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        <title xml:lang="la">Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam</title>
        <author>Gravesande, Willem Jakob</author>
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        <date>1721</date>
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  <text>
    <body xml:lang="la" type="free">
      <div type="section">
        <pb facs="0001" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0001-01" />
          <label>0001-01</label>
        </figure>
        <pb facs="0002" />
        <note />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0002-01" />
          <label>0002-01</label>
        </figure>
        <pb facs="0003" />
        <pb facs="0004" />
        <note />
        <note />
        <note />
        <note />
        <pb facs="0005" />
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="red">PHYSICES</hi> <lb />ELEMENTA <lb /><hi rend="red">MATHEMATICA,</hi> <lb />EXPERIMENTIS CONFIRMATA. <lb />Sive <lb />Introductio ad Philoſophiam <lb /><hi rend="red">NEWTONIANAM.</hi> <lb />Auctore <lb /><hi rend="red">GULIELMO JACOBO ’s GRAVESANDE,</hi> <lb />A. L. M., Fur. Vtr. &amp; Phil. Doctore, Regiæ Societ. Lond. Socio, <lb />Aſtron. &amp; Math. in Acad. Lugd. Bat. Profeſſore ordinario. <lb /><hi rend="red"><hi rend="small caps">Tomus</hi> <hi rend="small caps">Primus.</hi></hi> <lb />Editio Secunda, auctior &amp; emendatior.</head>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0005-01" />
          <label>0005-01</label>
        </figure>
      </div>
      <div type="section">
        <head xml:space="preserve">LUGDUNI BATAVORUM, <lb />Apud <hi rend="red">PETRUM VANDER As,</hi> <lb />Typographum Academiæ atque Civitatis.</head>
        <head xml:space="preserve">MDCC XXV. <lb />Cum Privilegio Præputent. Ordd. Hollandiæ &amp; Weſt-Friſiæ.</head>
        <pb facs="0006" />
        <fw type="head">PRIVILEGIE.</fw>
        <p rend="italics">
          <s xml:space="preserve">DE Staaten van Holland ende Weſt Vrieſtand, doen <lb />te weeten, alſoo ons vertoont is by Pieter vander <lb />Aa, Boekverkooper tot Leyden, hoe dat by Supplt. </s>
          <s xml:space="preserve">nu al-<lb />dereerſt nieuw hadde gedrukt, Guilielmi Jacobi <lb />’s Graveſande Phyſices Elementa Mathematica, <lb />experimentis confirmata; </s>
          <s xml:space="preserve">ſive Introductio ad <lb />Philoſophiam Newtonianam, in Quarto, cum fi-<lb />guris, het eerſte deel, ſynde het vervolg van het voorſz. <lb /></s>
          <s xml:space="preserve">werk by den ſupplt. </s>
          <s xml:space="preserve">meede tegenwoordigh onder de <lb />Pars, dog alſoo den Supplt beducht was, dat eenige <lb />nydige, off baetſoekende Menſchen, ’t ſy binnen off <lb />buytens Iands hem’tvoorn. </s>
          <s xml:space="preserve">werk ſouden mogen koo-<lb />men naa te drucken, waar door by van alle ſyne <lb />groote koſten en arbeyd tot nu toe gedaan en nog te <lb />doen, ſoude verſteken ſyn, ſoo keerde den Supplt, ſig <lb />tot Ons, verſoekende Ons Octroy, om het voorn werk <lb />en vervolg voor den tyd van vyſtien eerſt achter <lb />een volgende Faren, alleen met ſecluſie van allen an-<lb />deren hier te Lande te mogen drucken, uyt te geven, <lb />en te verkoopen in ſodanige taalen en formaten, als den <lb />Supplt. </s>
          <s xml:space="preserve">voor ſyn intreſt beſt oirbaar ſoude vinden, <lb />met expres verbod, waar by aan allen en eenen yge-<lb />lycken buyten hem Supplt. </s>
          <s xml:space="preserve">off die ſyn actie off recht <lb />naarmaels mochten verkrygen, door Ons verboden <lb />wiert, het voorn. </s>
          <s xml:space="preserve">werk off vervolg van dienin eeni-<lb />gerhande taalen te drucken, naa te drucken, tedoen <lb />naadrucken, uyt te geven, te verkopen, ofte ver-<lb />handelen, in ’t groot noch klein, in ’t geheel noch ten <lb />deelen, noch met, noch ſonder Platen, noch onder <lb />pretext van vermeerdering, verbeteringh, verande-<lb />ringh van naem, valſche tekens, ofte hoedanigh het <lb />ook genoemt ſoude mogen werden, ofte in eeniger-<lb />hande taal off taalen buyten deſen Lande gedrukt <lb />werdende, deſelve niet te mogen inbrengen, te ver-<lb />handelen, off te verkopen, alles telkens op verbeurte <lb />van alle de naagedrukte, ingebrachte, verhandelde off <lb />verkogte Exemplaren, ſo dikwils en menigmaal als <lb />deſelve ſouden werden achterhaelt, mitsgaders daar <lb />en boven een boete van drie duyſent guldens by Ons <lb />tegens de Contraventeurs te ſtellen. </s>
          <s xml:space="preserve">SO IST, dat Wy <lb />de ſaake, en’ verſoeck voorſz. </s>
          <s xml:space="preserve">overgemerkt hebbende, <lb />ende genegen weſende ter beede van den Supplt uyt <lb />Onſe rechte wetenſchap, Souveraine maght, en au-<lb />thoriteyt den ſelven Supplt. </s>
          <s xml:space="preserve">geconſenteert, geaccordeert, <lb />ende geoctroyeert hebben, conſenteeren, accordeeren, <lb />en octroyeren hem mitsdeſen, dat by geduyrende den <lb />tyd van vyftien eerſt achter een volgende Faren het <lb />voorſz. </s>
          <s xml:space="preserve">werk genaemt Guilielmi Jacobi’s Grave-<lb />ſande Phyſices Elementa Mathematica, expe-<lb />rimentis confirmata; </s>
          <s xml:space="preserve">ſive Introductio ad Phi-<lb />loſophiam Newtonianam, in Quarto cum figuris <lb />met het vervolg van dien, binnen den voorſz. </s>
          <s xml:space="preserve">On-<lb />ſen Landen alleen ſal mogen drucken, doen drucken, <lb />uytgeven, en verkoopen, in ſodanige taalen en for-<lb />maten, als den Supplt. </s>
          <s xml:space="preserve">voor ſyn intreſt beſt oirbaar <lb />ſal vinden, verbiedende daerom allen, ende een yge-<lb />gelyken het ſelve Werk en Vervolg in eenigerhande <lb />taalen in’t geheel, ofte ten deelen naa te drucken, <lb />te doen naadrucken, te verhandelen, ofte te verko-<lb />pen, ofte elders naergedrukt, binnen den ſelven On-<lb />ſen Lande te brengen, uyt te geven, te verhandelen <lb />ofte te verkoopen, op verbeurte van alle de naage-<lb />druckte, ingebragte, verhandelde ofte verkogte Exem-<lb />plaren, ende een boete van drie duyſent guldens daer <lb />en boven te verbeuren, te appliceeren een derde part <lb />voor den Officier, die de Calangie doen ſal, een derde <lb />part voor den Armen der plaatſe daer de caſus voor-<lb />vallen ſal, en de reſterende derde part voor den <lb />Supplt. </s>
          <s xml:space="preserve">ende dit telkens ſoo menigmael als deſelve ſullen <lb />werden achterhaelt, alles in dien verſtande, dat Wy <lb />den Supplt. </s>
          <s xml:space="preserve">met de ſen Onſen Octroye alleen uillende <lb />gratificeeren tot verhoedinge van ſyne ſchade door het <lb />naadrucken van het voorſz. </s>
          <s xml:space="preserve">Werk of Vervolg, daar <lb />door in geenen deele verſtaen den inhoude van dien <lb />te authoriſeeren ofte te advoueeren, ende veel min <lb />het ſelve onder Onſe protectie ende beſcherminge eenigh <lb />meerder credit, aanſien ofte reputatie te geven, ne-<lb />maar den Suppliant in cas daer in iets onbehoorlyks <lb />ſoude influeeren, alle het ſelve tot ſynen laſte ſal ge-<lb />houden weſen te verantwoorden, tot dien eynde wel <lb />expreſſelyck begeerende. </s>
          <s xml:space="preserve">dat by aldien by deſen On-<lb />ſen Octroye voor het ſelve Werk ſal willen ſtellen, <lb />daar van geen geæbbrevieerde oft gecontraheerde men-<lb />tie ſal mogen maeken, nemaer gehouden ſal weſen <lb />het ſelve Octroy in’t geheel ende ſonder eenige Omiſſie <lb />daer voor te drucken, ofte te doen drucken, ende <lb />dat by gehouden ſal ſyn een Exemplaer van het voorſz. </s>
          <s xml:space="preserve"><lb />werk gebonden en wel geconditioneert to brengen in <lb />de Bibliotheeck van Onſe Univerſiteyt tot Leyden, <lb />en daer van behoorlyk te doen blycken, alles op pœne <lb />van het effect van dien te verlieſen, ende ten eynde <lb />den Supple. </s>
          <s xml:space="preserve">deſen Onſen Conſente en Octroye moge ge-<lb />nieten als naer behooren, laſten Wy allen ende <lb />een ygelycken die’t aangaen mag, dat ſy den Supplt. </s>
          <s xml:space="preserve"><lb />van den inhoude van deſen doen laten ende gedogen, <lb />ruſtelyck, vredelyck ende volkomentlyk genieten ende <lb />gebruycken, ceſſerende alle beleth ter contrarie. </s>
          <s xml:space="preserve">Ge-<lb />daen in den Hage onder Onſen Grooten Zegele hier <lb />aen doen hangen op den aghſten November in’t Faer <lb />onſes Heeren en Zalighmakers ſeventien hondert en <lb />negentien.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Was getekent, <lb />A: </s>
          <s xml:space="preserve">HEINSIUS, vt <lb />Ter Ordonnantie van de Staten, <lb />SIMON <hi rend="small caps">van</hi> BEAUMONT.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0007" />
        <fw type="head">MONITUM</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">de hac Secunda Editione.</head>
        <p rend="italics">
          <s xml:space="preserve">CUm primùm ad hæc Elementa conſcribenda <lb />animum applicarem, hoc mihi fuit propo-<lb />ſitum, ut auditores, quæ fuſius explicata au-<lb />diviſſent, &amp; </s>
          <s xml:space="preserve">demonſtrata vidiſſent, illa <lb />facile in memoriam revocare poſſent. </s>
          <s xml:space="preserve">Etiam, ut le-<lb />ctoribus, quibus prima tantum Geometriæ elementa <lb />nota eſſent, ideam darem Philoſophiæ Naturalis Ma-<lb />thematicâ Methodo tractatæ. </s>
          <s xml:space="preserve">Cùmque, ut tironibus <lb />præcipuè liber hicce utilis eſſet, difficiliora omnia in-<lb />tacta relinquerem, ſæpe propoſitiones indicavi, de <lb />quibus tantum monui, has à Geometris probari.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ut autem ſecunda hæc editio, &amp; </s>
          <s xml:space="preserve">lectoribus magis <lb />in Mathematicis verſatis, uſui eſſet, propoſitiones ta-<lb />les omnes, in capite quocunque indicatas, Mathema-<lb />ticè demonſtratas in ſcholiis, capitibus ſubjunctis, adje-<lb />ci. </s>
          <s xml:space="preserve">Et ne hæc lectores alios turbarent, ipſa minore <lb />charactere imprimi curavi. </s>
          <s xml:space="preserve">Omnia tamen ita diſpo-<lb />ſui, ut illa ſola, quæ majore charactere edita ſunt, <lb />ſeparatum quaſi opus conſtituant.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">In ſcholiis etiam alia quædam tradidi, quæ in ipſo <lb />opere commode tractari non potuere, quamvis cum <lb />explicatis relationem habeant, aut ad hæc illuſtranda <lb />inſerviant.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Secunda hæc editio, &amp; </s>
          <s xml:space="preserve">aliis reſpectibus, eſt au-<lb />ctior &amp; </s>
          <s xml:space="preserve">magis accurata.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Novæ multæ Machinæ, &amp; </s>
          <s xml:space="preserve">antiquæ emendatæ in
</s>
          <pb facs="0008" />
          <s xml:space="preserve"><fw type="head">MONITUM</fw>
hujus tabulis exhibentur, &amp; </s>
          <s xml:space="preserve">Experimenta, ipſorum-<lb />que ſucceſſus, in hac majori cum curâ exponuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Novam etiam noſtram Percuſſionis Theoriam, quæ <lb />LEIBNITZIANAM, quam &amp; </s>
          <s xml:space="preserve">HUGENIANAM <lb />dicere auſim, de viribus inſitis doctrinam pro funda-<lb />mento habet, hîc plenius explicatam, noviſque variis <lb />experimentis fulcitam, &amp; </s>
          <s xml:space="preserve">illuſtratam tradimus.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Non animus unquam mihi fuit, nec adhucdum eſt, <lb />cum ullo, utcunque provocatus, in arenam deſcen-<lb />dere, ut de veritate contendam. </s>
          <s xml:space="preserve">Quod mihi verum vi-<lb />detur, hoc, ubi datur occaſio, pro viribus defendo; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in <lb />his ut, quantum poſſem, omnem contentionis ſpeciem re-<lb />moverem, argumenta, quibus memoratæ Theoriæ inniti <lb />mihi videntur, ita proponere conatus ſum, ut reſpon-<lb />ſa ad difficultates inde facile deduci queant, paucaſque <lb />tantum directe ſolvere ſuſcepi: </s>
          <s xml:space="preserve">lectorique dijudican-<lb />dum relinquo, an non Virium, Percuſſionum, ut &amp; </s>
          <s xml:space="preserve"><lb />Reſiſtentiarum, Retardationumque, corporum in flui-<lb />dis motorum, Theoriæ cum Phænomenis, &amp; </s>
          <s xml:space="preserve">inter ſe, <lb />quàm exactiſſime conveniant.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Noſtro labore quiſque pro arbitrio utatur, &amp; </s>
          <s xml:space="preserve">ne <lb />nos ad reſpondendum objectionibus, quæ proponi pote-<lb />runt, devinctos credat. </s>
          <s xml:space="preserve">Quamdiu illa pro veris habebimus <lb />quæ ſcripſimus, nos jure ſilere poſſe perſuaſum habe-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quamvis in multis, quæ ſpectant memoratas Theori-<lb />as, à NEWTONIAN Areceſſerim ſententia, non tamen <lb />titulum Introductionis ad Philoſophiam Newtonia-<lb />nam ſervare, &amp; </s>
          <s xml:space="preserve">huic ſecundæ editioni ipſum inſcri-
</s>
          <pb facs="0009" />
          <s xml:space="preserve"><fw type="head">AD LECTOREM</fw>
bere, ullo modo dubitavi. </s>
          <s xml:space="preserve">Varia enim in hiſce illu-<lb />ſtramus ex iis quæ ab eximio illo Philoſopho fuere tra-<lb />dita; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pleraque, quæ hîc explicamus, eo condu-<lb />cant, ut facilius intelligantur, à ſummis Philoſophis <lb />in perpetuum celebranda, &amp; </s>
          <s xml:space="preserve">a nemine unquam ſine <lb />admiratione legenda, NEWTONI ſcripta Philoſophica.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Qui tantum ex Phænomenis, omni fictâ rejectâ <lb />hypotheſi, in Phyſicis ratiocinatur, &amp;</s>
          <s xml:space="preserve">, quantum in <lb />ipſo eſt, caſte hanc methodum ſequitur, ille NEWTO-<lb />NIveſtigiis inſiſtere conatur, &amp; </s>
          <s xml:space="preserve">merito NEWTONIA-<lb />NAM ſe ſectari Philoſophiam profitetur; </s>
          <s xml:space="preserve">non au-<lb />tem ille, qui in verba jurat magiſtri.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ut autem augmenta, &amp; </s>
          <s xml:space="preserve">emendationes, hujus edi-<lb />tionis, &amp; </s>
          <s xml:space="preserve">illis, qui primam jam poſſident, inſer-<lb />virent, ſupplementum ſeparatum edi curavi: <lb /></s>
          <s xml:space="preserve">in quo, ut primæ editionis poſſeſſoribus utilis eſſem, <lb />præſtiti quod potui, non autem omne quod voluiſſem. </s>
          <s xml:space="preserve"><lb />In ſupplemento dedi omnium machinarum novarum <lb />deſcriptiones, additamenta omnia, &amp; </s>
          <s xml:space="preserve">propoſitiones <lb />mutatas. </s>
          <s xml:space="preserve">Non autem huic inſerere potui, machina-<lb />rum correctiones, neque illa, quibus, quæ in prima <lb />editione continentur, aut illuſtrantur, aut clarius &amp; </s>
          <s xml:space="preserve"><lb />magis accurate exprimuntur; </s>
          <s xml:space="preserve">ſupplementum omnibus <lb />partibus completum, lectori nimio fuiſſet labori, &amp; </s>
          <s xml:space="preserve"><lb />ipſius pretium nimium excreviſſet.</s>
          <s xml:space="preserve" />
        </p>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0009-01" />
          <label>0009-01</label>
        </figure>
        <pb facs="0010" />
        <fw type="head">ADDENDA.</fw>
        <p rend="italics">
          <s xml:space="preserve">In capite 22. </s>
          <s xml:space="preserve">lib. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">prætermiſſa ſunt quæ ſequuntur; </s>
          <s xml:space="preserve">lecto-<lb />rem ideo rogo ut hæc velit inſerere ad pag. </s>
          <s xml:space="preserve">119. </s>
          <s xml:space="preserve">poſt lin. </s>
          <s xml:space="preserve">26.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">TAB XIX. <lb />fig. 1</note>
        <p>
          <s xml:space="preserve">Si corpus cujus extremitas conica eſt ut E B F bis, in <lb />diverſis ſuperficiei argillæ partibus, in hanc incurrat, ve-<lb />locitatibus quæ ſunt ut unum ad duo, cavitates erunt ut u-<lb />num ad quatuor, ut ex ante dictis conſtat <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">immediatè,
<ptr xml:id="note-0010-02a" corresp="note-0010-02" type="noteAnchor" />
cavitates menſurando, detegitur. </s>
          <s xml:space="preserve">Tempus autem in quo ef-<lb />fectus hicce quadruplus editur majus eſt; </s>
          <s xml:space="preserve">ſed effectum et-<lb />iam quadruplum eſſe, quamvis minori tempore vim ſuam <lb />corpus amittat, experimento ſequenti clarum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0010-02" corresp="note-0010-02a" n="*" anchored="true" place="margin">447. 464. <lb />456.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Formatur ex ebore, aut ligno duriore, Cylindrus, qui <lb />ab una parte cono ut E B F terminatur, baſis oppoſita qua-<lb />tuor conis, omnino huic ſimilibus, obtegitur, qui ſinguli <lb />æqualiter prominent ita, ut planum, per quatuor vertices <lb />tranſiens, perpendiculare ſit ad axem cylindri; </s>
          <s xml:space="preserve">fuſpen-<lb />ditur hicce ut ille, quo in præcedenti experimento uſi ſu-<lb />mus, &amp; </s>
          <s xml:space="preserve">velocitate quacunque perpendiculariter in argillæ <lb />ſuperficiem incurrit, dum juxta directionem ad axim pa-<lb />rallelam fertur, cono unico in argillam impingente.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Converſo nunc Cylindro, mutatoque pyxidis ſitu, ve-<lb />locitate dupla in argillam incurrat cylindrus, moto iterum <lb />hoc juxta axis directionem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In priori caſu unica tantum formata fuit cavitas, in hoc <lb />quatuor formantur, quarum ſingulæ priori quàm exactiſſi-<lb />mè æquales ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum in utroque caſu ad eandem profunditatem in argil-<lb />lam penetraverit corpus, clarum eſt, minori tempore vim <lb />integram amiſiſſe, ubi velocitas major fuit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">Pag. 310. poſt. lin. 23. adde.</head>
        <p>
          <s xml:space="preserve">Hoc tamen difficilius continget, &amp; </s>
          <s xml:space="preserve">rarius extrahendi e-<lb />runt emboli, ſi hi ſinguli, in inferiori parte, inter duasla-<lb />minas æneas orbem contineant ex ſubere ita, ut annulus <lb />coriaceus intruſo embolo, ſeſe ſuberi non ipſi metallo ap-<lb />plicet. </s>
          <s xml:space="preserve">Quod in quibuſdam antliis minoribus Anglicanis <lb />obſervavi.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0011" />
      </div>
      <div type="section">
        <head xml:space="preserve">DEDICATIO PRIMÆ EDITIONI PRÆMISSA.</head>
        <head xml:space="preserve">ILLUSTRIBUS, NOBILISSIMIS, <lb />&amp; AMPLISSIMIS</head>
        <head xml:space="preserve">ACADEMIÆ BATAVÆ, <lb />quæ LEIDÆ eſt,</head>
        <head xml:space="preserve">CURATORIBUS,</head>
        <head xml:space="preserve">D. GULIELMO BARONI <lb /><hi rend="small caps">DE</hi> WASSENAER,</head>
        <head xml:space="preserve">TOPARCHÆ IN STERRENBERGH, EQUESTRI <lb />NOBILIUM HOLLANDIÆ ORDINI ADSCRIPTO, <lb />DELEGATORUM ILLUSTR. ET PRÆPOT. HOLLAN-<lb />DIÆ ORDINUM PRÆSIDI, ETC. ETC.</head>
        <head xml:space="preserve">D. HUBERTO ROSEBOOM, <hi rend="small caps">Jcto</hi>.</head>
        <head xml:space="preserve">TOPARCHÆ IN ’s GREVELSREGHT, SUPREMÆ <lb />BATAVORUM CURIÆ PRÆSIDI, ETC. ETC.</head>
        <head xml:space="preserve">D. HERMANN <hi rend="small caps">Ovanden</hi> HONERT, <hi rend="small caps">Jcto</hi>.</head>
        <head xml:space="preserve">REIPUBLICÆ DORDRACENÆ CONSULI, <lb />AGGERUM ALBLASSERW AERDENSIUM <lb />COMITI, ETC. ETC.</head>
        <pb facs="0012" />
      </div>
      <div type="section">
        <head xml:space="preserve">EORUMQUE COLLEGIS</head>
        <head xml:space="preserve">NOBILISSIMIS GRAVISSIMIS QUE <lb />VIRIS</head>
        <head xml:space="preserve">REIPUBLICÆ LUGDUNENSIS,</head>
        <head xml:space="preserve">CONSULIBUS,</head>
        <head xml:space="preserve">D. JOANNI <hi rend="small caps">VANDEN</hi> BERGH, <hi rend="small caps">Jcto</hi>.</head>
        <head xml:space="preserve">EX FOEDERATA HAC REPUBLICA OLIM, NO-<lb />MINE IMPERATORIS CAROLI VI., BRABANTIÆ, <lb />FLANDRIÆ, HANNONIÆ, ETC. EPHORO, ET <lb />AD RES EARUM ORDINANDAS DELEGATO.</head>
        <head xml:space="preserve">D. JOHANNI <hi rend="small caps">VAN</hi> ASSENDELFT, <hi rend="small caps">Jcto</hi>.</head>
        <head xml:space="preserve">D. HENRICO <hi rend="small caps">VAN</hi> WILLIGEN, <hi rend="small caps">Jcto</hi>.</head>
        <head xml:space="preserve">D. ABRAHAMO <hi rend="small caps">VAN</hi> GERWEN, <hi rend="small caps">Jcto</hi>.</head>
        <head xml:space="preserve">NEC NON</head>
        <head xml:space="preserve">VIRO SPECTATISSIMO</head>
        <head xml:space="preserve">D. PETRO GIJS, <hi rend="small caps">Jcto</hi>.</head>
        <head xml:space="preserve">REIPUBLICÆ LUGDUNENSIS SCABINO, <lb />AMPLISSIMIS CURATORIBUS ET CONSULIBUS <lb />A SECRETIS,</head>
        <head xml:space="preserve">Hæc Phyſices Elementa <lb />D. D. D. <lb />G. J. ’s GRAVESANDE.</head>
        <pb facs="0013" />
        <fw type="head">PRÆFATIO.</fw>
        <p>
          <s xml:space="preserve">QUi variorum Philoſophorum circa Phyſicam ſcri-<lb />pta contulerit, ſcientias omnino diverſas hoc <lb />nomine deſignari, in dubium vocare vix pote-<lb />rit, dum omnes ſe veram cauſam Phænome-<lb />nôn naturalium tradituros pollicentur. </s>
          <s xml:space="preserve">Nil mirum, Ma-<lb />theſis fallere neſcia non ſemper contentionem omnem a ſe <lb />removere potuit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sed ne nos ſententiarum varietas averitatis inquiſitione <lb />abducat, ſtudio &amp; </s>
          <s xml:space="preserve">labore, quantumvis abſcondita, in lu-<lb />cem protrahitur veritas, &amp; </s>
          <s xml:space="preserve">qui flagranti hujus amore ra-<lb />pitur, ſi errores non omnes, quod minime humanum, <lb />evitet, difficilius tamen in illos cadit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Caute in Phyſicis procedendum; </s>
          <s xml:space="preserve">circa Intelligentiæ ſu-<lb />premæ opera verſatur hæc ſcientia; </s>
          <s xml:space="preserve">tradit</s>
        </p>
        <p rend="italics">
          <s xml:space="preserve">quas, dum primordia rerum <lb />Pangeret, omniparens Leges violare Creator <lb />Noluit, æternique operis fundamina fixit:</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">quomodo hiſce Legibus univerſa rerum congeries rega-<lb />tur, &amp;</s>
          <s xml:space="preserve">, quomodo ordo, nunquam ſatis mirandus, qui-<lb />bus omnia peraguntur, iiſdem Legibus in Mundo ſervetur, <lb />explicat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cavendum ne fictum pro vero admittamus, eoipſoul-<lb />teriori examini januam claudimus; </s>
          <s xml:space="preserve">nulla vera Phænome-<lb />nôn explicatio ex falſo principio deduci poteſt; </s>
          <s xml:space="preserve">mentiſque <lb />humanæ figmentum diſcere, aut Intelligentiæ ſapientiſſi-<lb />mæ opus perpendere quantum intereſt? </s>
          <s xml:space="preserve">Cumque ſapien-<lb />tiæ divinæ inveſtigatio, &amp; </s>
          <s xml:space="preserve">cum hac ſemper conjuncta ve-<lb />neratio, ſcopus Phyſici eſſe debeat, hîc ex fictis hypo-
</s>
          <pb facs="0014" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
theſibus ratiocin andum non eſſe ulterius probare inutilefo-<lb />ret.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ipſa ergo Natura indefeſſo labore, animoque attento, <lb />continuo examinanda eſt. </s>
          <s xml:space="preserve">Lente quidem progredimur, <lb />ſed quæ deteguntur certa ſunt; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, ubi mortalium co-<lb />gnitionibus limites ponantur, ſæpe determinamus. </s>
          <s xml:space="preserve">Quod <lb />fere omnes in errorem duxit, eſt ſciendi immoderata cu-<lb />pido; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">non fatendæ ignorantiæ, ſæpe ſtudio acquiſitæ, <lb />a ratione ſuperandus, pudor. </s>
          <s xml:space="preserve">Sed, ſi in verbis ludere non <lb />vetitum, docta indoctæ ſcientiæ anteponenda ignorantia <lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Phyſica inter partes Matheſeos, cujus objectum eſt <lb />quantitas in genere, merito refertur. </s>
          <s xml:space="preserve">Dividitur Mathe-<lb />fis in puram &amp; </s>
          <s xml:space="preserve">mixtam. </s>
          <s xml:space="preserve">In generales figurarum proprie-<lb />tates inquirit illa, abſtractaſque ideas pro objecto ſuo ha-<lb />bet. </s>
          <s xml:space="preserve">In hac res ipſæ examinantur, conſequentiaſque non <lb />modo legitimas dari requiritur, ſed ut cum rebus ipſis con-<lb />gruant ideæ circa quas ratiocinamur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ad Matheſin mixtam pertinet Phyſica; </s>
          <s xml:space="preserve">ratiociniorum <lb />Mathematicorum baſes ſunt Corporis Proprietates, &amp; </s>
          <s xml:space="preserve">Na-<lb />turæ Leges, quod nemo, qui hujus ſcientiæ ſcopum exa-<lb />minavit, inficias ire poteſt. </s>
          <s xml:space="preserve">Quid autem pro Naturæ <lb />Lege ſit habendum, qua methodo ad has Leges inveſti-<lb />gandas procedendum, minime inter Philoſophos conve-<lb />nit. </s>
          <s xml:space="preserve">Neceſſe ideo duxi in hac Præfatione tueri quam in <lb />hoc Opere ſecutus ſum philoſophandi Methodum Newto-<lb />nianam, quæ in primo capite breviter exponitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Non agitur in Phyſicis de prima rerum formatione; </s>
          <s xml:space="preserve">ra-
</s>
          <pb facs="0015" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
tioni non modo conſentaneum eſt, quod Sacræ Litteræ <lb />tradunt, Mundum a DEO conditum; </s>
          <s xml:space="preserve">nequidem per mo-<lb />mentum temporis Naturam examinantem Intelligentiæ ſu-<lb />premæ veſtigia latent. </s>
          <s xml:space="preserve">Aſſerere ex quibuſdam generali-<lb />bus motus Legibus Mundum originem ducere potuiſſe, &amp; </s>
          <s xml:space="preserve"><lb />omnino parum referre quid de prima materiæ diviſione <lb />fingatur. </s>
          <s xml:space="preserve">Et vix aliquid ſupponi poſſe ex quo non idem <lb />effectus per eaſdem Naturæ Leges deduci poſſit: </s>
          <s xml:space="preserve">illudque <lb />hac de cauſa, quod cum illarum ope materia formas <lb />omnes quarum eſt capax ſucceſſive aſſumat, ſi formas iſtas <lb />ordine conſideremus, tandem ad illam, quæ eſt hujus Mun-<lb />di, nos poſſe devenire: </s>
          <s xml:space="preserve">adeo ut bîc nibil erroris ex falſa <lb />ſuppoſitione ſit timendum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hæc, inquam, aſſerere, &amp; </s>
          <s xml:space="preserve">notiones maxime claras e-<lb />vertere, vix differt, ut a plurimis Viris doctis abunde pro-<lb />batum, &amp; </s>
          <s xml:space="preserve">ad quod argumenta proferre inutile videbitur <lb />illi, cui ignotum, ſententiam, adeo a ratione remotam, <lb />&amp; </s>
          <s xml:space="preserve">Divino Numini contumelioſam, ab antiquis &amp; </s>
          <s xml:space="preserve">novis, <lb />etiam præclaris Philoſophis, &amp; </s>
          <s xml:space="preserve">ab omni Atheïſmi labe <lb />remotiſſimis, in medium prolatam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Poſitis ergo omnibus a DEO creatis, explicandum qui-<lb />bus Legibus omnia regantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ut ſolam Lunam memo-<lb />rem, dicendum:</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">qua cauſa argentea Phœbe <lb />Paſſibus haud æquis graditur, cur ſubdita nulli <lb />Hactenus Aſtronomo numerorum fræna recuſet; <lb /></s>
          <s xml:space="preserve">Cur remeant nodi, curque auges progrediuntur.</s>
        </p>
        <pb facs="0016" />
        <fw type="head">PRÆFATIO.</fw>
        <p>
          <s xml:space="preserve">quantis refluum vaga Cynthia Pontum <lb />Viribus impellit; </s>
          <s xml:space="preserve">dum fractis fluctibus ulvam <lb />Deſerit, ac nautis ſuſpectas nudat arenas; <lb /></s>
          <s xml:space="preserve">Alternisvicibus ſuprema ad littora pulſans.</s>
          <s xml:space="preserve">De inveſtigiatione autem Naturæ Legum ut dicam, res <lb />altius petenda eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Subſtantiæ quid ſint inter nobis ignota referendum eſt. <lb /></s>
          <s xml:space="preserve">Quaſdam ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">materiæ proprietates novimus, ſed in <lb />quo ſubjecto hæreant hæ nos omnino latet. </s>
          <s xml:space="preserve">An Corpori <lb />non multæ aliæ tribuendæ ſint proprietates, de quibus <lb />nullam habemus ideam, quis aſſerere poteſt? </s>
          <s xml:space="preserve">Cui etiam <lb />enotuit an, præter Corporis proprietates quæ a materiæ <lb />eſſentia pofluunt, non dentur aliæ a DEI libera poteſtate <lb />pendentes, ſubſtantiamque extenſam &amp; </s>
          <s xml:space="preserve">ſolidam (hæc e-<lb />nim a nobis Corpus vocatur) quibuſdam, ſine quibus exi-<lb />ſtere poſſet, proprietatibus ornari. </s>
          <s xml:space="preserve">De ignotis nihil af-<lb />firmandum aut negandum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quantum ab hac regula aberrant illi, qui, quaſi o-<lb />mnia quæ ad Corpus pertinent pleniſſime perſpecta habe-<lb />rent, in Phyſicis ratiocinantur, paucaſque Corporis pro-<lb />prietates notas ipſum Corpus conſtituere aſſerere non <lb />dubitant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quid obſecro ſibi vult proprietates ſubſtantiæ ipſam <lb />conſtituere ſubſtantiam? </s>
          <s xml:space="preserve">An quæ ſeparatim ſubſiſtere non <lb />poſſunt ſimul juncta ſubſiſtent? </s>
          <s xml:space="preserve">An extenſum, impenetra-<lb />bile, mobile eſſe, &amp; </s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">concipi poſſunt, ſine ſubjecto cui <lb />hæ proprietates @mpetant? </s>
          <s xml:space="preserve">Et an hujus ſubjecti ullam ha-<lb />bemus ideam?</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0017" />
        <fw type="head">PRÆFATIO.</fw>
        <p>
          <s xml:space="preserve">In incerto relinquendum quod incertum eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ne i-<lb />gnorantiam fateri pudeat: </s>
          <s xml:space="preserve">neque timendum de ignoto ni-<lb />mium affirmari, dum ſubjectum omnino ignotum quibuſ-<lb />dam incognitis proprietatibus forte præditum eſſe aſſeri-<lb />mus. </s>
          <s xml:space="preserve">Qui vero cum hoc axiomate ſe nixos dicunt, quod <lb />de incognitis non ſit ratiocinandum, pro ratiocinii tamen <lb />fundamento habent, nil circa Corpus ignoti dari, niſi <lb />forte fortuna errorem non vitabunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corporis proprietates a priori detegi nequeunt; </s>
          <s xml:space="preserve">Cor-<lb />pus ipſum ideo eſt examinandum, hujuſque proprietates <lb />exactiſſimè perpendendæ ſunt, ut poſſimus determinare <lb />quid in rerum Phænomenis ex illis proprietatibus ſequa-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus majori cum cura examinando, videmus quaſ-<lb />dam leges dari generales, ſecundum quas corpora moven-<lb />tur. </s>
          <s xml:space="preserve">Corpus motum in motu continuare: </s>
          <s xml:space="preserve">actioni ſemper <lb />æqualem eſſe &amp; </s>
          <s xml:space="preserve">contrariam reactionem extra omne du-<lb />bium eſt. </s>
          <s xml:space="preserve">Variæque aliæ ſimiles circa Corpus deteguntur <lb />Leges, quæ minime ex proprietatibus, quæ ipſum Cor-<lb />pus conſtituere dicuntur, deduci poſſunt; </s>
          <s xml:space="preserve">cumque hæ <lb />Leges ſemper, id eſt, in omnibus occaſionibus, &amp; </s>
          <s xml:space="preserve">ubi-<lb />que, obtineant, &amp; </s>
          <s xml:space="preserve">omnia corpora iis ſubjiciantur, pro <lb />generalibus Naturæ Legibus habendæ ſunt. </s>
          <s xml:space="preserve">Circa has <lb />in obſcuro eſt, an ex materiæ eſſentia fluant; </s>
          <s xml:space="preserve">an dedu-<lb />cendæ ſint ex proprietatibus corporibus, ex quibus conſtat <lb />Mundus, a DEO tributis, ſed Corpori minime eſſentialibus; <lb /></s>
          <s xml:space="preserve">tandem an non pendeant effectus, qui pro Naturæ Legibus <lb />habentur, a caufis extraneis nobis nequidem ideis attingen-<lb />dis.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0018" />
        <fw type="head">PRÆFATIO.</fw>
        <p>
          <s xml:space="preserve">Quis mortalium de omnibus aut ſingulis Naturæ Legi-<lb />bus hac in parte aliquid non temere aſſerere audebit? </s>
          <s xml:space="preserve">Mul-<lb />tas etiam Leges non eſſe detectas, circa alias varia deſide-<lb />rari, qui Naturæ Phænomena examinavit, pleniſſime <lb />perſuaſum habebit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Non tamen, ut ignoto fundamento nixum, contemnen-<lb />dum Philoſophiæ Naturalis ſtudium. </s>
          <s xml:space="preserve">Limitibus arctis circum-<lb />ſcribitur mentis humanæ cognoſcendi capacitas, &amp; </s>
          <s xml:space="preserve">qui <lb />niſi evidentiæ aſſenſum dare negat, omnibus momentis in <lb />dubio hæret, &amp; </s>
          <s xml:space="preserve">inter incognita refert multa, circa quæ <lb />vix per momentum temporis dubitandum plerique credunt. <lb /></s>
          <s xml:space="preserve">Cognita tamen ab ignotis rite ſeparare eſt animæ intelli-<lb />gentis perfectio, terræ incolam ſuperans, ſed ad quam <lb />acquirendam, continuo, animo attento, ſeſe applicare <lb />debet. </s>
          <s xml:space="preserve">Si in Phyſicis multa latent, quæ in hac ſcientia <lb />traduntur certa ſunt. </s>
          <s xml:space="preserve">Ex paucis generalibus principiis in-<lb />numera Phænomena peculiaria explicantur; </s>
          <s xml:space="preserve">hæcque ex <lb />illis Mathematica demonſtratione deducenda ſunt. </s>
          <s xml:space="preserve">Agi-<lb />tur ubique de motuum collatione, id eſt, de quantitatum <lb />comparatione, circa quam qui demonſtrationibus Mathe-<lb />maticis in ratiociniis non progreditur, ſi non in erro-<lb />rem, ſaltem in incertas concluſiones incidet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæcunque ergo habeat ignota Phyſica, vaſta &amp; </s>
          <s xml:space="preserve">cer-<lb />tiſſima eſt nihilominus hæc ſcientia, &amp; </s>
          <s xml:space="preserve">maxime utilis. <lb /></s>
          <s xml:space="preserve">Corrigit innumera circa res naturales, &amp; </s>
          <s xml:space="preserve">divinam ſapien-<lb />tiam, falſa judicia; </s>
          <s xml:space="preserve">omnibuſque momentis in DEI ope-<lb />ribus hanc ſapientiam ante oculos ponit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">multum dif-<lb />fert, ſupremi Numinis potentiam, ſapientiamque, argu-
</s>
          <pb facs="0019" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
mento Metaphyſico noviſſe, &amp; </s>
          <s xml:space="preserve">has omnibus momentis <lb />in effectibus ipſis contemplari.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Satis ergo patet, quinam ſit ſcopus Phyſices, exqui-<lb />bus Naturæ Legibus Phænomena ſint deducenda; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">qua-<lb />re, quando ad Leges generales pervenimus, non ulterius <lb />in cauſarum cognitionem penetrare poſſimus. </s>
          <s xml:space="preserve">Supereſt, <lb />ut de ipſarum Legum inveſtigatione dicamus, &amp; </s>
          <s xml:space="preserve">tres re-<lb />gulas Newtonianas in primo hujus Operis capite traditas <lb />ſequendas eſſe probemus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Prima eſt, cauſas rerum naturalium non plures admitti <lb />debere quam quæ veræ ſint, &amp; </s>
          <s xml:space="preserve">earum Phænomenis expli-<lb />candis ſufficiant. </s>
          <s xml:space="preserve">Pars prior ex ante dictis pleniſſime ſequi-<lb />tur. </s>
          <s xml:space="preserve">Altera a nemine, qui ſapientem rerum Conditorem <lb />non negat, in dubium vocari poteſt; </s>
          <s xml:space="preserve">ſi cauſa non ſuffi-<lb />cit, veram non eſſe ſponte ſequitur; </s>
          <s xml:space="preserve">ſi ſufficit aliam fu-<lb />peraddere inutile erit. </s>
          <s xml:space="preserve">Adde effectum ex duplici cauſa <lb />nunquam exactiſſime eundem eſſe cum effectu ex ſimplici; <lb /></s>
          <s xml:space="preserve">ergo duabus effectus explicetur, unica non ſufficiet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Regulæ duæ ſequentes ut probentur, quædam generalia <lb />præmittenda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Jam monuimus Demonſtrationes Mathematicas niſi <lb />circa ideas non verſari, &amp; </s>
          <s xml:space="preserve">ubi de rebus ipſis agitur ante <lb />omnia requiri, ut cum rebus ideæ conveniant, quod nul-<lb />lâ Mathematicâ demonſtratione probari poteſt. </s>
          <s xml:space="preserve">Cum <lb />tamen omnibus momentis circa resipſas ratiocinandum <lb />ſit, &amp; </s>
          <s xml:space="preserve">nil de rebus in mente dari poſſit præter ha-<lb />rum ideas, ratiociniaque omnia ideas immediate ſpe-<lb />ctent, ſequitur a DEO conſtitutas quaſdam regulas, qui-
</s>
          <pb facs="0020" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
bus de convenientia idearum cum rebus poſſimus judicium <lb />ferre.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Omnia ratiocinia Mathematica idearum tantum com-<lb />parationem ſpectant; </s>
          <s xml:space="preserve">unde ſequitur contrarium contradi-<lb />ctionem involvere. </s>
          <s xml:space="preserve">Triangulum rectilineum, cujus tres <lb />anguli duos rectos non æquant, impoſſibile eſt; </s>
          <s xml:space="preserve">quia idea <lb />trium angulorum trianguli, ipſa eſt idea duorum angulo-<lb />rum rectorum. </s>
          <s xml:space="preserve">Ubi de rebus ipſis agitur, contraria <lb />propoſitio impoſſibilis non ſemper datur. </s>
          <s xml:space="preserve">Indubitatum <lb />eſt, ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">Petrum vivere, licet certiſſimum ſit, illum heri <lb />potuiſſe mori. </s>
          <s xml:space="preserve">Cum autem in innumeris occaſionibus in ca-<lb />ſu ſimili, cum certitudine, affirmandum aut negandum <lb />ſit, cumque hoc clare ex rerum conſtitutione, deduca-<lb />tur: </s>
          <s xml:space="preserve">ſequitur, in talibus occaſionibus, ratiocinia dari certa, <lb />a Mathematicis demonſtrationibus neceſſario diverſa, vo-<lb />luiſſe rerum conditorem. </s>
          <s xml:space="preserve">Qui enim homines neceſſita-<lb />te cogit, de veritate aut falſitate propoſitionis pronun-<lb />ciare, aſſentiendum eſſe, clare indicat, argumentis, qui-<lb />bus judicium neceſſario nititur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">non digne de DEO ſen-<lb />tit qui aliter ratiocinatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut ad Phyſicam redeamus, in hac de convenientia re-<lb />rum cum ideis ſenſibus dijudicandum. </s>
          <s xml:space="preserve">Extenſio, ex. </s>
          <s xml:space="preserve">gr. <lb /></s>
          <s xml:space="preserve">materiæ &amp; </s>
          <s xml:space="preserve">hujus ſoliditas, quæ hocfundamento affirman-<lb />tur, extra omne dubium ſunt. </s>
          <s xml:space="preserve">Non hîc agitur, an ſen-<lb />ſus quibuſdam in occaſionibus fallant, &amp; </s>
          <s xml:space="preserve">quomodo error <lb />vitetur, rem in genere hic examinamus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Phyſicis de omnibus non poſſumus immediate ſenſi-<lb />bus judicium ferre; </s>
          <s xml:space="preserve">datur &amp; </s>
          <s xml:space="preserve">alia legitima, licet non Ma-
</s>
          <pb facs="0021" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
thematica, ratiocinandi methodus, hoc axiomate funda-<lb />ta; </s>
          <s xml:space="preserve">Pro vero habendum omne quod ſi negetur ſocietas inter <lb />homines deſtruitur, aut his vivendi ratio adimitur. </s>
          <s xml:space="preserve">Ex <lb />qua propoſitione, quæ a nemine in dubium vocari po-<lb />teſt, regulæ philoſophandi Newtonianæ ſecunda &amp; </s>
          <s xml:space="preserve">tertia <lb />evidentiſſime deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Niſi enim, quæ ubique obtinent ubi Experimenta inſti-<lb />tuere licet, pro generaliter veris habeantur, effectuſque ſimi-<lb />les ex cauſa ſimili oriri ponantur, quis per momentum <lb />temporis tranquille vivere poterit?</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quotidie, nequidem ad illud attendendo, ſequentia ra-<lb />tiocinia unuſquiſque pro indubitatis habet, &amp; </s>
          <s xml:space="preserve">clare videt <lb />horum concluſiones, ſine præſentis rerum conſtitutionis <lb />deſtructione, in dubium vocari minime poſſe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ædificium, hodie in omnibus partibus firmiſſimum, cra-<lb />ſtino die ſponte non ruet: </s>
          <s xml:space="preserve">id eſt, partium corporum cohæ-<lb />ſiohorumque gravitas, quas, niſi interveniente cauſa extra-<lb />nea, nunquam mutatas vidi, aut audivi, hac nocte non <lb />mutabuntur; </s>
          <s xml:space="preserve">quia cauſa cohæſionis &amp; </s>
          <s xml:space="preserve">gravitatis eadem <lb />erit craſtino die ac hodie. </s>
          <s xml:space="preserve">Quod ratiocinium certum eſſe, <lb />niſi ex memorato principio deduci non poſſe, quis non <lb />videt?</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Tigna &amp; </s>
          <s xml:space="preserve">lapides, quæ in quacunque regione ad ædifi-<lb />cium conſtruendum apta ſunt, ſepoſita omni mutatione ex <lb />cauſa extranea, hîc tranſlata inſervire poterunt, &amp; </s>
          <s xml:space="preserve">de <lb />ruina non magis ſollicitus ero, ac in prima regione incolæ <lb />fuiſſent, ſi non tranſlatis tignis &amp; </s>
          <s xml:space="preserve">lapidibus, ipſi exhis do-<lb />mum conſtruxiſſent; </s>
          <s xml:space="preserve">id eſt, vis, qua partes cohærent, &amp;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0022" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
illa, qua corpora gravia ſunt, in variis regionibus non <lb />differunt.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Tali cibo per tot annos uſus ſum, &amp; </s>
          <s xml:space="preserve">hodie eo ſine timore <lb />veſcar.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ubi cicutam video, venenum ibi dari concludo, licet de <lb />hac ipſa quam video nullum experimentum ſumſero.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hæc omnia ratiocinia analogiam pro fundamento ha-<lb />bent, &amp; </s>
          <s xml:space="preserve">extra omne dubium eſt, nos a rerum Conditore <lb />neceſſitate cogi per analogiam ratiocinari &amp; </s>
          <s xml:space="preserve">hanc ideo ra-<lb />tiociniorum legitimum eſſe fundamentum. </s>
          <s xml:space="preserve">Analogiæ au-<lb />tem fundamentum eſt hoc; </s>
          <s xml:space="preserve">rerum univerſam congeriem <lb />legibus immutatis regi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quibus ſemel probatis, hac ratiocinandi methodo uti po-<lb />terimus etiam in illis occaſionibus, in quibus non ſimilis <lb />ratiocinandi neceſſitas datur. </s>
          <s xml:space="preserve">Argumento, quod in uno <lb />caſu procedit, in alio aſſenſum negare non debemus. </s>
          <s xml:space="preserve">Quis <lb />enim concipiet, quæ eodem modo probantur non æque <lb />certa eſſe? </s>
          <s xml:space="preserve">Adde ex neceſſitate quidem generaliter deduci, <lb />ratiocinandi methodum eſſe legitimam, ratiocinia vero pe-<lb />culiaria ab hac neceſſitate non pendere. </s>
          <s xml:space="preserve">Ex analogia <lb />concludo, cibum non eſſe veneſicum; </s>
          <s xml:space="preserve">an argumentum <lb />non procedit niſi cum eſurio? </s>
          <s xml:space="preserve">Ex neceſſitate ratiocinandi <lb />per analogiam, Mundum fixis legibus a rerum conditore <lb />regi, probamus; </s>
          <s xml:space="preserve">unde deducimus, &amp; </s>
          <s xml:space="preserve">ſublatâ neceſſitate, <lb />ratiocinia hæc extra dubium eſſe poſita.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Phyſicis ergo per Phænomena Naturæ Leges ſunt <lb />detegendæ; </s>
          <s xml:space="preserve">per inductionem pro generalibus habendæ; <lb /></s>
          <s xml:space="preserve">de cetero Mathematice ratiocinandum. </s>
          <s xml:space="preserve">Qui, quo hæc tra-
</s>
          <pb facs="0023" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
ctandæ Phyſices methodus fundamento nitatur, ſerio exa-<lb />minaverit, ſolam hanc eſſe legitimam, hypotheſeſque <lb />omnes eſſe rejiciendas, facillime percipiet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hæc de philoſophandi Methodo; </s>
          <s xml:space="preserve">reſtat ut deipſo Opere <lb />quid dicatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dividitur totum Opus in quatuor libros. </s>
          <s xml:space="preserve">Primus agit de <lb />corpore in genere, &amp; </s>
          <s xml:space="preserve">corporum ſolidorum motu. </s>
          <s xml:space="preserve">Secun-<lb />dus fluida ſpectat. </s>
          <s xml:space="preserve">Quæ ad lucem pertinent, in tertio tra-<lb />ctantur. </s>
          <s xml:space="preserve">In quarto tandem motus corporum cœleſtium, <lb />&amp; </s>
          <s xml:space="preserve">quæ in terris ad hos relationem habent, explicantur. <lb /></s>
          <s xml:space="preserve">Primi duo libri hoc Tomo continentur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut Phyſices ſtudium quantum fieri poteſt amœnum &amp; </s>
          <s xml:space="preserve"><lb />facile reddatur, omnia Experimentis eſſe elucidanda, i-<lb />pſaſque concluſiones Mathematicas, hac Methodo ſub o-<lb />culos eſſe ponendas, neceſſarium duxi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Qui ſcientiæ elementa conſcribit, non quid novi, quan-<lb />tum ad materiam, Orbi Litterato pollicetur; </s>
          <s xml:space="preserve">ideoque <lb />inutile duxi monere ubi reperiantur quæ hîc traduntur. <lb /></s>
          <s xml:space="preserve">Pro meo ſumſi quodcunque propoſito meo utile mihi vi-<lb />ſum eſt, credidique ſatis eſſe de hoc monere ad omnem <lb />furti ſuſpicionem vitandam. </s>
          <s xml:space="preserve">Malo gloriam, ſi quam ex <lb />paucis novis, quæ ſparſim in hoc Tractatu dantur, ſpe-<lb />rare poſſum amittere, quam alii ſuam detrahere; </s>
          <s xml:space="preserve">ſumat <lb />ergo quiſque quod ſuum credit, nihil mihi vindico.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quod Machinas attinet, quibus Experimenta inſtituen-<lb />da ſunt, varias aliorum Auctorum imitari curavi, multas <lb />inter has mutavi perfectioreſque reddidi, plures novas ad-<lb />didi. </s>
          <s xml:space="preserve">Neque mirum in hanc neceſſitatem illum incidiſſe,
</s>
          <pb facs="0024" />
          <s xml:space="preserve"><fw type="head">PRÆFATIO.</fw>
qui ad experimentum vocavit multa, de quibus nil ſimile <lb />nemo antea forte tentavit. </s>
          <s xml:space="preserve">Mathematicus enim circailla <lb />quæ Mathematicè demonſtrantur Experimenta ſuperflua <lb />credit: </s>
          <s xml:space="preserve">nos autem Mathematicas demonſtrationes, ſem-<lb />per abſtractas, faciliores reddi, ſi experimentis conclu-<lb />ſiones ſub oculos ponantur, extra omne dubium habuimus; <lb /></s>
          <s xml:space="preserve">in hoc imitati Anglos, quorum docendæ Philoſophiæ na-<lb />turalis Methodus nobis occaſionem dedit cogitandi de hac <lb />quam in hoc Opere ſecuti ſumus; </s>
          <s xml:space="preserve">illorum veſtigia tenere <lb />ſemper gloriabimur, qui, Principe Philoſophorum duce, <lb />primi in Philoſophicis detegendæ veritatis viam ingreſſi <lb />ſunt, fictas omnes hypotheſes ex Phyſicis amandantes.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Circa Machinas ulterius monebo, pleraſque conſtructas <lb />eſſe ab Artifice in hac urbe ingenioſiſſimo, &amp; </s>
          <s xml:space="preserve">ſimul Phi-<lb />loſopho non imperito, Joanne van Muſſchenbroek, cui <lb />omnes quæ hîc explicantur pleniſſime notæ ſunt; </s>
          <s xml:space="preserve">quod mo-<lb />nere non ingratum fore iis credidi, qui fortè quaſdam <lb />Machinas imitatas deſiderarent.</s>
          <s xml:space="preserve" />
        </p>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0024-01" />
          <label>0024-01</label>
        </figure>
        <pb facs="0025" />
        <fw type="head">MONITUM</fw>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De Demonſtrationibus quæ quantitates in-<lb />finitè exiguas pro fundamento habent.</head>
        <p>
          <s xml:space="preserve">IN multis demonſtrationibus, in ſcholiis datis, quantitates conſi-<lb />deramus infinite exiguas, &amp; </s>
          <s xml:space="preserve">ita haſce proponimus, ut &amp; </s>
          <s xml:space="preserve">a le-<lb />ctoribus intelligi poſſint, quibus illa, quæ de talibus quantitatibus <lb />a Geometris fuere explicata, ignota ſunt. </s>
          <s xml:space="preserve">Ne autem ipſis ſcrupulus <lb />ullus circa demonſtrationes in mente hæreat, &amp; </s>
          <s xml:space="preserve">ne ſibi de talibus de-<lb />monſtrationibus non exactam forment ideam, monitum præmittere <lb />non inutile credidi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit curva quæcunque ABC; </s>
          <s xml:space="preserve">quam in B tangit linea DE; </s>
          <s xml:space="preserve">ſint <lb />
<ptr xml:id="note-0025-01a" corresp="note-0025-01" type="noteAnchor" />
rectæ duæ quæcunque FB, fG, parallelæ, junctæ lineâ Ff; </s>
          <s xml:space="preserve">qua-<lb />rum fG curvam ſecat in b; </s>
          <s xml:space="preserve">ſit etiam Hb parallela Ff, ſecans tangen-<lb />tem DE in g. </s>
          <s xml:space="preserve">Si nunc concipiamus, Ff minui, id eſt lineam, fG <lb />motu parallelo ferri, dum etiam, per interſectionem hujus lineæ <lb />cum curva, motu parallelo fertur gbH, clarum eſt rationes inter <lb />gB, gH, HB, non mutari, donec, coincidentibus fG, FB li-<lb />neolæ omnes ſimul evaneſcant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0025-01" corresp="note-0025-01a" place="margin">TAB. XLVII <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In codem lineæ fG motu, rationes inter bB, bH, HB, con-<lb />tinuò mutantur, donec ubi evanuere nullæ rationes dentur; </s>
          <s xml:space="preserve">in ipſo <lb />autem momento evaneſcentiæ dantur rationes ab omnibus, quæ in <lb />præcedentibus momentis locum habuere diverſæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sic corpus quod cadit, &amp; </s>
          <s xml:space="preserve">libere cadendo continuò celerius move-<lb />tur, ubi ad punctum quodcunque pervenit, velocitatem habet majo-<lb />rem omnibus velocitatibus quas antequam ibi perveniret habuit, mi-<lb />norem autem omnibus illis, quas babebit poſtquam punctum præter-<lb />greſſum erit, peculiariſque eſt velocitas qua ad punctum appellit, ab <lb />omnibusaliis, quibus ad puncta alia quæcunque pervenit, diverſa. </s>
          <s xml:space="preserve">Eodem <lb />modo non agitur hîc de rationibus, quas habent quantitates ante eva-<lb />neſcentiam, aut poſtquam evanuere, ſed quas habent dum evaneſcunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In ipſo autem hoc momento evaneſcentiæ, quia curva in puncto <lb />contactus cum tangente conincidit, confunduntur puncta G, g, b, &amp; </s>
          <s xml:space="preserve"><lb />rationes inter bB, bH, HB, non differunt a rationibus gB, gH, <lb />HB, aut GB, GI, IB.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ubi in demonſtrationibus Bb infinitè exiguam ponimus, hanc <lb />pro recta habemus, &amp; </s>
          <s xml:space="preserve">memoratam æqualitatem rationum, etiam <lb />ponimus: </s>
          <s xml:space="preserve">Hæc tamen Mathematicè vera non ſunt, niſi in momen-<lb />to evaneſcentiæ ubi ergo loquimur de quantitatibus infinitè exiguis,
</s>
          <pb facs="0026" />
          <s xml:space="preserve"><fw type="head">MONITUM</fw>
intellige evaneſcentes, &amp; </s>
          <s xml:space="preserve">demonſtrationes nulli Mathematicæ demon-<lb />ſtrationi firmitate cedent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Clarum etiam eſt in momento evaneſcentiæ fb &amp; </s>
          <s xml:space="preserve">FB confundi <lb />reveraque æquales eſſe, ergo in demonſtratione quacunque in qua <lb />portionem curvæ bB infinite exiguam ponimus, quia hanc evane-<lb />ſcentem intelligimus, tuto lineas ut fb, &amp; </s>
          <s xml:space="preserve">FB pro æqualibus habemus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Demonſtrationes hæ diſtingui debent a demonſtrationibus in qui-<lb />bus error, licet inſenſibilis, datur, qualis eſt demonſtratio n. </s>
          <s xml:space="preserve">1222. <lb /></s>
          <s xml:space="preserve">ex qua deducimus ſonum, ſive majorem ſive minorem, eâdem ſemper <lb />velocitate per eundem aërem moveri; </s>
          <s xml:space="preserve">quod Mathematice verum non <lb />eſt, ſed differentia velocitatum, quando datur, ita exigua eſt, ut <lb />nulla arte percipi poſſit, quare differentiam in Phyſicis negligimus; </s>
          <s xml:space="preserve"><lb />eodem modo ac in praxi geometriæ, ubi montis altitudinem conſi-<lb />deramus, hanc non pro mutata habebimus, quamvis arenula adjecta <lb />ſit. </s>
          <s xml:space="preserve">In talibus autem demonſtrationibus non agitur de quantitatibus <lb />infinitè exiguis, ſed de quantitatibus finitis; </s>
          <s xml:space="preserve">numero enim finito <lb />non modo exprimi poteſt ratio inter arenulæ diametrum &amp; </s>
          <s xml:space="preserve">montis <lb />altitudinem, ſed &amp; </s>
          <s xml:space="preserve">inter illam diametrum &amp; </s>
          <s xml:space="preserve">telluris diametrum, aut <lb />ſi velis diſtantiam ſtellæ fixæ cujuſcunque a Tellure.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hiſce demonſtrationibus in quibus pro æqualibus habemus quan-<lb />titates, quæ tali inſenſibili quantitate differunt, error in demonſtra-<lb />tione ſenſibilis non erit, &amp; </s>
          <s xml:space="preserve">ideò, ubi de rebus ipſis agitur, de qui-<lb />bus ſenſibus dijudicamus, demonſtrationes hæ a Mathematicis jure <lb />admittuntur; </s>
          <s xml:space="preserve">ex Matheſi pura removentur, quæ tamen admittit, <lb />ut demonſtravimus, demonſtrationes quæ infinitè exiguas, aut eva-<lb />neſcentes, quantitates pro fundamento habent.</s>
          <s xml:space="preserve" />
        </p>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01" />
          <label>0026-01</label>
        </figure>
        <pb facs="0027" />
      </div>
      <div type="section">
        <head xml:space="preserve">INDEX CAPITUM.</head>
        <head xml:space="preserve">LIBRII. PARSI.</head>
        <head xml:space="preserve">De Corpore in Genere.</head>
        <note xml:space="preserve" place="margin"> <lb />CAP. I. # De Scopo Phyſices, &amp; Regulis Philoſophandi. # Pag. 1 <lb /># II. De Corpore in genere. # 3 <lb /># III. De Extenſione, Soliditate, &amp; Vacuo. # 5 <lb /># IV. De Diviſibilitate corporis in infinitum, &amp; Particularum ſubtilitate. # 6 <lb /><hi rend="small caps">Schol</hi>. 1. De Materiæ Diviſibilitate. # 8 <lb /># Infinitum Finito contineri. # ibid. <lb /># De Spirali Logarithmica, &amp; hujus Menſura. # 9 <lb /># De Infinitorum Claſſibus. # 10 <lb /># 2. De Partium ſubtilitate. # 12 <lb />CAP. V. De Cohæſione partium, ubi de Duritie, Mollitie, Fluiditate, &amp; E-<lb /># laſticitate agitur. # 13 <lb /><hi rend="small caps">Schol</hi>. De Effectu attractionis vitri in aquam. # 19 <lb /># De tubis Capillarihus. # ibid. <lb /># De Aſcenſu aquæ inter plana. # ibid. <lb /># De Motu guttæ inter plana. # 20 <lb />CAP. VI. De Motu in genere, ubi de loco &amp; Tempore. # 21 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">LIBRI I. PARS II.</head>
        <head xml:space="preserve">De Actionibus Potentiarum.</head>
        <note xml:space="preserve" place="margin"> <lb />CAP. VII. De Actionibus Potentiarum comparandis. # 22 <lb /># VIII. Generalia circa Gravitatem. # 24 <lb /># IX. De Trochlea ſimplici, Libra, &amp; Centro Gravitatis. # 28 <lb /><hi rend="small caps">Schol</hi>. 1. De Centro Gravitatis. # 33 <lb /># De centri Gravitatis inveſtigatione. # 34 <lb /># 2. Arithmetica Mechanica. # 35 <lb />CAP. X. De Vecte Machinarum ſimplicium prima. # 36 <lb /># XI. De Axe in Peritrochio, ſecundâ Machinarum ſimplicium, &amp; Rotis <lb /># dentatis. # 39 <lb /># XII. De Trochleâ, Machinarum ſimplicium tertiâ. # 40 <lb /># XIII. De Cuneo &amp; Cochleâ, Machinarum ſimplicium Quartâ &amp; Quintâ. # 43 <lb /><hi rend="small caps">Schol</hi>. 1. De Ligno findendo. # 46 <lb /># 2. Machinæ cujuſdam Examen. # 47
</note>
        <pb facs="0028" />
        <note xml:space="preserve" place="margin">
CAP. XIV. De Machinis compoſitis. # 47 <lb /># XV. De Potentiis obliquis. # 49 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">LIBRI I. PARS III.</head>
        <head xml:space="preserve">De Motibus, Potentiarum Actionibus, Variatis.</head>
        <note xml:space="preserve" place="margin"> <lb />CAP. XVI. De Naturæ legibus Newtonianis. # 57 <lb /># XVII. De Acceleratione &amp; Retardatione Gravium. # 59 <lb /># XVIII. De Deſcenſu Gravium ſuper plano inclinato. # 62 <lb /># XIX. De Oſcillatione Pendulorum. # 66 <lb /><hi rend="small caps">Schol</hi>. 1. De Motu in Cycloïde. # 71 <lb /># 2. De Centro Oſcillationis determinando. # 72 <lb /># 3. De quibusdam Cycloïdis proprietatibus. # 74 <lb /># 4. De Lineâ celerrimi deſcenſus. # 75 <lb />CAP. XX. De Projectione Gravium. # 77 <lb /># XXI. De Viribus centralibus. # 83 <lb /><hi rend="small caps">Schol</hi>. 1. Generalia de viribus centralibus. # 98 <lb /># 2. De Motu in circulo. # 99 <lb /># 3. De Motu in Ellipſi. # 101 <lb /># 4. De Motu in Orbitâ agitatâ. # 103 <lb /># 5. De Motu in Ellipſi agitatâ. # 106 <lb /># 6. De Computatione Motuum Apſidum in curvis parum a circulis diffe-<lb /># rentibus. # 108 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">LIBRI I. PARS IV.</head>
        <head xml:space="preserve">De Viribus inſitis, &amp; Colliſione corporum.</head>
        <note xml:space="preserve" place="margin"> <lb />CAP. XXII. De Viribus corporibus motis inſitis. # 109 <lb /># XXIII. De Colliſione Corporum. # 120 <lb /><hi rend="small caps">Schol</hi>. 1. De viribus amiſſis &amp;c. # 141 <lb /># 2. De Percuſſione Corporum lineis rigidis inter ſe cohærentium, &amp; cir-<lb /># ca centra agitatorum. # 143 <lb /># 3. Examen Experimenti circa corpora in lancem, aut Brachium, libræ <lb /># impingentia. # 146 <lb /># 4. De Centro Oſcillationis, &amp; Percuſſionis. # 150 <lb />CAP. XXIV. De Congreſſu corporum Elaſticorum. # 151 <lb /><hi rend="small caps">Schol</hi>. 1 Uberior demonſtratio de æqualitate virium ante &amp; poſt ictum. # 160 <lb /># 2. Illuſtratio circa mutuam Corporum elaſticorum Actionem. # 161 <lb /># 3. Paradoxi explicatio. # 163
</note>
        <pb facs="0029" />
        <note xml:space="preserve" place="margin">
CAP. XXV. De Motu compoſito. # Pag. 164 <lb /># XXVI. De Percuſſione obliqua. # 168 <lb /># XXVII. De Colliſione compoſita. # 172 <lb /><hi rend="small caps">Schol</hi>. 1. Demonſtrationes concurſutrium corporum ineadem linea motorum. # 180 <lb /># 2. De concurſu trium Corporum elaſticorum, poſitâ elaſterii relaxatione <lb /># minus ſubitâ. # 182 <lb /># 3. De virium æqualitate in corporibus elaſticis ante &amp; poſt ictum. # 184 <lb />CAP. XXVIII. De Motu Centri gravitatis. # ibid. <lb /><hi rend="small caps">Schol</hi>. 1. De Motu abſoluto &amp; relativo variorum corporum ſimul conſiderato-<lb /># rum. # 187 <lb /># 2. De Motu Centri gravitatis trium corporum, in quibuſdam caſibus. # 188 <lb /># 3. Motus determinatio in caſu peculiari. # 189 <lb />CAP. XXIX. De Legibus Elaſticitatis. # 190 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">LIBRI II. PARS I.</head>
        <head xml:space="preserve">De Gravitate &amp; Preſſione Fluidorum.</head>
        <note xml:space="preserve" place="margin"> <lb />CAP. I. De Gravitate partium Fluidorum, &amp; illius effectu in ipſis Fluidis. # 200 <lb /># II. De Actione Fluidorum in Fundos, Latera, &amp; Opercula vaſorum qui-<lb /># bus continentur. # 204 <lb /># III. De Solidis Fluidis immerſis. # 211 <lb /># IV. De Comparandis Fluidorum Denſitatibus. # 219 <lb /># V. De Hydroſtatica Solidorum Comparatione. # 222 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">LIBRI II. PARS II.</head>
        <head xml:space="preserve">De Motu &amp; Reſiſtentia Fluidorum.</head>
        <note xml:space="preserve" place="margin"> <lb /># CAP. VI. De Celeritate Fluidi ex preſſione fluidi ſuperincumbentis. # 226 <lb /># VII. De Fluidis proſilientibus. # 229 <lb /># VIII. De Fluido ex Vaſis profluente, &amp; Irregularitatibus in hoc motu. # 238 <lb /><hi rend="small caps">Schol</hi>. Computatio de quantitate fluidi ex foramine fluentis. # 246 <lb />CAP. IX. De Curſu Fluminum. # ibid. <lb /># X. De Motu Undarum. # 252 <lb /># XI. De Reſiſtentia Fluidorum. # 257 <lb /><hi rend="small caps">Schol</hi>. De Reſiſtentiarum differentiis pro diverſis corporum figuris. # 274 <lb />CAP. XII. De Retardatione Corporum in Fluidis motorum. # 275 <lb /><hi rend="small caps">Schol</hi>. 1. De Logarithmica. # 283
</note>
        <pb facs="0030" />
        <note xml:space="preserve" place="margin">
<hi rend="small caps">Schol</hi>. 2. De Retardatione in genere. # 284 <lb /># 3. De Retardatione ex prima cauſa. # 285 <lb /># 4. De Retardatione ex ſecunda cauſa. # 286 <lb /># 5. De ambabus Retardationibus conjunctim. # 287 <lb /># 6. De Corporibus in altum projectis. # 290 <lb /># 7. De Corporibus in Fluidis cadentibus. # 291 <lb /># 8. Illuſtratio quorundam quæ ad Retardationem ſpectant. # 292 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">LIBRI II. PARS III.</head>
        <head xml:space="preserve">De Aëre &amp; aliis Fluidis Elaſticis.</head>
        <note xml:space="preserve" place="margin"> <lb />CAP. XIII. Aërem Fluidorum Proprietates habere. # 296 <lb /># XIV. De Aëris Elaſticitate. # 299 <lb /># XV. De quibuſdam aliis Fluidis Elaſticis. # 306 <lb /># XVI. De Antlia Pneumatica. # 309 <lb /># XVII. Experimenta varia circa Aëris gravitatem, &amp; hujus Elaſticita-<lb /># tem. # 313 <lb /># XVIII. Variarum Machinarum, quarum actio ab Aëre pendet, Deſcriptio, <lb /># &amp; harum effectuum Explicatio. # 322 <lb /># XIX. De Aëris motu Undulatorio, ubi de ſone. # 327 <lb /><hi rend="small caps">Schol</hi>. 1. De Agitatione particularum aërearum, &amp; Soni velocitate. # 342 <lb /># 2. De Soni intenſitate. # 344 <lb /></note>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-01" />
          <label>0030-01</label>
        </figure>
        <pb facs="0031" n="1" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0031-01" />
          <label>0031-01</label>
        </figure>
      </div>
      <div type="section">
        <head xml:space="preserve">PHYSICES</head>
        <head xml:space="preserve">ELEMENTA MATHEMATICA, <lb />EXPERIMENTIS CONFIRMATA.</head>
        <head rend="italics" xml:space="preserve">LIBER I. <lb />Pars I. de Corpore in genere.</head>
        <head xml:space="preserve">CAPUT I. <lb />De Scopo Phyſices &amp; Regulis philoſophandi.</head>
        <p>
          <s xml:space="preserve">PHyſica circa res naturales &amp; </s>
          <s xml:space="preserve">illarum Phænomena ver-<lb />ſatur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1. &amp; 2.</head>
        <p>
          <s xml:space="preserve">Res naturales ſunt omnia corpora; </s>
          <s xml:space="preserve">congerieſque illorum <lb />
<ptr xml:id="note-0031-01a" corresp="note-0031-01" type="noteAnchor" />
omnium univerſum vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0031-01" corresp="note-0031-01a" place="margin">1.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Phænomena naturalia, ſunt omnes ſitus &amp; </s>
          <s xml:space="preserve">omnes mo-<lb />
<ptr xml:id="note-0031-02a" corresp="note-0031-02" type="noteAnchor" />
tus corporum naturalium, ab actione entis intelligentis imme-<lb />diate non pendentes, &amp; </s>
          <s xml:space="preserve">qui a nobis ſenſibus obſervari poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0031-02" corresp="note-0031-02a" place="margin">2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non excludimus ex numero Phænomenorum natu-<lb />ralium motus, qui in corpore noſtro ad voluntatem fiunt, <lb />pendent enim a motu muſculorum, qui etiam motu alio <lb />agitantur, in hiſce ſolus motus ex actione immediata men-<lb />tis oriundus, &amp; </s>
          <s xml:space="preserve">nobis omnino ignotus, non eſt Phænome-<lb />non naturale.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0032" n="2" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Omnes hi motus regulis certis peraguntur &amp; </s>
          <s xml:space="preserve">legibus ſem-<lb />per iisdem adſtricti ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sol quotidie oritur &amp; </s>
          <s xml:space="preserve">occidit, tempuſque ortus &amp; </s>
          <s xml:space="preserve">occa-<lb />ſus, pro anni tempeſtate &amp; </s>
          <s xml:space="preserve">loco, ſemper determinatur, ejuſ-<lb />dem ſpeciei plantæ, iiſdem poſitis circumſtantiis, eodemmo-<lb />do producuntur &amp; </s>
          <s xml:space="preserve">creſcunt, &amp; </s>
          <s xml:space="preserve">ſic de cæteris. </s>
          <s xml:space="preserve">In iis ipſis <lb />quæ nobis omnino fortuita &amp; </s>
          <s xml:space="preserve">incerta apparent, certas ob-<lb />ſervari regulas extra omne dubium eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Phyſica Phænomena naturalia explicat, id eſt, illorum <lb />
<ptr xml:id="note-0032-01a" corresp="note-0032-01" type="noteAnchor" />
cauſas tradit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0032-01" corresp="note-0032-01a" place="margin">3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum in illas cauſas inquirimus, ipſum corpus in genere <lb />examinandum eſt, deinde quibus regulis rerum conditor <lb />omnes motus peragi voluerit. </s>
          <s xml:space="preserve">Hæ regulæ, vocantur leges <lb />Naturæ.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p rend="italics">
          <s xml:space="preserve">Naturæ lex ergo eſt, Regula &amp; </s>
          <s xml:space="preserve">norma, ſecundum quam <lb />
<ptr xml:id="note-0032-02a" corresp="note-0032-02" type="noteAnchor" />
Deus voluit certos motus ſemper, id eſt, in omnibus occaſio-<lb />nibus, peragi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0032-02" corresp="note-0032-02a" place="margin">4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eſt ideo noſtri reſpectu lex naturæ, omnis effectus, qui <lb />
<ptr xml:id="note-0032-03a" corresp="note-0032-03" type="noteAnchor" />
in omnibus occaſionibus idem eſt, cujus cauſa nobis eſt <lb />ignota, &amp; </s>
          <s xml:space="preserve">quem videmus exnulla lege, nobis nota, fluere <lb />poſſe, licet ex ſimpliciori lege, nobis ignota, fluat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0032-03" corresp="note-0032-03a" place="margin">5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Noſtri enim reſpectu non intereſt, utrum quid immedi-<lb />ate a Dei voluntate pendeat, an vero mediante cauſa, cu-<lb />jus nullam ideam habemus, producatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Leges naturæ, niſi ex examine Phænomenorum naturali-<lb />um, non poſſunt elici.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ope legum hac methodo detectarum Phænomena alia ex-<lb />plicari debent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In inveſtigatione Naturæ legum, ſequentes Regulæ New-<lb />tonianæ obſervandæ veniunt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Regula</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Cauſas rerum Naturalium non plures admitti debere <lb />
<ptr xml:id="note-0032-04a" corresp="note-0032-04" type="noteAnchor" />
quam quæ &amp; </s>
          <s xml:space="preserve">veræ ſint, &amp; </s>
          <s xml:space="preserve">earum Phænomenis explicandis <lb />ſufficiant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0032-04" corresp="note-0032-04a" place="margin">6.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0033" n="3" />
        <fw type="head">MATHEMATICA, LIB. I. CAP. I.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Regula</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Effectuum Naturalium ejuſdem generis eaſdem eſſe cauſas. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0033-01a" corresp="note-0033-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0033-01" corresp="note-0033-01a" place="margin">7.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Regula</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Qualitates corporum, quæ intendi &amp; </s>
          <s xml:space="preserve">remitti nequeunt, quæ-<lb />
<ptr xml:id="note-0033-02a" corresp="note-0033-02" type="noteAnchor" />
que corporibus omnibus competunt, in quibus experimenta in-<lb />ſtituere licet, pro qualitatibus corporum univer ſorum haben-<lb />das eſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0033-02" corresp="note-0033-02a" place="margin">8.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT II.</head>
        <head rend="italics" xml:space="preserve">De Corpore in genere.</head>
        <p>
          <s xml:space="preserve">QUod primum in corpore conſiderandum venit eſt exten-<lb />
<ptr xml:id="note-0033-03a" corresp="note-0033-03" type="noteAnchor" />
ſio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0033-03" corresp="note-0033-03a" place="margin">9.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Extenſio quid ſit, nemoignorat, hujus idea fere ſem-<lb />per menti noſtræ obverſatur, &amp; </s>
          <s xml:space="preserve">eſt ſimpliciſſima; </s>
          <s xml:space="preserve">unde, li-<lb />cet diſtinctiſſima ſit, verbis tamen nullis deſcribi poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Omne corpus eſt extenſum, ſublata corporis extenſione <lb />integrum tollitur corpus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Omne extenſum non eſt corpus, in quo vero corpus a <lb />ſpatio differat, non poteſt determinari, niſi prius examinatis <lb />aliis corporis proprietatibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Secunda quæ corpus conſideranti ſeſe offert eſt ſoliditas. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0033-04a" corresp="note-0033-04" type="noteAnchor" />
Corpus, omne aliud corpus ex loco a ſe occupato excludit, <lb />&amp; </s>
          <s xml:space="preserve">corpora fluidiſſima æque ac maxime dura ea proprietate <lb />gaudent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0033-04" corresp="note-0033-04a" place="margin">10.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tertia corporis proprietas eſt diviſibilitas, eo quod cor-<lb />
<ptr xml:id="note-0033-05a" corresp="note-0033-05" type="noteAnchor" />
pus eſt extenſum, etiam eſt diviſibile. </s>
          <s xml:space="preserve">Extenſio enim alia <lb />extenſione minor ſemper poteſt concipi, unde videmus in <lb />omni extenſione partes dari, quæ partes in corpore a ſein-<lb />vicem poſſunt ſeparari; </s>
          <s xml:space="preserve">quia</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0033-05" corresp="note-0033-05a" place="margin">11.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus quarta proprietate præditum eſt, quod poſſit de <lb />
<ptr xml:id="note-0033-06a" corresp="note-0033-06" type="noteAnchor" />
loco in locum transferri, unde corpus mobile dicitur. </s>
          <s xml:space="preserve">Vi <lb />autem inſitâ in motu perſeverat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0033-06" corresp="note-0033-06a" place="margin">12.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando nullum datur obſtaculum, corpus ictui minimo <lb />
<ptr xml:id="note-0033-07a" corresp="note-0033-07" type="noteAnchor" />
cedit, major tamen vis requiritur ad corpus movendum ma-<lb />jori celeritate quam minori, &amp; </s>
          <s xml:space="preserve">ad movendum corpus ma-<lb />jus quam minus, ſi æqualis fuerit velocitas; </s>
          <s xml:space="preserve">vis etiam ma-
</s>
          <pb facs="0034" n="4" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
jor iisdem in caſibus requiritur, ut corpus in motu ſiſtatur; <lb /></s>
          <s xml:space="preserve">corpus ergo quieſcens motui &amp; </s>
          <s xml:space="preserve">corpus motum quieti reſiſtit: </s>
          <s xml:space="preserve"><lb />illud oritur ex materiæ Inertia, quæ in omnibus corporibus <lb />quantitati materiæ proportinalis eſt; </s>
          <s xml:space="preserve">quia omnibus materiæ <lb />particulis æqualiter competit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0033-07" corresp="note-0033-07a" place="margin">13.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omne corpus figura eſt præditum, &amp; </s>
          <s xml:space="preserve">Figurabile; </s>
          <s xml:space="preserve">ſiab omni <lb />
<ptr xml:id="note-0034-01a" corresp="note-0034-01" type="noteAnchor" />
parte in corpore diviſiones fiant, &amp; </s>
          <s xml:space="preserve">partes removeantur, <lb />quod in medio remanet ab omni parte terminatum eſt, &amp; </s>
          <s xml:space="preserve"><lb />neceſſario figura præditum; </s>
          <s xml:space="preserve">Idem corpus varias poteſt in-<lb />duere figuras, quia in partes poteſt reſolvi, &amp; </s>
          <s xml:space="preserve">quia hæ, quæ mo-<lb />biles ſunt, in vario ordine erga ſe invicem diſponi queunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0034-01" corresp="note-0034-01a" place="margin">14.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT III.</head>
        <head rend="italics" xml:space="preserve">De Extenſione, Soliditate, &amp; Vacuo.</head>
        <p>
          <s xml:space="preserve">HIc conſideranda venit in Scholis decantata quæſtio de Va-<lb />
<ptr xml:id="note-0034-02a" corresp="note-0034-02" type="noteAnchor" />
cuo; </s>
          <s xml:space="preserve">fcilicet an detur extenſio omni materia deſtituta, <lb />hæc enim extenſio vocatur Vacuum, Inane, aut Spatium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0034-02" corresp="note-0034-02a" place="margin">15.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vacuum revera dari ex Phænomenis probatur, &amp; </s>
          <s xml:space="preserve">ideo <lb />in cap. </s>
          <s xml:space="preserve"><hi rend="small caps">XII</hi>. </s>
          <s xml:space="preserve">lib. </s>
          <s xml:space="preserve"><hi rend="small caps">IV</hi>. </s>
          <s xml:space="preserve">quæſtionem hanc ad examen voca-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vacuum poſſibile eſſe ex ſolo examine idearum deduci-<lb />tur. </s>
          <s xml:space="preserve">Omne enim quod clare concipimus exiſtere poſſe, poſ-<lb />ſibile eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæſtio ergo eo redit, an habeamus ideam extenſionis <lb />non ſolidæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Soliditatis ideam acquirimus contactu; </s>
          <s xml:space="preserve">corpora quæ-<lb />
<ptr xml:id="note-0034-03a" corresp="note-0034-03" type="noteAnchor" />
dam nobis reſiſtere ſentimus, &amp; </s>
          <s xml:space="preserve">quidem omnibus momen-<lb />tis nobis illa reſiſtunt, quæ deſcenſum verſus inferiora loca <lb />impediunt; </s>
          <s xml:space="preserve">ex qua reſiſtentia apparet corpus ex loco a ſe oc-<lb />cupato omne aliud corpus excludere; </s>
          <s xml:space="preserve">id eſt, illud ſolidita-<lb />te præditum eſſe, quam ſoliditatis ideam ad corpora ſubtilio-<lb />ra, quæ propter partium tenuitatem ſub ſenſus non cadunt, <lb />transferimus: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">experientia conſtat, hæc ipſa, æque ac <lb />duriſſima, aliis corporibus reſiſtere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0034-03" corresp="note-0034-03a" place="margin">16.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0035" n="5" />
        <fw type="head">MATHEMATICA, LIB. I. CAP. III.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Aër in quo vivimus fere ſemper viſum &amp; </s>
          <s xml:space="preserve">tactum noſtrum <lb />
<ptr xml:id="note-0035-01a" corresp="note-0035-01" type="noteAnchor" />
fugit, in antlia tamen exacte clauſa embolo reſiſtit, ita ut nul-<lb />la vi ad antliæ fundum protrudi poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0035-01" corresp="note-0035-01a" place="margin">17.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In extenſionis autem idea non continetur idea ſolidita-<lb />tis, hanc non niſi ex contactu, illam vero ſine illo acquiri-<lb />mus, &amp; </s>
          <s xml:space="preserve">ſi quis nunquam corpus tetigiſſet, ei ſoliditas omni-<lb />no ignota eſſet.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Conſpiciat quis idolum inter ſpeculum cavum &amp; </s>
          <s xml:space="preserve">obje-<lb />
<ptr xml:id="note-0035-02a" corresp="note-0035-02" type="noteAnchor" />
ctum ſpeculo expoſitum; </s>
          <s xml:space="preserve">idolum tale non reſiſtit, corpus <lb />tamen æque denſum ac corpus repræſentatum videtur: </s>
          <s xml:space="preserve">poſ-<lb />ſunt enim colores magis vividi in idolo quam ipſius objecti <lb />colores repræſentari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0035-02" corresp="note-0035-02a" place="margin">18.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si homo nihil unquam præter talia idola vidiſſet, &amp; </s>
          <s xml:space="preserve">ipſi-<lb />us corpus tali idolo ſimile eſſet, an ullam ſoliditatis haberet <lb />ideam? </s>
          <s xml:space="preserve">non videtur; </s>
          <s xml:space="preserve">extenſionis tamen certiſſime habebit. <lb /></s>
          <s xml:space="preserve">Hic non agitur de eo quid ſit tale idolum, de ideis diſpu-<lb />tamus, ſat eſt illud dari.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In ſoliditatis privatione non omnis ſita eſt differentia inter <lb />Spatium &amp; </s>
          <s xml:space="preserve">Corpus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Spatium eſt infinitum, ac nullis terminari poſſe limitibus, <lb />
<ptr xml:id="note-0035-03a" corresp="note-0035-03" type="noteAnchor" />
rem attente conſideranti patebit. </s>
          <s xml:space="preserve">Corpora autem finita <lb />dantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0035-03" corresp="note-0035-03a" place="margin">19.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſpatio partes dari clare videmus, a ſe invicem vero <lb />
<ptr xml:id="note-0035-04a" corresp="note-0035-04" type="noteAnchor" />
ſeparari nequeunt, immobiles ſunt, ut &amp; </s>
          <s xml:space="preserve">ipſum ſpatium. </s>
          <s xml:space="preserve">Cor-<lb />poris vero partes ſeparationem patiuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0035-04" corresp="note-0035-04a" place="margin">20.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Spatii idea ſimpliciſſima eſt; </s>
          <s xml:space="preserve">corporis magis eſt compo-<lb />ſita.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Soliditas a quibuſdam impenetrabilitas vocatur, &amp; </s>
          <s xml:space="preserve">ex na-<lb />
<ptr xml:id="note-0035-05a" corresp="note-0035-05" type="noteAnchor" />
tura extenſionis illam deducere conantur; </s>
          <s xml:space="preserve">pedi cubico ex. <lb /></s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">extenſionis, pes alter cubicus extenſionis addi non poteſt, <lb />quin habeamus duos pedes cubicos, ſinguli enim habent om-<lb />nia quæ ad illam magnitudinem conſtituendam requirun-<lb />tur; </s>
          <s xml:space="preserve">pars ergo una ſpatii partes omnes alias excludit &amp; </s>
          <s xml:space="preserve">ipſa <lb />illas admittere non poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0035-05" corresp="note-0035-05a" place="margin">21.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0036" n="6" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Reſp. </s>
          <s xml:space="preserve">partem ſpatii in alium locum translatam contradi-<lb />ctionem involvere; </s>
          <s xml:space="preserve">ex immobilitate ergo partium ſpatii, <lb />non ex impenetrabilitate, ſeu ſoliditate, ſequitur, duas par-<lb />tes ſpatii confundi non poſſe.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IV.</head>
        <head rend="italics" xml:space="preserve">De Diviſibilitate Corporis in infinitum, &amp; parti-<lb />cularum Subtilitate.</head>
        <p>
          <s xml:space="preserve">EO quod corpus eſt extenſum etiam eſt diviſibile, ideſt, <lb />in eo partes conſiderari poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Differt tamen corporis diviſibilitas, ab extenſionis divi-<lb />ſibilitate, illius enim partes a ſe invicem ſeparari poſſunt. <lb /></s>
          <s xml:space="preserve">Hæc vero proprietas cum ab extenſione pendeat, in exten-<lb />ſione examinari debet: </s>
          <s xml:space="preserve">demonſtrata deinde facile ad corpus <lb />transferri poterunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus eſt diviſibile in infinitum, id eſt, in ejus exten-<lb />
<ptr xml:id="note-0036-01a" corresp="note-0036-01" type="noteAnchor" />
ſione nulla pars quantumvis parva poteſt concipi, quin de-<lb />tur adhuc alia minor.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0036-01" corresp="note-0036-01a" place="margin">22.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit linea AD, ad BF, perpendicularis; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">GH, ad <lb />
<ptr xml:id="note-0036-02a" corresp="note-0036-02" type="noteAnchor" />
parvam ab A diſtantiam, ad eandem etiam perpendicula-<lb />ris; </s>
          <s xml:space="preserve">centris C,C,C,&amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">radiis CA, CA, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">deſcribantur <lb />circuli ſecantes lineam GH, in punctis e, e &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">quo major <lb />eſt radius AC, eo minor eſt pars e G: </s>
          <s xml:space="preserve">radius poteſt in infi-<lb />nitum augeri &amp; </s>
          <s xml:space="preserve">ſic ergo minui pars e G; </s>
          <s xml:space="preserve">quæ tamen nunquam <lb />ad nihilum poteſt redigi, quia circulus cum linea recta BF, <lb />coincidere nunquam poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0036-02" corresp="note-0036-02a" place="margin">TAB. II. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Partes ergo magnitudinis cujuſcunque in infinitumpoſſunt <lb />minui &amp; </s>
          <s xml:space="preserve">nullus diviſionis datur finis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Innumeris aliis idem probari poteſt Mathematicis demon-<lb />ſtrationibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hac diviſibilitate deducimus, data quavis materiæ par-<lb />
<ptr xml:id="note-0036-03a" corresp="note-0036-03" type="noteAnchor" />
ticula quantumvis exigua, &amp; </s>
          <s xml:space="preserve">dato ſpatio quovis finito ut-<lb />cunque amplo, poſſibile eſſe, ut materia iſtius arenulæ per <lb />totum illud ſpatium diffundatur, atque ipſum ita adimpleat,
</s>
          <pb facs="0037" n="7" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA, LIB. I. CAP. IV.</fw>
ut nullus ſit in eo porus cujus diameter minimam datam ſu-<lb />peret lineam. </s>
          <s xml:space="preserve">Quod ut demonſtremus, ſpatium implendum, <lb />diviſum concipimus in cellulas cubicas, quarum latera æqua-<lb />lia aut minora ſint minimâ lineâ datâ: </s>
          <s xml:space="preserve">numerus cellularum <lb />finitus erit, &amp; </s>
          <s xml:space="preserve">in tot partes arenula data dividi poterit, quot <lb />cellulæ dantur; </s>
          <s xml:space="preserve">ita ut in ſingulis cellulis particulam unam <lb />poſitam concipere poſſimus: </s>
          <s xml:space="preserve">concipiendum ulterius ex ſin-<lb />gulis hiſce particulis minimis globum cavum formari. </s>
          <s xml:space="preserve">Pro-<lb />pter materiæ diviſibilitatem poteſt globus cavus ſemper au-<lb />geri minuendo materiæ craſſitiem, cum autem in ſingulis <lb />cellulis globus talis detur, poterunt ſinguli augeri, donec <lb />vicini ſeſe mutuo tangant, ut omnes ſimul ſpatium impleant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0036-03" corresp="note-0036-03a" place="margin">23.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Objectiones præcipuæ, contra diviſibilitatem materiæ in <lb />
<ptr xml:id="note-0037-01a" corresp="note-0037-01" type="noteAnchor" />
infinitum, ſunt, infinitum finito contineri non poſſe; </s>
          <s xml:space="preserve">ex di-<lb />viſibilitate in infinitum ſequi, omnia corpora eſſe æqualia, <lb />aut infinitum alio infinito majus dari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0037-01" corresp="note-0037-01a" place="margin">24.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sed hiſce reſponſio facilis eſt, infinito non tribuendæ ſunt <lb />proprietates quantitatis finitæ &amp; </s>
          <s xml:space="preserve">determinatæ. </s>
          <s xml:space="preserve">Partes infinite <lb />parvas, numero infinito, in quantitate finita darinon poſle, quis <lb />unquam probavit; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">omnia infinita eſſe æqualia? </s>
          <s xml:space="preserve">Con-<lb />trarium in Scholio ſequenti demonſtratur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si, examinatâ poſſibili materia diviſibilitate, partium ſub-<lb />
<ptr xml:id="note-0037-02a" corresp="note-0037-02" type="noteAnchor" />
tilitatem in corporibus ad examen revocemus, hanc captum <lb />noſtrum in immenſumſuperare conſtabit; </s>
          <s xml:space="preserve">innumeraque in re-<lb />rum natura dantur exempla talium particularum a ſe invicem <lb />ſeparatarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0037-02" corresp="note-0037-02a" place="margin">25.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Boileus hæc variis probat argumentis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Loquitur de filo ſerico trecentis ulnis Anglicanis longo &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0037-03a" corresp="note-0037-03" type="noteAnchor" />
ponderis duorum granorum cum ſemiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0037-03" corresp="note-0037-03a" place="margin">26.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Folia auri menſuravit, &amp; </s>
          <s xml:space="preserve">ponderavit, &amp; </s>
          <s xml:space="preserve">reperit quinqua-<lb />
<ptr xml:id="note-0037-04a" corresp="note-0037-04" type="noteAnchor" />
ginta pollices quadratos unicum tantum ponderare granum; <lb /></s>
          <s xml:space="preserve">ſi unius pollicis longitudo dividatur in ducentas partes, omnes <lb />oculo diſtingui poterunt, dantur ergo in pollice quadrato <lb />partes viſibiles quadraginta millia, &amp; </s>
          <s xml:space="preserve">in uno auri grano par-<lb />tium numerus eſt duarum millionum, quas partes viſibiles <lb />adhuc poſſe dividi nemo negabit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0037-04" corresp="note-0037-04a" place="margin">27.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0038" n="8" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Octo granis auri deaurari poteſt integra argenti uncia, <lb />
<ptr xml:id="note-0038-01a" corresp="note-0038-01" type="noteAnchor" />
quæ deinde porrigitur in filum longitudinis tredecim millium <lb />pedum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0038-01" corresp="note-0038-01a" place="margin">28.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In corporibus odoriferis majorem adhuc partium percipi-<lb />
<ptr xml:id="note-0038-02a" corresp="note-0038-02" type="noteAnchor" />
mus ſubtilitatem &amp; </s>
          <s xml:space="preserve">quidem a ſe invicem ſeparatarum, plura <lb />longo tempore fere nihil ſui ponderis amittunt &amp; </s>
          <s xml:space="preserve">ſpatium <lb />fatis magnum particulis odoriferis continuo implent, qui <lb />computum de tali ſubtilitate inire voluerit in illarum nume-<lb />ro quid portenti facile reperiet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0038-02" corresp="note-0038-02a" place="margin">29.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ope microſcopiorum objecta quæ viſum fugiunt magna <lb />
<ptr xml:id="note-0038-03a" corresp="note-0038-03" type="noteAnchor" />
videntur, dantur animalcula per optima microſcopia vix vi-<lb />ſibilia, habent tamen partes omnes ad vitam neceſſarias, ſan-<lb />guinem, &amp; </s>
          <s xml:space="preserve">alia liquida: </s>
          <s xml:space="preserve">ſubtilitas partium illa componentium <lb />quanta ſit quis non videt?</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0038-03" corresp="note-0038-03a" place="margin">30.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM.</head>
        <head rend="italics" xml:space="preserve">De Materiæ Diviſibilitate</head>
        <p>
          <s xml:space="preserve">In finitum vocant quidam illud, quo non datur majus, &amp; </s>
          <s xml:space="preserve">negant materiam, <lb />eſſe diviſibilem in infinitum, quod, hac Infiniti data definitione, libenter <lb />concedimus. </s>
          <s xml:space="preserve">Corpus in talem numerum partium, qui ſit omuium maximus, <lb />non poſſe dividi, nullumque diviſionis dari limitem, defendimus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">Infinitum finito contineri.</head>
        <p>
          <s xml:space="preserve">Infinitum eſt quod finitum ſuperat; </s>
          <s xml:space="preserve">partes autem numero, omnem finitum nu-<lb />
<ptr xml:id="note-0038-04a" corresp="note-0038-04" type="noteAnchor" />
merum ſuperante, in quantitate finita contineri, ex conſideratione progreſſionis <lb />geometricæ decreſcentis deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0038-04" corresp="note-0038-04a" place="margin">31.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Progreſſionem hanc Ex gr. </s>
          <s xml:space="preserve">{1/2}, {1/4}, {1/8}, {1/16} &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">in infinitum poſſe continuari, <lb />nullumque dari continuationis limitem quis non videt? </s>
          <s xml:space="preserve">Omnium tamen ter-<lb />minorum ſummam nunquam excedere unitatem; </s>
          <s xml:space="preserve">imo exacte unitati æquari <lb />demonſtramus, ſi revera in infinitum continuatam concipiamus progreſſio-<lb />nem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit linea AE unitas; </s>
          <s xml:space="preserve">hujus dimidium AB eſt primus terminus {1/2}; </s>
          <s xml:space="preserve">BC di-<lb />
<ptr xml:id="note-0038-05a" corresp="note-0038-05" type="noteAnchor" />
midium reliqui eſt terminus ſecundus {1/4}; </s>
          <s xml:space="preserve">tertius terminus erit CD {1/8}; </s>
          <s xml:space="preserve">dividen-<lb />do DE in duas partes æquales habetur terminus ſequens; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eodem modo <lb />in infinitum continuari poteſt ſeries, ſemperque defectus ſummæ termino-<lb />rum ſeriei AB, BC, CD, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">ab integra linea AE ultimo termino ipſius <lb />ſeriei æqualis erit quantumvis hæc continuetur. </s>
          <s xml:space="preserve">Quamdiu autem numerus <lb />terminorum eſt finitus denominator fractionis, ultimum terminum exprimen-<lb />tis, eſt numerus finitus, &amp; </s>
          <s xml:space="preserve">ultimus terminus eſt pars finita, qua ſumma ſeriei <lb />ab integra unitate deficit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0038-05" corresp="note-0038-05a" place="margin">TAB. I. <lb />fig 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sivero numerus terminorum lomnem finitum numerum ſuperet, denomi-<lb />nator ultimi termini omnem numerum finitum ſuperabit, partemque lineæ <lb />AE exprimet omni parte finita minorem, ideoque differentia ſumman ſeriei
</s>
          <pb facs="0039" n="9" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I CAP. IV.</fw>
&amp; </s>
          <s xml:space="preserve">lineam AE inter evaneſcet, id eſt erunt æquales quantitates hæ. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">E. </s>
          <s xml:space="preserve">D.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Infiniti ideam non habemus; </s>
          <s xml:space="preserve">ideo ideis non aſſequimur, quæ de infinito de-<lb />monſtramus; </s>
          <s xml:space="preserve">quæ tamen ex indubitatis principiis immediate ſequuntur, cer-<lb />ta ſunt, &amp;</s>
          <s xml:space="preserve">, quæ ex hiſce deducuntur, etiam in dubium vocari nequeunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Innumera circa Materiæ diviſibilitatem captum noſtrum ſuperantia eviden-<lb />tiſſime demonſtrantur, inter hæc notatu maximedigna ſunt, quæ ſpectant cur-<lb />vam ſpiralem logarithmicam dictam.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De Spirali logaritbmicâ, &amp; bujus menſurâ.</head>
        <p>
          <s xml:space="preserve">Hujus curvæ proprietas eſt, quod cum omnibus lineis ad centrum curvæ <lb />
<ptr xml:id="note-0039-01a" corresp="note-0039-01" type="noteAnchor" />
ductis angulos efficiat inter ſe æquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0039-01" corresp="note-0039-01a" place="margin">32.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit centrum C: </s>
          <s xml:space="preserve">in A angulus curvæ, id eſt tangentis ad curvam, cum radio <lb />
<ptr xml:id="note-0039-02a" corresp="note-0039-02" type="noteAnchor" />
AC, nempe BAC, æqualis eſt angulo EDC, quem tangens, in puncto alio <lb />quocunque D, cum linea DC efficit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0039-02" corresp="note-0039-02a" place="margin">TAB. I. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si angulus hic fuerit rectus, ſpiralis in circulum ſe convertet, ſi autem <lb />fuerit acutus, ad centrum continuo accederefacile patet: </s>
          <s xml:space="preserve">non tamen niſi poſt <lb />infinitos gyros ad hoc pervenire poterit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponamus revolutionem primam, poſito curvæ initio in A, terminari in F, <lb />puncto medio inter A &amp; </s>
          <s xml:space="preserve">centrum C. </s>
          <s xml:space="preserve">In hoc caſu angulus BAC paululum <lb />excedet 80. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">57′. </s>
          <s xml:space="preserve">Secunda revolutio ad FC illam habet relationem, quam <lb />prima ad AC; </s>
          <s xml:space="preserve">ideoque terminabitur in G, puncto medio inter F &amp; </s>
          <s xml:space="preserve">C, quod <lb />ad gyros ſequentes etiam applicari debet; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">punctum quod in curva movetur <lb />
<ptr xml:id="note-0039-03a" corresp="note-0039-03" type="noteAnchor" />
in integra revolutione quacunque, accedendo ad centrum, percurrit dimidi-<lb />um diſtantiæ ſuæ a centro in principio revolutionis. </s>
          <s xml:space="preserve">Licet ergo ad diſtanti-<lb />am a centro quantumvis exiguam pervenerit, non unicâ revolutione ad hoc per-<lb />venire poterit; </s>
          <s xml:space="preserve">auctoque numero revolutionum, quantum quis voluerit, non-<lb />dum ultimam attinget; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">numerus revolutionum omnem numer um finitum ſupe-<lb />rabit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0039-03" corresp="note-0039-03a" place="margin">33</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ad centrum tamen curvam pertingere, ibique terminari, etiam conſtat. </s>
          <s xml:space="preserve">Sit por-<lb />
<ptr xml:id="note-0039-04a" corresp="note-0039-04" type="noteAnchor" />
tio curvæ ABEG; </s>
          <s xml:space="preserve">cujus centrum C; </s>
          <s xml:space="preserve">quo eodem centro, radio CG, deſcri-<lb />
<ptr xml:id="note-0039-05a" corresp="note-0039-05" type="noteAnchor" />
batur circuli portio GL, ſecans lineam C A in L.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0039-04" corresp="note-0039-04a" place="margin">34</note>
              <note xml:space="preserve" xml:id="note-0039-05" corresp="note-0039-05a" place="margin">TAB. I. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus LA diviſam in partes æquales, ſed exiguas, AD, DI, IL, <lb />per quarum ſeparationes concipiamus circulorum portiones, centro C de-<lb />ſcriptas, ſecantes curvam in B &amp; </s>
          <s xml:space="preserve">E; </s>
          <s xml:space="preserve">ductiſque radiis BC, EC, formentur <lb />triangula rectangula ADB, BFE, EHG, in quibus propter exiguas AD, <lb />DI, IL, hypotenuſæ, licet portiones curvæ, pro rectis haberi poſſunt; </s>
          <s xml:space="preserve">nume-<lb />rus enim partium in AL in infinitum poteſt concipi auctus, manentibus, quæ <lb />huc uſque ſunt expoſita, ut &amp; </s>
          <s xml:space="preserve">iis, quæ ſequuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Triangula memorata ſunt omnia ſimilia inter ſe; </s>
          <s xml:space="preserve">quia ſunt rectangula, &amp; </s>
          <s xml:space="preserve"><lb />præterea ex natura Curvæ angulos habent æquales BAD, EBF, GEH. </s>
          <s xml:space="preserve">Sunt <lb />etiam æqualia, propter latera homologa æqualia AD, BF, EH, quod ex æ-<lb />qualitate partium AD, DI, IL, ſ quitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex A ducatur linea A c, cum C A angulum efficiens CA c, æqualem an-<lb />gulo CAB; </s>
          <s xml:space="preserve">ad AC in centro C &amp; </s>
          <s xml:space="preserve">punctis L, I, D, erigantur perpendicu-<lb />lares C c, L g, I e, D b, ſecantes A c in punctis c, g, e, b; </s>
          <s xml:space="preserve">ductiſque bf <lb />&amp; </s>
          <s xml:space="preserve">eb parallelis ad AC, formantur triangula AD b, bfe, ebg, ſimilia &amp; </s>
          <s xml:space="preserve">æ-<lb />qualia inter ſe, ut &amp; </s>
          <s xml:space="preserve">triangulis ABD, BFE, EHG, ut ex conſtructione li-<lb />quet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Idcirco hypotenuſæ A b, be, eg, æquales ſunt hypotenuſis AB, BE, EG, id <lb />eſt, linea A g æqualis eſt curvæ portioni AG.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hinc patet quomodo portio quæcunque curvæ menſuranda ſit, curvam-<lb />
<ptr xml:id="note-0039-06a" corresp="note-0039-06" type="noteAnchor" />
</s>
          <pb facs="0040" n="10" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
que non æquari lineæ A c, niſi ad centrum uſque continuetur, illam autem <lb />finitæ eſſe longitudinis, licet inſinitos gyros peragat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0039-06" corresp="note-0039-06a" place="margin">35.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc concipiamus punctum, quod ex A procedat, &amp; </s>
          <s xml:space="preserve">velocitate quacun-<lb />que finita moveatur ita, ut hujus directio ad lineas ad C ductas ſemper æqua-<lb />liter in clinetur, augulos efficiens æquales angulo c AC, perveniet punctum <lb />
<ptr xml:id="note-0040-01a" corresp="note-0040-01" type="noteAnchor" />
hoc ad C tempore finito, in co nempe in quo eadem velocitate rectam Ac <lb />potuiſſet percurrere; </s>
          <s xml:space="preserve">id eſt finito tempore, velocitate finita, in ſpatio finito, per-<lb />aget infinitos gyros.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0040-01" corresp="note-0040-01a" place="margin">36.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De infinitorum Inæqualitate</head>
        <p>
          <s xml:space="preserve">Non omnia infinita eſſe æqualia, evidentiſſime patebit, ſi conſideremus lineam, <lb />
<ptr xml:id="note-0040-02a" corresp="note-0040-02" type="noteAnchor" />
quæ ad partem quamcunque extenditur, in infinitum poſſe produci, talemque <lb />lineam in finitam eſſe; </s>
          <s xml:space="preserve">minor tamen erit aliâ lineâ, quam partem utram que ver-<lb />ſus productam concipimus in infinitum, hanc etiam ambarum ſumma ſupe-<lb />rabit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0040-02" corresp="note-0040-02a" place="margin">37.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Infinita linea continet numerum infinitum pedum, duodecuplum numerum <lb />pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Infinitorum inæqualitatem etiam detegimus, comparando diverſas curvas <lb />ſpirales logarhthmicas ſtatim indicatas.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Præter jam memoratam, &amp; </s>
          <s xml:space="preserve">pro parte hic delineatam, curvam, concipiamus <lb />
<ptr xml:id="note-0040-03a" corresp="note-0040-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">aliam ſpitalem logarithmiam, ex A exeuntem, &amp; </s>
          <s xml:space="preserve">ad centrum ita tenden-<lb />
<ptr xml:id="note-0040-04a" corresp="note-0040-04" type="noteAnchor" />
tem, ut duabus revolutionibus pertingat ad F, duabus aliis pertinget ad G; <lb /></s>
          <s xml:space="preserve">quia duæ requiruntur revolutiones, ut accedendo ad centrum dimidium di-<lb />ſtantiæ ab hoc percurrat, numerus revolutionum in hac duplus eſt nu-<lb />meri revolutionum in ſpirali prima, quando æqualiter cum hac prima ADF <lb />ad centrum accedit; </s>
          <s xml:space="preserve">duploque numero revolutionum ad centrum pertinget: </s>
          <s xml:space="preserve"><lb />utraque tamen curva niſi poſt infinitas revolutiones ad centrum non accedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0040-03" corresp="note-0040-03a" place="margin">38.</note>
              <note xml:space="preserve" xml:id="note-0040-04" corresp="note-0040-04a" place="margin">TAB. I. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De infinitorum claſſibus.</head>
        <p>
          <s xml:space="preserve">Quæ de infinito omnium maxime paradoxa demonſtrantur, ideaſque no-<lb />ſtras in immenſum ſuperant, ſunt quæ ſpectant infinitorum claſſes va rias.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Detur curva ABC parabola, cujus abſciſſa quæqcunque ſit AD ordinata <lb />
<ptr xml:id="note-0040-05a" corresp="note-0040-05" type="noteAnchor" />
huic reſpondens DC. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0040-06a" corresp="note-0040-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0040-05" corresp="note-0040-05a" place="margin">93.</note>
              <note xml:space="preserve" xml:id="note-0040-06" corresp="note-0040-06a" place="margin">TAB. I. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nota eſt hujus curvæ proprietas, ordinatam mediam eſſe proportionalem <lb />inter abſciſſam &amp; </s>
          <s xml:space="preserve">determinatam quandam lineam, quæ parameter dicitur: <lb /></s>
          <s xml:space="preserve">quare ſi abſciſſa quæcunque dicatur x, ordinata reſpondens y, parameter a, <lb />
<ptr xml:id="note-0040-07a" corresp="note-0040-07" type="noteAnchor" />
in omnibus parabolæ punctis habemus {.</s>
          <s xml:space="preserve">./.</s>
          <s xml:space="preserve">.} x, y, a; </s>
          <s xml:space="preserve">ideo ax = yy <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">quæ ergo
æquatio naturam parabolæ exprimit. </s>
          <s xml:space="preserve">Evaneſcente x evaneſcit y, &amp; </s>
          <s xml:space="preserve">Parabo-<lb />la cum AF, per A parallelâ ad abſciſſas, non congruit, daturque tota infra hanc <lb />lineam, quæ illam tangit, &amp; </s>
          <s xml:space="preserve">cum qua efficit angulum mixtum FAC.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0040-07" corresp="note-0040-07a" n="*" anchored="true" place="margin"> La Hire. <lb />ſict. cou. <lb />lib. 3. <lb />pro. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si augeatur a manente x augetur y, &amp; </s>
          <s xml:space="preserve">ſeſe expandit Parabola, aut potius <lb />formatur nova, in qua omnes ordinatæ aliûs curvæ ordinatas reſpondentes <lb />ſuperant; </s>
          <s xml:space="preserve">ita ut curva prima ſecundâ includatur, quæ inter primam &amp; </s>
          <s xml:space="preserve">tan-<lb />gentem AF tranſit, minoremque angulum mixtum cum hac efficit. </s>
          <s xml:space="preserve">Para-<lb />meter autem in infinitum poteſt augeri, &amp; </s>
          <s xml:space="preserve">eo in infinitum minui angulus, <lb />quem cum tangente efficit Parabola.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Servato axe AD &amp; </s>
          <s xml:space="preserve">vertice A, detur alia curva AEG, cujus ordinatæ di-<lb />
<ptr xml:id="note-0040-08a" corresp="note-0040-08" type="noteAnchor" />
cantur z, quarum relatio cum reſpondentibus abſciſſis x exprimatur hac æ-<lb />quatione bbx = z<hi rend="superscript">3</hi>: </s>
          <s xml:space="preserve">b deſignat lineam conſtantem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0040-08" corresp="note-0040-08a" place="margin">40.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Augendo b augentur omnes z, &amp; </s>
          <s xml:space="preserve">mutatur curva in magis apertam, minui-<lb />turque angulus contactus, qui augendo b in infinitum minui poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Habemus ergo duasclaſſes angulorum decr eſcentium in infinitum; </s>
          <s xml:space="preserve">barum integra ſe-<lb />
<ptr xml:id="note-0040-09a" corresp="note-0040-09" type="noteAnchor" />
</s>
          <pb facs="0041" n="11" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. IV.</fw>
cunda infinite exigua eſt reſpectu primæ, demonſtramus enim angulum quemcun-<lb />quein ſecunda ſuperari ab angulo quocunque, id eſt, utcumque exiguo, in prima.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0040-09" corresp="note-0040-09a" place="margin">41.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit c tertia proportionalis ipſis a &amp; </s>
          <s xml:space="preserve">b, utcunque ſumtis; </s>
          <s xml:space="preserve">ergo ac = bb. <lb /></s>
          <s xml:space="preserve">Multiplicando per c æquationem ax = yy, habemus acx = yyc, id eſt bbx = yyc. </s>
          <s xml:space="preserve"><lb />in ſecunda curva bbx valet z<hi rend="superscript">3</hi>; </s>
          <s xml:space="preserve">ergo z<hi rend="superscript">3</hi> = yyc, ſi abſciſſa x fuerit eademiu <lb />utraque curva.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex æquatione hac deducimus z, c:</s>
          <s xml:space="preserve">:yy, z<hi rend="superscript">2</hi>: </s>
          <s xml:space="preserve">unde patet yy ſuperari à zz, id <lb />eſt, y minorem eſſe z, quamdiu hæc ac ſuperatur, unde ſequitur curvam ſe-<lb />cundam dum ex A profluit, antequam z valeat c, inter tangentem &amp; </s>
          <s xml:space="preserve">curvam <lb />primam dari quod univerſaliter obtineri hac demonſtratione conſtat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponamus nunc tertiam dari curvam AI, cujus axis etiam eſt AD, &amp; </s>
          <s xml:space="preserve">cujus æ-<lb />
<ptr xml:id="note-0041-01a" corresp="note-0041-01" type="noteAnchor" />
quatio, manentibus iiſdem abſciſſis x, ſit dx = u<hi rend="superscript">4</hi>; </s>
          <s xml:space="preserve">u eſt ordinata quæ-<lb />cunque; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">d linea determinata; </s>
          <s xml:space="preserve">hanc ſi augeamus, mutamus curvam &amp; </s>
          <s xml:space="preserve">mi-<lb />nuimus angulum quem curva cum tangente AF efficit; </s>
          <s xml:space="preserve">formaturque hiſce <lb />curvis tertia claſſis angulorum, qui in infinitum minui poſſunt, &amp; </s>
          <s xml:space="preserve">in qua <lb />nullus datur angulus, qui non ſuperetur ab angulo quocunque in ſecunda.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0041-01" corresp="note-0041-01a" place="margin">42.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datis b &amp; </s>
          <s xml:space="preserve">d quibuſcunque, ſit bb ad dd; </s>
          <s xml:space="preserve">ut dad quartam quam dicamus e; </s>
          <s xml:space="preserve">erit <lb />ergo bbe = d<hi rend="superscript">3</hi>, &amp; </s>
          <s xml:space="preserve">æquatio curvæ bbx = z<hi rend="superscript">3</hi> mutabitur in hanc bbex = d<hi rend="superscript">3</hi> x <lb /> = z<hi rend="superscript">3</hi> e; </s>
          <s xml:space="preserve">ideoque z<hi rend="superscript">3</hi> e = u<hi rend="superscript">4</hi>, ſi agatur de iiſdem abſciſſis in utraque curva; </s>
          <s xml:space="preserve">id-<lb />circo u, e:</s>
          <s xml:space="preserve">:z<hi rend="superscript">3</hi>, u<hi rend="superscript">3</hi>; </s>
          <s xml:space="preserve">ergo u ſuperat z, quamdiu e ſuperat u, &amp;</s>
          <s xml:space="preserve">, exeundo ex A, <lb />curva, cujus abſciſſæ ſunt u, tranſit inter AF &amp; </s>
          <s xml:space="preserve">aliam curvam Q. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Curvæ, quarum æquatio eſt f<hi rend="superscript">4</hi> x = t<hi rend="superscript">3</hi> poſita f quantitate determinatâ in ſin-<lb />gulis curvis, &amp; </s>
          <s xml:space="preserve">t ordinata quæcunque, dabunt novam claſſem angulorum mino-<lb />
<ptr xml:id="note-0041-02a" corresp="note-0041-02" type="noteAnchor" />
rum omnibus memoratis, &amp; </s>
          <s xml:space="preserve">eodem modo claſſes in infinitum formari poſſunt, <lb />ſemperque omnes anguli in claſſe quacunque ſuperantur ab omnibus angulis in claſ-<lb />ſe præcedenti, &amp; </s>
          <s xml:space="preserve">ſuperant omnes angulos in claſſe ſequenti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0041-02" corresp="note-0041-02a" place="margin">43.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Inter duas claſſes quaſcunque datur ſeries infinita claſſium; </s>
          <s xml:space="preserve">quæ omnes eandem <lb />
<ptr xml:id="note-0041-03a" corresp="note-0041-03" type="noteAnchor" />
proprietatem babent, ut angulus quicunque unius ſit infinite parvus reſpectu angulo-<lb />rum claſſis præcedentis, id eſt, ut ab omnibus ſuperetur, &amp; </s>
          <s xml:space="preserve">infinite magnusre-<lb />ſpectu claſſis ſequentis, cujus omnes angulos ſuperat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0041-03" corresp="note-0041-03a" place="margin">44.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Curvæ ax = yy &amp; </s>
          <s xml:space="preserve">bbx = z<hi rend="superscript">3</hi> claſſes formant diverſas; </s>
          <s xml:space="preserve">quia ordinatarum di-<lb />menſio z<hi rend="superscript">3</hi> id ſecunda unitate ſuperat dimenſionem y<hi rend="superscript">2</hi> primæ curvæ; </s>
          <s xml:space="preserve">demon-<lb />ſtrabimus autem claſſes differre, quantumvis parum hæ dimenſiones differant, <lb />unde conſtabit propoſitum: </s>
          <s xml:space="preserve">quia inter hoſce numeros 2 &amp; </s>
          <s xml:space="preserve">3, &amp; </s>
          <s xml:space="preserve">alios quoſ-<lb />cunque, innumeridaripoſſunt, quiinter ſe differunt, quorum nulli, quantumvis <lb />parum differentes, dari poſſunt, inter quos iterum non alii innumeri dari <lb />poſſint.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit ax = yy &amp; </s>
          <s xml:space="preserve">g 1 {1/10} x = s 2 {1/10} id eſt, g {11/10} x = s {21/10}; </s>
          <s xml:space="preserve">ordinatas deſignat s, &amp; </s>
          <s xml:space="preserve">g <lb />conſtantem lineam, quamdiu curva non mutatur. </s>
          <s xml:space="preserve">Fiat ut a ad g, ita g {1/10} ad <lb />quartam quantitatem, quæ dicatur b {1/10}; </s>
          <s xml:space="preserve">ergo g{11/10} = ab{1/10}; </s>
          <s xml:space="preserve">multiplican-<lb />do per b {1/10} æquationem ax = yy datur ab {1/10} x = g {11/10} x = y<hi rend="superscript">2</hi> b {1/10} = s {21/10}; <lb /></s>
          <s xml:space="preserve">under deducimus s {1/10}, b {1/10}:</s>
          <s xml:space="preserve">: yy. </s>
          <s xml:space="preserve">ss. </s>
          <s xml:space="preserve">Idcirco in viciniis puncti A, ubi s <lb />neceſſario minor eſt determinatâ b, erit etiam y minor s unde liquet quod de <lb />angulis dictum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Inter duas claſſes quaſcunque, quantitatum, quæ in infinitum differunt, da-<lb />
<ptr xml:id="note-0041-04a" corresp="note-0041-04" type="noteAnchor" />
ri in infinitum claſſes intermedias ex conſideratione mediarum proportiona-<lb />lium etiam deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0041-04" corresp="note-0041-04a" place="margin">45.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0042" n="12" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Si A ſit infinite magnum reſpectu a, media quæcunque proportionalis b <lb />inter has quantitates minor eſt A, &amp; </s>
          <s xml:space="preserve">major a, non tamen finitam habet rationem <lb />ad A aut a; </s>
          <s xml:space="preserve">ratio enim A ad a componitur ex rationibus A ad b, &amp; </s>
          <s xml:space="preserve">b ad a, &amp; </s>
          <s xml:space="preserve"><lb />ratio ex duabus finitis rationibus compoſita eſt etiam finita; </s>
          <s xml:space="preserve">ideo cum A &amp; </s>
          <s xml:space="preserve">a in <lb />infinitum differant, ratio inter A &amp; </s>
          <s xml:space="preserve">b, aut b &amp; </s>
          <s xml:space="preserve">a, omnem finitam rationem <lb />ſuperat; </s>
          <s xml:space="preserve">quare etiam infinita eſt. </s>
          <s xml:space="preserve">In infinitum mediæ proportionales inter <lb />duas quantitates dari poſſunt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">De partium Subtilitate.</head>
        <p>
          <s xml:space="preserve">Pondus auri, quo in n°. </s>
          <s xml:space="preserve">28. </s>
          <s xml:space="preserve">diximus argentum deaurari, eſt {1/60} ponderis ipſius <lb />
<ptr xml:id="note-0042-01a" corresp="note-0042-01" type="noteAnchor" />
argenti. </s>
          <s xml:space="preserve">Volumen auri ſe habet ad volumen argenti, quando pondera <lb />ſunt æqualia, ut 10 and 19, ergo volumen auri quo argentum obtegitur ad <lb />volumen ipſius argenti obtecti, ut 1 ad 114. </s>
          <s xml:space="preserve">nam 10. </s>
          <s xml:space="preserve">19:</s>
          <s xml:space="preserve">:60.</s>
          <s xml:space="preserve">, 114.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0042-01" corresp="note-0042-01a" place="margin">46.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pes cubicus aquæ ponderat libras 63 {1/2} decies gravius eſt argentum; </s>
          <s xml:space="preserve">ergo <lb />pes cubicus argenti libras 635. </s>
          <s xml:space="preserve">pondo eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cubus eſt ad cylindrum, ejuſdem diametri &amp; </s>
          <s xml:space="preserve">altitudinis, circiter ut 14 ad <lb />11; </s>
          <s xml:space="preserve">pondus ergo pedis cylindrici argenti eſt librarum 499. </s>
          <s xml:space="preserve">aut unciarum 7984.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Uncia una porrigitur in filum 14000. </s>
          <s xml:space="preserve">pedum, &amp; </s>
          <s xml:space="preserve">in pede cylindrico datur <lb />filum 111776000. </s>
          <s xml:space="preserve">pedum, id eſt, tot dantur fila unius pedis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Circulorum ſuperficies ſunt ut quadrata diametrorum, ideo quadratum di-<lb />ametri fili ad quadratum unius pedis, ut 1. </s>
          <s xml:space="preserve">ad 111776000; </s>
          <s xml:space="preserve">quorum numero-<lb />rum radices ſunt 1 &amp; </s>
          <s xml:space="preserve">10572, in qua ratione ſunt dictæ diametri; </s>
          <s xml:space="preserve">eſt ergo fili <lb />diameter {1/10572} pedis, aut {1/881} pollicis. </s>
          <s xml:space="preserve">Aurum circumponitur &amp; </s>
          <s xml:space="preserve">volumen <lb />augetur {1/114}, id eſt ſectio circularis fili ea quantitate augetur, quod fiet ſi <lb />filo circumponatur lamina, cujus craſſities eſt pars quarta partis {1/114} diame-<lb />tri, area enim circuli habetur multiplicando circumferentiam per quartam <lb />diametri partem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Eſt ergo auri craſſities {1/456} diametri fili, quæ eſt {1/881} poll. </s>
          <s xml:space="preserve">ita ut auri <lb />craſſities ſit {1/401736} pollicis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Filahæctenuia deaurata, ut filis ſericis circumvolvantur, plana fiunt, quo ſu-<lb />perficies ad minimum triplicatur, &amp; </s>
          <s xml:space="preserve">in eadem ratione craſſities auri minuitur, <lb />ita ut ſit {1/1205208}.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Non æqualiter in omnibus punctis filum deauratur, &amp; </s>
          <s xml:space="preserve">auri craſſities in qui-<lb />buſdam locis forte duplo minor eſt, quare nihil a vero remotum ponimus, <lb />ſi craſſitiem determinemus {1/2000000} pollicis, id eſt milleſima pars pollicis <lb />in bis mille partes dividitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Talis actu datur auri diviſio; </s>
          <s xml:space="preserve">ideoque particulæ, quæ arte ſeparantur, non <lb />majorem diametrum habent, &amp; </s>
          <s xml:space="preserve">talium partium in ſphæra aurea unius pollicis <lb />dantur 8.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">; &amp; </s>
          <s xml:space="preserve">in arenula minima, cujus nempe <lb />diameter eſt pars centeſima pollicis, dantur particulæ 8,000.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">000.</s>
          <s xml:space="preserve">000: <lb /></s>
          <s xml:space="preserve">particula itaque ſe habet ad arenulam, ut hæc ad globum, cujus diameter ſu-<lb />peraret 10. </s>
          <s xml:space="preserve">pedes, &amp; </s>
          <s xml:space="preserve">non majorem numerum arenularum contineret globus <lb />hic, quam particularum continet arenula. </s>
          <s xml:space="preserve">Globus vero continet 4096. </s>
          <s xml:space="preserve"><lb />globosunius pedis.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0043" n="13" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. V.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT V.</head>
        <head rend="italics" xml:space="preserve">De cobæſione partium, ubi de Duritie, Mollitie, Fluidi-<lb />tate, &amp; Elaſticitate agitur.</head>
        <p>
          <s xml:space="preserve">OMne corpus quod in ſenſus noſtros cadit, ex particu-<lb />
<ptr xml:id="note-0043-01a" corresp="note-0043-01" type="noteAnchor" />
lis quam minimis conſtat, nulla illarum in ſe eſt in-<lb />diviſibilis, noſtri reſpectu omnes ſunt, diviſio enim quæ a <lb />nobis fieri poteſt, eſt particularum ſeparatio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0043-01" corresp="note-0043-01a" place="margin">47.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando magna vis ad illam ſeparationem requiritur, cor-<lb />pus durum vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si partes facilius cedant &amp; </s>
          <s xml:space="preserve">cum ſublapſu partium intro-<lb />cedant molle vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sed hæc in ſignificatione vulgari, vis magna &amp; </s>
          <s xml:space="preserve">minor ni-<lb />hil determinati denotant, &amp; </s>
          <s xml:space="preserve">corpus durum reſpectu unius ho-<lb />minis, alteri molle videtur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Philoſophicè corpus durum vocatur, cujus partes inter <lb />
<ptr xml:id="note-0043-02a" corresp="note-0043-02" type="noteAnchor" />
ſe cobærent, &amp; </s>
          <s xml:space="preserve">neutiquam introcedunt, ita ut partes nullo mo-<lb />tu affici poſſint quin diſrumpatur corpus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0043-02" corresp="note-0043-02a" place="margin">48.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus tale perfectè durum nullum novimus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Philoſophice corpus molle vocatur cujus partes introce-<lb />
<ptr xml:id="note-0043-03a" corresp="note-0043-03" type="noteAnchor" />
dunt &amp; </s>
          <s xml:space="preserve">ſublabuntur, licet ad illud mallei ictus requirantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0043-03" corresp="note-0043-03a" place="margin">49.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Corpus cujus partes cuicunque impreſſioni cedunt &amp; </s>
          <s xml:space="preserve">ce-<lb />
<ptr xml:id="note-0043-04a" corresp="note-0043-04" type="noteAnchor" />
dendo facillime moventur inter ſe vocatur fluidum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0043-04" corresp="note-0043-04a" place="margin">50.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc omnia a cohæſione partium pendent, quo arctior <lb />eſt eo magis ad perfectam duritiem corpus accedit. </s>
          <s xml:space="preserve">Durities <lb />vero particularum minimarum ab illarum ſoliditate non dif-<lb />fert, &amp; </s>
          <s xml:space="preserve">eſt proprietas eſſentialis corporis, quæ non magis <lb />explicanda eſt, quam quare corpus ſit extenſum &amp; </s>
          <s xml:space="preserve">mens <lb />cogitet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">An omnia corpora ex particulis æqualibus &amp; </s>
          <s xml:space="preserve">ſimilibus con-<lb />ſtent omnino ignoro, &amp; </s>
          <s xml:space="preserve">circa cauſam cohæſionis particula-<lb />rum adhuc multa obſcura ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Naturæ leges quæ hic locum habentex Phænomenis dedu-<lb />cuntur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0044" n="14" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Cohæſionis lex peculiaris eſt, omnes particulas vi attra-<lb />
<ptr xml:id="note-0044-01a" corresp="note-0044-01" type="noteAnchor" />
ctiva gaudere, ideſt ſi vicinæ fuerint, ſponte ad ſe mutuo <lb />tendunt, cujus motus cauſa nos latet, ſed cum hunc ge-<lb />neraliter locum habere obſervemus, ipſum inter leges natu-<lb />ræ referimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0044-02a" corresp="note-0044-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0044-01" corresp="note-0044-01a" place="margin">51</note>
              <note xml:space="preserve" xml:id="note-0044-02" corresp="note-0044-02a" n="*" anchored="true" place="margin">5.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p>
          <s xml:space="preserve">Nomine attractionis intelligo vim quamcunque qua duo <lb />
<ptr xml:id="note-0044-03a" corresp="note-0044-03" type="noteAnchor" />
corpora ad ſe invicem tendunt; </s>
          <s xml:space="preserve">licet forte illud per impul-<lb />ſum fiat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0044-03" corresp="note-0044-03a" place="margin">52.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Attractio autem, quæ in cohæſione partium locum habet, <lb />
<ptr xml:id="note-0044-04a" corresp="note-0044-04" type="noteAnchor" />
hiſce legibus ſubjicitur, ut in ipſo particularum contactu ſit <lb />perquam magna, &amp; </s>
          <s xml:space="preserve">ſubito decreſcat, ita ut ad diſtantiam <lb />quam minimam, quæ ſub ſenſus cadit, non amplius agat, imo <lb />etiam ad majorem diſtantiam ſeſe mutet in vim repellentem, <lb />qua particulæ ſeſe mutuo fugiunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0044-04" corresp="note-0044-04a" place="margin">53.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ope hujus legis multa Phænomena facillime explicantur, <lb />&amp; </s>
          <s xml:space="preserve">innumeris experimentis chemicis illa attractio &amp; </s>
          <s xml:space="preserve">repulſio <lb />pleniſſime probantur, etiam exſequentibus experimentis illas <lb />dari ſatis patet.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">In omnibus corporibus fluidis partes omnes ſeſe mutuo <lb />
<ptr xml:id="note-0044-05a" corresp="note-0044-05" type="noteAnchor" />
attrahere videmus, ex figura ſphærica quam guttæ ſemper <lb />habent; </s>
          <s xml:space="preserve">ex eo etiam quod nullum detur fluidum, cujus par-<lb />tes non ſint quaſi conglutinatæ, quod in ipſo Mercurio cla-<lb />re apparet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0044-05" corresp="note-0044-05a" place="margin">54.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Sed multo melius hæc mutua particularum attractio pro-<lb />
<ptr xml:id="note-0044-06a" corresp="note-0044-06" type="noteAnchor" />
batur, ex eo quod in omnibus fluidis duæ guttæ ut A &amp; </s>
          <s xml:space="preserve">B, <lb />
<ptr xml:id="note-0044-07a" corresp="note-0044-07" type="noteAnchor" />
ſtatim ac ſe invicem quam minime tangunt, in unam guttam <lb />majorem F redigantur; </s>
          <s xml:space="preserve">quæ omnia cum etiam in metallis <lb />liquefactis locum habeant, ſequitur particulas illa compo-<lb />nentes &amp; </s>
          <s xml:space="preserve">tum ſeſe mutuo attrahere, cum motu ignis a jun-<lb />ctione arcentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0044-06" corresp="note-0044-06a" place="margin">55.</note>
              <note xml:space="preserve" xml:id="note-0044-07" corresp="note-0044-07a" place="margin">TAB. II. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc non oriuntur ab aëris preſſione, quia &amp; </s>
          <s xml:space="preserve">in locoaë-<lb />re vacuo procedunt, neque ab alius materiæ cujuſcunque <lb />preſſione ab omni parte æquali; </s>
          <s xml:space="preserve">tali enim preſſione figura,
</s>
          <pb facs="0045" n="15" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. V.</fw>
quæcunque fuerit, minime mutari poteſt, ut in cap. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">lib. <lb /></s>
          <s xml:space="preserve">2, ex legibus preſſionis fluidorum deducemus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Etiam primo intuitu patet in gutta acbd, preſſiones in ſu-<lb />
<ptr xml:id="note-0045-01a" corresp="note-0045-01" type="noteAnchor" />
perficies ad &amp; </s>
          <s xml:space="preserve">cb minores eſſe preſſionibus in ſuperficies <lb />ac, db, ſi ab omni parte gutta æqualiter prematur. </s>
          <s xml:space="preserve">Non <lb />tamen gutta fiet rotunda, quin preſſiones iſtæ minores, ma-<lb />jores vincant, quod eſt abſurdum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0045-01" corresp="note-0045-01a" place="margin">TAB. II. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In attractione contra, quo major eſt numerus particula-<lb />rum ſe mutuo attrahentium inter duas particulas, eo ma-<lb />jori vi ſe mutuo verſus feruntur; </s>
          <s xml:space="preserve">unde motus in gutta, donec <lb />diſtantiæ inter puncta oppoſita in ſuperficie ſint ubique æ-<lb />quales, quod in ſola figura ſphærica locum habet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pleraque corpora attractione illa agunt in corpora extra-<lb />nea. </s>
          <s xml:space="preserve">Exempla pauca dabo, in quibus effectus attractionis <lb />illius ſunt maxime notabiles.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Tubuli vitrei exigui ab utraque extremitate aperti aquæ <lb />
<ptr xml:id="note-0045-02a" corresp="note-0045-02" type="noteAnchor" />
immerguntur, ut in ſchemate repræſentatur. </s>
          <s xml:space="preserve">Aqua in eos <lb />
<ptr xml:id="note-0045-03a" corresp="note-0045-03" type="noteAnchor" />
ſponte aſcendit, &amp; </s>
          <s xml:space="preserve">ad majorem altitudinem quo diameter <lb />tubuli eſt minor. </s>
          <s xml:space="preserve">Tubuli hi dicuntur capillares; </s>
          <s xml:space="preserve">ſed <lb />in majoribus, quorum ex. </s>
          <s xml:space="preserve">gr, diametri æquant ſextam pol-<lb />licis partem, experimentum etiam procedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0045-02" corresp="note-0045-02a" place="margin">56.</note>
              <note xml:space="preserve" xml:id="note-0045-03" corresp="note-0045-03a" place="margin">TAB. II. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Effectum hunc preſſioni aëris tribuendum non eſſe, ſe-<lb />quenti experimento liquet.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Suberiannectuntur tubuli, &amp; </s>
          <s xml:space="preserve">filo æneo AB ſuſtinentur, dein-<lb />
<ptr xml:id="note-0045-04a" corresp="note-0045-04" type="noteAnchor" />
de ope machinæ pneumaticæ aër ex recipiente R, laminæ æ-<lb />
<ptr xml:id="note-0045-05a" corresp="note-0045-05" type="noteAnchor" />
neæ impoſito, exhauritur, &amp; </s>
          <s xml:space="preserve">motu fili AB, aquâin vitro CD <lb />contentæ immerguntur tubuli, aqua in eo caſu eodem mo-<lb />do ac in experimento præcedenti in eos aſcendit. </s>
          <s xml:space="preserve">Quo-<lb />modo filum ſine ingreſſu aëris moveri poſſit, in ſequentibus, <lb />dicetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0045-04" corresp="note-0045-04a" place="margin">57.</note>
              <note xml:space="preserve" xml:id="note-0045-05" corresp="note-0045-05a" place="margin">TAB. II. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Vitrea duo plana ABCD junguntur in AB, at in CD <lb />
<ptr xml:id="note-0045-06a" corresp="note-0045-06" type="noteAnchor" />
interpoſitâ laminâ paululum ſeparantur; </s>
          <s xml:space="preserve">latera CB aquâ ali-<lb />
<ptr xml:id="note-0045-07a" corresp="note-0045-07" type="noteAnchor" />
quo colore tinctâ immerguntur tia, ut latera AB &amp; </s>
          <s xml:space="preserve">CD
</s>
          <pb facs="0046" n="16" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſint verticalia; </s>
          <s xml:space="preserve">antea iiſdem planis intus eodem liquore ma-<lb />defactis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0045-06" corresp="note-0045-06a" place="margin">58.</note>
              <note xml:space="preserve" xml:id="note-0045-07" corresp="note-0045-07a" place="margin">TAB. II. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aqua inter hæc plana, planorum attractione, aſcendit, <lb />&amp; </s>
          <s xml:space="preserve">ad majorem altitudinem aſcendit pro minori inter plana <lb />diſtantiâ; </s>
          <s xml:space="preserve">cum vero continuo à CD, verſus AB, minua-<lb />tur hæc, aqua ubique ad diverſas altitudines aſcendit, &amp; </s>
          <s xml:space="preserve">for-<lb />mat lineam curvam efg.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">ABCD ſunt duæ laminæ vitreæ planæ, junctæ in AB, <lb />
<ptr xml:id="note-0046-01a" corresp="note-0046-01" type="noteAnchor" />
in CD vero paululum ſeparantur, interpoſitâ lami-<lb />nâ cujuſcunque materiæ. </s>
          <s xml:space="preserve">Rectangulo ligneo HILM <lb />ſuſtinentur; </s>
          <s xml:space="preserve">latera ſeparata DC regulæ ligneæ, cum la-<lb />tere ML rectanguli cohærente, imponuntur; </s>
          <s xml:space="preserve">ad horizontem <lb />utcunque inclinantur laminæ, elevando latera conjuncta <lb />AB; </s>
          <s xml:space="preserve">Cylindro NO laminæ in quocunque ſitu ſuſtinentur; <lb /></s>
          <s xml:space="preserve">Cochleâ P cylindrus ad altitudinem quamcunque ſirmatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0046-01" corresp="note-0046-01a" place="margin">59.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Gutta aquæ aut olei G interponitur, ita ut ambo plana, <lb />antea eodem liquore madefacta, tangat; </s>
          <s xml:space="preserve">ab utroque plano <lb />attrahitur, ſed attractio majorem in guttam edit effectum; <lb /></s>
          <s xml:space="preserve">ubi plana minus diſtant, id eſt, in e quam in f; </s>
          <s xml:space="preserve">gutta i-<lb />deo verſus e movetur, id eſt, aſcendit, &amp; </s>
          <s xml:space="preserve">eo celerius quo <lb />altius aſcendit, ſuperficiebus quibus gutta vitra tangit, cre-<lb />ſcentibus ubi diſtantia inter plana minuitur. </s>
          <s xml:space="preserve">Angulus inclina-<lb />tionis plani ita poteſt augeri, ut gravitas guttæ æque polleat <lb />cum effectu attractionis, &amp; </s>
          <s xml:space="preserve">tunc gutta quieſcit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſi in eo <lb />caſu magis elevetur planorum pars AB, gutta de-<lb />ſcendit propter guttæ gravitatem præpollentem.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Mercurius Auro &amp; </s>
          <s xml:space="preserve">Stanno ſeſe jungit, etiam aqua, &amp; </s>
          <s xml:space="preserve">o-<lb />
<ptr xml:id="note-0046-02a" corresp="note-0046-02" type="noteAnchor" />
leum ligno &amp; </s>
          <s xml:space="preserve">vitro nitido adhærent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0046-02" corresp="note-0046-02a" place="margin">60.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Repulſionis exempla habemus inter aquam &amp; </s>
          <s xml:space="preserve">oleum, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0046-03a" corresp="note-0046-03" type="noteAnchor" />
in genere inter aquam &amp; </s>
          <s xml:space="preserve">omnia corpora pinguia, inter Mer-<lb />curium &amp; </s>
          <s xml:space="preserve">Ferrum, ut &amp; </s>
          <s xml:space="preserve">etiam inter particulas pulveris cu-<lb />juſcunque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0046-03" corresp="note-0046-03a" place="margin">61.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Si corpus quoddam pingue, quod aqua levius ſit, ſuper-<lb />
<ptr xml:id="note-0046-04a" corresp="note-0046-04" type="noteAnchor" />
</s>
          <pb facs="0047" n="17" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. V.</fw>
ficiei aquæ imponatur, aut fruſtum Ferri Mercurio, ſuper-<lb />ficies liquidorum deprimentur circum corpora immerſa, ut <lb />circum globum A repræſentantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eodem modo ac in <lb />
<ptr xml:id="note-0047-01a" corresp="note-0047-01" type="noteAnchor" />
caſibus ubi vis attractiva locum habet, ſuperficies fluidi cir-<lb />cum corpora immerſa altior eſt, ut circum globum B, &amp; </s>
          <s xml:space="preserve"><lb />gravitate ad libellam non defluit; </s>
          <s xml:space="preserve">ſic in hiſce ubi vis <lb />repellens actionem ſuam exerit, fluida pondere ſuo non <lb />defluunt ad implendas cavitate, quæ circum corpora im-<lb />merſa formantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0046-04" corresp="note-0046-04a" place="margin">62.</note>
              <note xml:space="preserve" xml:id="note-0047-01" corresp="note-0047-01a" place="margin">TAB. II. <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Huc pertinent omnia Phænomena globorum vitreorum le-<lb />
<ptr xml:id="note-0047-02a" corresp="note-0047-02" type="noteAnchor" />
viſſimorum aquâ innatantium; </s>
          <s xml:space="preserve">quando nitidi ſunt aqua ab <lb />omni parte circa eos aſcendit, ut in B; </s>
          <s xml:space="preserve">quando pinguedine <lb />quadam obteguntur, aqua ab omni parte quaſi excavatur, <lb />ut in A;</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0047-02" corresp="note-0047-02a" place="margin">63.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In vaſe vitreo, in quo experimenta fiunt, aqua a lateribus <lb />vitri ab omni parte etiam ſuſtinetur, &amp; </s>
          <s xml:space="preserve">ibi altior eſt, ut in <lb />C, &amp; </s>
          <s xml:space="preserve">D; </s>
          <s xml:space="preserve">quando vitrum ita repletur, ut aqua ab omni par-<lb />te defluat, attractione mutua partium aquæ, altior eſt in <lb />medio quam ad latera, &amp; </s>
          <s xml:space="preserve">ſuperficiem convexam format <lb />
<ptr xml:id="note-0047-03a" corresp="note-0047-03" type="noteAnchor" />
ABC: </s>
          <s xml:space="preserve">ex hiſce ſolis ſequentia Experimenta explicantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0047-03" corresp="note-0047-03a" place="margin">TAB. II. <lb />fig. 9.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9. 10. 11. 12. 13.</head>
        <p>
          <s xml:space="preserve">Quando vitreum vas non omnino aquâ impletur, globus <lb />
<ptr xml:id="note-0047-04a" corresp="note-0047-04" type="noteAnchor" />
nitidus ſemper, ſi, ad diſtantiam non admodum magnam <lb />a latere vaſis, aquâ imponitur, latus verſus fertur &amp; </s>
          <s xml:space="preserve">ei ſeſe <lb />jungit. </s>
          <s xml:space="preserve">Globus ab omni parte æqualiter ab aqua premitur, <lb />quando autem accedit ad latus vaſis, vis, qua ibi aqua ele-<lb />vatur, tollit pro parte preſſionem illam; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">preſſio a parte <lb />oppoſita præpollet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0047-04" corresp="note-0047-04a" place="margin">64.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando vas repletur ita, ut aqua defluat, globus a late-<lb />
<ptr xml:id="note-0047-05a" corresp="note-0047-05" type="noteAnchor" />
re vitri ſponte medium verſus fertur; </s>
          <s xml:space="preserve">vi, qua aqua in medio <lb />magis elevatur, ab ea parte preſſionem circa globum minuente.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0047-05" corresp="note-0047-05a" place="margin">65.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Contrarium in utroque caſu obtinet, quando globus pin-<lb />
<ptr xml:id="note-0047-06a" corresp="note-0047-06" type="noteAnchor" />
guedine obtegitur, quia vis, qua aqua &amp; </s>
          <s xml:space="preserve">globus ſeſe mutuo <lb />repellunt, major eſt, ubi aqua magis elevata eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0047-06" corresp="note-0047-06a" place="margin">66.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Duo globi nitidi, aut pinguedine induti, ſeſe mutuo pe-<lb />
<ptr xml:id="note-0047-07a" corresp="note-0047-07" type="noteAnchor" />
tunt. </s>
          <s xml:space="preserve">Si nitidi fuerint, cauſa eadem eſt ex qua globus ad
</s>
          <pb facs="0048" n="18" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
latus vitri fertur: </s>
          <s xml:space="preserve">quando pinguedine obtecti ſunt, cavitas <lb />circum illos datur, ubi cavitates juguntur preſſio minuitur, <lb />&amp; </s>
          <s xml:space="preserve">verſus illam partem globus uterque fertur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0047-07" corresp="note-0047-07a" place="margin">67.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si Globus unus ſit nitidus, &amp; </s>
          <s xml:space="preserve">alter pinguedine obtectus, <lb />
<ptr xml:id="note-0048-01a" corresp="note-0048-01" type="noteAnchor" />
ſeſe mutuo fugiunt; </s>
          <s xml:space="preserve">eodem modo ac globus pinguedine ob-<lb />tectus latus vitri fugit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0048-01" corresp="note-0048-01a" place="margin">68.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In cryſtalliſationibus etiam pulcherrima attractionis exem-<lb />
<ptr xml:id="note-0048-02a" corresp="note-0048-02" type="noteAnchor" />
pla habemus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0048-02" corresp="note-0048-02a" place="margin">69.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p>
          <s xml:space="preserve">Elaſticitas, vocatur corporum proprietas, qua, ſi figura <lb />
<ptr xml:id="note-0048-03a" corresp="note-0048-03" type="noteAnchor" />
illorum vi aliqua mutetur, ad priſtinam figuram redeunt; <lb /></s>
          <s xml:space="preserve">Si enim corpus quoddam ſit compactum, flectat ſe, &amp; </s>
          <s xml:space="preserve">cum <lb />prematur introcedat ſine ullo partium ſuarum ſublapſu, cor-<lb />pus revertet ad figuram ſuam vi illa, quæ ex mutua ſuarum <lb />partium attractione oritur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0048-03" corresp="note-0048-03a" place="margin">70.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Illam vero aëris proprietatem, quæ illius elaſticitas dici-<lb />
<ptr xml:id="note-0048-04a" corresp="note-0048-04" type="noteAnchor" />
tur, oriri ex vi, qua partes ſeſe mutuo repellunt, ſuo tem-<lb />pore dicetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0048-04" corresp="note-0048-04a" place="margin">71.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Et ne quis credat, quia cauſam prædictæ attractionis &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0048-05a" corresp="note-0048-05" type="noteAnchor" />
repulſionis non damus, illas inter qualitates occultas eſſe re-<lb />cenſendas. </s>
          <s xml:space="preserve">Cum Newtono reſpondemus, „ nos illa principia <lb />„ conſiderare, non ut occultas qualitates, quæ ex ſpecificis <lb />„ rerum formis oriri finguntur; </s>
          <s xml:space="preserve">ſed ut univer ſales naturæ <lb />„ leges, quibus res ipſæ ſunt formatæ; </s>
          <s xml:space="preserve">nam principia qui-<lb />„ dem talia revera exiſtere oſtendunt Phænomena naturæ, <lb />„ licet, ipſorum cauſæ quæ ſint, nondum fuerit explicatum. <lb /></s>
          <s xml:space="preserve">„ Affirmare ſingulas rerum ſpecies ſpecificis præditas eſſe <lb />„ qualitatibus occultis, per quas eæ vim certam in agendo <lb />„ habeant, hoc utique eſt nihil dicere. </s>
          <s xml:space="preserve">At ex Phænome-<lb />„ nis naturæ duo vel tria derivare generalia motus princi-<lb />„ pia, &amp; </s>
          <s xml:space="preserve">deinde explicare quemadmodum proprietates, &amp; </s>
          <s xml:space="preserve"><lb />„ actiones rerum omnium, ex principiis iſtis conſequuntur; </s>
          <s xml:space="preserve"><lb />„ id vero magnus eſſet factus in Philoſophia progreſſus, et-<lb />„ iamſi principiorum iſtorum cauſæ nondum eſſent cognitæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0048-05" corresp="note-0048-05a" place="margin">72.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0049" n="19" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. V.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM</head>
        <head rend="italics" xml:space="preserve">De efſectu attractionis vitri in aquam.</head>
        <p>
          <s xml:space="preserve">Singulæ particulæ aqueæ ad exiguam a vitro diſtantiam ab hoc attrahuntur, <lb />
<ptr xml:id="note-0049-01a" corresp="note-0049-01" type="noteAnchor" />
id eſt, per lineas rectas tendunt ad ſingulas vitri particulas, quarum diſtantia <lb />non ſuperat illam ad quam vitrum &amp; </s>
          <s xml:space="preserve">aqua in ſe mutuo agere poſſunt. </s>
          <s xml:space="preserve">Sit <lb />
<ptr xml:id="note-0049-02a" corresp="note-0049-02" type="noteAnchor" />
vitri ſuperficies AB; </s>
          <s xml:space="preserve">particula C; </s>
          <s xml:space="preserve">hæc ad vitrum tendit per lineam CD, ad <lb />ſuperficiem perpendicularem; </s>
          <s xml:space="preserve">tendit etiam ad punctum e, ſed eodem tem-<lb />pore æquali vi tendit ad omnia puncta in ſuperficie æqualiter cum e à D di-<lb />ſtantia, id eſt in cir cumferentia circuli poſita, cujus diameter eſt e f: </s>
          <s xml:space="preserve">propter <lb />harum omnium virium æqualitatem non poterit punctum magis ad punctum u-<lb />num ferri, quam ad aliud; </s>
          <s xml:space="preserve">ideo, omnibus viribus ſimul agentibus, par-<lb />ticula etiam trahitur per CD. </s>
          <s xml:space="preserve">Similem demonſtrationem aliis particulis vitri <lb />in aquæ particulam agentibus applicando conſtabit, hanc ad vitrum tendere per <lb />
<ptr xml:id="note-0049-03a" corresp="note-0049-03" type="noteAnchor" />
lineam ad ſuperficiem bujus perpendicularem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0049-01" corresp="note-0049-01a" place="margin">73.</note>
              <note xml:space="preserve" xml:id="note-0049-02" corresp="note-0049-02a" place="margin">TAB. I. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0049-03" corresp="note-0049-03a" place="margin">74.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur ſuper plano vitreo AB gutta G. </s>
          <s xml:space="preserve">Particulæ ſingulæ parum a vitro <lb />
<ptr xml:id="note-0049-04a" corresp="note-0049-04" type="noteAnchor" />
diſtantes ad hoc directe tendunt, particulaſque cum quibus cohærent ſecum <lb />trahunt, unde in gutta oritur motus ſimilis illi, qui in gutta daretur, ſi plano <lb />CD ad AB parallelo hoc verſus premeretur; </s>
          <s xml:space="preserve">qua preſſione gutta ſeſe expan-<lb />deret quaqua verſum, &amp; </s>
          <s xml:space="preserve">expanſio hæc eſt effectus attractionis. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0049-05a" corresp="note-0049-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0049-04" corresp="note-0049-04a" place="margin">TAB. I. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0049-05" corresp="note-0049-05a" place="margin">75.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit AB aquæ ſuperficies; </s>
          <s xml:space="preserve">huic pro parte immergatur perpendiculariter <lb />
<ptr xml:id="note-0049-06a" corresp="note-0049-06" type="noteAnchor" />
vitreum planum FD, cujus craſſitiem hic repræſentamus. </s>
          <s xml:space="preserve">Aqua a plano at <lb />
<ptr xml:id="note-0049-07a" corresp="note-0049-07" type="noteAnchor" />
trahitur, quo premitur juxta directionem BD <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">conatur quaqua verſum
<ptr xml:id="note-0049-08a" corresp="note-0049-08" type="noteAnchor" />
ſuper plano ſeſe expandere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quo motu non poſſunt agitari niſi particulæ in
<ptr xml:id="note-0049-09a" corresp="note-0049-09" type="noteAnchor" />
D, motibus contrariis infra ſuperficiem ſeſe mutuo deſtruentibus; </s>
          <s xml:space="preserve">elevabitur <lb />ideo aqua, &amp; </s>
          <s xml:space="preserve">aſcendentem ſequetur illa, quæ cum ipſa cohæret, ſuſtinebi-<lb />turque ita aqua a vitro, ut pondus aquæ elevatæ valeat vim qua elevatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0049-06" corresp="note-0049-06a" place="margin">76.</note>
              <note xml:space="preserve" xml:id="note-0049-07" corresp="note-0049-07a" place="margin">TAB. I. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0049-08" corresp="note-0049-08a" n="*" anchored="true" place="margin">74.</note>
              <note xml:space="preserve" xml:id="note-0049-09" corresp="note-0049-09a" n="*" anchored="true" place="margin">75.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit altitudo hæc, quam juſto majorem repræſentamus, DC; </s>
          <s xml:space="preserve">ſuſtinetur autem <lb />aqua in CDG ſolâ vi qua particulæ in C ſurſum pelluntur: </s>
          <s xml:space="preserve">nam ubi aqua <lb />quieſcit, vires, quibus aqua inter C &amp; </s>
          <s xml:space="preserve">D ſeſe quaqua verſum expandere cona-<lb />tur <ptr type="noteAnchor" />, ſeſe mutuo deſtruunt: </s>
          <s xml:space="preserve">particula ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">in e æqualiter ſurſum &amp; </s>
          <s xml:space="preserve">deor-
<ptr xml:id="note-0049-10a" corresp="note-0049-10" type="noteAnchor" />
ſum pellitur. </s>
          <s xml:space="preserve">Vis ergo quæ ſuſtinet aquam, proportionem ſequitur latitudinis <lb />
<ptr xml:id="note-0049-11a" corresp="note-0049-11" type="noteAnchor" />
ſuperficiei juxta quam aqua adſcendit, menſuratæ, ad altitudinem ad quam aqua <lb />pertingit, in linea ad ſuperficiem ipſius aquæ parallela: </s>
          <s xml:space="preserve">quam eandem rationem <lb />ſequitur pondus aquæ elevatæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0049-10" corresp="note-0049-10a" n="*" anchored="true" place="margin">75.</note>
              <note xml:space="preserve" xml:id="note-0049-11" corresp="note-0049-11a" place="margin">77.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De Tubis Capillaribus.</head>
        <p>
          <s xml:space="preserve">Aquam in tubos vitreos minores ſponte adſcendere debere, ex explicatis <lb />facile deducitur. </s>
          <s xml:space="preserve">Quantitas autem aquæ, quæ ſuſtinetur, ſequitur rationem o-<lb />
<ptr xml:id="note-0049-12a" corresp="note-0049-12" type="noteAnchor" />
ræ aquæ elevatæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">orahæc, ſiagatur detubis cylindricis, perpendiculariter im-
<ptr xml:id="note-0049-13a" corresp="note-0049-13" type="noteAnchor" />
merſis ad inſtar diametri creſcit aut minuitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0049-12" corresp="note-0049-12a" place="margin">78.</note>
              <note xml:space="preserve" xml:id="note-0049-13" corresp="note-0049-13a" n="*" anchored="true" place="margin">77.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint duo tubi quorum diametri dicantur D, d; </s>
          <s xml:space="preserve">altitudines aquæ A, a; <lb /></s>
          <s xml:space="preserve">quantitates aquæ ergo erunt inter ſe ut D<hi rend="superscript">q</hi> x A ad d<hi rend="superscript">q</hi> x a <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideo D<hi rend="superscript">q</hi> x A, d<hi rend="superscript">q</hi> x a
<ptr xml:id="note-0049-14a" corresp="note-0049-14" type="noteAnchor" />
:</s>
          <s xml:space="preserve">: D, d<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">dividendo antecedentia per D<hi rend="superscript">q</hi>, &amp; </s>
          <s xml:space="preserve">conſequentia per dq habemus,
<ptr xml:id="note-0049-15a" corresp="note-0049-15" type="noteAnchor" />
A, a :</s>
          <s xml:space="preserve">: {1/D}, {1/d}, id eſt altitudines ſunt inverſe ut diametri. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0049-16a" corresp="note-0049-16" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0049-14" corresp="note-0049-14a" n="*" anchored="true" place="margin">2. II. 14. <lb />El. XII.</note>
              <note xml:space="preserve" xml:id="note-0049-15" corresp="note-0049-15a" n="*" anchored="true" place="margin">78.</note>
              <note xml:space="preserve" xml:id="note-0049-16" corresp="note-0049-16a" place="margin">79.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De aſcènſu aquæ inter plana, de quo in n. 58.</head>
        <p>
          <s xml:space="preserve">Sint AC, BC, lineæ repræſentantes planorum ſectionem horizontalem a <lb />
<ptr xml:id="note-0049-17a" corresp="note-0049-17" type="noteAnchor" />
ſuperficie aquæ; </s>
          <s xml:space="preserve">ponamus ſpatium, angulo ACB contentum, dividi lineis <lb />
<ptr xml:id="note-0049-18a" corresp="note-0049-18" type="noteAnchor" />
</s>
          <pb facs="0050" n="20" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ut de, fg, hi, l m, &amp;</s>
          <s xml:space="preserve">c parum admodum, ſed æqualiter, a ſe mutuo di-<lb />ſtantibus; </s>
          <s xml:space="preserve">manifeſtum eſt æquales aquæ quantitates in ſpatiis dfeg, himl, <lb />elevari <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ibique ideo dari priſmata æqualia, quorum altitudines ſunt inverſe
<ptr xml:id="note-0050-01a" corresp="note-0050-01" type="noteAnchor" />
ut baſes <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hæ autem, quia pro parallelogrammis haberi poſſunt, &amp; </s>
          <s xml:space="preserve">propter la-
<ptr xml:id="note-0050-02a" corresp="note-0050-02" type="noteAnchor" />
titudines df, hl, æquales, ſunt inter ſe ut de ad hi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ ſunt ut d C ad h C.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0050-03a" corresp="note-0050-03" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0049-17" corresp="note-0049-17a" place="margin">80.</note>
              <note xml:space="preserve" xml:id="note-0049-18" corresp="note-0049-18a" place="margin">TAB. I. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0050-01" corresp="note-0050-01a" n="*" anchored="true" place="margin">77.</note>
              <note xml:space="preserve" xml:id="note-0050-02" corresp="note-0050-02a" n="*" anchored="true" place="margin">34. El. <hi rend="small caps">XI</hi>.</note>
              <note xml:space="preserve" xml:id="note-0050-03" corresp="note-0050-03a" n="*" anchored="true" place="margin">1. El. <hi rend="small caps">VI</hi>.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Deducimus ex his curvam efg eſſe Hyperbolam cujus Aſymptoti ſunt lineæ <lb />
<ptr xml:id="note-0050-04a" corresp="note-0050-04" type="noteAnchor" />
AB, in qua vitra ſeſe mutuo tangunt, &amp; </s>
          <s xml:space="preserve">BC, ſuperficies aquæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Propter
<ptr xml:id="note-0050-05a" corresp="note-0050-05" type="noteAnchor" />
angulum rectum ABC Hyperbola eſt æquilatera <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">examinavimus enim
<ptr xml:id="note-0050-06a" corresp="note-0050-06" type="noteAnchor" />
caſum in quo linea, in qua vitra ſeſe mutuo tangunt, ad ſuperficiem aquæ <lb />perpendicularis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0050-04" corresp="note-0050-04a" place="margin">81.</note>
              <note xml:space="preserve" xml:id="note-0050-05" corresp="note-0050-05a" place="margin">TAB. II. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0050-06" corresp="note-0050-06a" n="*" anchored="true" place="margin">La Hire <lb /><hi rend="small caps">S. C</hi>. l. <hi rend="small caps">IV</hi>. <lb />p. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Facile etiam confertur altitudo in tubo cum altitudine inter plana.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">ibid. l. <hi rend="small caps">V</hi>. <lb />p. 13.</note>
        <p>
          <s xml:space="preserve">Sit tubi cylindrici ſectio M, cujus ſemidiameter æqualis eſt diſtantiæ e d inter <lb />plana. </s>
          <s xml:space="preserve">Clarum eſt vim, quæ ſuſtinet priſma aqueum cujus baſis eſt def pro-<lb />
<ptr xml:id="note-0050-08a" corresp="note-0050-08" type="noteAnchor" />
portionem ſequi lineæ df; </s>
          <s xml:space="preserve">ambabus enim df &amp; </s>
          <s xml:space="preserve">eg proportionalis eſt vis quæ pa-<lb />
<ptr xml:id="note-0050-09a" corresp="note-0050-09" type="noteAnchor" />
rallelopipedum, cujus baſis eſt dfeg, ſuſtinet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0050-10a" corresp="note-0050-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0050-08" corresp="note-0050-08a" place="margin">82.</note>
              <note xml:space="preserve" xml:id="note-0050-09" corresp="note-0050-09a" place="margin">TAB I. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0050-10" corresp="note-0050-10a" n="*" anchored="true" place="margin">77.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In tubo vis quæ ſuſtinet priſma, cujus baſis eſt nop, proportionalis eſt ipſi np; <lb /></s>
          <s xml:space="preserve">quia tota circumferentia proportionalis eſt illi quæ integrum aqueum cylin-<lb />drum vitro contentum ſuſtinet. </s>
          <s xml:space="preserve">Si np &amp; </s>
          <s xml:space="preserve">df fuerint æquales; </s>
          <s xml:space="preserve">vires quæ pri-<lb />ſmata ſuſtinent æquales ſunt; </s>
          <s xml:space="preserve">ideoque &amp; </s>
          <s xml:space="preserve">ipſa priſmata æqualia; </s>
          <s xml:space="preserve">ſunt etiam <lb />in hoc caſu baſes nop, def, æquales, quare priſmatum altitudines non <lb />difterunt, &amp; </s>
          <s xml:space="preserve">aqua in tubum &amp; </s>
          <s xml:space="preserve">inter plana ad eandem adſcendit altitudinem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Variarimultis modis poteſt experimentum de adſcenſu aquæ inter plana.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Nimium longum &amp; </s>
          <s xml:space="preserve">ſatis inutile foret, omnia quæ huc ſpectant perpendere; <lb /></s>
          <s xml:space="preserve">ſatis eſt caſum præcipuum examinaſſe; </s>
          <s xml:space="preserve">Circa duos alios in quibus angulus <lb />
<ptr xml:id="note-0050-11a" corresp="note-0050-11" type="noteAnchor" />
ABC, quem linea, in qua vitra junguntur, cum ſuperficie aquæ efficit, eſt <lb />
<ptr xml:id="note-0050-12a" corresp="note-0050-12" type="noteAnchor" />
acutus aut obtuſus, manentibus planis vitreis ad aquæ ſuperficiem perpendi-<lb />cularibus, notabo, aquam etiam terminari Hyperbolica linea, cujus aſym-<lb />ptos una eſt aquæ ſuperficies, altera habetur erigendo perpendicularem BF <lb />ad CB, in puncto B, aſvmptos quæſita erit BE, quæ dividit bifariam FD, <lb />perpendicularem in puncto quocunque ad BF, &amp; </s>
          <s xml:space="preserve">terminatam linea BA.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0050-11" corresp="note-0050-11a" place="margin">83.</note>
              <note xml:space="preserve" xml:id="note-0050-12" corresp="note-0050-12a" place="margin">TAB. I. <lb />fig. 8. 9.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si DF per punctum D Hyperbolæ tranſect, BF erit ſemidiameter con-<lb />jugata cum ſemidiametro BD.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Fig. </s>
          <s xml:space="preserve">9. </s>
          <s xml:space="preserve">ultra F Hyperbola non continuatur; </s>
          <s xml:space="preserve">aqua tamen ulterius adſcen-<lb />dit, ſed aliâ terminatur Curvâ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Fig. </s>
          <s xml:space="preserve">8. </s>
          <s xml:space="preserve">licet Hyperbola vitrorum latera juncta ſecet in D non ibi ad-<lb />ſcenſus aquæ terminatur, ſed ad certam, &amp; </s>
          <s xml:space="preserve">quidem pro diverſo, quem in-<lb />ter ſe vitra continent, angulo, diverſam ab AB diſtantiam, ab Hyperbola <lb />deflectitur curva, adſcenſuſque juxta BA continuatur. </s>
          <s xml:space="preserve">Ubi enim exigua <lb />
<ptr xml:id="note-0050-13a" corresp="note-0050-13" type="noteAnchor" />
admodum eſt inter vitra diſtantia attractiones oppoſitæ ſeſe mutuo juvant, quo au-<lb />getur aquæ adſcenſus. </s>
          <s xml:space="preserve">Simile augmentum actionis in n ſequenti memoratur; <lb /></s>
          <s xml:space="preserve">in luminis attractione a corporibus etiam locum habet, ut notamus in nume-<lb />ro ultimo cap. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">lib. </s>
          <s xml:space="preserve">3.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0050-13" corresp="note-0050-13a" place="margin">84.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De motu guttæ in n. 59,</head>
        <p>
          <s xml:space="preserve">Concipiamus plana, inter quæ gutta movetur, ſecari plano ad plana, &amp; </s>
          <s xml:space="preserve">ad <lb />
<ptr xml:id="note-0050-14a" corresp="note-0050-14" type="noteAnchor" />
lineam in qua junguntur perpendicularem: </s>
          <s xml:space="preserve">repræſentatur ſectio hæc; </s>
          <s xml:space="preserve">ſed, cum <lb />
<ptr xml:id="note-0050-15a" corresp="note-0050-15" type="noteAnchor" />
motus ab inclinatione planorum ad ſe invicem pendeat, hanc juſto majorem <lb />repræſentamus, ut &amp; </s>
          <s xml:space="preserve">diſtantiam inter vitra, &amp; </s>
          <s xml:space="preserve">diſtantiam ad quam vitrum in <lb />oleum agit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0050-14" corresp="note-0050-14a" place="margin">85.</note>
              <note xml:space="preserve" xml:id="note-0050-15" corresp="note-0050-15a" place="margin">TAB. I. <lb />fig. 10.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint plana AB, CD; </s>
          <s xml:space="preserve">gutta e eff; </s>
          <s xml:space="preserve">gh diſtantia ad quam vitrum oleum tra-<lb />hit: </s>
          <s xml:space="preserve">omne ergo oleum inter iehf ad planum trahitur, &amp; </s>
          <s xml:space="preserve">conatur ſeſe quaqua
</s>
          <pb facs="0051" n="21" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. V.</fw>
verſum ſuper plano expandere <ptr type="noteAnchor" /> non autem poteſt propter cohærentiam par-
<ptr xml:id="note-0051-01a" corresp="note-0051-01" type="noteAnchor" />
tium guttæ, vireſque oppoſitæ in e &amp; </s>
          <s xml:space="preserve">f ſeſe mutuo deſtruunt, guttaque, ſi pla-<lb />na parallela forent non moveretur. </s>
          <s xml:space="preserve">Nunc vero, quia actio attractionis per-<lb />pendiculariter dirigitur ad vitrum, oleum in ſpatio flh a ſuperficie fg attra-<lb />hitur, ceditque, quia nulla actione contraria deſtruitur hæc, quo motu agi-<lb />tatur tota gutta cujus partes cohærent inter ſe. </s>
          <s xml:space="preserve">Tendit idcirco gutta illam <lb />partem verſus in qua vitra concurrunt, quamdiu inferius plani inclinatio ad <lb />horizontem talis eſt, ut vis, qua gravitate ſuper plano conatur deſcendere, <lb />minor eſt illâ qua ex attractione ſurſum fertur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-01" corresp="note-0051-01a" n="*" anchored="true" place="margin">75.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ubi autem exigua eſt inter vitra diſtantia attractiones oppoſitæ ſeſe mutuo <lb />juvant’, viſque magis augetur quam ad inſtar diametri guttæ, quod augmen-<lb />tum in ratione diametri ex ſuperius demonſtratis deduci facile poteſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VI.</head>
        <head rend="italics" xml:space="preserve">De Motu in genere, ubi de Loco &amp; Tempore.</head>
        <p>
          <s xml:space="preserve">MOtus eſt tranſlatio de loco in locum, ſive continua loci <lb />
<ptr xml:id="note-0051-02a" corresp="note-0051-02" type="noteAnchor" />
mutatio. </s>
          <s xml:space="preserve">Unusquiſque illius habet ideam, quæ ſim-<lb />plex eſt, &amp; </s>
          <s xml:space="preserve">verbis explicari nequit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-02" corresp="note-0051-02a" place="margin">86.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Locus eſt ſpatium a corpore occupatum, &amp; </s>
          <s xml:space="preserve">de eo idem ac <lb />
<ptr xml:id="note-0051-03a" corresp="note-0051-03" type="noteAnchor" />
de motu dicendum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-03" corresp="note-0051-03a" place="margin">87.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Duplex eſt, verus ſeu abſolutus, &amp; </s>
          <s xml:space="preserve">relativus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Locus verus eſt pars ſpatii immobilis, quæ a corpore occu-<lb />
<ptr xml:id="note-0051-04a" corresp="note-0051-04" type="noteAnchor" />
patur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-04" corresp="note-0051-04a" place="margin">88.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Locus relativus, qui ſolus ſenſibus diſtinguitur, eſt ſitus <lb />
<ptr xml:id="note-0051-05a" corresp="note-0051-05" type="noteAnchor" />
corporis reſpectu aliorum corporum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-05" corresp="note-0051-05a" place="margin">89.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sæpe mutatur locus verus manente relativo, &amp; </s>
          <s xml:space="preserve">vice <lb />verſa.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Unde motus alter eſt verus ſeu abſolutus, alter relativus. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0051-06a" corresp="note-0051-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-06" corresp="note-0051-06a" place="margin">90.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum corpus movetur, tempus labitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tempus etiam duplex eſt; </s>
          <s xml:space="preserve">verum ſeu abſolutum, &amp; </s>
          <s xml:space="preserve">re-<lb />
<ptr xml:id="note-0051-07a" corresp="note-0051-07" type="noteAnchor" />
lativum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-07" corresp="note-0051-07a" place="margin">91.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Verum nullam habet relationem ad motum corporum, <lb />
<ptr xml:id="note-0051-08a" corresp="note-0051-08" type="noteAnchor" />
neque ad ſucceſſionem idearum in Ente intelligenti, ſed ſua <lb />natura ſemper æqualiter fluit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-08" corresp="note-0051-08a" place="margin">92.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Tempus relativum eſt pars temporis veri per motum cor-<lb />
<ptr xml:id="note-0051-09a" corresp="note-0051-09" type="noteAnchor" />
porum menſurata, hoc ſolum ſub ſenſus cadit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0051-09" corresp="note-0051-09a" place="margin">93.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0052" n="22" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Motus omnis poteſt celerior fieri, &amp; </s>
          <s xml:space="preserve">etiam corpus tardi-<lb />us quam ante poteſt moveri; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">veriſimillimum eſt nullum <lb />dari motum corporum omnino æquabilem; </s>
          <s xml:space="preserve">unde ſequitur <lb />tempus relativum a vero differri, hoc enim nunquam ci-<lb />tius, nunquam tardius fluit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p rend="italics">
          <s xml:space="preserve">Illa motus afſectio, qua in certo tempore certum ſpatium <lb />
<ptr xml:id="note-0052-01a" corresp="note-0052-01" type="noteAnchor" />
a corpore moto percurritur, vocatur celeritas aut velocitas; <lb /></s>
          <s xml:space="preserve">quæ ergo major aut minor eſt pro magnitudine illius ſpatii, <lb />&amp; </s>
          <s xml:space="preserve">illi ſpatio ſemper proportionalis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0052-01" corresp="note-0052-01a" place="margin">94.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Spatium percurſum ad inſtar temporis augetur ſi veloci-<lb />
<ptr xml:id="note-0052-02a" corresp="note-0052-02" type="noteAnchor" />
tas maneat; </s>
          <s xml:space="preserve">ideo generaliter ſpatium percurſum ſequitur <lb />rationem compoſitam temporis &amp; </s>
          <s xml:space="preserve">velocitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0052-02" corresp="note-0052-02a" place="margin">95.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datis variis corporibus, ſi pro ſingulis velocitas multi-<lb />plicetur per tempus, producta erunt ut ſpatia percurſa.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p rend="italics">
          <s xml:space="preserve">Motus directio eſt recta, quæ ducta concipitur ver ſus par-<lb />
<ptr xml:id="note-0052-03a" corresp="note-0052-03" type="noteAnchor" />
tem qua tendit mobile.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0052-03" corresp="note-0052-03a" place="margin">96.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p rend="italics">
          <s xml:space="preserve">Potentia aut preſſio eſt vis continua in corpus agens ad il-<lb />
<ptr xml:id="note-0052-04a" corresp="note-0052-04" type="noteAnchor" />
lud ex loco movendum, &amp; </s>
          <s xml:space="preserve">quæ actionem in corpus exerere <lb />poteſt, hoc non moto, aut motu jam impreſſo non mutato. </s>
          <s xml:space="preserve">Si <lb />nempe preſſionis actio contraria preſſione deſtruatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0052-04" corresp="note-0052-04a" place="margin">97.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">LIBRI I. PARS II.</head>
        <head xml:space="preserve">De Actionibus Potentiarum.</head>
        <head xml:space="preserve">CAPUT VII.</head>
        <head rend="italics" xml:space="preserve">De Actionibus Potentiarum comparandis.</head>
        <p rend="italics">
          <s xml:space="preserve">PReſſiones, id eſt, Potentiarum actiones æquales eſſe has, <lb />
<ptr xml:id="note-0052-05a" corresp="note-0052-05" type="noteAnchor" />
quæ æqualibus temporibus æquales edunt effectus, pri-<lb />mo intuitu patet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0052-05" corresp="note-0052-05a" place="margin">98.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Preſſionem contrariam poſſe vincere Preſſionem, in du-<lb />bium nemo vocabit. </s>
          <s xml:space="preserve">Preſſiones æquales ſeſe mutuo deſtrue-<lb />
<ptr xml:id="note-0052-06a" corresp="note-0052-06" type="noteAnchor" />
</s>
          <pb facs="0053" />
          <s xml:space="preserve">
<ptr xml:id="fig-0053-01a" corresp="fig-0053-01" type="figureAnchor" />
<pb facs="0053a" />
<ptr xml:id="fig-0053a-01a" corresp="fig-0053a-01" type="figureAnchor" />
<pb facs="0054" />
<pb facs="0055" n="23" /><fw type="head">MATHEMATICA. LIB. I CAP. VII.</fw>
re, &amp; </s>
          <s xml:space="preserve">has eſſe æquales quæ ſeſe mutuo deſtruunt, ſi pro <lb />axiomate non habeatur, ex dictis haud difficulter deduci po-<lb />terit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0052-06" corresp="note-0052-06a" place="margin">99.</note>
              <figure xml:id="fig-0053-01" corresp="fig-0053-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-01" />
                <label>0053-01</label>
              </figure>
              <figure xml:id="fig-0053a-01" corresp="fig-0053a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053a-01" />
                <label>0053a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex quibus etiam patet, Preſſiones eſſe inter ſe ut effectus <lb />
<ptr xml:id="note-0055-01a" corresp="note-0055-01" type="noteAnchor" />
æqualibus temporibus editos.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-01" corresp="note-0055-01a" place="margin">100.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si prematur obſtaculum &amp; </s>
          <s xml:space="preserve">hoc ex loco non recedat, con-<lb />
<ptr xml:id="note-0055-02a" corresp="note-0055-02" type="noteAnchor" />
trariâ preſſione deſtruitur preſſio; </s>
          <s xml:space="preserve">aliter enim hæc nullum <lb />ederet effectum. </s>
          <s xml:space="preserve">Si ergo non deſtruatur, cedit obſtaculum. <lb /></s>
          <s xml:space="preserve">Hìc non conſideranda eſt vis quæ in quibuſdam occaſioni-<lb />bus obſtaculo communicatur &amp; </s>
          <s xml:space="preserve">qua in motu perſeverat <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0055-03a" corresp="note-0055-03" type="noteAnchor" />
agitur tantum in tota hac parte ſecunda de translatione quæ <lb />
<ptr xml:id="note-0055-04a" corresp="note-0055-04" type="noteAnchor" />
eſt effectus immediatus preſſionis, &amp; </s>
          <s xml:space="preserve">quæ ſemper tantum ſo-<lb />la locum habet in momento primo infinite exiguo, quando <lb />actione potentiæ obſtaculum movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-02" corresp="note-0055-02a" place="margin">101.</note>
              <note xml:space="preserve" xml:id="note-0055-03" corresp="note-0055-03a" n="*" anchored="true" place="margin">12.</note>
              <note xml:space="preserve" xml:id="note-0055-04" corresp="note-0055-04a" place="margin">102.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum effectus preſſionis contraria preſſione non deſtructæ <lb />ſit obſtaculi translatio, ſequitur actiones variarum poten-<lb />
<ptr xml:id="note-0055-05a" corresp="note-0055-05" type="noteAnchor" />
tiarum tantum inter ſe poſſe differre reſpectu obſtaculorum <lb />in quæ agunt potentiæ, &amp; </s>
          <s xml:space="preserve">reſpectu ſpatiorum ab obſtaculis per-<lb />cuſſorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-05" corresp="note-0055-05a" place="margin">103.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p>
          <s xml:space="preserve">Magnitudo preſſionis conſiderata cum relatione ad obſta-<lb />
<ptr xml:id="note-0055-06a" corresp="note-0055-06" type="noteAnchor" />
culum quod ab illa removetur vocatur Potentiæ intenſitas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-06" corresp="note-0055-06a" place="margin">104.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Sunt igitur potentiarum intenſitates ut obſtacula in quæ <lb />
<ptr xml:id="note-0055-07a" corresp="note-0055-07" type="noteAnchor" />
illæ agunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-07" corresp="note-0055-07a" place="margin">105.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si æqualibus temporibus per ſpatia æqualia obſtacula ce-<lb />
<ptr xml:id="note-0055-08a" corresp="note-0055-08" type="noteAnchor" />
dunt, actiones Potentiarum ſunt ut harum intenſitates, ideſt, <lb />ut obſtacula <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0055-09a" corresp="note-0055-09" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-08" corresp="note-0055-08a" place="margin">106.</note>
              <note xml:space="preserve" xml:id="note-0055-09" corresp="note-0055-09a" n="*" anchored="true" place="margin">100. <lb />103. 105.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si Potentiarum intenſitates fuerint æquales, id eſt, ſi in <lb />
<ptr xml:id="note-0055-10a" corresp="note-0055-10" type="noteAnchor" />
obſtacula æqualia agant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Potentiarum actiones ſunt ut
<ptr xml:id="note-0055-11a" corresp="note-0055-11" type="noteAnchor" />
ſpatia, æqualibus temporibus, ab obſtaculis percurſa <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0055-12a" corresp="note-0055-12" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-10" corresp="note-0055-10a" place="margin">107.</note>
              <note xml:space="preserve" xml:id="note-0055-11" corresp="note-0055-11a" n="*" anchored="true" place="margin">105.</note>
              <note xml:space="preserve" xml:id="note-0055-12" corresp="note-0055-12a" n="*" anchored="true" place="margin">100. 102. <lb />103.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si autem &amp; </s>
          <s xml:space="preserve">obſtacula &amp; </s>
          <s xml:space="preserve">viæ ab his æqualibus temporibus <lb />
<ptr xml:id="note-0055-13a" corresp="note-0055-13" type="noteAnchor" />
percurſæ differant, ſunt potentiarum actiones ut intenſitates, <lb />aut ut obſtacula, &amp; </s>
          <s xml:space="preserve">ut viæ percurſæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, in harum ra-
<ptr xml:id="note-0055-14a" corresp="note-0055-14" type="noteAnchor" />
tionum ratione compoſita.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0055-13" corresp="note-0055-13a" place="margin">108.</note>
              <note xml:space="preserve" xml:id="note-0055-14" corresp="note-0055-14a" n="*" anchored="true" place="margin">106. 107.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex. </s>
          <s xml:space="preserve">Gr. </s>
          <s xml:space="preserve">ſi unius potentiæ intenſitas fuerit dupla; </s>
          <s xml:space="preserve">id eſt, ſi <lb />obſtaculum fuerit duplum, &amp; </s>
          <s xml:space="preserve">per ſpatium triplum transfera-
</s>
          <pb facs="0056" n="24" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tur, actio erit bis dupla, aut ter tripla, id eſt, ſextupla. </s>
          <s xml:space="preserve">Si, <lb />datis numeris in ratione intenſitatum, &amp; </s>
          <s xml:space="preserve">aliis in ratione ſpa-<lb />tiorum percurſorum, pro ſingulis potentiis intenſitas per ſpa-<lb />tium ab obſtaculo percurſum multiplicetur, producta ha-<lb />bebunt quæſitam compoſitam rationem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si numeri dentur, qui actiones potentiarum variarum de-<lb />
<ptr xml:id="note-0056-01a" corresp="note-0056-01" type="noteAnchor" />
ſignant, erunt hi ut producta obſtaculorum per ſpatia, ergo <lb />ſi ſinguli ex datis numeris per ſpatium ab obſtaculo ſuo per-<lb />curſum dividantur, quotientes erunt ut ipſa obſtacula.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0056-01" corresp="note-0056-01a" place="margin">109.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ideo eo majora ſunt obſtacula, quo actiones ſunt majo-<lb />res, &amp; </s>
          <s xml:space="preserve">ſpatia percurſa minora; </s>
          <s xml:space="preserve">ideſt, obſtacula ſunt in ratio-<lb />
<ptr xml:id="note-0056-02a" corresp="note-0056-02" type="noteAnchor" />
ne compoſita directæ actionum, &amp; </s>
          <s xml:space="preserve">inverſæ ſpatiorum percur-<lb />ſorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0056-02" corresp="note-0056-02a" place="margin">110.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si numeri qui exprimunt producta obſtaculorum per <lb />ſpatia, id eſt, qui potentiarum actiones exprimunt, ſinguli <lb />dividantur per numeros, qui obſtacula deſignant, quotientes <lb />erunt ut ſpatia, quæ ergo ſunt directe ut actiones, &amp; </s>
          <s xml:space="preserve">inver-<lb />
<ptr xml:id="note-0056-03a" corresp="note-0056-03" type="noteAnchor" />
ſe ut obſtacula.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0056-03" corresp="note-0056-03a" place="margin">111.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Potentiarum actiones ſunt æquales, ſi ſpatia percurſa fue-<lb />
<ptr xml:id="note-0056-04a" corresp="note-0056-04" type="noteAnchor" />
rint in ratione inverſa obſtaculorum aut intenſit atum poten-<lb />tiarum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quantum enim potentia intenſitate alteram ſupe-
<ptr xml:id="note-0056-05a" corresp="note-0056-05" type="noteAnchor" />
rat, in tantum reſpectu ſpatii percurſi ſuperatur. </s>
          <s xml:space="preserve">Ex. </s>
          <s xml:space="preserve">Gr. </s>
          <s xml:space="preserve">ſi obſta-<lb />cula fuerint ut octo &amp; </s>
          <s xml:space="preserve">ſex, viæ percurſæ ut tria ad quatuor, u-<lb />traque actio exprimetur per numerum viginti quatuor <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0056-06a" corresp="note-0056-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0056-04" corresp="note-0056-04a" place="margin">112.</note>
              <note xml:space="preserve" xml:id="note-0056-05" corresp="note-0056-05a" n="*" anchored="true" place="margin">100.</note>
              <note xml:space="preserve" xml:id="note-0056-06" corresp="note-0056-06a" n="*" anchored="true" place="margin">108.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VIII.</head>
        <head rend="italics" xml:space="preserve">Generalia circa Gravitatem.</head>
        <head xml:space="preserve"><hi rend="small caps">Phænomenon i</hi>.</head>
        <p rend="italics">
          <s xml:space="preserve">Omnia Corpora in Terræ viciniis, ſi nullo obſtaculo co-<lb />
<ptr xml:id="note-0056-07a" corresp="note-0056-07" type="noteAnchor" />
hibeantur, Terram verſum feruntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0056-07" corresp="note-0056-07a" place="margin">113.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>. 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Vis qua corpora Tellurem verſus pelluntur, vocatur gravitas. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0056-08a" corresp="note-0056-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0056-08" corresp="note-0056-08a" place="margin">114.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Vis illa cum relatione ad corpus, quod vi illa propellitur, <lb />
<ptr xml:id="note-0056-09a" corresp="note-0056-09" type="noteAnchor" />
vocatur corporis pondus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0056-09" corresp="note-0056-09a" place="margin">115.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0057" n="25" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. VIII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Phænomenon</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Vis gravitatis ubique in Terræ viciniis, &amp; </s>
          <s xml:space="preserve">omnibus mo-<lb />
<ptr xml:id="note-0057-01a" corresp="note-0057-01" type="noteAnchor" />
mentis, æqualiter agit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0057-01" corresp="note-0057-01a" place="margin">116.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Parva quidem datur gravitatis differentia in regionibus di-<lb />verſis, de qua agemus in cap. </s>
          <s xml:space="preserve">17. </s>
          <s xml:space="preserve">libri IV, nimis tamen <lb />eſt exigua ut hìc conſideretur, præcipue cum in regionibus, <lb />quæ inter ſe ſunt vicinæ, omnino ſit inſenſibilis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando corporis deſcenſus obſtaculo impeditur, pondere <lb />
<ptr xml:id="note-0057-02a" corresp="note-0057-02" type="noteAnchor" />
ſuo ſemper æqualiter obſtaculum premit, Terræ centrum <lb />verſus tendens; </s>
          <s xml:space="preserve">poteſt ergo haberi pro potentia in obſtacu-<lb />lum agenti, &amp; </s>
          <s xml:space="preserve">quæ de potentiis in capite præcedenti ſunt <lb />demonſtrata, hìc etiam locum habent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0057-02" corresp="note-0057-02a" place="margin">117.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Phænomenon</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Corpora quæ vi gravitatis deſcendunt, ſi omnis tollatur <lb />
<ptr xml:id="note-0057-03a" corresp="note-0057-03" type="noteAnchor" />
reſiſtentia, ſunt æque velocia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0057-03" corresp="note-0057-03a" place="margin">118.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Phænomenon hoc Experimento ſequenti patet.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <p rend="italics">
          <s xml:space="preserve">Qua duo corpora eodem momento in vacuo dimittuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pneumaticam dicimus machinam illam, cujus ope aër <lb />
<ptr xml:id="note-0057-04a" corresp="note-0057-04" type="noteAnchor" />
ex vaſe extrahitur, de hac agemus in parte 3<hi rend="superscript">2</hi>. </s>
          <s xml:space="preserve">lib. </s>
          <s xml:space="preserve">II.</s>
          <s xml:space="preserve">, hìc <lb />
<ptr xml:id="note-0057-05a" corresp="note-0057-05" type="noteAnchor" />
repræſentatur in N.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0057-04" corresp="note-0057-04a" place="margin">119.</note>
              <note xml:space="preserve" xml:id="note-0057-05" corresp="note-0057-05a" place="margin">TAB. I@.. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut magis commode experimentum, quod nunc explican-<lb />dum eſt, inſtituatur, a pede ſuo tollitur machina pneuma-<lb />tica, &amp; </s>
          <s xml:space="preserve">depreſſo ſuſtentaculo SS ſuperimponitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lamina ænea, cui vitra, ex quibus aër extrahitur, impo-<lb />nuntur, eſt L.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ad latera hujus duæ firmantur columnæ ligneæ AE, AE; <lb /></s>
          <s xml:space="preserve">harum pedes infra tabulam Machinæ pneumaticæ ſuperiorem <lb />penetrant, &amp; </s>
          <s xml:space="preserve">transverſis lignis, ut t, firmantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Columnarum altitudo excedit pedes quinque; </s>
          <s xml:space="preserve">junguntur <lb />hæ tabellis ligneis quatuor BB, CC, DD, EE. </s>
          <s xml:space="preserve">Diſtantia <lb />inter L &amp; </s>
          <s xml:space="preserve">BB eſt novem aut decem pollicum; </s>
          <s xml:space="preserve">BC, CD, DE, <lb />ſingulæ æquales ſunt octodecim pollicibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tabellæ hæ ligneæ latiores ſunt in medio, ut in ſingulis <lb />apertura, aut foramen rotundum, detur, cujus diameter æ-<lb />quat pollices quinque cum ſemiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0058" n="26" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Quatuor vitra cylindrica, quorum oræ exactiſſime inter <lb />ſe conveniunt, (quo pervenimus atterendo oras cum are-<lb />na madida ſuper plano), ſuperimponuntur Laminæ L, &amp; </s>
          <s xml:space="preserve"><lb />ſibi mutuo.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cylindrorum ſingulorum diametri interiores ſunt quatuor <lb />pollicum, &amp; </s>
          <s xml:space="preserve">altitudines ſeſquipedis. </s>
          <s xml:space="preserve">Transeunt hi cylindri per <lb />foramina in tabellis ligneis, &amp; </s>
          <s xml:space="preserve">firmantur ſinguli, tribus cuneis li-<lb />gneis x, x, &amp;</s>
          <s xml:space="preserve">c, formatis, ut cum vitro &amp; </s>
          <s xml:space="preserve">foramine con-<lb />gruant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Obtegitur cylindrus ſuperior operculo æneo o, quod in <lb />O ſeparatim repræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum hoc conjungitur pyxis ænea P, aut p, ope cochleæ <lb />G, quæ intra vitrum per operculum penetrat ita, ut ope <lb />ejuſdem cum operculo jungatur lamina elaſtica, flexa, in-<lb />curvata, &amp; </s>
          <s xml:space="preserve">perforata in ſuperiori parte, ut repræſentatur in I <lb />&amp; </s>
          <s xml:space="preserve">i.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Laminæ extrema r, r, elaſticitate conveniunt, ultimis <lb />tamen extremitatibus paululum deflexis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Huic laminæ includitur lamina ænea ovalis H, cujus mi-<lb />nor diameter intra laminam I contineri poteſt, hujus extre-<lb />mis non ſeparatis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Intra eandem laminam I aut i, penetrat filum æneum F <lb />(f), quod tranſit per pyxidem P (p), &amp; </s>
          <s xml:space="preserve">eò etiam per o-<lb />perculum O (o), ut &amp; </s>
          <s xml:space="preserve">per pyxidis operculum Q (q).</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Fili F extremum inferius V quadratum eſt &amp; </s>
          <s xml:space="preserve">cavum, ut <lb />cum filo jungatur lamina H, quæ, juncto cum eodem filo <lb />manubrio M (m), agitari poteſt, &amp; </s>
          <s xml:space="preserve">circumvolvi, quo ex-<lb />trema r, r, laminæ I ſeparantur, longiore diametro ovalis H <lb />ſuperante diſtantiam inter oppoſitas partes laminæ I, quando <lb />ipſius extrema elaſticitate junguntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cerâ molli circumpoſitâ cohibetur ne aër inter laminam <lb />&amp; </s>
          <s xml:space="preserve">vitrum transeat, ut &amp; </s>
          <s xml:space="preserve">inter operculum o &amp; </s>
          <s xml:space="preserve">vitrum; </s>
          <s xml:space="preserve">et-<lb />iam cerâ circumdantur vitra ubi duo junguntur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cochlea <lb />G eâdem obducitur, antequam pyxis P (p) cum operculo <lb />O (o) jungatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ne aër juxta filum f (F) vitra intret, pyxis p (P) annulis
</s>
          <pb facs="0059" n="27" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. VIII.</fw>
coreaceis cerâ &amp; </s>
          <s xml:space="preserve">oleo imbutis impletur, quæ comprimuntur <lb />operculo q(Q) ita, ut quam exactiſſime cum filo æneo, quod <lb />hæc pertranſit, congruant.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi></head>
        <p>
          <s xml:space="preserve">Omnibus ut explicatum dispoſitis, antequam operculum <lb />
<ptr xml:id="note-0059-01a" corresp="note-0059-01" type="noteAnchor" />
o, cum adjunctis, vitro ſuperiori imponatur, fruſtum au-<lb />ri cum plumulâ ita diſponenda ſunt, ut hæreant inter ex-<lb />trema laminæ i, ibique elaſticitate firmiter retineantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0059-01" corresp="note-0059-01a" place="margin">120.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Impoſito tunc operculo, cerâ aëris ingreſſus inter hoc &amp; </s>
          <s xml:space="preserve"><lb />vitrum, ut ſuperius dictum, cohibeatur; </s>
          <s xml:space="preserve">agitatâ antliâ ex-<lb />hauriatur aër ex vitris.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si nunc manubrium m circumvolvatur; </s>
          <s xml:space="preserve">clarum eſt eodem <lb />momento aurum &amp; </s>
          <s xml:space="preserve">plumulam relaxari, &amp; </s>
          <s xml:space="preserve">dimitti, exactiſſi-<lb />me etiam eodem momento ad laminam L pervenient.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpora cadentia percipiet ſpectator ad talem diſtan-<lb />tiam poſitus, ut unico intuitu omnia percipiat vitra, ſi ad <lb />minorem detur diſtantiam oculos dirigat ad ipſam lami-<lb />nam L.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex alio etiam Experimento, in ſequentibus memorando, <lb />idem hocce Phænomenon deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur, gravitate obſtacula quæcunque per æqua-<lb />lia ſpatia æqualibus temporibus transferri, ex actione imme-<lb />diata gravitatis; </s>
          <s xml:space="preserve">patet enim corpora in primo momento eo-<lb />dem modo moveri, &amp; </s>
          <s xml:space="preserve">ſingulis momentis ſequentibus corpus <lb />utrumque eodem modo accelerari; </s>
          <s xml:space="preserve">ſunt ergo actiones gra-<lb />
<ptr xml:id="note-0059-02a" corresp="note-0059-02" type="noteAnchor" />
vitatis in corpora ut ipſa corpora <ptr type="noteAnchor" />, id eſt pondera ſunt ut
<ptr xml:id="note-0059-03a" corresp="note-0059-03" type="noteAnchor" />
quantitates materiæ; </s>
          <s xml:space="preserve">ſingulæque materiæ particulæ æqua-<lb />les æqualiter ponderant, cujuſcunque corporis particulæ <lb />fuerint.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0059-02" corresp="note-0059-02a" n="*" anchored="true" place="margin">106.</note>
              <note xml:space="preserve" xml:id="note-0059-03" corresp="note-0059-03a" place="margin">121.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando pondus conſideratur ut potentia, intenſitas po-<lb />
<ptr xml:id="note-0059-04a" corresp="note-0059-04" type="noteAnchor" />
tentiæ proportionalis eſt quantitati materiæ in corpore pon-<lb />deranti, &amp; </s>
          <s xml:space="preserve">potentiæ directio eſt verſus Terræ centrum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0059-04" corresp="note-0059-04a" place="margin">122.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc de gravitate notanda erant, quia ponderibus in Ex-<lb />perimentis circa preſſiones inſtituendis utimur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0060" n="28" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IX.</head>
        <p rend="italics">
          <s xml:space="preserve">De Trochlea ſimplici, Libra, &amp; </s>
          <s xml:space="preserve">Centro gravitatis.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">TRochlea ſimplex, eſt orbiculus circa axem volubilis, <lb />
<ptr xml:id="note-0060-01a" corresp="note-0060-01" type="noteAnchor" />
cui circumpo ſitus funis ductarius dictus, Trochlea ex-<lb />
<ptr xml:id="note-0060-02a" corresp="note-0060-02" type="noteAnchor" />
hibetur in A, funis ductarius eſt d c e.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-01" corresp="note-0060-01a" place="margin">123.</note>
              <note xml:space="preserve" xml:id="note-0060-02" corresp="note-0060-02a" place="margin">TAB. II. <lb />48. 19.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hac Machinâ potentiæ directio mutatur, nec ullîus alîus <lb />uſus eſt, quando ſuo loco eſt fixa; </s>
          <s xml:space="preserve">in hoc enim caſu, vis, <lb />
<ptr xml:id="note-0060-03a" corresp="note-0060-03" type="noteAnchor" />
ſeu potentia, funi ductario applicata, ut M, æqualis impedi-<lb />mento P, æquipollet impedimento <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam potentia moveri
<ptr xml:id="note-0060-04a" corresp="note-0060-04" type="noteAnchor" />
non poteſt, quin impedimentum eodem tempore ſpatium <lb />æquale percurrat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-03" corresp="note-0060-03a" place="margin">124.</note>
              <note xml:space="preserve" xml:id="note-0060-04" corresp="note-0060-04a" n="*" anchored="true" place="margin">100.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondera explorantur, id eſt, quantitates materiæ in ſin-<lb />gulis corporibus comparantur <ptr type="noteAnchor" />, adhibitâ librâ aut bilance,
<ptr xml:id="note-0060-05a" corresp="note-0060-05" type="noteAnchor" />
inſtrumento notiſſimo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-05" corresp="note-0060-05a" n="*" anchored="true" place="margin">121.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Axis libræ vocatur linea circa quam libra movetur, aut <lb />
<ptr xml:id="note-0060-06a" corresp="note-0060-06" type="noteAnchor" />
potius rotatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-06" corresp="note-0060-06a" place="margin">125.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Quando longitudinem brachiorum ſive jugi conſideramus, <lb />
<ptr xml:id="note-0060-07a" corresp="note-0060-07" type="noteAnchor" />
axis conſideratur ut punctum, &amp; </s>
          <s xml:space="preserve">vocatur centrum libræ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-07" corresp="note-0060-07a" place="margin">126.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p>
          <s xml:space="preserve">Puncta ſuſpenſionis, aut applicationis, vocantur, puncta <lb />
<ptr xml:id="note-0060-08a" corresp="note-0060-08" type="noteAnchor" />
in quibus vel actu ſunt, vel liberè dependent pondera, aut lan-<lb />ces, quibus pondera imponuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-08" corresp="note-0060-08a" place="margin">127.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa hanc Machinam ſequentia notanda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Pondus æqualiter gravat punctum, ſi liberè ab eo depen-<lb />
<ptr xml:id="note-0060-09a" corresp="note-0060-09" type="noteAnchor" />
deat, ad quamcunque altitudinem, ac ſi pondus in ipſo poſitum <lb />intelligeretur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-09" corresp="note-0060-09a" place="margin">128.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondus enim corporis ad omnes altitudines æqualiter tra-<lb />hit funem quo ſuſpenditur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0060-10a" corresp="note-0060-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-10" corresp="note-0060-10a" n="*" anchored="true" place="margin">115. 116.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">In libra AB, pondus P, ope funis BD, ad varias ſuſpen-<lb />
<ptr xml:id="note-0060-11a" corresp="note-0060-11" type="noteAnchor" />
ditur altitudines; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eo ſitus libræ non mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-11" corresp="note-0060-11a" place="margin">TAB. III. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Actio ponderis ad movendam libram eo major eſt, quoma-<lb />
<ptr xml:id="note-0060-12a" corresp="note-0060-12" type="noteAnchor" />
</s>
          <pb facs="0061" />
          <s xml:space="preserve">
<ptr xml:id="fig-0061-01a" corresp="fig-0061-01" type="figureAnchor" />
<pb facs="0061a" />
<ptr xml:id="fig-0061a-01a" corresp="fig-0061a-01" type="figureAnchor" />
<pb facs="0062" />
<pb facs="0063" n="29" /><fw type="head">MATHEMATICA. LIB. I. CAP. IX.</fw>
gis punctum a pondere gravatum a centro libræ diſtat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />actio illa ſequitur proportionem diſtantiæ prædicti punctiab <lb />illo centro.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0060-12" corresp="note-0060-12a" place="margin">129.</note>
              <figure xml:id="fig-0061-01" corresp="fig-0061-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061-01" />
                <label>0061-01</label>
              </figure>
              <figure xml:id="fig-0061a-01" corresp="fig-0061a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061a-01" />
                <label>0061a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando libra rotatur, in eodem libræ motu, punctum <lb />
<ptr xml:id="note-0063-01a" corresp="note-0063-01" type="noteAnchor" />
B percurrit arcum B b, &amp; </s>
          <s xml:space="preserve">punctum A arcum A a, quo-<lb />rum ultimus maximus eſt; </s>
          <s xml:space="preserve">in illo ergo libræ motu actio e-<lb />juſdem ponderis varia eft, pro puncto cui applicatur, &amp; </s>
          <s xml:space="preserve"><lb />ſequitur proportionem ſpatii ab hoc puncto percurſi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eſt
<ptr xml:id="note-0063-02a" corresp="note-0063-02" type="noteAnchor" />
ergo in A, ut Aa, in B, ut Bb; </s>
          <s xml:space="preserve">arcus verò hi ſuntinter <lb />ſe ut CA, CB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0063-01" corresp="note-0063-01a" place="margin">TAB. III. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0063-02" corresp="note-0063-02a" n="*" anchored="true" place="margin">107. 117.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Libræ AB, cujus jugi longitudo eſt duorum pedum, bra-<lb />
<ptr xml:id="note-0063-03a" corresp="note-0063-03" type="noteAnchor" />
chia ſingula in partes centum æquales dividuntur, poſito <lb />
<ptr xml:id="note-0063-04a" corresp="note-0063-04" type="noteAnchor" />
diviſionum initio in ipſo centro libræ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0063-03" corresp="note-0063-03a" place="margin">130.</note>
              <note xml:space="preserve" xml:id="note-0063-04" corresp="note-0063-04a" place="margin">TAB. III. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Actio unciæ unius, applicatæ 60 diviſioni, æqualis eſt <lb />actioni trium unciarum, 20 diviſioni ſuſpenſarum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut hoc Experimentum cum quibusdam ſequentibus com-<lb />mode inſtituatur, varia dantur pondera ænea unius unciæ, <lb />ut P, quæ diviſionibus jugi applicari poſſunt, &amp; </s>
          <s xml:space="preserve">in inferiori <lb />parte uncum habent. </s>
          <s xml:space="preserve">Dantur etiam lances variæ, ut L, quæ <lb />ſingulæ cum filis, &amp; </s>
          <s xml:space="preserve">unco, cui ſuspenduntur exactiſſime et-<lb />iam ponderant unciam unam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur, actionem ponderis ad movendum li-<lb />
<ptr xml:id="note-0063-05a" corresp="note-0063-05" type="noteAnchor" />
bram eſſe in ratione compoſita ip ſius ponderis &amp; </s>
          <s xml:space="preserve">diſtantiæ a <lb />centro <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">nam hæc diſtantia eſt ut ſpatium percurſum in mo-
<ptr xml:id="note-0063-06a" corresp="note-0063-06" type="noteAnchor" />
tu libræ. </s>
          <s xml:space="preserve">Multiplicando ſingula pondera per ſuas diſtantias <lb />a centro producta ſunt ut actiones in libram.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0063-05" corresp="note-0063-05a" place="margin">131.</note>
              <note xml:space="preserve" xml:id="note-0063-06" corresp="note-0063-06a" n="*" anchored="true" place="margin">10@.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p>
          <s xml:space="preserve">Libra in æquilibrio dicitur, quando actiones ponderum in <lb />
<ptr xml:id="note-0063-07a" corresp="note-0063-07" type="noteAnchor" />
utrumque brachium ad movendam libram, ſunt æquales; </s>
          <s xml:space="preserve">i-<lb />ta ut ſeſe mutuo deſtruant, ut in præcedenti Experimento.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0063-07" corresp="note-0063-07a" place="margin">132.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p>
          <s xml:space="preserve">Quando libra eſt in æquilibrio, pondera ab utraque par-<lb />
<ptr xml:id="note-0063-08a" corresp="note-0063-08" type="noteAnchor" />
te dicuntur æquiponderare.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0063-08" corresp="note-0063-08a" place="margin">133.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondera inæqualia poſſunt æquiponderare; </s>
          <s xml:space="preserve">quando <lb />
<ptr xml:id="note-0063-09a" corresp="note-0063-09" type="noteAnchor" />
diſtantiæ a centro ſunt reciprocè ut pondera <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0063-10a" corresp="note-0063-10" type="noteAnchor" />
</s>
          <pb facs="0064" n="30" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
In hoc caſu, ſi unumquodque pondus per ſuam diſtantiam <lb />multiplicetur, producta erunt æqualia. </s>
          <s xml:space="preserve">Confirmatur hoc <lb />præcedenti experimento.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0063-09" corresp="note-0063-09a" place="margin">134.</note>
              <note xml:space="preserve" xml:id="note-0063-10" corresp="note-0063-10a" n="*" anchored="true" place="margin">132. <gap reason="illegible" /></note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hoc fundamento nititur Statera Romana, qua unico pon-<lb />
<ptr xml:id="note-0064-01a" corresp="note-0064-01" type="noteAnchor" />
dere omnia ponderantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0064-01" corresp="note-0064-01a" place="margin">135.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Statera Romana A B habet duo brachia admodum inæ-<lb />
<ptr xml:id="note-0064-02a" corresp="note-0064-02" type="noteAnchor" />
qualia; </s>
          <s xml:space="preserve">in breviori lanx ſuſpenditur: </s>
          <s xml:space="preserve">longiſſimum in partes æ-<lb />
<ptr xml:id="note-0064-03a" corresp="note-0064-03" type="noteAnchor" />
quales dividitur, poſito diviſionum initio in centro motus; <lb /></s>
          <s xml:space="preserve">diviſiones majores numeris notantur, &amp; </s>
          <s xml:space="preserve">ſingula in octo mi-<lb />nores iterum dividuntur. </s>
          <s xml:space="preserve">Pondus tale ei applicatur, ut <lb />in prima diviſione majori æquiponderet cum ſemiliberâ lan-<lb />ci impoſitâ: </s>
          <s xml:space="preserve">tum corpus ponderandum lanci imponitur, &amp; </s>
          <s xml:space="preserve"><lb />pondus ſtatim memoratum per longitudinem brachii longi-<lb />oris movetur, donec detur æquilibrium; </s>
          <s xml:space="preserve">diviſiones majores <lb />inter pondus &amp; </s>
          <s xml:space="preserve">centrum, ſemi librarum numerum denotant, <lb />quas corpus ponderat; </s>
          <s xml:space="preserve">ſubdiviſiones uncias indicant. </s>
          <s xml:space="preserve">Mi-<lb />nus etiam pondus quodcunque adhiberi poteſt quo minores <lb />differentiæ inter corporum pondera determinari queunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0064-02" corresp="note-0064-02a" place="margin">136.</note>
              <note xml:space="preserve" xml:id="note-0064-03" corresp="note-0064-03a" place="margin">TAB. VIII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem etiam nititur fundamento bilanx fallax, cujus nem-<lb />
<ptr xml:id="note-0064-04a" corresp="note-0064-04" type="noteAnchor" />
pe brachia ſunt inæqualia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0064-04" corresp="note-0064-04a" place="margin">137.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Libræ ſæpius memoratæ duæ lances, ponderis inæqua-<lb />
<ptr xml:id="note-0064-05a" corresp="note-0064-05" type="noteAnchor" />
lis, ut detur æquilibrium, applicantur ab una parte cente-<lb />
<ptr xml:id="note-0064-06a" corresp="note-0064-06" type="noteAnchor" />
fimæad alteram nonageſimæ quintæ diviſioni. </s>
          <s xml:space="preserve">Si tunc duo <lb />pondera dentur quæcumque, quæ ſint inter ſe ut 19 ad <lb />20, &amp; </s>
          <s xml:space="preserve">illud primæ lanci, hoc vero ſecundæ, imponatur æ-<lb />quiponderabunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0064-05" corresp="note-0064-05a" place="margin">138.</note>
              <note xml:space="preserve" xml:id="note-0064-06" corresp="note-0064-06a" place="margin">TAB IV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Plurima pondera ad varias diſtantias ab una parte, cum <lb />
<ptr xml:id="note-0064-07a" corresp="note-0064-07" type="noteAnchor" />
unico pondere ad aliam partem, poſſunt æquiponderare. </s>
          <s xml:space="preserve">Re-<lb />quiritur, ut productum hujus ponderis, per ſuam diſtantiam <lb />a centro, æquale ſit ſummæ productorum omnium aliorum <lb />ponderum, ſingulatim unumquodque per ſuam diſtantiam a <lb />centro multiplicatorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0064-07" corresp="note-0064-07a" place="margin">139.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <note xml:space="preserve" place="margin">140.</note>
        <p>
          <s xml:space="preserve">Ad unam partem pondus duarum unciarum 20 diviſioni, <lb />
<ptr xml:id="note-0064-09a" corresp="note-0064-09" type="noteAnchor" />
</s>
          <pb facs="0065" n="31" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. IX.</fw>
pondus unius unciæ 30, &amp; </s>
          <s xml:space="preserve">tandem pondus trium unciarum <lb />60 diviſioni applicantur, &amp; </s>
          <s xml:space="preserve">æquilibrium datur, ſi pondus <lb />unicum quinque unciarum 50 diviſioni, alterius brachii, <lb />ſuſpendatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0064-09" corresp="note-0064-09a" place="margin">TAB. III. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Multiplicando 50 per 5, productum habemus 250. </s>
          <s xml:space="preserve">In a-<lb />lio brachio tria habemus producta, 20 x 2 ideſt 40, 30 x 1, <lb />ideſt 30, &amp; </s>
          <s xml:space="preserve">60 x 3, nempe 180. </s>
          <s xml:space="preserve">Colligendo nunc 40, 30, <lb />180, in unam ſummam etiam habemus 250.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Plurima pondera, numero inæquali, ab utraque parte, <lb />
<ptr xml:id="note-0065-01a" corresp="note-0065-01" type="noteAnchor" />
poſſunt æquiponderare. </s>
          <s xml:space="preserve">In eo caſu, ſi unumquodque mul-<lb />tiplicetur per ſuam diſtantiam a centro, ſummæ producto-<lb />rum ab utraque parte erunt æquales: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſi ſummæ iſtæ ſunt <lb />æquales, datur æquilibrium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-01" corresp="note-0065-01a" place="margin">141.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Ex inſpectione figuræ Experimentum hoc ſatis patet. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0065-02a" corresp="note-0065-02" type="noteAnchor" />
Multiplicando ſingula pondera, per ſuas a centro diſtantias, <lb />
<ptr xml:id="note-0065-03a" corresp="note-0065-03" type="noteAnchor" />
habemus ab una parte producta 15, 40, 110, 80. </s>
          <s xml:space="preserve">90. </s>
          <s xml:space="preserve">500, <lb />ad aliam partem 70, 105, 300, 360: </s>
          <s xml:space="preserve">quorum ſumma utra-<lb />que eſt 835.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-02" corresp="note-0065-02a" place="margin">142.</note>
              <note xml:space="preserve" xml:id="note-0065-03" corresp="note-0065-03a" place="margin">TAB. III. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p rend="italics">
          <s xml:space="preserve">Centrum gravitatis vocatur punctum in corpore, circa <lb />
<ptr xml:id="note-0065-04a" corresp="note-0065-04" type="noteAnchor" />
quod omnes partes corporis, in quocumque ſitu poſiti, in æ-<lb />quilibrio ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-04" corresp="note-0065-04a" place="margin">143.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando duo aut plura corpora junguntur, ſive ſint conti-<lb />
<ptr xml:id="note-0065-05a" corresp="note-0065-05" type="noteAnchor" />
gua, ſive ſeparata, commune centrum gravitatis habent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-05" corresp="note-0065-05a" place="margin">144.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quando centrum gravitatis ſuſtinetur, corpus quieſcere <lb />
<ptr xml:id="note-0065-06a" corresp="note-0065-06" type="noteAnchor" />
poteſt; </s>
          <s xml:space="preserve">quia inter partes oppoſitas æquilibrium datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-06" corresp="note-0065-06a" place="margin">145.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Corpus A ſuſtinetur &amp; </s>
          <s xml:space="preserve">quieſcit, quia centrum illius gra-<lb />
<ptr xml:id="note-0065-07a" corresp="note-0065-07" type="noteAnchor" />
vitatis c, ſuſtinetur a fulcro F.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-07" corresp="note-0065-07a" place="margin">146.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. IV. <lb />fig. 2.</note>
        <p rend="italics">
          <s xml:space="preserve">Quando centrum gravitatis non ſuſtinetur, corpus movetur <lb />
<ptr xml:id="note-0065-09a" corresp="note-0065-09" type="noteAnchor" />
donec ſuſtineatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-09" corresp="note-0065-09a" place="margin">147.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <note xml:space="preserve" place="margin">148.</note>
        <p>
          <s xml:space="preserve">Corpus A menſæ impoſitum cadet, &amp; </s>
          <s xml:space="preserve">corpus B in ſitu, <lb />
<ptr xml:id="note-0065-11a" corresp="note-0065-11" type="noteAnchor" />
in quo repræſentatur, non manebit, quia horum centra gra-<lb />vitatis non ſuſtinentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0065-11" corresp="note-0065-11a" place="margin">TAB. IV. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0066" n="32" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Ex hiſce ratio redditur, quare corpora quædam planis <lb />inclinatis impoſita, devolvantur, &amp; </s>
          <s xml:space="preserve">alia ſimpliciter laban-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Corpus A labitur, quia centrum gravitatis illius a plano <lb />
<ptr xml:id="note-0066-01a" corresp="note-0066-01" type="noteAnchor" />
inclinato ſuſtinetur, id eſt, linea verticalis quæ tranſit per <lb />
<ptr xml:id="note-0066-02a" corresp="note-0066-02" type="noteAnchor" />
centrum illud c, ſecat planum inclinatum intra corpus. </s>
          <s xml:space="preserve">Cor-<lb />pus vero B devolvitur, quia verticalis linea, quæ tranſit per <lb />centrum gravitatis, ſecat planum inclinatum extra corpus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0066-01" corresp="note-0066-01a" place="margin">149.</note>
              <note xml:space="preserve" xml:id="note-0066-02" corresp="note-0066-02a" place="margin">TAB. IV. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex prædictis etiam ſequitur, corpus deſcendere quando <lb />
<ptr xml:id="note-0066-03a" corresp="note-0066-03" type="noteAnchor" />
gravitatis centrum deſcendit, id eſt, Terræ centrum ver-<lb />ſus movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0066-03" corresp="note-0066-03a" place="margin">150.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aliquando in illo caſu corpus adſcendere videtur, &amp; </s>
          <s xml:space="preserve">ſæpe <lb />etiam revera, ſi integram ipſius maſſam conſideremus, aſcen-<lb />dit, quando centrum figuræ corporis cum centro gravitatis <lb />non coincidit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 10.</head>
        <p>
          <s xml:space="preserve">Rota A, cujus axis formatur ex duobus conis quorum ba-<lb />
<ptr xml:id="note-0066-04a" corresp="note-0066-04" type="noteAnchor" />
ſes rotæ applicantur, ſi ponatur inter duo plana, quorum <lb />
<ptr xml:id="note-0066-05a" corresp="note-0066-05" type="noteAnchor" />
latera DG, FH, continuata formant angulum FCD, baſin <lb />apice magis elevatam habentem, ab inferiori parte HG, verſus <lb />planorum partem maxime elevatam FD, movebitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0066-04" corresp="note-0066-04a" place="margin">151.</note>
              <note xml:space="preserve" xml:id="note-0066-05" corresp="note-0066-05a" place="margin">TAB. IV. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propter majorem inter plana diſtantiam in FD, rota A, <lb />cujus axis ab utraque parte eſt conus, magis deſcendit inter <lb />plana, quando illam partem verſus movetur, &amp; </s>
          <s xml:space="preserve">ſic gravita-<lb />te ſua huc fertur, ſi modo deſcenſus inter plana ſuperet ad-<lb />ſcenſum ex anguli FCD inclinatione ad horizontem.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 11.</head>
        <p>
          <s xml:space="preserve">Cylindrus ligneus A, intus a latere continet cylindrum <lb />
<ptr xml:id="note-0066-06a" corresp="note-0066-06" type="noteAnchor" />
plumbeum; </s>
          <s xml:space="preserve">centrum gravitatis commune illorum eſt in ſe-<lb />
<ptr xml:id="note-0066-07a" corresp="note-0066-07" type="noteAnchor" />
ctione ad baſin parallela, cylindrum in duas partes æquales <lb />dividente, &amp; </s>
          <s xml:space="preserve">in puncto, reſpondenti, puncto baſis c.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0066-06" corresp="note-0066-06a" place="margin">152.</note>
              <note xml:space="preserve" xml:id="note-0066-07" corresp="note-0066-07a" place="margin">TAB. IV. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cylindrus hic utcunque poſitus, movebitur, donec cen-<lb />trum gravitatis memoratum ſit in infimo ad quem perveni-<lb />re poteſt loco.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si plano inclinato imponatur, in eo ſitu in quo hic delinea-
</s>
          <pb facs="0067" />
          <s xml:space="preserve">
<ptr xml:id="fig-0067-01a" corresp="fig-0067-01" type="figureAnchor" />
<pb facs="0067a" />
<ptr xml:id="fig-0067a-01a" corresp="fig-0067a-01" type="figureAnchor" />
<pb facs="0068" />
<pb facs="0069" n="33" /><fw type="head">MATHEMATICA. LIB. I. CAP. IX.</fw>
tur; </s>
          <s xml:space="preserve">deſcendet centrum gravitatis, dum corpus juxta pla-<lb />num adſcendit, poſita juſta plani inclinatione.</s>
          <s xml:space="preserve" />
        </p>
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          <body>
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              <figure xml:id="fig-0067-01" corresp="fig-0067-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01" />
                <label>0067-01</label>
              </figure>
              <figure xml:id="fig-0067a-01" corresp="fig-0067a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067a-01" />
                <label>0067a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aſcendit corpus dum rotatur partem plani ſuperiorem <lb />verſus; </s>
          <s xml:space="preserve">ſed dum ſicrotatur cavendum eſt, ne juxta planum <lb />labatur, ad quod requiritur funis, quo pro parte cylindrus <lb />circumdatur, cujus extremitas una cylindro in f connecti-<lb />tur, extremitate alterâ in d plano affixâ manente.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ulterius ex iis, quæ de centro gravitatis dicta ſunt, de-<lb />ducitur; </s>
          <s xml:space="preserve">Punctum in quocunque corpore, aut machina, quod <lb />
<ptr xml:id="note-0069-01a" corresp="note-0069-01" type="noteAnchor" />
ſuſtinet centrum gravitatis alicujus ponderis, totum pondus <lb />ſuſtinere: </s>
          <s xml:space="preserve">totamque vim, qua corpus terram verſus tendit, <lb />in hoc centro quaſi coactam dari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0069-01" corresp="note-0069-01a" place="margin">153.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 13.</head>
        <p>
          <s xml:space="preserve">Si corpus A B, cujus centrum gravitatis brachio libræ <lb />
<ptr xml:id="note-0069-02a" corresp="note-0069-02" type="noteAnchor" />
imponitur, aliquo in ſitu æquiponderat cum pondere P, <lb />
<ptr xml:id="note-0069-03a" corresp="note-0069-03" type="noteAnchor" />
in omni alio ſitu, ab, ab, manente centro gravitatis C, <lb />æquiponderabit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0069-02" corresp="note-0069-02a" place="margin">154.</note>
              <note xml:space="preserve" xml:id="note-0069-03" corresp="note-0069-03a" place="margin">TAB. IV. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ad perfectionem libræ requiruntur 1. </s>
          <s xml:space="preserve">ut puncta ſuſpen-<lb />
<ptr xml:id="note-0069-04a" corresp="note-0069-04" type="noteAnchor" />
ſionis lancium, aut ponderum, ſint exactè in eadem linea <lb />cum centro libræ; </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">ut ab utraque parte exactè ab iſto <lb />centro æqualiter diſtent; </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">ut libræ brachia, quantum com-<lb />modè fieri poteſt, ſint longa; </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">ut in motu jugi &amp; </s>
          <s xml:space="preserve">lancium, <lb />quantum fieri poteſt, parvus ſit attritus; </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">ut centrum <lb />gravitatis jugi ponatur paululum infra centrum motus; </s>
          <s xml:space="preserve">6. <lb /></s>
          <s xml:space="preserve">tandem ut partes axis, quæ jugo ſeparantur, ſint exa-<lb />ctiſſimè in eadem linea recta, quæ ſitum maximè commo-<lb />dum habebit, ſi cum jugo angulum efficiat rectum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0069-04" corresp="note-0069-04a" place="margin">155.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM</head>
        <head rend="italics" xml:space="preserve">De centro Gravitatis.</head>
        <p>
          <s xml:space="preserve">Centrum gravitatis diximus eſſe punctum in corpore, circa quod omnes <lb />partes ipſius, in quocunque ſitu poſiti, ſunt in æquilibrio: </s>
          <s xml:space="preserve">tale punctum <lb />in corpore quocunque revera dari, cum pleriſque Mechanicis poſuimus, hoc <lb />nunc demonſtrabimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sint puncta duo gravia A &amp; </s>
          <s xml:space="preserve">B, inæqualem quamcunque gravitatem haben-<lb />
<ptr xml:id="note-0069-05a" corresp="note-0069-05" type="noteAnchor" />
tia; </s>
          <s xml:space="preserve">concipiantur hæc juncta, lineâ inflexili, rectâ, ſine pondere; </s>
          <s xml:space="preserve">Detur in <lb />
<ptr xml:id="note-0069-06a" corresp="note-0069-06" type="noteAnchor" />
hac punctum C tale, ut CA ſit ad CB, ut pondus puncti B ad pondus pun-<lb />cti A. </s>
          <s xml:space="preserve">Pondera hæc in æquilibrio erunt circa C, &amp; </s>
          <s xml:space="preserve">quidem in ſitu quocun-
</s>
          <pb facs="0070" n="34" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
que, ut ex ante demonſtratis <ptr type="noteAnchor" /> deducitur; </s>
          <s xml:space="preserve">ideò ſi ſuſtineatur punctum C, ſu-
<ptr xml:id="note-0070-01a" corresp="note-0070-01" type="noteAnchor" />
ſtinentur puncta A &amp; </s>
          <s xml:space="preserve">B, &amp; </s>
          <s xml:space="preserve">harum actio in puncto C quaſi coacta eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0069-05" corresp="note-0069-05a" place="margin">156.</note>
              <note xml:space="preserve" xml:id="note-0069-06" corresp="note-0069-06a" place="margin">TAB. VIII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0070-01" corresp="note-0070-01a" n="*" anchored="true" place="margin">129.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur tertium punctum grave D, ponderis cujuſcunque; </s>
          <s xml:space="preserve">jungantur D &amp; </s>
          <s xml:space="preserve"><lb />C, etiam rectâ inflexili, ponderis experti; </s>
          <s xml:space="preserve">ſitque in hac punctum E, ita de-<lb />terminatum, ut EC ſe habeat ad ED, ut pondus puncti D ad ſummam pon-<lb />derum punctorum A &amp; </s>
          <s xml:space="preserve">B.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si A &amp; </s>
          <s xml:space="preserve">B juncta darentur in C, circa E daretur æquilibrium, poſitâ li-<lb />neâ CD in ſitu quocunque <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ſed A &amp; </s>
          <s xml:space="preserve">B, ut demonſtravimus, in ſitu quo-
<ptr xml:id="note-0070-02a" corresp="note-0070-02" type="noteAnchor" />
cunque lineæ AB, agunt quaſi in C juncta eſſent; </s>
          <s xml:space="preserve">ergo tria pondera A,B,D, <lb />lineis inflexilibus conjuncta, in ſitu quocunque, in æquilibrio ſunt circa <lb />punctum E; </s>
          <s xml:space="preserve">quod ergo eſt centrum gravitatis trium punctorum. </s>
          <s xml:space="preserve">Puncta <lb />hæc etiam nullum aliud habere centrum gravitatis, præter punctum E, ex eâ-<lb />dem demonſtratione conſtat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0070-02" corresp="note-0070-02a" n="*" anchored="true" place="margin">129</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si quartum daretur punctum grave, lineâ inflexili, rectâ, jungendum hoc <lb />foret cum E, &amp; </s>
          <s xml:space="preserve">ſimili demonſtratione conſtaret, quatuor puncta commune <lb />habere gravitatis centrum, &amp; </s>
          <s xml:space="preserve">unicum hoc eſſe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum vero eadem demonſtratio ad numerum quemcunque punctorum re-<lb />ferri poſſit, applicari poterit omnibus punctis gravibus, ex quibus corpus quod-<lb />
<ptr xml:id="note-0070-03a" corresp="note-0070-03" type="noteAnchor" />
cunque conſtat: </s>
          <s xml:space="preserve">habet ideò corpus centrum gravitatis, &amp; </s>
          <s xml:space="preserve">unicum tale habet cen-<lb />trum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0070-03" corresp="note-0070-03a" place="margin">157.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De Centri gravitatis inveſtigatione.</head>
        <p>
          <s xml:space="preserve">Dentur corpora, numero quocunque, quorum commune gravitatis cen-<lb />
<ptr xml:id="note-0070-04a" corresp="note-0070-04" type="noteAnchor" />
trum ſit C; </s>
          <s xml:space="preserve">per hoc concipiamus planum horizontale, quod ſit planum ipſi-<lb />
<ptr xml:id="note-0070-05a" corresp="note-0070-05" type="noteAnchor" />
us figuræ. </s>
          <s xml:space="preserve">Sint centra gravitatis ipſorum corporum A, B, D, E, F; </s>
          <s xml:space="preserve">ſi <lb />centra hæc ipſo plano horizontali memorato non dentur, ad hoc referenda <lb />ſunt lineis verticalibus &amp; </s>
          <s xml:space="preserve">eodem modo planum corpora gravabunt ac ſi i-<lb />pſorum centra gravitatis darentur in punctis, in quibus lineæ hæ verticales <lb />
<ptr xml:id="note-0070-06a" corresp="note-0070-06" type="noteAnchor" />
planum ſecant <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0070-04" corresp="note-0070-04a" place="margin">158.</note>
              <note xml:space="preserve" xml:id="note-0070-05" corresp="note-0070-05a" place="margin">TAB. VIII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0070-06" corresp="note-0070-06a" n="*" anchored="true" place="margin">128.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Suſtineatur planum linea GH; </s>
          <s xml:space="preserve">habentur actiones ponderum ad movendum <lb />planum circa lineam GH, multiplicando pondus unumquodque per ſuam diſtanti-<lb />
<ptr xml:id="note-0070-07a" corresp="note-0070-07" type="noteAnchor" />
am a linea GH <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſumma productorum dat integram actionem, qua omnia
<ptr xml:id="note-0070-08a" corresp="note-0070-08" type="noteAnchor" />
pondera ſimul planum premunt ad hoc circa GH movendum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0070-07" corresp="note-0070-07a" place="margin">159.</note>
              <note xml:space="preserve" xml:id="note-0070-08" corresp="note-0070-08a" n="*" anchored="true" place="margin">131.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omnia autem pondera agunt, quaſi eſſent in C <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">idcirco habetur etiam i-
<ptr xml:id="note-0070-09a" corresp="note-0070-09" type="noteAnchor" />
pſorum actio, multiplicando ſummam ponderum per diſtantiam puncti C a <lb />linea GH: </s>
          <s xml:space="preserve">Si ergo ſumma memorata productorum, quæ, ut patet, huic ul-<lb />timo producto æqualis eſt, dividatur per ſummam ponderum, datur in quotiente <lb />diſtantia centri gravitatis a linea GH.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0070-09" corresp="note-0070-09a" n="*" anchored="true" place="margin">153.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando agitur de ponderibus, quæ lineis verticalibus ad planum horizon-<lb />tale referuntur, diſtantiæ punctorum, ad quæ pondera referuntur, à lineâ <lb />GH, ſunt æquales diſtantiis centrorum gravitatis ipſorum corporum à pla-<lb />no verticali, per GH tranſeunti.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum verò hæc demonſtratio locum habeat in quocunque ſitu corpora den-<lb />tur, ſi lineis inflexilibus, &amp; </s>
          <s xml:space="preserve">ſine pondere, corpora inter ſe coh@reant, nul-<lb />lum poteſt concipi planum, quod non, ſervato ipſius ſitu reſpectu corporum, <lb />
<ptr xml:id="note-0070-10a" corresp="note-0070-10" type="noteAnchor" />
poſſit fieri verticale; </s>
          <s xml:space="preserve">unde ſequitur datis corporibus &amp; </s>
          <s xml:space="preserve">plano quocunque, diſtan-<lb />tiam centri gravitatis a plano detegi, multiplicando corpus unumquodque per ſui <lb />centri gravitatis diſtantiam a plano, &amp; </s>
          <s xml:space="preserve">dividendo productorum ſummam per ipſo-<lb />rum corporum ſummam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0070-10" corresp="note-0070-10a" place="margin">160.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſimilem demonſtrationem applicemus plano, quod inter corpora tranſit, <lb />
<ptr xml:id="note-0070-11a" corresp="note-0070-11" type="noteAnchor" />
differentia inter ſummas productorum ab utraque parte per corporum ſum-
</s>
          <pb facs="0071" />
          <s xml:space="preserve">
<ptr xml:id="fig-0071-01a" corresp="fig-0071-01" type="figureAnchor" />
<pb facs="0071a" />
<ptr xml:id="fig-0071a-01a" corresp="fig-0071a-01" type="figureAnchor" />
<pb facs="0072" />
<pb facs="0073" n="35" /><fw type="head">MATHEMATICA. LIB. 1. CAP. IX.</fw>
mam dividenda erit, ad detegendam memoratam diſtantiam centri gravitatis a <lb />plano.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0070-11" corresp="note-0070-11a" place="margin">161.</note>
              <figure xml:id="fig-0071-01" corresp="fig-0071-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0071-01" />
                <label>0071-01</label>
              </figure>
              <figure xml:id="fig-0071a-01" corresp="fig-0071a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0071a-01" />
                <label>0071a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ex hiſce deducimus methodum, qua inveſtigatur centrum gravitatis; </s>
          <s xml:space="preserve">quæ-<lb />
<ptr xml:id="note-0073-01a" corresp="note-0073-01" type="noteAnchor" />
rendo bujus diſtantiam a tribus planis <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quæ eadem methodus ad corpus quodcun-
<ptr xml:id="note-0073-02a" corresp="note-0073-02" type="noteAnchor" />
que peculiare applicari poteſt, referendo adhujus partes, quæ de corporibus ſunt de-<lb />
<ptr xml:id="note-0073-03a" corresp="note-0073-03" type="noteAnchor" />
monſtrata.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-01" corresp="note-0073-01a" place="margin">162.</note>
              <note xml:space="preserve" xml:id="note-0073-02" corresp="note-0073-02a" place="margin">163.</note>
              <note xml:space="preserve" xml:id="note-0073-03" corresp="note-0073-03a" n="*" anchored="true" place="margin">160</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si Corpora, quorum commune gravitatis centrum quæritur, ſua peculiaria <lb />
<ptr xml:id="note-0073-04a" corresp="note-0073-04" type="noteAnchor" />
gravitatis centra in eodem plano babeant, determinatur quæſitum centrum, dete-<lb />gendo bujus diſtantiam â duabus lineis <ptr type="noteAnchor" />, utcunque in eodem hoc plano ductis.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0073-05a" corresp="note-0073-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-04" corresp="note-0073-04a" place="margin">164.</note>
              <note xml:space="preserve" xml:id="note-0073-05" corresp="note-0073-05a" n="*" anchored="true" place="margin">159.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quando peculiaria gravitatis centra in eâdem lineâ dantur, detegitur commune <lb />
<ptr xml:id="note-0073-06a" corresp="note-0073-06" type="noteAnchor" />
gravitatis centrum operatione unicâ, qua nempe ipſius diſtantia à puncto quocun-<lb />que, in eâdem illâ lineâ ſumto, determinatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-06" corresp="note-0073-06a" place="margin">165.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">Arithmetica Mechanica.</head>
        <p>
          <s xml:space="preserve">Regulæ quatuor Arithmeticæ, Additic, Subtractio, Multiplicatio, &amp; </s>
          <s xml:space="preserve">Diviſio, ope <lb />libræ ſuperius memoratæ <ptr type="noteAnchor" />, cujus brachia in partes æquales ſunt diviſa fa-
<ptr xml:id="note-0073-07a" corresp="note-0073-07" type="noteAnchor" />
cile inſtitui poſſunt, operationumque demonſtratio ex ante memoratis quam <lb />facillimè deducitur; </s>
          <s xml:space="preserve">ſatis ideò erit ipſas regulas exemplis illuſtrare.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-07" corresp="note-0073-07a" n="*" anchored="true" place="margin">130.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Habeatur pondus quodcunque pro unitate; </s>
          <s xml:space="preserve">uncia Ex gr.</s>
          <s xml:space="preserve">; decima pars un-<lb />ciæ eodem modo poſſet adhiberi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit numerus 364 libræ applicandus; </s>
          <s xml:space="preserve">tres uncias centeſimæ applico divi-<lb />
<ptr xml:id="note-0073-08a" corresp="note-0073-08" type="noteAnchor" />
ſioni, &amp; </s>
          <s xml:space="preserve">unciam unam diviſioni 64<hi rend="superscript">tæ</hi>.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-08" corresp="note-0073-08a" place="margin">166.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Gravetur brachium libræ urcunque; </s>
          <s xml:space="preserve">quem numerum valeat actio hæc, de-<lb />
<ptr xml:id="note-0073-09a" corresp="note-0073-09" type="noteAnchor" />
terminamus, ſuſpendendo in centeſimâ diviſione brachii oppoſiti pondus, <lb />quod augeatur additâ ſucceſſivè unciâ atque unciâ; </s>
          <s xml:space="preserve">ponamus novem uncias <lb />nondum æquilibrium dare, decem autem excedere; </s>
          <s xml:space="preserve">relictis novem mo-<lb />tu unius juxta brachium quæro æquilibrium, detur hoc ubi pondus ad 47 di-<lb />viſionem pervenit, actio quæſita valebit 947.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-09" corresp="note-0073-09a" place="margin">167.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">ADDITIO. </s>
          <s xml:space="preserve">Sint addenda 34, 54, 268, 407, 45. </s>
          <s xml:space="preserve">65. </s>
          <s xml:space="preserve">Separatim numeros <lb />
<ptr xml:id="note-0073-10a" corresp="note-0073-10" type="noteAnchor" />
hos applico eidem brachio libræ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæro hujus actionis valorem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">dete-
<ptr xml:id="note-0073-11a" corresp="note-0073-11" type="noteAnchor" />
go 873, ſummam quæſitam. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0073-12a" corresp="note-0073-12" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-10" corresp="note-0073-10a" place="margin">168.</note>
              <note xml:space="preserve" xml:id="note-0073-11" corresp="note-0073-11a" n="*" anchored="true" place="margin">166.</note>
              <note xml:space="preserve" xml:id="note-0073-12" corresp="note-0073-12a" n="*" anchored="true" place="margin">167.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">SUBTRACTIO. </s>
          <s xml:space="preserve">Ex ſumma numerorum 567, 258, ſubtrahenda ſunt 489 <lb />
<ptr xml:id="note-0073-13a" corresp="note-0073-13" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">56. </s>
          <s xml:space="preserve">Numeros primos uni applico brachio <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſubtrahendos alteri applico <ptr type="noteAnchor" />,
<ptr xml:id="note-0073-14a" corresp="note-0073-14" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">quæro quantum valeat actio, qua actio in brachium unum alteram <lb />
<ptr xml:id="note-0073-15a" corresp="note-0073-15" type="noteAnchor" />
actionem ſuperat <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">detego differentiam quæſitam 280.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0073-16a" corresp="note-0073-16" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-13" corresp="note-0073-13a" place="margin">169.</note>
              <note xml:space="preserve" xml:id="note-0073-14" corresp="note-0073-14a" n="*" anchored="true" place="margin">166.</note>
              <note xml:space="preserve" xml:id="note-0073-15" corresp="note-0073-15a" n="*" anchored="true" place="margin">166.</note>
              <note xml:space="preserve" xml:id="note-0073-16" corresp="note-0073-16a" n="*" anchored="true" place="margin">167.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">MULTIPLICATIO. </s>
          <s xml:space="preserve">Detur numerus 67, multiplicandus per 15. </s>
          <s xml:space="preserve">Pon-<lb />
<ptr xml:id="note-0073-17a" corresp="note-0073-17" type="noteAnchor" />
dus 15. </s>
          <s xml:space="preserve">ſuſpendo diviſioni 67 &amp; </s>
          <s xml:space="preserve">quæro valorem <ptr type="noteAnchor" />, quo productum quæſitum
<ptr xml:id="note-0073-18a" corresp="note-0073-18" type="noteAnchor" />
detego 1005.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-17" corresp="note-0073-17a" place="margin">170.</note>
              <note xml:space="preserve" xml:id="note-0073-18" corresp="note-0073-18a" n="*" anchored="true" place="margin">167.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">DIVISIO. </s>
          <s xml:space="preserve">Sit 1005. </s>
          <s xml:space="preserve">numerus dividendus per 15, Numerum dividendum <lb />
<ptr xml:id="note-0073-19a" corresp="note-0073-19" type="noteAnchor" />
applico libræ <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">movendo pondus quindecim juxta brachium, quæro æqui-
<ptr xml:id="note-0073-20a" corresp="note-0073-20" type="noteAnchor" />
librium, quod datur ubi pondus ad 67 diviſionem, quotientem deſignantem, <lb />pervenit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0073-19" corresp="note-0073-19a" place="margin">171.</note>
              <note xml:space="preserve" xml:id="note-0073-20" corresp="note-0073-20a" n="*" anchored="true" place="margin">166.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Præſtat in hiſce duabus ultimis operationibus, minori pondere pro unita-<lb />te uti.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0074" n="36" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT X.</head>
        <head xml:space="preserve">De Vecte, Machinarum ſimplicium prima.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">VEctis à Matbematicis vocatur linearecta inflexilis, pon-<lb />
<ptr xml:id="note-0074-01a" corresp="note-0074-01" type="noteAnchor" />
deribus ſuſtinendis, aut elevandis, accommodata, pon-<lb />
<ptr xml:id="note-0074-02a" corresp="note-0074-02" type="noteAnchor" />
deris vel nullius, vel ſaltem æquabilis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0074-01" corresp="note-0074-01a" place="margin">172.</note>
              <note xml:space="preserve" xml:id="note-0074-02" corresp="note-0074-02a" place="margin">TAB. V. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inter Machinas, quæ ſimplices vocantur, primum locum <lb />occupat, eſt omnium ſimpliciſſima; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">uſu venit, quando <lb />pondera ad parvam altitudinem elevanda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quatuor aliæ dantur Machinæ ſimplices, de quibus in tri-<lb />bus capitibus ſequentibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Circa Vectem tria conſiderari debent. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Pondus ſuſti-<lb />
<ptr xml:id="note-0074-03a" corresp="note-0074-03" type="noteAnchor" />
nendum, aut elevandum, P. </s>
          <s xml:space="preserve">2, Potentia, qua ſuſtinetur, aut <lb />elevatur, quæ hîc pondere M deſignatur, &amp; </s>
          <s xml:space="preserve">vulgo eſtactio <lb />hominis. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Fulcrum, id eſt, illud quo Vectis ſuſtinetur, <lb />&amp; </s>
          <s xml:space="preserve">ſuper quo movetur, aut potius rotatur, dum ipſum im-<lb />mobile manet, F.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0074-03" corresp="note-0074-03a" place="margin">173.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vectes triplicis ſunt generis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">174.</note>
        <p>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Aliquando fulerum inter pondus &amp; </s>
          <s xml:space="preserve">potentiam ponitur. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0074-05a" corresp="note-0074-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0074-05" corresp="note-0074-05a" place="margin">TAB. V. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Aliquando pondus inter fulcrum &amp; </s>
          <s xml:space="preserve">potentiam.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">TAB. V. <lb />fig. 2.</note>
        <p>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Sæpe etiam ipſa potentia agit inter pondus &amp; </s>
          <s xml:space="preserve">fulcrum. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0074-07a" corresp="note-0074-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0074-07" corresp="note-0074-07a" place="margin">TAB. V. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In omnibus caſibus regulæ eædem locum habent, quæ ex <lb />iis, quæ de libra dicta ſunt <ptr type="noteAnchor" />, ſequuntur, &amp; </s>
          <s xml:space="preserve">quæ analogiam in-
<ptr xml:id="note-0074-08a" corresp="note-0074-08" type="noteAnchor" />
ter libram &amp; </s>
          <s xml:space="preserve">vectem oſtendunt. </s>
          <s xml:space="preserve">Vectis primi generis eſt qua-<lb />ſi ſtatera Romana ad elevanda pondera accommodata.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0074-08" corresp="note-0074-08a" n="*" anchored="true" place="margin">129.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Actio potentiæ, &amp; </s>
          <s xml:space="preserve">ponderis reſiſtentia, creſcunt in ratio-<lb />
<ptr xml:id="note-0074-09a" corresp="note-0074-09" type="noteAnchor" />
ne diſtantiæ à fulcro <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideòque, ut potentia valeat ad ſuſti-
<ptr xml:id="note-0074-10a" corresp="note-0074-10" type="noteAnchor" />
nendum pondus, requiritur, ut diſtantia puncti in vecte, <lb />cui applicatur, ſit ad ponderis diſtantiam, ut pondas ad po-<lb />tentiæ intenſitatem <ptr type="noteAnchor" />, quæ ſi paululum adaugeatur, pondus
<ptr xml:id="note-0074-11a" corresp="note-0074-11" type="noteAnchor" />
elevabitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0074-09" corresp="note-0074-09a" place="margin">175.</note>
              <note xml:space="preserve" xml:id="note-0074-10" corresp="note-0074-10a" n="*" anchored="true" place="margin">119.</note>
              <note xml:space="preserve" xml:id="note-0074-11" corresp="note-0074-11a" n="*" anchored="true" place="margin">134.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1. 2. &amp; 3.</head>
        <p>
          <s xml:space="preserve">Hæc regula experimentis confirmatur erga memoratos <lb />
<ptr xml:id="note-0074-12a" corresp="note-0074-12" type="noteAnchor" />
tres vectes, ut patet ex fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">3, Tab. </s>
          <s xml:space="preserve">v.</s>
          <s xml:space="preserve">; æquilibrium <lb />
<ptr xml:id="note-0074-13a" corresp="note-0074-13" type="noteAnchor" />
enim datur, quando pondera P, &amp; </s>
          <s xml:space="preserve">pondera M quæpoten-<lb />tias repræſentant, ut &amp; </s>
          <s xml:space="preserve">diſtantiæ à fulcro F, proportionem
</s>
          <pb facs="0075" n="37" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. X.</fw>
habent, quæ datur inter numeros in figuris. </s>
          <s xml:space="preserve">Conſtructio ma-<lb />chinarum, quibus hæc experimenta inſtituuntur, ex ſola <lb />inſpectione Tabulæ ſatis patet, &amp; </s>
          <s xml:space="preserve">nulla ulteriori explicatio-<lb />ne indiget.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0074-12" corresp="note-0074-12a" place="margin">176.</note>
              <note xml:space="preserve" xml:id="note-0074-13" corresp="note-0074-13a" place="margin">TAB. V. <lb />fig. 1. 2. &amp; 3.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Vectis formatur compoſitus ex variis vectibus junctis. </s>
          <s xml:space="preserve">In <lb />
<ptr xml:id="note-0075-01a" corresp="note-0075-01" type="noteAnchor" />
hoc caſu adhibito ſecundo vecte movetur primus; </s>
          <s xml:space="preserve">ſecundus <lb />tertio poteſt agitari; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſic ulterius ſi libuerit, ultimo tandem <lb />applicatur potentia, cujus ratso ad pondus, quando cum pondere <lb />æquè pollet, componitur ex rationibus potentiarum ad ponde-<lb />ra in ſingulis vectibus, quando ſeparatim adbibentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0075-01" corresp="note-0075-01a" place="margin">177.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Tres vectes A, B, D, ita diſponuntur, ut potentiâ Mpon-<lb />
<ptr xml:id="note-0075-02a" corresp="note-0075-02" type="noteAnchor" />
dus P ſuſtineatur. </s>
          <s xml:space="preserve">In vecte A, ſi ſolus adhiberetur, po-<lb />
<ptr xml:id="note-0075-03a" corresp="note-0075-03" type="noteAnchor" />
tentia eſſet ad pondus, ut 1. </s>
          <s xml:space="preserve">ad 5.</s>
          <s xml:space="preserve">; in vecte B, ut 1. </s>
          <s xml:space="preserve">ad 4.</s>
          <s xml:space="preserve">; <lb />&amp; </s>
          <s xml:space="preserve">in vecte D, ut 1. </s>
          <s xml:space="preserve">ad 6. </s>
          <s xml:space="preserve">Ratio, ex his tribus compoſita, <lb />eſt 1. </s>
          <s xml:space="preserve">ad 120; </s>
          <s xml:space="preserve">unica etiam uncia M ſuſtinet pondus P cen-<lb />tum &amp; </s>
          <s xml:space="preserve">viginti unciarum. </s>
          <s xml:space="preserve">Notandum, in motu hujus machi-<lb />næ ſpatia à potentia &amp; </s>
          <s xml:space="preserve">pondere eodem tempore percurſa eſ-<lb />ſe ut 120. </s>
          <s xml:space="preserve">ad 1.</s>
          <s xml:space="preserve">, id eſt, in ratione prædictainverſa, quod <lb />requiritur ut detur æquilibrium <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0075-04a" corresp="note-0075-04" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0075-02" corresp="note-0075-02a" place="margin">178.</note>
              <note xml:space="preserve" xml:id="note-0075-03" corresp="note-0075-03a" place="margin">TAB. V. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0075-04" corresp="note-0075-04a" n="*" anchored="true" place="margin">212.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vecte etiam ſæpe utuntur artifices ad pondera vehenda; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hujus uſus vectis varii dantur caſus, digni quinotentur, &amp; </s>
          <s xml:space="preserve"><lb />quorum demonſtratio ex dictis facile deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Circa omnes caſus generaliter obſervandum, intenſitatem <lb />
<ptr xml:id="note-0075-05a" corresp="note-0075-05" type="noteAnchor" />
potentiæ, aut intenſitates potentiarum junctas, quando plu-<lb />rimæ dantur, æquè pollere debere cumgravitate ponderum ve-<lb />dorum, aut ſuſtinendorum: </s>
          <s xml:space="preserve">in omnibus enim caſibus potentiæ <lb />&amp; </s>
          <s xml:space="preserve">obſtacula æquales vias percurrunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0075-05" corresp="note-0075-05a" place="margin">179.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si duabus potentiis ſuſtineri aut vehi debeat pondus, in-<lb />
<ptr xml:id="note-0075-06a" corresp="note-0075-06" type="noteAnchor" />
ter potentias collocandum erit, &amp; </s>
          <s xml:space="preserve">diſtantiæ potentiarum ab <lb />utraque parte à pondere debent eſſe in ratione inverſa po-<lb />téntiarum intenſitatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0075-06" corresp="note-0075-06a" place="margin">180.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Potentiarum enim actiones ſeſe mutuo turbabunt, niſi in-<lb />ter has æquilibrium detur circa punctum ſuſpenſionis pon-<lb />deris; </s>
          <s xml:space="preserve">quo æquilibrio poſito, in puncto hoc potentiarum <lb />actiones ſunt coactæ, &amp; </s>
          <s xml:space="preserve">cum pondere contrarie agunt; </s>
          <s xml:space="preserve">id-
</s>
          <pb facs="0076" n="38" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
eòque hoc ſuſtinent, propter æqualitatem inter potentias <lb />&amp; </s>
          <s xml:space="preserve">pondus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Confirmatur propſitio hæc Experimento in Fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">de-<lb />
<ptr xml:id="note-0076-01a" corresp="note-0076-01" type="noteAnchor" />
lineato, quod ulteriori explicatione non indiget.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0076-01" corresp="note-0076-01a" place="margin">181.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB V. <lb />fig. 4.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p rend="italics">
          <s xml:space="preserve">Quando unâ potentiâ duo pondera ſuſtinenda ſunt, potentiam <lb />
<ptr xml:id="note-0076-03a" corresp="note-0076-03" type="noteAnchor" />
inter pondera poni neceſſe eſt, &amp; </s>
          <s xml:space="preserve">tunc quæ ſtatim de duabus <lb />
<ptr xml:id="note-0076-04a" corresp="note-0076-04" type="noteAnchor" />
potentiis dicta ſunt, ad pondera applicari debent. </s>
          <s xml:space="preserve">Ponde-<lb />ra enim ſuſtineri non poſſunt, niſi horum commune cen-<lb />trum gravitatis ſuſtineatur<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0076-03" corresp="note-0076-03a" place="margin">182.</note>
              <note xml:space="preserve" xml:id="note-0076-04" corresp="note-0076-04a" place="margin">TAB. VI. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">147.</note>
        <p>
          <s xml:space="preserve">Plurima pondera ſæpe unâ, aut plurimis potentiis, ſuſti-<lb />nentur aut vehuntur. </s>
          <s xml:space="preserve">Circa quod notandum, omnia pon-<lb />
<ptr xml:id="note-0076-06a" corresp="note-0076-06" type="noteAnchor" />
dera, babere commune centrum gravitatis; </s>
          <s xml:space="preserve">quod centrum <lb />tale eſt, ut ſi ab utraque parte unumquodque pondus mul-<lb />tiplicetur per ſuam diſtantiam ab iſto puncto, ſumma produ-<lb />ctorum ab utraque parte ſit eadem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0076-07a" corresp="note-0076-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0076-06" corresp="note-0076-06a" place="margin">183.</note>
              <note xml:space="preserve" xml:id="note-0076-07" corresp="note-0076-07a" n="*" anchored="true" place="margin">143. 141.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Potentiæ etiam utcunque diſpoſitæ commune babent gravi-<lb />tatis centrum; </s>
          <s xml:space="preserve">poſſunt enim per pondera repræſentari <ptr type="noteAnchor" />,
<ptr xml:id="note-0076-08a" corresp="note-0076-08" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">hìc intenſitas uniuſcujuſque potentiæ perſuam diſtantiam à <lb />centro multiplicari debet, &amp; </s>
          <s xml:space="preserve">ſummæ productorum tunc <lb />erunt ab utraque parte æquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0076-08" corresp="note-0076-08a" n="*" anchored="true" place="margin">117.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vt potentiæ ad pondera ſuſtinenda valeant, requiritur po-<lb />tentiarum &amp; </s>
          <s xml:space="preserve">ponderum idem eſſe gravitatis centrum. </s>
          <s xml:space="preserve">Tunc <lb />omnium ponderum, omniumque potentiarum, vires in u-<lb />num &amp; </s>
          <s xml:space="preserve">idem punctum reducuntur, quod viribus æqualibus <lb />ſurſum &amp; </s>
          <s xml:space="preserve">deorſum trahitur, ideoque ſuſtinetur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7. &amp; 8.</head>
        <p>
          <s xml:space="preserve">Ex dictis explicatio figurarum ſatis patet, in quibus C de-<lb />
<ptr xml:id="note-0076-09a" corresp="note-0076-09" type="noteAnchor" />
notat centrum gravitatis &amp; </s>
          <s xml:space="preserve">ponderum &amp; </s>
          <s xml:space="preserve">potentiarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0076-09" corresp="note-0076-09a" place="margin">184.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. VI. <lb />fig. 2. &amp; 3.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9</head>
        <p>
          <s xml:space="preserve">Prædicta etiam locum habent, ſi vectis ab utraque parte <lb />
<ptr xml:id="note-0076-11a" corresp="note-0076-11" type="noteAnchor" />
à potentiis trahatur; </s>
          <s xml:space="preserve">quod videmus in vecte, qui ab utra-<lb />
<ptr xml:id="note-0076-12a" corresp="note-0076-12" type="noteAnchor" />
que parte horizontaliter trahitur, in quo æquilibrium non <lb />datur niſi in caſu memoratarum regularum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0076-11" corresp="note-0076-11a" place="margin">185.</note>
              <note xml:space="preserve" xml:id="note-0076-12" corresp="note-0076-12a" place="margin">TAB. VI. <lb />fig 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa octo prima hujus cap. </s>
          <s xml:space="preserve">Exp. </s>
          <s xml:space="preserve">notandum, vectes ipſos <lb />ſuſtineri debere.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0077" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0077-01" />
          <label>0077-01</label>
        </figure>
        <pb facs="0077a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0077a-01" />
          <label>0077a-01</label>
        </figure>
        <pb facs="0078" />
        <pb facs="0079" n="39" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XI.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XI.</head>
        <p>
          <s xml:space="preserve">De Axe in Peritrochio, ſecundâ Machinarum ſimplicium, <lb />&amp; </s>
          <s xml:space="preserve">Rotis dentatis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">VEctis, ut in principio capitis præcedentis dictum, in-<lb />ſervit ad elevanda pondera ad parvam altitudinem; <lb /></s>
          <s xml:space="preserve">quando altitudo major eſt, Axis in Peritrochio uſu venit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi></head>
        <p>
          <s xml:space="preserve">Axis in Peritrochio vocatur rota cum axe volubilis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">186.</note>
        <p>
          <s xml:space="preserve">Potentia in hac machinâ applicatur peripheriæ rotæ, cu-<lb />
<ptr xml:id="note-0079-02a" corresp="note-0079-02" type="noteAnchor" />
jus motu funis, cui affixum eſt pondus, axi circumvolvitur, <lb />quo pondus elevatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0079-02" corresp="note-0079-02a" place="margin">TAB. VI. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit a b rota; </s>
          <s xml:space="preserve">d e axis; </s>
          <s xml:space="preserve">p pondus elevandum; </s>
          <s xml:space="preserve">m potentia; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0079-03a" corresp="note-0079-03" type="noteAnchor" />
hujus actione moveatur rota, puncta b &amp; </s>
          <s xml:space="preserve">d arcus ſimiles eo <lb />
<ptr xml:id="note-0079-04a" corresp="note-0079-04" type="noteAnchor" />
motu deſcribunt; </s>
          <s xml:space="preserve">arcus illi ſunt viæ percurſæ à potentiâ &amp; </s>
          <s xml:space="preserve"><lb />pondere, &amp; </s>
          <s xml:space="preserve">ſunt inter ſe, ut c b ad c d, id eſt ut rotæ dia-<lb />meter ad axis diametrum, ex quo ſequensregula deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0079-03" corresp="note-0079-03a" place="margin">187.</note>
              <note xml:space="preserve" xml:id="note-0079-04" corresp="note-0079-04a" place="margin">TAB. VI. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Potentia eo plus valet, quo major eſt rota, &amp; </s>
          <s xml:space="preserve">illius actio <lb />
<ptr xml:id="note-0079-05a" corresp="note-0079-05" type="noteAnchor" />
creſcit in eâdem ratione cum rotæ diametro. </s>
          <s xml:space="preserve">Pondus eo mi-<lb />nus reſiſtit, quo axis diameter minor eſt, &amp; </s>
          <s xml:space="preserve">illius reſiſten-<lb />tia in eadem ratione cum axis diametro minuitur. </s>
          <s xml:space="preserve">Et ut de-<lb />tur æquilibrium inter potentiam &amp; </s>
          <s xml:space="preserve">pondus, requiritur, ut <lb />rotædiameter ſit ad axis diametrum, in ratione inverſa <lb />potentiæ ad pondus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0079-06a" corresp="note-0079-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0079-05" corresp="note-0079-05a" place="margin">188.</note>
              <note xml:space="preserve" xml:id="note-0079-06" corresp="note-0079-06a" n="*" anchored="true" place="margin">112.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Notandum, axis diametro funis diametrum eſſe addendum.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Hæc regula diverſimodæ confirmatur ope Machinæ hìc <lb />
<ptr xml:id="note-0079-07a" corresp="note-0079-07" type="noteAnchor" />
delineatæ, in qua dantur rotæ &amp; </s>
          <s xml:space="preserve">axes variæ magnitudinis. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0079-08a" corresp="note-0079-08" type="noteAnchor" />
Quando axis diameter eſt pars duodecima rotæ diametri, <lb />ſemilibra ſex libras ſuſtinet, &amp; </s>
          <s xml:space="preserve">ſic de cæteris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0079-07" corresp="note-0079-07a" place="margin">189.</note>
              <note xml:space="preserve" xml:id="note-0079-08" corresp="note-0079-08a" place="margin">TAB. VI <lb />fig. 1</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Potentia poteſt etiam ſcytalæ applicari, ut in D, &amp; </s>
          <s xml:space="preserve">tunc <lb />diſtantia puncti, cui applicatur, à centro, pro rotæ ſemi-<lb />diametro habenda eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Eodem omnino cum hac Machina nituntur fundamento <lb />rotæ dentatæ reſpectu axis in peritrochio ſunt, quod <lb />vectis compoſitus reſpectu vectis ſimplicis.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0080" n="40" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Si axis rotæ ſit dentatus, valet ad movendam rotam, cu-<lb />
<ptr xml:id="note-0080-01a" corresp="note-0080-01" type="noteAnchor" />
jus peripheria dentes habet, &amp; </s>
          <s xml:space="preserve">cujus axis tertiæ rotæ motum <lb />communicare poteſt, &amp; </s>
          <s xml:space="preserve">ſic ulterius. </s>
          <s xml:space="preserve">In eo caſu</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0080-01" corresp="note-0080-01a" place="margin">TAB. VI. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ratio potentiæ ad pondus ut æquè polleant, eſt ratio compo-<lb />
<ptr xml:id="note-0080-02a" corresp="note-0080-02" type="noteAnchor" />
ſita ex ratione diametri axis ultimæ rotæ, ad diametrum pri-<lb />mæ &amp; </s>
          <s xml:space="preserve">ratione circumvolutionum ultimæ rotæ, ad circum-<lb />volutiones primæ, eodem tempore.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0080-02" corresp="note-0080-02a" place="margin">190.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cujus regulæ demonſtratio etiam ex comparatione viarum <lb />percurſarum à pondere &amp; </s>
          <s xml:space="preserve">potentia deducitur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Rotæ AB potentia, quæ per pondus M repræſentatur, <lb />
<ptr xml:id="note-0080-03a" corresp="note-0080-03" type="noteAnchor" />
applicatur, pondus P axi rotæ FG; </s>
          <s xml:space="preserve">axis illius diameter eſt <lb />
<ptr xml:id="note-0080-04a" corresp="note-0080-04" type="noteAnchor" />
octava pars diametri rotæ AB, &amp; </s>
          <s xml:space="preserve">hæc rota quinquies cir-<lb />cumvolvitur, dum rota FG ſemel: </s>
          <s xml:space="preserve">ratio ergo potentiæ ad <lb />pondus componitur ex rationibus 1. </s>
          <s xml:space="preserve">ad 8.</s>
          <s xml:space="preserve">; &amp; </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">ad 5.</s>
          <s xml:space="preserve">; eſt <lb />ergo ratio 1. </s>
          <s xml:space="preserve">ad 40.</s>
          <s xml:space="preserve">; ſemilibra ſuſtinet in eo caſu viginti li-<lb />bras.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0080-03" corresp="note-0080-03a" place="margin">191.</note>
              <note xml:space="preserve" xml:id="note-0080-04" corresp="note-0080-04a" place="margin">TAB. VI. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XII. <lb />De Trochlea, Machinarum ſimplicium tertia.</head>
        <p>
          <s xml:space="preserve">MUltis in occaſionibus axis in peritrochio ad elevanda <lb />pondera inſervire nequit; </s>
          <s xml:space="preserve">trochleis in iis caſibus u-<lb />tendum, &amp; </s>
          <s xml:space="preserve">Machina, quæ ex iſtis formatur, eſt admodum <lb />compendioſa, &amp; </s>
          <s xml:space="preserve">facillime de loco in locum transfertur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quid ſit Trochlea, jam ante dictum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">123.</note>
        <p>
          <s xml:space="preserve">Si pondus trochleæ conjunctum ſit ita, ut cum ea traha-<lb />tur, utraque extremitas funis ductarii ſuſtinet partem dimi-<lb />diam ponderis. </s>
          <s xml:space="preserve">Quando ergo extremitas una, unco alliga-<lb />
<ptr xml:id="note-0080-06a" corresp="note-0080-06" type="noteAnchor" />
ta, aut aliter fixa eſt, vis movens alteri extremitati appli-<lb />cata, quæ dimidium ponderis valet, pondus ſuſtinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0080-06" corresp="note-0080-06a" place="margin">192.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Pondus P, duarum librarum trochleæ conjungitur, ita ta-<lb />
<ptr xml:id="note-0080-07a" corresp="note-0080-07" type="noteAnchor" />
men, ut rotatio orbiculi eo non impediatur; </s>
          <s xml:space="preserve">unco funis e f <lb />
<ptr xml:id="note-0080-08a" corresp="note-0080-08" type="noteAnchor" />
alligatur, &amp; </s>
          <s xml:space="preserve">altera funis extremitas cd circumit trochleam <lb />fixam ad directionem mutandam <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">tunc pondus M, unius
<ptr xml:id="note-0080-09a" corresp="note-0080-09" type="noteAnchor" />
</s>
          <pb facs="0081" />
          <s xml:space="preserve">
<ptr xml:id="fig-0081-01a" corresp="fig-0081-01" type="figureAnchor" />
<pb facs="0081a" />
<ptr xml:id="fig-0081a-01a" corresp="fig-0081a-01" type="figureAnchor" />
<pb facs="0082" />
<pb facs="0083" n="41" /><fw type="head">MATHEMATICA. LIB. I. CAP XII.</fw>
libræ, huic extremitati applicatum ſuſtinet pondus P.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0080-07" corresp="note-0080-07a" place="margin">193.</note>
              <note xml:space="preserve" xml:id="note-0080-08" corresp="note-0080-08a" place="margin">TAB. VII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0080-09" corresp="note-0080-09a" n="*" anchored="true" place="margin">124.</note>
              <figure xml:id="fig-0081-01" corresp="fig-0081-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081-01" />
                <label>0081-01</label>
              </figure>
              <figure xml:id="fig-0081a-01" corresp="fig-0081a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081a-01" />
                <label>0081a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Plurimi orbiculi utcunque conjungi poſſunt, &amp; </s>
          <s xml:space="preserve">pondus iis <lb />
<ptr xml:id="note-0083-01a" corresp="note-0083-01" type="noteAnchor" />
annecti; </s>
          <s xml:space="preserve">ſi tunc unum extremum funis fixum ſit, &amp; </s>
          <s xml:space="preserve">funis <lb />circumeat omnes orbiculosillos, &amp; </s>
          <s xml:space="preserve">fixos æquali numero, par-<lb />vâ potentiâ magnum pondus elevari poteſt; </s>
          <s xml:space="preserve">in hoc caſu quo <lb />numerus orbiculorum ponderi conjunctorum major eſt, (fi-<lb />xis enim actio potentiæ non mutatur <ptr type="noteAnchor" />) eo minor potentia
<ptr xml:id="note-0083-02a" corresp="note-0083-02" type="noteAnchor" />
valet ad ſuſtinendum pondus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">potentia, quæ eſt ad pon-<lb />
<ptr xml:id="note-0083-03a" corresp="note-0083-03" type="noteAnchor" />
dus, ut unitas ad duplum numeri or biculorum, cum pondere æ-<lb />que pollet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0083-01" corresp="note-0083-01a" place="margin">194.</note>
              <note xml:space="preserve" xml:id="note-0083-02" corresp="note-0083-02a" n="*" anchored="true" place="margin">124.</note>
              <note xml:space="preserve" xml:id="note-0083-03" corresp="note-0083-03a" place="margin">195.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hic enim eſt numerus funium, quibus pondus ſuſti-<lb />netur, &amp; </s>
          <s xml:space="preserve">unico funi potentia applicatur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Pondus P ſex librarum regulæ AB annectitur, in quatres <lb />
<ptr xml:id="note-0083-04a" corresp="note-0083-04" type="noteAnchor" />
orbiculi libere rotantur. </s>
          <s xml:space="preserve">Unco extremitas funis alligatur, <lb />
<ptr xml:id="note-0083-05a" corresp="note-0083-05" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">funis circumit tres illos orbiculos, &amp; </s>
          <s xml:space="preserve">totidem alios fixos; <lb /></s>
          <s xml:space="preserve">alteri extremo pondus unius libræ alligatur, &amp; </s>
          <s xml:space="preserve">datur æqui-<lb />librium,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0083-04" corresp="note-0083-04a" place="margin">196.</note>
              <note xml:space="preserve" xml:id="note-0083-05" corresp="note-0083-05a" place="margin">TAB. VII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3. &amp; 4</head>
        <p>
          <s xml:space="preserve">Non intereſt quomodocunque orbiculi conjungantur; </s>
          <s xml:space="preserve">ad <lb />
<ptr xml:id="note-0083-06a" corresp="note-0083-06" type="noteAnchor" />
elevanda pondera haud facile præcedens diſpoſitio adhibetur; <lb /></s>
          <s xml:space="preserve">artifices ideò inæqualibus orbiculis utuntur diſpoſitis ut in <lb />fig. </s>
          <s xml:space="preserve">3.</s>
          <s xml:space="preserve">; magnitudo enim orbiculorum nihil immutat. </s>
          <s xml:space="preserve">Sæpe <lb />
<ptr xml:id="note-0083-07a" corresp="note-0083-07" type="noteAnchor" />
etiam, quæ diſpoſitio eſt omnium maxime compendioſa, <lb />orbiculi circa eundem axem volubiles ſunt, ut in fig. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0083-08a" corresp="note-0083-08" type="noteAnchor" />
in hiſce duobus caſibus experimentum eodem modo proce-<lb />dit, ac in 2<hi rend="superscript">do</hi> experimento.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0083-06" corresp="note-0083-06a" place="margin">197.</note>
              <note xml:space="preserve" xml:id="note-0083-07" corresp="note-0083-07a" place="margin">TAB. VII. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0083-08" corresp="note-0083-08a" place="margin">TAB. VII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando extremitas funis ductarii, quæ in experimentis <lb />
<ptr xml:id="note-0083-09a" corresp="note-0083-09" type="noteAnchor" />
præcedentibus fixa eſt, annectitur ponderi aut orbiculis <lb />
<ptr xml:id="note-0083-10a" corresp="note-0083-10" type="noteAnchor" />
mobilibus, ratio potentiæ ad pondus non eſt ut 1. </s>
          <s xml:space="preserve">ad du-<lb />plum numeri orbiculorum ponderi affixorum; </s>
          <s xml:space="preserve">ſed unitate <lb />augeri debet numerus hicce duplus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hîc, ubi duo orbicu-<lb />li ponderi annectuntur, ratio eſt ut 1 ad 5; </s>
          <s xml:space="preserve">tot enim dan-<lb />tur funes, quibus pondus ſuſtinetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0083-09" corresp="note-0083-09a" place="margin">198.</note>
              <note xml:space="preserve" xml:id="note-0083-10" corresp="note-0083-10a" place="margin">TAB. VII. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <note xml:space="preserve" place="margin">199.</note>
        <p>
          <s xml:space="preserve">Plurimi orbiculi ſeparati &amp; </s>
          <s xml:space="preserve">mobiles, habentes ſinguli <lb />
<ptr xml:id="note-0083-12a" corresp="note-0083-12" type="noteAnchor" />
</s>
          <pb facs="0084" n="42" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſuum funem peculiarem, ſi ita diſponantur, ut in hac figura, <lb />multo magis actionem potentiæ augent. </s>
          <s xml:space="preserve">Actio enim du-<lb />plicatur pro unoquoque orbiculo, ita ut produobus ſit qua-<lb />drupla, pro tribus octupla, &amp; </s>
          <s xml:space="preserve">ſic de cæteris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0083-12" corresp="note-0083-12a" place="margin">TAB. VIII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sæpius memorata regula, ſcilicet ſpatia percurſa à po-<lb />tentia &amp; </s>
          <s xml:space="preserve">pondere, quando æquè pollent, eſſe inter ſe inver-<lb />ſè, ut potentia ad pondus, in omnibus prædictis locum ha-<lb />bet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hic ſemper ſunes paralleli ponuntur; </s>
          <s xml:space="preserve">quid ſunium obli-<lb />quitas diſcriminis adſerat, in ſequentibus videbimus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIII.</head>
        <head rend="italics" xml:space="preserve">De Cuneo &amp; Cocbleâ, Machinarum Simplicium quartâ, &amp; <lb />quintâ.</head>
        <p>
          <s xml:space="preserve">Ex prædictis ſatis patet, quomodo ope parvæ potentiæ <lb />pondus magnum ſuſtineri aut elevari poſſit;</s>
          <s xml:space="preserve">ad hoſce uſus <lb />non reſtringitur Ars Mechanica: </s>
          <s xml:space="preserve">intenſitates potentiarum <lb />in omni caſu augeri poſſunt; </s>
          <s xml:space="preserve">exemplum pulcherrimum ſup-<lb />peditat Cuneus, inſtrumentum findendo ligno, pluribuſque <lb />aliis uſibus, inſerviens.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> I.</head>
        <p>
          <s xml:space="preserve">Cuneus eſt priſma non admodum altum, cujus baſes ſunt <lb />
<ptr xml:id="note-0084-01a" corresp="note-0084-01" type="noteAnchor" />
<ptr xml:id="note-0084-02a" corresp="note-0084-02" type="noteAnchor" />
triangula æquicrura; </s>
          <s xml:space="preserve">ut A.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0084-01" corresp="note-0084-01a" place="margin">200.</note>
              <note xml:space="preserve" xml:id="note-0084-02" corresp="note-0084-02a" place="margin">TAB. VII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Altitudo trianguli eſt cunei altitudo; </s>
          <s xml:space="preserve">ut db.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">201.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Trianguli baſis vocatur etiam cunei baſis; </s>
          <s xml:space="preserve">ut ce.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">202.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p>
          <s xml:space="preserve">Acies cunei eſt linea recta, quæ conjungit triangulorum <lb />
<ptr xml:id="note-0084-05a" corresp="note-0084-05" type="noteAnchor" />
vertices, ut bf.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0084-05" corresp="note-0084-05a" place="margin">203.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ligno findendo, aut corporibus ſeparandis, acies cunei <lb />applicatur, &amp; </s>
          <s xml:space="preserve">ictibus mallei, loco preſſionis, cuneus intruditur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando totus cuneus intruditur, ſpatium a puncto d, cui <lb />ictus mallei applicantur, percurſum, eſt altitudo cunei d b, <lb />quæ ideo proſpatio à potentia percurſo haberi debet; </s>
          <s xml:space="preserve">ſpa-
</s>
          <pb facs="0085" n="43" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CCP. XIII.</fw>
tìum verò, per quod ligni partes, aut corpora, a ſe mutuo <lb />recedunt, eſt baſis cunei. </s>
          <s xml:space="preserve">Unde ſequitur,</s>
        </p>
        <p rend="italics">
          <s xml:space="preserve">‘Potentiam ſe habere ad corporum ſeparandorum reſiſten-<lb />
<ptr xml:id="note-0085-01a" corresp="note-0085-01" type="noteAnchor" />
tiam, quando cum hac æquè pollet, ut baſis cunei, adillius al-<lb />titudinem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0085-01" corresp="note-0085-01a" place="margin">204.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">112.</note>
        <p>
          <s xml:space="preserve">Quando agitur de ligno findendo, regula hæclocum non <lb />
<ptr xml:id="note-0085-03a" corresp="note-0085-03" type="noteAnchor" />
habet; </s>
          <s xml:space="preserve">quia non per æqualia ſpatia ſingulæ ligni partes ce-<lb />dunt, &amp; </s>
          <s xml:space="preserve">quia, partibus quam minime ſeparatis, cohæren-<lb />tia in totum toliitur. </s>
          <s xml:space="preserve">Quæ ad lignum findendum ſpectant <lb />in ſequenti Scholio explicantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0085-03" corresp="note-0085-03a" place="margin">205.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head xml:space="preserve">Qua cunei affectiones demonſtrantur.</head>
        <p>
          <s xml:space="preserve">Tabella T, longitudinis ſex poll.</s>
          <s xml:space="preserve">, latitudinis quatuor poll. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0085-04a" corresp="note-0085-04" type="noteAnchor" />
cum ſemiſſe, in ſitu horizontali firmatur, ad altitudinem <lb />
<ptr xml:id="note-0085-05a" corresp="note-0085-05" type="noteAnchor" />
circiter trium pedum ſupra menſam M.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0085-04" corresp="note-0085-04a" place="margin">206.</note>
              <note xml:space="preserve" xml:id="note-0085-05" corresp="note-0085-05a" place="margin">TAB. VIII <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hoc commodè fit ope columnæ firmæ C, cui in ſuperio-<lb />ri parte cohæret lignum horizontale B, in cujus extre-<lb />mo cavum quadratum datur, in quo intruditur cauda li-<lb />gnèa, quæ cum tabella cohæret, &amp; </s>
          <s xml:space="preserve">quæ cum cavo exa-<lb />cte congruit; </s>
          <s xml:space="preserve">quare facile &amp; </s>
          <s xml:space="preserve">firmatur, &amp; </s>
          <s xml:space="preserve">ex ſitu tollitur, <lb />tabella T.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ad quatuor hujus angulos foramina dantur a, a, b, b. <lb /></s>
          <s xml:space="preserve">per quæ funes tranſeunt, in ipſis foraminibus fixi; </s>
          <s xml:space="preserve">ſunt hi <lb />æquales inter ſe circiter tres pedes longi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hiſce funibus ſuſpenduntur lamellæ æneæ quatuor, ut e <lb />&amp; </s>
          <s xml:space="preserve">e; </s>
          <s xml:space="preserve">ſed quæ diſtinctius, &amp; </s>
          <s xml:space="preserve">juxta veras dimenſiones, repræ-<lb />ſentantur in E aut E.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ope harum duo ſuſpenduntur cylindri lignei h, h; </s>
          <s xml:space="preserve">ſe-<lb />ctio juxta axem repræſentatur in H; </s>
          <s xml:space="preserve">altitudo inter t &amp; </s>
          <s xml:space="preserve">t, <lb />ubi baſes paulum prominent, æqualis eſt diſtantiæ inter fo-<lb />ramina a &amp; </s>
          <s xml:space="preserve">b in tabella T: </s>
          <s xml:space="preserve">cylindrorum axes ulterius prominent, <lb />chalybei ſunt, &amp; </s>
          <s xml:space="preserve">tenues, ut tr, tr; </s>
          <s xml:space="preserve">hi per lamellarum, ut E, <lb />foramina majora tranſeunt, cum quibus congruunt; </s>
          <s xml:space="preserve">ita ta-<lb />men ut in his quam liberrimè rotari poſſint.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cylindrorum diametri ſunt duorum pollicum cum ſemiſ-<lb />ſe; </s>
          <s xml:space="preserve">in medio pars datur tenuior, long tudinis quatuor pol-
</s>
          <pb facs="0086" n="44" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
licum, cujus diameter eſt ſeſquipollicis. </s>
          <s xml:space="preserve">Pars hæc tenui-<lb />or duobus annulis ii, oo, ex ipſo ligno, circumdatur ita, <lb />ut lamina lignea F, quæ tenuiori huic parti applicatur, an-<lb />nulos tantum tangat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In tabella T dantur &amp; </s>
          <s xml:space="preserve">duo alia foramina inter a, a, &amp; </s>
          <s xml:space="preserve"><lb />b, b, nempe l, l, per quæ funes tranſeunt, qui in ſuperiori <lb />parte tabellæ cum paxillis s, s, cohærent. </s>
          <s xml:space="preserve">Hiſce funibus <lb />trochleæ duæ æneæ ſuſtinentur, ut t, aut T, ita ſuſpenſæ <lb />ut liberrime circa axes ſuos chalybeos, in foraminibus in la-<lb />mellis æneis rotari poſſint.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Trochlea, ut T, cum cylindro uno conjungitur ope la-<lb />mellæ E, &amp; </s>
          <s xml:space="preserve">funium m; </s>
          <s xml:space="preserve">cum oppoſitâ lamellâ E funis n n co-<lb />hæret, qui trochleæ circumponitur &amp; </s>
          <s xml:space="preserve">pondere P trahitur. <lb /></s>
          <s xml:space="preserve">Simile pondus, ad aliam partem cylindrorum, eodem mo-<lb />do, ſuſpenditur, quibus duobus ponderibus ad ſe mutuotra-<lb />huntur cylindri.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ope paxillorum s, s, elevantur, aut deprimuntur trochleæ, <lb />donec funes n &amp; </s>
          <s xml:space="preserve">m ſint in ſitu horizontali.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cuneus formatur ex duabus laminis ligneis F, F, verti-<lb />eulis inter ſe conjunctis; </s>
          <s xml:space="preserve">quæ angulum quemcunque inter <lb />ſe efficere poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Per haſce ipſas tranſit cochlea, circulariter incurvata, ſu-<lb />per qua duo fruſta ænea exigua, duæ nempe cochleæ ex-<lb />teriores, moventur. </s>
          <s xml:space="preserve">Hiſce plana F, F ſeparantur, &amp;</s>
          <s xml:space="preserve">, ne an-<lb />gulus, quem efficiunt, minuatur, cohibent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Appenſâ lance, cum pondere Q, cuneus hic inter cylin-<lb />dros intruditur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut ita conſtituatur cuneus, ut ratio inter baſim&amp; </s>
          <s xml:space="preserve">altitudi -<lb />nem determinetur, formantur ex ligno triangula iſocelia mino-<lb />ra, ad verticem paululum truncata; </s>
          <s xml:space="preserve">quibus altitudo, &amp; </s>
          <s xml:space="preserve">baſis lon-<lb />gitudo inſcribuntur, datâ menſurâ quacunque. </s>
          <s xml:space="preserve">Commodum <lb />eſt exprimere altitudinem per numerum 16, ſi integris libris <lb />cylindri ad ſe mutuo trahantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi></head>
        <p>
          <s xml:space="preserve">Rebus, ut in machinæ deſcriptione dictum, diſpoſitis, <lb />
<ptr xml:id="note-0086-01a" corresp="note-0086-01" type="noteAnchor" />
ſi pondus, quo cuneus inter cylindros intruditur, (id eſt,
</s>
          <pb facs="0087" n="45" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XIII.</fw>
pondus cunei, cochleæ g g, &amp; </s>
          <s xml:space="preserve">lancis cum pondere impoſi-<lb />to) ſe habet ad ſummam ponderum P,P, ut baſis cunei <lb />ad ipſius altitudinem, æquilibrium datur, inter vim qua <lb />cylindri ſeparantur, &amp; </s>
          <s xml:space="preserve">illam qua ad ſe mutuo trahuntur. <lb /></s>
          <s xml:space="preserve">Hoc exinde elicitur, quia agitatione minimâ cuneus eleva-<lb />tur aut deprimitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0086-01" corresp="note-0086-01a" place="margin">207.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magnam cum cuneo affinitatem habet cochlea. </s>
          <s xml:space="preserve">Ex dua-<lb />bus partibus conſtat.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p>
          <s xml:space="preserve">Prima, quæ vocatur cochlea interior, eſt cylindrus ad for-<lb />
<ptr xml:id="note-0087-01a" corresp="note-0087-01" type="noteAnchor" />
mam belicis ſulcatus, ut AB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0087-01" corresp="note-0087-01a" place="margin">208.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. VII. <lb />fig. 8.</note>
        <p>
          <s xml:space="preserve">Secunda, quæ vocatur cochlea exterior, &amp; </s>
          <s xml:space="preserve">cujus figura <lb />
<ptr xml:id="note-0087-03a" corresp="note-0087-03" type="noteAnchor" />
differt pro vario uſu Machinæ, eſt ſolidum cylindricè excava-<lb />tum, cujus ſuperficies concava eodem modo ſulcata eſt, ita ut bu-<lb />jus eminentiæ alterius cavitatibus congruant, ut DE.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0087-03" corresp="note-0087-03a" place="margin">209.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæ duæ partes in ſe mutuo moveri poſſunt, quod in uſu <lb />hujus machinæ requiritur. </s>
          <s xml:space="preserve">Inſervit præcipuè ad compri-<lb />menda corpora, quæ jungi &amp; </s>
          <s xml:space="preserve">firmiter connecti debent; </s>
          <s xml:space="preserve">in <lb />hac enim Machinâ potentia minima quam arctiſſimé corpo-<lb />ra comprimit. </s>
          <s xml:space="preserve">Poteſt etiam cochlea ad elevanda ponde-<lb />ra adaptari. </s>
          <s xml:space="preserve">In unaquaque revolutione hujus machinæ, quie-<lb />ſcente parte una, altera protruditur ad diſtantiam æqualem in-<lb />tervallo duarum proximarum ſpiralium converſionum. </s>
          <s xml:space="preserve">Po-<lb />tentia, quâ cochlea movetur, applicatur manubrio, aut ſcy-<lb />talæ &amp; </s>
          <s xml:space="preserve">potentia eſt ad compreſſionem, quam generat, ut <lb />
<ptr xml:id="note-0087-04a" corresp="note-0087-04" type="noteAnchor" />
prædicta diſtantia, inter duas proximas ſpiralium converſio-<lb />nes, ad peripheriam circulià puncto manubrii aut ſcytalæ, <lb />cui potentia applicatur, percurſi; </s>
          <s xml:space="preserve">via enim a puncto aut pla-<lb />no, quo reſiſtentia ſuperatur, percurſa, illam ad viam po-<lb />tentiæ rationem habet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0087-04" corresp="note-0087-04a" place="margin">210.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hic obſervandum eſt, quando potentia cum pondere æquè <lb />pollet in machinâ quacunque, ſi potentia parte quantumvis <lb />exiguâ augeatur, illam præpollere, machinâ omnium parti-<lb />um attritu carente; </s>
          <s xml:space="preserve">quando verò attritus datur, potentiâ <lb />&amp; </s>
          <s xml:space="preserve">hic ſuperari debet, &amp; </s>
          <s xml:space="preserve">quantum ad illud requiritur ſu-<lb />peraddi debet, quod ratiocinio mathematico determinari non
</s>
          <pb facs="0088" n="46" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
poteſt. </s>
          <s xml:space="preserve">In Cochleis attritus admodum eſt ſenſibilis, &amp; </s>
          <s xml:space="preserve">et-<lb />
<ptr xml:id="note-0088-01a" corresp="note-0088-01" type="noteAnchor" />
iam magni uſus; </s>
          <s xml:space="preserve">nam eo machina in ſitu ſuo ſervatur, &amp; </s>
          <s xml:space="preserve"><lb />actione corporum, quæ comprimuntur, aut gravitate pon-<lb />derum quæ elevantur, ceſſante actione potentiæ, motu con-<lb />trario non agitatur, &amp; </s>
          <s xml:space="preserve">ad priſtinum ſitum non redit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0088-01" corresp="note-0088-01a" place="margin">211.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM I.</head>
        <head xml:space="preserve">De ligno findendo.</head>
        <p>
          <s xml:space="preserve">Detur lignum, cujus partes jam ſeparatæ efficiant angulum EFL; </s>
          <s xml:space="preserve">ſit hoc <lb />
<ptr xml:id="note-0088-02a" corresp="note-0088-02" type="noteAnchor" />
ulterius findendum ope cunei ACB, cujus baſis eſt AB, &amp; </s>
          <s xml:space="preserve">cujus alti-<lb />
<ptr xml:id="note-0088-03a" corresp="note-0088-03" type="noteAnchor" />
tudinem menſurat CD.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0088-02" corresp="note-0088-02a" place="margin">212.</note>
              <note xml:space="preserve" xml:id="note-0088-03" corresp="note-0088-03a" place="margin">TAB. VIII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ubi partes, ut ſuperius monuimus, quantumvis parum ſeparantur, omnis <lb />tollitur reſiſtentia; </s>
          <s xml:space="preserve">antequam autem ſeparentur partes in F, puncta E, L, <lb />paululum moveri debent, id eſt augendus eſt angulus E F L; </s>
          <s xml:space="preserve">de-<lb />terminaada ideò eſt vis, qua angulus hic augeri poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponamus angulum auctum, ut ſit e F l; </s>
          <s xml:space="preserve">cuneus intravit, &amp; </s>
          <s xml:space="preserve">datur in a c b; <lb /></s>
          <s xml:space="preserve">partes ligni E, L, translatæ fuere per E e, L l, ſed quæ minus ab F diſtant <lb />per minus ſpatium moventur, lineæque EF, LF, motibus ſuis deſeribunt <lb />areas triangulorum æqualium inter ſe F E, l FL.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ductis e f &amp; </s>
          <s xml:space="preserve">f F, parallelis EF &amp; </s>
          <s xml:space="preserve">e E, formetur parallelogrammum e E F f; <lb /></s>
          <s xml:space="preserve">ſunt æqualia triangula e F E &amp; </s>
          <s xml:space="preserve">f e F <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">parallelogrammum valet ambo tri-
<ptr xml:id="note-0088-04a" corresp="note-0088-04" type="noteAnchor" />
angula e F E &amp; </s>
          <s xml:space="preserve">L F l conjuncta: </s>
          <s xml:space="preserve">ideò translationes memoratæ linearum <lb />ambarum EF, LF, conjunctæ, valent translationem ſolius lineæ E F per ſpa-<lb />tium E e aut F f: </s>
          <s xml:space="preserve">quæ lineola ergo diſtantiam repræſentat, qua partes ligni à <lb />ſe invicem ſeparantur, cum autem de hac ſeparatione hìc agatur, eſt hæci-<lb />pſa lineola ſpatium, ab obſtaculo quod ſuperandum eſt, percurſum, dum <lb />ſpatium, quod percurrit potentia, eſt C c, ſpatium nempe per quod cuneus <lb />fuit tranſlatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0088-04" corresp="note-0088-04a" n="*" anchored="true" place="margin">34. El. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis ergo, qua cuneus intruditur, eſt ad ligni reſiſtentiam, quando æquè pol-<lb />lent, ut e E ad C c. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /></s>
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">112.</note>
        <p>
          <s xml:space="preserve">Ducatur C g ipſi E e parallela, erunt hæ lineæ æquales <ptr type="noteAnchor" />, quia motu parallelo
<ptr xml:id="note-0088-06a" corresp="note-0088-06" type="noteAnchor" />
latus cunei AG fuit tranſlatum;</s>
          <s xml:space="preserve">ratio memorata eſt ergo quæ datur inter g C&amp;</s>
          <s xml:space="preserve">Cc.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0088-06" corresp="note-0088-06a" n="*" anchored="true" place="margin">34. El. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lineola E e, ideò etiam g C, perpendicularis eſt ad F E;</s>
          <s xml:space="preserve">eſt enim E e arcus cir-<lb />culi, adeo exiguus ut pro rectâ lineâ haberi poſſit; </s>
          <s xml:space="preserve">cujus circuli radius eſt <lb />F E.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Per punctum baseos medium D linea ducatur DH, ad latus AC cunei per-<lb />
<ptr xml:id="note-0088-07a" corresp="note-0088-07" type="noteAnchor" />
veniens in H &amp; </s>
          <s xml:space="preserve">cum FE latere ligni ſeparato, continuato, angulum efficiens re-<lb />ctum; </s>
          <s xml:space="preserve">quare ipſi Cg parallela eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0088-07" corresp="note-0088-07a" place="margin">213.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propter latera c C, CD, in eadem linea, &amp; </s>
          <s xml:space="preserve">reliqua parallela, ſunt ſimilia <lb />triangula C gc, DHC; </s>
          <s xml:space="preserve">idcirco DH ſe babet ad DC, id eſt altitudinem cu-<lb />nei, ut g C ad C c, id eſt, ut vis qua cuneus intruditur ad ligni reſiſtentiam, quan-<lb />do neutra alteram vincere poteſt, auctâ paulum potentiâ ſeparantur ligni par-<lb />tes.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando ligni partes non ſeparantur, niſi quo uſque cuneus intruditur, lineæ AC <lb />
<ptr xml:id="note-0088-08a" corresp="note-0088-08" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">EF con veniunt, &amp; </s>
          <s xml:space="preserve">angulus DHC eſt rectus, ideoque ſimilia ſunt trian-
</s>
          <pb facs="0089" n="47" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XIV.</fw>
gula CHD, CAD <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">DH ad DC, ut AD ad AC. </s>
          <s xml:space="preserve">In hoc caſu
<ptr xml:id="note-0089-01a" corresp="note-0089-01" type="noteAnchor" />
ergo eſt vis, qua Cuneus intruditur, ad ligni reſiſtentiam, ubi æque pollent, ut ſe-<lb />mibaſis cunei ad bujus latus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0088-08" corresp="note-0088-08a" place="margin">214.</note>
              <note xml:space="preserve" xml:id="note-0089-01" corresp="note-0089-01a" n="*" anchored="true" place="margin">8. El. VI.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head xml:space="preserve">Machinæ cujuſdam examen.</head>
        <p>
          <s xml:space="preserve">Machinam ad cunei proprietates demonſtrandum, à ſuperius deſcriptâ <ptr type="noteAnchor" />
<ptr xml:id="note-0089-02a" corresp="note-0089-02" type="noteAnchor" />
<ptr xml:id="note-0089-03a" corresp="note-0089-03" type="noteAnchor" />
diverſam, adhibuere alii; </s>
          <s xml:space="preserve">ipſe olim talem paululum tantum immuta-<lb />tam, eodem tamen principio nixam, conſtrui curavi, quæ hìc exhibetur;</s>
          <s xml:space="preserve">ſed in <lb />quo failat breviter dicam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0089-02" corresp="note-0089-02a" place="margin">215.</note>
              <note xml:space="preserve" xml:id="note-0089-03" corresp="note-0089-03a" n="*" anchored="true" place="margin">206.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hac cuneus, illi ſimilis cum quo experimenta in noſtra machina inſti-<lb />
<ptr xml:id="note-0089-04a" corresp="note-0089-04" type="noteAnchor" />
tuuntur, eodem modo ac ubi de noſtra egimus dictum, pondere M inter cy-<lb />lindros E, E, trahitur; </s>
          <s xml:space="preserve">cylindri autem moventur juxta regulas æneas CC, <lb />CC, ſuper quibus chalybei axes prominentes ponuntur, &amp; </s>
          <s xml:space="preserve">quæ cum regulis <lb />ligneis AA, AA, parallelis inter ſe cohærent. </s>
          <s xml:space="preserve">Cylindri trahuntur ponderibus <lb />P,P, ſuſpenſis funibus, qui cum lamellis æneis cohærent, in quibus forami-<lb />na dantur per quæ axes chalybei cylindrorum tranſeunt; </s>
          <s xml:space="preserve">funes trochleis nt d, d, <lb />in regulis AA, AA, fixis, &amp; </s>
          <s xml:space="preserve">circa axes mobilibus, circumponuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0089-04" corresp="note-0089-04a" place="margin">TAB. VII. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hac machina datur æquilibrium, ſi vis, qua cuneus intruditur, ſe ha-<lb />beat ad ſummam ponderum P,P, ut ſemibaſis cunei ad ipſius altitudinem, quæ <lb />proportio in cuneo locum non habet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">204.</note>
        <p>
          <s xml:space="preserve">Machina hæc non repræſentat quæ in actione cunei, quo corpora ſeparan-<lb />tur, obtinent; </s>
          <s xml:space="preserve">pondera enim P,P, non repræſentant vim qua cylindri inter ſe <lb />cohærent; </s>
          <s xml:space="preserve">ſed cylindri ſinguli dimidio ponderum P,P, ad trochleam fixam <lb />trahuntur; </s>
          <s xml:space="preserve">in noſtra autem machina, ponderibus integris P,P, inter ſe co-<lb />hærent cylindri.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIV.</head>
        <head xml:space="preserve">De Machinis compoſitis.</head>
        <p>
          <s xml:space="preserve">JAm vidimus, quomodo Machina ex plurimis vectibus <ptr type="noteAnchor" />,
<ptr xml:id="note-0089-06a" corresp="note-0089-06" type="noteAnchor" />
aut plurimis rotis <ptr type="noteAnchor" />, componi poſſit, &amp; </s>
          <s xml:space="preserve">quomodo in iſtis
<ptr xml:id="note-0089-07a" corresp="note-0089-07" type="noteAnchor" />
machinis potentia, ut cum reſiſtentia æquè polleat, ſit adre-<lb />
<ptr xml:id="note-0089-08a" corresp="note-0089-08" type="noteAnchor" />
ſiſtentiam, in ratione compoſita ex omnibus rationibus, quas in <lb />ſingulis machinis potentia ad reſiſtentias baberent, ſi ſepa-<lb />ratim adhiberentur; </s>
          <s xml:space="preserve">hæc eadem regula in omnibus aliis <lb />machinis compoſitis obtinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0089-06" corresp="note-0089-06a" n="*" anchored="true" place="margin">177.</note>
              <note xml:space="preserve" xml:id="note-0089-07" corresp="note-0089-07a" n="*" anchored="true" place="margin">190.</note>
              <note xml:space="preserve" xml:id="note-0089-08" corresp="note-0089-08a" place="margin">216.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non modo plurimæ machinæ ejuſdem generis poſſunt <lb />jungi, ex machinis diverſis, variis modis, machina componi <lb />poteſt; </s>
          <s xml:space="preserve">exemplo uno &amp; </s>
          <s xml:space="preserve">altero id ſatis patebit.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0090" n="48" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> I.</head>
        <p>
          <s xml:space="preserve">Axi in peritrochio funis ductarius trochleæ jungitur, po-<lb />
<ptr xml:id="note-0090-01a" corresp="note-0090-01" type="noteAnchor" />
tentia rotæ applicatur, &amp; </s>
          <s xml:space="preserve">hìc ubi trochleâ quinquies vis au-<lb />
<ptr xml:id="note-0090-02a" corresp="note-0090-02" type="noteAnchor" />
getur, &amp; </s>
          <s xml:space="preserve">ubi diameter axis eſt pars tertia diametri rotæ, <lb />ratio potentiæ ad pondus componitur ex rationibus 1 ad 5 <ptr type="noteAnchor" />,
<ptr xml:id="note-0090-03a" corresp="note-0090-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">1 ad 3 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eſt ergo ut 1 ad 15; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideo unica libra M
<ptr xml:id="note-0090-04a" corresp="note-0090-04" type="noteAnchor" />
ſuſtinet pondus P quindecim librarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0090-01" corresp="note-0090-01a" place="margin">217.</note>
              <note xml:space="preserve" xml:id="note-0090-02" corresp="note-0090-02a" place="margin">TAB. VIL. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0090-03" corresp="note-0090-03a" n="*" anchored="true" place="margin">194.</note>
              <note xml:space="preserve" xml:id="note-0090-04" corresp="note-0090-04a" n="*" anchored="true" place="margin">188.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Axis in peritrochio moveri poteſt adhibitâ cochleâ ro-<lb />
<ptr xml:id="note-0090-05a" corresp="note-0090-05" type="noteAnchor" />
ta in hoc caſu dentata requiritur, cujus dentes ſint inclinati, <lb />
<ptr xml:id="note-0090-06a" corresp="note-0090-06" type="noteAnchor" />
ut cum ſulco cochleæ congruant Talis eſt rota A, quæ <lb />ope cochleæ BC movetur. </s>
          <s xml:space="preserve">Hoc in caſu cochlea perpetua <lb />dicitur, &amp; </s>
          <s xml:space="preserve">mirum admodum hujus ope potentia minima <lb />exerit effectum; </s>
          <s xml:space="preserve">tot enim in ſingul is rotæ revolutionibus, <lb />revolutiones requiruntur cochleæ, id eſt, manubrii quo <lb />cochlea movetur, quot dentes rota habet; </s>
          <s xml:space="preserve">ſi huic rotæ ul-<lb />terior rota dentata addatur, potentia eadem majus ob-<lb />ſtaculum agitare poterit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0090-05" corresp="note-0090-05a" place="margin">218.</note>
              <note xml:space="preserve" xml:id="note-0090-06" corresp="note-0090-06a" place="margin">TAB. VII. <lb />fig. 9.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Machina, quam hìc exhibemus, conſtat ex duabus rotis, <lb />
<ptr xml:id="note-0090-07a" corresp="note-0090-07" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">cochleâ perpetuâ, quæ manubrio DE movetur. </s>
          <s xml:space="preserve">In hac <lb />
<ptr xml:id="note-0090-08a" corresp="note-0090-08" type="noteAnchor" />
ratio potentiæ ad pondus, quando æquè pollent, componitur <lb />ex ratione ſemidiametri axis ultimæ rotæ F, ad manubrii <lb />longitudinem DE, &amp; </s>
          <s xml:space="preserve">ratione revolutionum hujus rotæ ad <lb />manubrii aut cochleæ revolutiones. </s>
          <s xml:space="preserve">Prima ratio in hac ma-<lb />china eſt 1 ad 30; </s>
          <s xml:space="preserve">ſecunda ex numero dentium colligitur. <lb /></s>
          <s xml:space="preserve">Rota ultima F habet in peripheria dentes 35, axis primæ rotæ <lb />A continet dentes 7; </s>
          <s xml:space="preserve">quinquies ergo prima rota revolvi-<lb />tur, dum ſecunda ſemel; </s>
          <s xml:space="preserve">hæc verò prima continet dentes <lb />36, totidem igitur revolutiones peragit cochlea, dum hæc <lb />rota ſemel revolvitur <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ratio ex hiſce duabus compoſita
<ptr xml:id="note-0090-09a" corresp="note-0090-09" type="noteAnchor" />
eſt, 1 ad 180, quæ eſt ſecunda ratio quæſita; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ratio ex <lb />hac &amp; </s>
          <s xml:space="preserve">prima 1 ad 30 compoſita, eſt ratio 1 ad 5400, quæ <lb />eſt ratio potentiæ ad pondus in caſu æquilibrii; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quan-<lb />tumvis parum auctâ potentia pondus elevaretur, ſinullus da-<lb />retur attritus, qui cum in omnibus hiſce machinis non ſit <lb />contemnendus; </s>
          <s xml:space="preserve">ſatis ſenſibiliter potentia, antequam pon-
</s>
          <pb facs="0091" />
          <s xml:space="preserve">
<ptr xml:id="fig-0091-01a" corresp="fig-0091-01" type="figureAnchor" />
<pb facs="0091a" />
<ptr xml:id="fig-0091a-01a" corresp="fig-0091a-01" type="figureAnchor" />
<pb facs="0092" />
<pb facs="0093" n="49" /><fw type="head">MATHEMATICA. LIB. I. CAP. XV.</fw>
dus ſuperet, adaugeri debet; </s>
          <s xml:space="preserve">pontentiâ tamen minimâ pon-<lb />dus maximum elevatur. </s>
          <s xml:space="preserve">Longitudo ſcytalæ ED duplicari, <lb />aut etiam ulterius augeri poteſt, quo actio potentiæ dupli-<lb />catur, aut magis augetur; </s>
          <s xml:space="preserve">in hoc caſu capillo tenuiſſimo ho-<lb />mo fortis ſuperatur.</s>
          <s xml:space="preserve" />
        </p>
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            <div type="float">
              <note xml:space="preserve" xml:id="note-0090-07" corresp="note-0090-07a" place="margin">219.</note>
              <note xml:space="preserve" xml:id="note-0090-08" corresp="note-0090-08a" place="margin">TAB. VII. <lb />fig. 9.</note>
              <note xml:space="preserve" xml:id="note-0090-09" corresp="note-0090-09a" n="*" anchored="true" place="margin">218.</note>
              <figure xml:id="fig-0091-01" corresp="fig-0091-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0091-01" />
                <label>0091-01</label>
              </figure>
              <figure xml:id="fig-0091a-01" corresp="fig-0091a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0091a-01" />
                <label>0091a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Innumeræ aliæ Machinæ compoſitæ conſtrui poſſunt, <lb />quarum vires eodem modo computatione determinantur, <lb />ope regulæ initio hujus capitis memoratæ, aut etiam compa-<lb />rando viam percurſam a potentiâ cum viâ à pondere, aut <lb />alio quocumque impedimento, percurſâ; </s>
          <s xml:space="preserve">harum enim ratio <lb />eſt ratio inverſa potentiæ &amp; </s>
          <s xml:space="preserve">ponderis autimpedimenti, quando <lb />potentiæ actio cum reſiſtentiâ impedimenti æquè pollet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Preſſiones, quæ contrarie agentes æquè pollent, ſemper <lb />ſunt æquales; </s>
          <s xml:space="preserve">ſi ergo potentia intenſitate minor eſt impe-<lb />dimento, reſpectu viæ percurſæ illud ſuperare debet, &amp; </s>
          <s xml:space="preserve"><lb />quidem toties quoties ab illo intenſitate ſuperatur; </s>
          <s xml:space="preserve">nullo e-<lb />nim alio reſpectu preſſionum effectus differre poſſunt, etiam <lb />nulla alia compenſatio dari poteſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XV.</head>
        <head xml:space="preserve">De Potentiis obliquis.</head>
        <p>
          <s xml:space="preserve">Detur punctum A, quod tribus potentiis filis applicatis <lb />
<ptr xml:id="note-0093-01a" corresp="note-0093-01" type="noteAnchor" />
per AB, <hi rend="small caps">A</hi>E, &amp; </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>D, trabitur, quieſcit, ſi poten-<lb />
<ptr xml:id="note-0093-02a" corresp="note-0093-02" type="noteAnchor" />
tiæ fuerint inter ſe ut latera trianguli formati lineis juxta <lb />directiones potentiarum poſitis; </s>
          <s xml:space="preserve">id eſt, ſi potentiæ fuerint <lb />inter ſe ut latera trianguli A Db. </s>
          <s xml:space="preserve">In quo caſu poſitis AB, <lb />AE &amp; </s>
          <s xml:space="preserve">AD, reſpectivè ut preſſiones per has lineas agentes, <lb />ſi duabus ut AD &amp; </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>E formetur parallelogrammum, pa-<lb />tet tertiam <hi rend="small caps">Ba</hi> continuatam fore parallelogrammi diagona-<lb />lem &amp; </s>
          <s xml:space="preserve">AB, Ab, æquales eſſe inter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0093-01" corresp="note-0093-01a" place="margin">220.</note>
              <note xml:space="preserve" xml:id="note-0093-02" corresp="note-0093-02a" place="margin">TAB. X. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Punctum autem A in hoc caſu quieſcere ut demonſtremus, <lb />concipere debemus, ſepoſitâ potentiâ per <hi rend="small caps">A</hi>B, preſſiones per <lb />AE &amp; </s>
          <s xml:space="preserve">AD deſtrui, punctumque quieſcere, actione quacunque, <lb />&amp; </s>
          <s xml:space="preserve">in hanc actionem inquirendum eſt. </s>
          <s xml:space="preserve">Sint lineæ minimæ A d, <lb />A e, inter ſe ut A D, AE, id eſt, ut preſſiones juxta haſce lineas <lb />agentes;</s>
          <s xml:space="preserve">æquali tempore punctum A per haſce lineas minimas
</s>
          <pb facs="0094" n="50" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
poſſet transferri, ſi ſingulæ ſolæ agerent &amp; </s>
          <s xml:space="preserve">non deſtruerentur <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0094-01a" corresp="note-0094-01" type="noteAnchor" />
cum punctum quieſcat, integras ſuas actiones ambæ ſimul in <lb />hoc exerunt, &amp; </s>
          <s xml:space="preserve">conatur hoc per ambas ſimul lineas eodem tem-<lb />pore moveri; </s>
          <s xml:space="preserve">ſi autem per ambas ſimul transferatur dabitur in <lb />b, in diagonali Ab, ductis eb ad Ad, &amp; </s>
          <s xml:space="preserve">db ad Ae parallelis; </s>
          <s xml:space="preserve">am-<lb />babus ergo potentiis conatur lineam Ab percurrer@ eo tempo-<lb />re, quo poſſet percurrere Ae aut Ad; </s>
          <s xml:space="preserve">duæ ergo memo-<lb />
<ptr xml:id="note-0094-02a" corresp="note-0094-02" type="noteAnchor" />
ratæ potentiæ adunicam per Ab agentem reducuntur, &amp; </s>
          <s xml:space="preserve">eſt <lb />hæc potentia ad reliquas duas ut Ab ad Ad &amp; </s>
          <s xml:space="preserve">Ae, <lb />id eſt, ut AB ad AD &amp; </s>
          <s xml:space="preserve">AE. </s>
          <s xml:space="preserve">Æqualis eſt idcirco <lb />potentia, qua punctum A trahitur per AB, poten-<lb />tiæ, ad quam reliquæ duæ reducuntur, &amp; </s>
          <s xml:space="preserve">cum hac con-<lb />trarie agit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0094-01" corresp="note-0094-01a" n="*" anchored="true" place="margin">107.</note>
              <note xml:space="preserve" xml:id="note-0094-02" corresp="note-0094-02a" place="margin">221.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nota eſt triangulorum proprietas, latera eſſe inter ſe ut <lb />ſinus angulorum oppoſitorum; </s>
          <s xml:space="preserve">ſunt ergo in æquilibrio po-<lb />
<ptr xml:id="note-0094-03a" corresp="note-0094-03" type="noteAnchor" />
tentiæ tres, quæ ſunt inter ſe ut ſinus angulorum directioni-<lb />bus potentiarum oppoſitarum formatorum. </s>
          <s xml:space="preserve">Id eſt, poten-<lb />tia quæ per <hi rend="small caps">A</hi>E agit, eſt ut ſinus anguli BAD, &amp; </s>
          <s xml:space="preserve">ſic de <lb />cæteris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0094-03" corresp="note-0094-03a" place="margin">222.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head rend="italics" xml:space="preserve">Qua demonſtrantur quæ ſpectant punctum quod filis ad <lb />partes diverſas trabitur.</head>
        <p>
          <s xml:space="preserve">Machina hæc conſtat ex orbe ligneo, diametri circiter o-<lb />
<ptr xml:id="note-0094-04a" corresp="note-0094-04" type="noteAnchor" />
cto pollicum, horizontalis eſt &amp; </s>
          <s xml:space="preserve">pede ſuſtinetur; </s>
          <s xml:space="preserve">in medio <lb />
<ptr xml:id="note-0094-05a" corresp="note-0094-05" type="noteAnchor" />
craſſitiei ſulco circumdatur, quo Trochleæ ad libitum, in <lb />quocunque circumferentiæ puncto, Machinæ junguntur. <lb /></s>
          <s xml:space="preserve">Sulco enim huic inſeritur lamina ænea, cui Trochlea per-<lb />pendiculariter cohæret, ut in Frepræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0094-04" corresp="note-0094-04a" place="margin">223.</note>
              <note xml:space="preserve" xml:id="note-0094-05" corresp="note-0094-05a" place="margin">TAB X <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Orbis prædictus in ſuperiori parte paululum excavatur, <lb />ut recipiat orbem minorem <hi rend="small caps">DFa</hi>, craſſitiei quartæ partis u-<lb />nius pollicis, &amp; </s>
          <s xml:space="preserve">paululum ſupra orbem primum prominen-<lb />tem; </s>
          <s xml:space="preserve">ita ut filum ſuper Trochleâ, ut dictum, Machinæ an-<lb />nexâ, horizontaliter extenſum ſuperficiem <hi rend="small caps">Da</hi>F perſtrin-<lb />gat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Varii, pro variis Experimentis, tales requiruntur orbes <lb />minores. </s>
          <s xml:space="preserve">Charta ab utraque parte obteguntur, ut com-
</s>
          <pb facs="0095" />
          <s xml:space="preserve">
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</s>
          <pb facs="0095a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0095a-01a" corresp="fig-0095a-01" type="figureAnchor" />
</s>
          <pb facs="0096" />
          <s xml:space="preserve">
</s>
          <pb facs="0097" n="51" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA, LIB. I. CAP. XV.</fw>
mode lineæ, in ſequentibus memorandæ, in iis duci poſ-<lb />ſint.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0095-01" corresp="fig-0095-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0095-01" />
                <label>0095-01</label>
              </figure>
              <figure xml:id="fig-0095a-01" corresp="fig-0095a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0095a-01" />
                <label>0095a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Sit C centrum orbis minoris memorati, &amp; </s>
          <s xml:space="preserve">in hoc deli-<lb />
<ptr xml:id="note-0097-01a" corresp="note-0097-01" type="noteAnchor" />
neatum triangulum <hi rend="small caps">A</hi>BC, cujus latera ſunt inter ſe ut 2. <lb /></s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve">; Detur linea CE lateri AB trianguli parallela, &amp; </s>
          <s xml:space="preserve"><lb />continuetur latus AC verſus D.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0097-01" corresp="note-0097-01a" place="margin">224.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nunc dentur tria fila in C juncta, &amp; </s>
          <s xml:space="preserve">juxta lineas CD, <lb />CE, &amp; </s>
          <s xml:space="preserve">CB protenſa ſuper Trochleis majori orbi junctis; <lb /></s>
          <s xml:space="preserve">Si filis CD, CE, &amp; </s>
          <s xml:space="preserve">CF, appendantur pondera quæ ſint inter <lb />ſe ut 4. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">fila non moventur, &amp; </s>
          <s xml:space="preserve">nodus in C quieſcit; </s>
          <s xml:space="preserve"><lb />ſi ex eo puncto dimoveatur nodus, non quieſcit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hac propoſitione duæ potentiæ quæcunque cum tertia æ-<lb />què pollent, id eſt, valent unicam potentiam, quæ in eadem <lb />directione cum illa tertia, ſed contrarie, agit, &amp; </s>
          <s xml:space="preserve">illi ter-<lb />tiæ æqualis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando quatuor potentiis punctum trahitur, dabitur æ-<lb />
<ptr xml:id="note-0097-02a" corresp="note-0097-02" type="noteAnchor" />
quilibrium, ſi reductis duabus potentiis ad unicam, hæc <lb />potentia nova, cum duabus reliquis, ſit in conditione n. <lb /></s>
          <s xml:space="preserve">220; </s>
          <s xml:space="preserve">id eſt, ſi hiſce reliquis etiam ad unicam reductis, po-<lb />tentia ex eo orta æqualis ſit, &amp; </s>
          <s xml:space="preserve">contrarie agat, cum poten-<lb />tia nova ſtatim memorata.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0097-02" corresp="note-0097-02a" place="margin">225.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Punctum C trahitur quatuor filis, B verſus pondere dua-<lb />
<ptr xml:id="note-0097-03a" corresp="note-0097-03" type="noteAnchor" />
rum unciarum, F verſus pondere ſex unciarum, E verſus <lb />
<ptr xml:id="note-0097-04a" corresp="note-0097-04" type="noteAnchor" />
pondere quatuor unciarum &amp; </s>
          <s xml:space="preserve">tandem D verſus pondere o-<lb />cto unciarum, &amp; </s>
          <s xml:space="preserve">datur æ quilibrium: </s>
          <s xml:space="preserve">formato triangulo <lb />CFa, aut parallelogrammo CFaE, potentiæ prædictæ per <lb />CF &amp; </s>
          <s xml:space="preserve">CE reducuntur ad unicam agentem per Ca, cum <lb />vi ponderis octo unciarum, &amp; </s>
          <s xml:space="preserve">tunc tres potentiæ per CB, <lb />CD, Ca exhibent caſum n. </s>
          <s xml:space="preserve">220; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideo ſi potentiæ per <lb />CB &amp; </s>
          <s xml:space="preserve">CD reducantur ad unicam per CA, aget in eadem <lb />directione ſed contrarie cum potentia per Ca, &amp; </s>
          <s xml:space="preserve">huic æ-<lb />qualis erit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0097-03" corresp="note-0097-03a" place="margin">226.</note>
              <note xml:space="preserve" xml:id="note-0097-04" corresp="note-0097-04a" place="margin">TAB. X. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quæ hìc de quatuor potentiis dicuntur, de quinque <lb />
<ptr xml:id="note-0097-05a" corresp="note-0097-05" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">pluribus dici potuiſſent; </s>
          <s xml:space="preserve">ex quinque enim ſi duæ ad u-
</s>
          <pb facs="0098" n="52" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
nam reducantur, incidimus in exemplum præcedens.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0097-05" corresp="note-0097-05a" place="margin">227.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Punctum C quinque potentiis trahitur, filis CA, CB, <lb />
<ptr xml:id="note-0098-01a" corresp="note-0098-01" type="noteAnchor" />
CD, CE, &amp; </s>
          <s xml:space="preserve">CF; </s>
          <s xml:space="preserve">potentiæ ſunt inter ſe ut pondera qui-<lb />
<ptr xml:id="note-0098-02a" corresp="note-0098-02" type="noteAnchor" />
bus fila trahuntur, &amp; </s>
          <s xml:space="preserve">illa habent inter ſe proportionem nu-<lb />merorum Trochleis in figura adſcriptorum, &amp; </s>
          <s xml:space="preserve">æquilibrium <lb />datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0098-01" corresp="note-0098-01a" place="margin">228.</note>
              <note xml:space="preserve" xml:id="note-0098-02" corresp="note-0098-02a" place="margin">TAB. IX. <lb />fig. 1</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Potentiæ per CB &amp; </s>
          <s xml:space="preserve">CD ad unicam reducuntur per <lb />CG; </s>
          <s xml:space="preserve">potentiæ agentes per CE &amp; </s>
          <s xml:space="preserve">CF ad unicam reducun-<lb />tur per CH, &amp; </s>
          <s xml:space="preserve">ita verſamur in caſu n. </s>
          <s xml:space="preserve">220; </s>
          <s xml:space="preserve">tandem iſtæ <lb />duæ novæ potentiæ, per CH &amp; </s>
          <s xml:space="preserve">CG, ad unicam reducun-<lb />tur per Ca, quæ quintæ per CA æqualis eſt, &amp; </s>
          <s xml:space="preserve">cum hac <lb />in eadem linea, ſed contrarie, agit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex memorata propoſitione n. </s>
          <s xml:space="preserve">220. </s>
          <s xml:space="preserve">deducimus ulterius, <lb />
<ptr xml:id="note-0098-03a" corresp="note-0098-03" type="noteAnchor" />
actionem potentiæ cujusvis poſſe reſolvi in actiones <lb />duarum aliarum potentiarum, &amp; </s>
          <s xml:space="preserve">illud quidem innumeris <lb />modis, propter innumera triangula, quæ formari poſſunt <lb />ſervato eodem latere. </s>
          <s xml:space="preserve">Eo poſſumus in omnibus Machinis <lb />reducere potentiam oblique agentem ad directam, &amp; </s>
          <s xml:space="preserve">pro-<lb />portionem inter directam &amp; </s>
          <s xml:space="preserve">obliquam determinare; </s>
          <s xml:space="preserve">quod <lb />exemplis ſequentibus, Experimentis confirmatis, patebit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0098-03" corresp="note-0098-03a" place="margin">229.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Vecti <hi rend="small caps">A</hi>B, cujus brachia ſunt æqualia, applicatur in B <lb />
<ptr xml:id="note-0098-04a" corresp="note-0098-04" type="noteAnchor" />
pondus P duarum librarum, &amp; </s>
          <s xml:space="preserve">in A potentia oblique agens <lb />
<ptr xml:id="note-0098-05a" corresp="note-0098-05" type="noteAnchor" />
per <hi rend="small caps">A</hi>D, &amp; </s>
          <s xml:space="preserve">quæ repræſentatur per pondus M. </s>
          <s xml:space="preserve">Concipia-<lb />tur linea DE vecti in ſitu horizontali parallela, &amp; </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>E ad il-<lb />lam &amp; </s>
          <s xml:space="preserve">vectem perpendicularis; </s>
          <s xml:space="preserve">nunc ſi <hi rend="small caps">A</hi>D ſit ad <hi rend="small caps">A</hi>E, ut <lb />duo ad tria, &amp; </s>
          <s xml:space="preserve">pondus M ſit trium librarum, datur æqui-<lb />librium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0098-04" corresp="note-0098-04a" place="margin">230.</note>
              <note xml:space="preserve" xml:id="note-0098-05" corresp="note-0098-05a" place="margin">TAB. IX. <lb />fig. 2. &amp; 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Directio motus puncti A ex motu vectis eſt vecti perpen-<lb />
<ptr xml:id="note-0098-06a" corresp="note-0098-06" type="noteAnchor" />
dicularis, tendit ergo juxta lineam <hi rend="small caps">Ea</hi> prolongatam; </s>
          <s xml:space="preserve">di-<lb />ſtantia BA cum maneat ſemper eadem, in fig. </s>
          <s xml:space="preserve">2 impeditur A ne <lb />magis accedat ad B, &amp; </s>
          <s xml:space="preserve">quaſi repellitur per directionem <lb />BA; </s>
          <s xml:space="preserve">in fig. </s>
          <s xml:space="preserve">3 receſſus puncti A à B cohibetur, &amp; </s>
          <s xml:space="preserve">ſic A qua-<lb />ſi trahitur B verſus. </s>
          <s xml:space="preserve">Ulterius punctum A pondere M trahitur <lb />D verſus: </s>
          <s xml:space="preserve">tribus ergo punctum hocce trahitur potentiis, qua-
</s>
          <pb facs="0099" n="53" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XV.</fw>
rum directiones ſunt parallelæ lateribus trianguli AED; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />quæ ergo, ut detur æquilibrium, ſunt inter ſe ut iſta latera.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0098-06" corresp="note-0098-06a" place="margin">231.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Punctum A, ob æqualitatem diſtantiarum punctorum A <lb />&amp; </s>
          <s xml:space="preserve">B a fulcro, juxta <hi rend="small caps">Ea</hi> continuatam, trahitur eadem vi <lb />qua pondus P deſcendit, id eſt, pondere duarum librarum; <lb /></s>
          <s xml:space="preserve">vis ergo per AD requiritur trium librarum, quia latera AD <lb />&amp; </s>
          <s xml:space="preserve">AE ſunt inter ſe ut tria ad duo. </s>
          <s xml:space="preserve">Latus DE exprimit <lb />quid fulcrum patiatur vi qua punctum A in fig. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">premitur <lb />B verſus, &amp; </s>
          <s xml:space="preserve">in fig. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">à B retrahitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Idem omnino dicendum de potentia obliqua axi in peri-<lb />trochio applicata.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Pondus P, trochleæ annexum, ſuſtinetur potentiis ab u-<lb />
<ptr xml:id="note-0099-01a" corresp="note-0099-01" type="noteAnchor" />
traque parte funi ductario applicatis, ſed oblique trahenti-<lb />
<ptr xml:id="note-0099-02a" corresp="note-0099-02" type="noteAnchor" />
bus per CA &amp; </s>
          <s xml:space="preserve">CB; </s>
          <s xml:space="preserve">hæ potentiæ ſunt æquales inter ſe, quia <lb />omnis funis trochleam circumdans non quieſcit, niſi ab u-<lb />traque parte æqualiter trahatur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ipſum pondus P eſt qua-
<ptr xml:id="note-0099-03a" corresp="note-0099-03" type="noteAnchor" />
ſi tertia potentia, &amp; </s>
          <s xml:space="preserve">ita punctum C tribus potentiis trahi-<lb />tur. </s>
          <s xml:space="preserve">Concipiatur linea CE ad horizontem perpendicularis, <lb />&amp; </s>
          <s xml:space="preserve">linea AE parallela lineæ CB: </s>
          <s xml:space="preserve">ſi CE ſit ad AE aut AC, <lb />(hæ enim duæ lineæ ſunt æquales, propter memoratam æ-<lb />qualitatem potentiarum trahentium per CB, CA <ptr type="noteAnchor" />,) ut
<ptr xml:id="note-0099-04a" corresp="note-0099-04" type="noteAnchor" />
ſex ad quinque, pondus P ſex librarum a ponderibus Q &amp; </s>
          <s xml:space="preserve"><lb />Q quinque librarum ſuſtinetur; </s>
          <s xml:space="preserve">cujus ratio patet ex n. </s>
          <s xml:space="preserve">220.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0099-01" corresp="note-0099-01a" place="margin">232.</note>
              <note xml:space="preserve" xml:id="note-0099-02" corresp="note-0099-02a" place="margin">TAB. IX. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0099-03" corresp="note-0099-03a" n="*" anchored="true" place="margin">124.</note>
              <note xml:space="preserve" xml:id="note-0099-04" corresp="note-0099-04a" n="*" anchored="true" place="margin">220.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si extremitas una funis ductarii annectatur clavo, unico <lb />pondere ut Q, pondus P ſuſtinetur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Si pondus P Trochleæ non conjungatur, ſed funibus <hi rend="small caps">Ca</hi> <lb />
<ptr xml:id="note-0099-05a" corresp="note-0099-05" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">CB, ei annexis, ſuſtineatur, poterit ſuſtineri poten-<lb />
<ptr xml:id="note-0099-06a" corresp="note-0099-06" type="noteAnchor" />
tiis duabus inæqualibus; </s>
          <s xml:space="preserve">formetur ut in Experimento præ-<lb />cedenti triangulum <hi rend="small caps">Ca</hi>E, &amp; </s>
          <s xml:space="preserve">ſit AE undecim, <hi rend="small caps">Ca</hi> duo-<lb />decim cum ſemiſſe, &amp; </s>
          <s xml:space="preserve">CE duodecim; </s>
          <s xml:space="preserve">dabitur æquilibri-<lb />um, ſi pondera Q &amp; </s>
          <s xml:space="preserve">Q ſint ad P ut primi numeri ad ulti-<lb />mum; </s>
          <s xml:space="preserve">cujus Experimenti ratio iterum patet ex n. </s>
          <s xml:space="preserve">220.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0099-05" corresp="note-0099-05a" place="margin">233.</note>
              <note xml:space="preserve" xml:id="note-0099-06" corresp="note-0099-06a" place="margin">TAB. IX. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hic in tranſitu obſervandum, ex datis inclinationibus fi-<lb />
<ptr xml:id="note-0099-07a" corresp="note-0099-07" type="noteAnchor" />
lorum <hi rend="small caps">Ca</hi> &amp; </s>
          <s xml:space="preserve">CB ad horizontem, proportionem ponderum
</s>
          <pb facs="0100" n="54" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
Q, Q ad pondus P, ex tabulis Trigonometriæ poſſe deter-<lb />minari. </s>
          <s xml:space="preserve">Si in triangulo <hi rend="small caps">A</hi>CE concipiatur linea <hi rend="small caps">A</hi>e, per <lb />punctum <hi rend="small caps">A</hi> ad horizontem parallela, &amp; </s>
          <s xml:space="preserve">illa habeatur pro <lb />radio circuli, <hi rend="small caps">Ca</hi> erit ſecans, &amp; </s>
          <s xml:space="preserve">eC tangens anguli, quem <lb />efficit <hi rend="small caps">Ca</hi> cum horizonte; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>E erit ſecans, &amp; </s>
          <s xml:space="preserve">eE tan-<lb />gens anguli inclinationis fili CB ad horizontem: </s>
          <s xml:space="preserve">unde pa-<lb />tet pondera Q, Q, proportionalia eſſe prædictis ſecantibus, <lb />&amp; </s>
          <s xml:space="preserve">pondus P proportionem ſequi ſummæ memoratarum tan-<lb />gentium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0099-07" corresp="note-0099-07a" place="margin">234.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Machina, qua hæc ultima Experimenta peraguntur, <lb />(cujus conſtructio ex ſola figura, ſi conferatur cum fig. </s>
          <s xml:space="preserve">4. <lb /></s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">V. </s>
          <s xml:space="preserve">abunde liquet) ducantur lineæ, juxta quas fila, <lb />quæ trochleas circumdant, extendi poſſint; </s>
          <s xml:space="preserve">in medio linea-<lb />rum adſcribantur numeri, deſignantes fecantes angulorum, <lb />quos illæ lineæ cum horizonte efficiunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">extremitatibus <lb />linearum adſcribantur tangentes horum angulorum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Nunc in omni caſu ubi datur æquilibrium, pondera Q &amp; </s>
          <s xml:space="preserve"><lb />Q ſunt ut numeri in medio linearum, juxta quas fila pro-<lb />tenſa ſunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pondus P ut ſumma numerorum extremita-<lb />tibus ambarum harum linearum adſcriptorum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vis qua corpus ſuper plano inclinato deſcendere cona-<lb />tur, per ea quæ de puncto, quod tribus potentiis trahitur, <lb />dicta ſunt, determinatur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Planum inclinatum vocatur, quod cum horizonte efficit <lb />
<ptr xml:id="note-0100-01a" corresp="note-0100-01" type="noteAnchor" />
angulum obliquum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0100-01" corresp="note-0100-01a" place="margin">235.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">CB repræſentat lineam horizonti parallelam, <hi rend="small caps">A</hi>B cum <lb />
<ptr xml:id="note-0100-02a" corresp="note-0100-02" type="noteAnchor" />
illa efficit angulum obliquum <hi rend="small caps">A</hi>BC, &amp; </s>
          <s xml:space="preserve">planum inclinatum re-<lb />præſentat. </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>b extremitate ſuperiori plani dimittitur per-<lb />pendicularis linea <hi rend="small caps">A</hi>C ad horizontem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0100-02" corresp="note-0100-02a" place="margin">TAB. X. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Longitudo AB vocatur Longitudo Plani.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">236.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3</head>
        <p>
          <s xml:space="preserve">Linea AC vocatur Altitudo Plani.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">237.</note>
        <p>
          <s xml:space="preserve">Corpus P plano <hi rend="small caps">A</hi>B impoſitum juxta directionem <hi rend="small caps">A</hi>B <lb />ſuper Plano conatur deſcendere; </s>
          <s xml:space="preserve">ponamus filo huic lineæ
</s>
          <pb facs="0101" n="55" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XV.</fw>
parallelo retineri ut quieſcat, plano ſuſtinetur, id eſt quaſi <lb />pellitur, juxta directionem dc plano perpendicularem, tan-<lb />dem gravitate verticaliter per ce conatur deſcendere. </s>
          <s xml:space="preserve">Cor-<lb />pus ergo P tribus quaſi trahitur potentiis, quarum directio-<lb />nes lateribus trianguli ced parallelæ ſunt, ſed corpus qui-<lb />eſcit, ſunt idcirco potentiæ inter ſe ut latera hujus triangu-<lb />
<ptr xml:id="note-0101-01a" corresp="note-0101-01" type="noteAnchor" />
li<ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ideo, vis qua corpus ſuper plano conatur deſcendere eſt
<ptr xml:id="note-0101-02a" corresp="note-0101-02" type="noteAnchor" />
ad vim qua verticaliter conatur deſcendere, pondus nempe <lb />corporis, ut de ad ce aut ut <hi rend="small caps">A</hi>C ad <hi rend="small caps">A</hi>B, id eſt, ut alti-<lb />tudo plani ad hujus longitudinem, ſunt enim ſimilia triangula <lb />rectangula cde, <hi rend="small caps">A</hi>BC, habentia angulos æquales ced, CAB <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0101-01" corresp="note-0101-01a" n="*" anchored="true" place="margin">210.</note>
              <note xml:space="preserve" xml:id="note-0101-02" corresp="note-0101-02a" place="margin">238.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">29. El. I.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi>,</head>
        <head rend="italics" xml:space="preserve">Qua plani inclinati affectiones exhibentur.</head>
        <p>
          <s xml:space="preserve">Planum NOQL in ſitu ponitur horizontali; </s>
          <s xml:space="preserve">Planum AB <lb />
<ptr xml:id="note-0101-04a" corresp="note-0101-04" type="noteAnchor" />
IH circa cardines volvitur, &amp; </s>
          <s xml:space="preserve">ad inclinationem quam-<lb />
<ptr xml:id="note-0101-05a" corresp="note-0101-05" type="noteAnchor" />
cunque conſtituitur, ope cochleæ V &amp; </s>
          <s xml:space="preserve">quadrantis circu-<lb />li t.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0101-04" corresp="note-0101-04a" place="margin">239.</note>
              <note xml:space="preserve" xml:id="note-0101-05" corresp="note-0101-05a" place="margin">TAB. X. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Regula lignea EF extremitati uni trochleam connexam <lb />habet G; </s>
          <s xml:space="preserve">circa alteram volvitur; </s>
          <s xml:space="preserve">caputque D, in quo mo-<lb />vetur, ubique in ſciſſura rs, cum plano NOQL connecti-<lb />tur, auxilio cochleæ infra planum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">M eſt cylindrus ligneus, cujus axis eſt chalybeus, &amp; </s>
          <s xml:space="preserve">cu-<lb />jus baſes cylindrum paululum excedunt; </s>
          <s xml:space="preserve">ita ut in revolu-<lb />tione ſuper plano <hi rend="small caps">A</hi>BIH baſes ſolæ planum tangant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Suſtinetur cylindrus filo tranſeunte ſuper trochlea G; </s>
          <s xml:space="preserve">quod <lb />filum annectitur regulæ tenui æneæ, ita inflexæ, ut per e-<lb />jus extremitates axis cylindri tranſeat, &amp; </s>
          <s xml:space="preserve">rotetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Experimentis ita diſponitur trochlea, inclinando re-<lb />gulam EF, &amp; </s>
          <s xml:space="preserve">movendo caput Dper ſciſſuram rs; </s>
          <s xml:space="preserve">ut fi-<lb />lum, quo cylindrus ſuſtinetur, ſit parallelum plano inclina-<lb />to <hi rend="small caps">A</hi>BIH.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Inclinetur utcumque planum <hi rend="small caps">A</hi>BIH, pondus corporis <lb />
<ptr xml:id="note-0101-06a" corresp="note-0101-06" type="noteAnchor" />
Meam habet rationem ad pondus P, quam longitudo plani <lb /><hi rend="small caps">A</hi>B ad illius altitudinem <hi rend="small caps">A</hi>C; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pondere P corpus M ſuſti-<lb />ne tur ſuper plano inclinato, ubicunque ponatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0101-06" corresp="note-0101-06a" place="margin">240.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0102" n="56" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Ut exactiſſimè experimenta inſtituantur, minora trian-<lb />gula rectangula chartacea, aut potius lignea, ſunt adhiben-<lb />da, &amp; </s>
          <s xml:space="preserve">ſuper his planum inclinandum; </s>
          <s xml:space="preserve">ut commode &amp; </s>
          <s xml:space="preserve">ex-<lb />acte longitudo plani cum altitudine conferatur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">In hoc Experimento eâdem ac in præcedenti utimur Ma-<lb />
<ptr xml:id="note-0102-01a" corresp="note-0102-01" type="noteAnchor" />
chinâ. </s>
          <s xml:space="preserve">Corpus M plano inclinato AB impoſitum, ſuſtinetur <lb />
<ptr xml:id="note-0102-02a" corresp="note-0102-02" type="noteAnchor" />
potentiâ trahente per MS; </s>
          <s xml:space="preserve">concipiantur linea MR, ad ho-<lb />rizontem perpendicularis, &amp; </s>
          <s xml:space="preserve">ASR ad plani ſuperficiem <lb />normalis: </s>
          <s xml:space="preserve">in omni caſu ubi pondus P eſt ad pondus corpo-<lb />ris M, ut MS ad <hi rend="small caps">Mr</hi>, corpus quieſcit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0102-01" corresp="note-0102-01a" place="margin">241.</note>
              <note xml:space="preserve" xml:id="note-0102-02" corresp="note-0102-02a" place="margin">TAB. IX. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondere ſuo corpus M trahitur juxta directionem RM, <lb />plano inclinato ſuſtinetur directione ad planum perpendicu-<lb />lari, &amp; </s>
          <s xml:space="preserve">Experimentum reducitur ad propoſitionem n. <lb /></s>
          <s xml:space="preserve">220.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Vectis <hi rend="small caps">A</hi>CB brachia ſunt æqualia, &amp; </s>
          <s xml:space="preserve">angulum formant, <lb />
<ptr xml:id="note-0102-03a" corresp="note-0102-03" type="noteAnchor" />
ita ut ſi <hi rend="small caps">A</hi>C continuetur verſus D, &amp; </s>
          <s xml:space="preserve">BD ad CD perpen-<lb />
<ptr xml:id="note-0102-04a" corresp="note-0102-04" type="noteAnchor" />
dicularis ducatur, DC ſit dimidia pars ipſius BC aut CA. <lb /></s>
          <s xml:space="preserve">Appenſo in <hi rend="small caps">A</hi> pondere p unius libræ, &amp; </s>
          <s xml:space="preserve">in B pondere P <lb />duarum librarum, poſitoque brachio <hi rend="small caps">Ca</hi> in ſitu horizonta-<lb />li, datur æquilibrium <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quia pondus Pagit quaſi in vecte
<ptr xml:id="note-0102-05a" corresp="note-0102-05" type="noteAnchor" />
recto in puncto D eſſet ſuſpenſum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0102-03" corresp="note-0102-03a" place="margin">242.</note>
              <note xml:space="preserve" xml:id="note-0102-04" corresp="note-0102-04a" place="margin">TAB. IX. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0102-05" corresp="note-0102-05a" n="*" anchored="true" place="margin">175.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">128.</note>
        <p>
          <s xml:space="preserve">Mutentur pondera, &amp; </s>
          <s xml:space="preserve">majus ſuſpendatur in A, minus <lb />
<ptr xml:id="note-0102-07a" corresp="note-0102-07" type="noteAnchor" />
vero imponatur brachio BC in B; </s>
          <s xml:space="preserve">ſi plano verticali illius ca-<lb />ſus impediatur, dabitur iterum æquilibrium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0102-07" corresp="note-0102-07a" place="margin">TAB. IX. <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Brachia vectis ſunt æqualia, &amp; </s>
          <s xml:space="preserve">æqualiter motu vectis mo-<lb />ventur: </s>
          <s xml:space="preserve">vi ergo ponderis P pondus p quaſi trahitur verſus <lb />E in directione ad brachium BC perpendiculari; </s>
          <s xml:space="preserve">Ex actio-<lb />ne plani verticalis premitur corpus illud horizontaliter; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />tandem vi gravitatis verticaliter pellitur. </s>
          <s xml:space="preserve">Tribus igitur po-<lb />tentiis trahitur pondus p, quæ ſunt inter ſe ut latera trian-<lb />guli <hi rend="small caps">BE</hi>D <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Vis ergo tendens terram verſus (pondus p)
<ptr xml:id="note-0102-08a" corresp="note-0102-08" type="noteAnchor" />
ſe habet ad vim trahentem E verſus (pondus P), ut BD ad BE, <lb />aut DC ad CB <ptr type="noteAnchor" />, ſeu <hi rend="small caps">Ca</hi>; </s>
          <s xml:space="preserve">id eſt, ut unum ad duo; </s>
          <s xml:space="preserve">quæ
<ptr xml:id="note-0102-09a" corresp="note-0102-09" type="noteAnchor" />
etiam eſt ratio inter pondera p &amp; </s>
          <s xml:space="preserve">P. </s>
          <s xml:space="preserve">Et hìc ergo ratio Ex-
</s>
          <pb facs="0103" />
          <s xml:space="preserve">
<ptr xml:id="fig-0103-01a" corresp="fig-0103-01" type="figureAnchor" />
</s>
          <pb facs="0103a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0103a-01a" corresp="fig-0103a-01" type="figureAnchor" />
</s>
          <pb facs="0104" />
          <s xml:space="preserve">
</s>
          <pb facs="0105" n="57" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XVI.</fw>
perimenti ex ſæpius memoraton. </s>
          <s xml:space="preserve">220. </s>
          <s xml:space="preserve">deducitur; </s>
          <s xml:space="preserve">ad quem <lb />omnes alii caſus potentiarum obliquarum, quæ excogitari <lb />poſſunt, etiam pertient.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0102-08" corresp="note-0102-08a" n="*" anchored="true" place="margin">220.</note>
              <note xml:space="preserve" xml:id="note-0102-09" corresp="note-0102-09a" n="*" anchored="true" place="margin">8. El. VI.</note>
              <figure xml:id="fig-0103-01" corresp="fig-0103-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-01" />
                <label>0103-01</label>
              </figure>
              <figure xml:id="fig-0103a-01" corresp="fig-0103a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103a-01" />
                <label>0103a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">LIBRI I. PARS III.</head>
        <head xml:space="preserve">De Motibus, Potentiarum actionibus, <lb />variatis.</head>
        <head xml:space="preserve">CAPUT XVI.</head>
        <head rend="italics" xml:space="preserve">De Naturæ legibus Newtonianis.</head>
        <p>
          <s xml:space="preserve">Preſſiones contrariis preſſionibus deſtructas, &amp; </s>
          <s xml:space="preserve">obſtacu-<lb />la immediatâ potentiæ actione translata, huc uſque <lb />conſideravimus. </s>
          <s xml:space="preserve">Nunc preſſiones in corpora ſibi per-<lb />miſſa &amp; </s>
          <s xml:space="preserve">in motu perſeverantia, agentes examinabimus; <lb /></s>
          <s xml:space="preserve">hìc ut in omnibus Phyſicis ex Phænomenis ratiocinandum eſt, <lb />&amp; </s>
          <s xml:space="preserve">ex iis naturæ leges deduci debent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tres a Newtono traduntur, quibus omnia, quæ ad mo-<lb />tum pertinent, explicari poſſe credimus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Lex</hi> I.</head>
        <p rend="italics">
          <s xml:space="preserve">Corpus omne perſeverat in ſtatu ſuo quieſcendi vel mo-<lb />
<ptr xml:id="note-0105-01a" corresp="note-0105-01" type="noteAnchor" />
vendi uniformiter in directum, niſi quatenus a viribus im-<lb />preſſis cogitur ſtatum illum mutare.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0105-01" corresp="note-0105-01a" place="margin">243.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Videmus Corpus ſuâ naturâ eſſe iners &amp; </s>
          <s xml:space="preserve">incapax ſeſe mo-<lb />vendi, unde niſi cauſâ extraneâ moveatur, in quiete ſem-<lb />per neceſſario manet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus etiam ſemel motum in motu ſecundum eandem <lb />rectam lineam eadem cum velocitate continuare quotidia-<lb />nis Experimentis pleniſhme conſtat; </s>
          <s xml:space="preserve">nullam enim unquam <lb />mutationem in motu fieri videmus niſi aliqua ex cauſa.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus vi inſitâ transfertur, &amp; </s>
          <s xml:space="preserve">vis hæc, ut ex lege hac <lb />
<ptr xml:id="note-0105-02a" corresp="note-0105-02" type="noteAnchor" />
ſequitur, non mutatur niſi actione cauſæ extraneæ,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0105-02" corresp="note-0105-02a" place="margin">244.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Lex</hi> II.</head>
        <p rend="italics">
          <s xml:space="preserve">Mutatio motus eſt ſemper proportionalis vi motrici impreſ-<lb />
<ptr xml:id="note-0105-03a" corresp="note-0105-03" type="noteAnchor" />
</s>
          <pb facs="0106" n="58" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſæ, &amp; </s>
          <s xml:space="preserve">fit ſemper ſecundum rectam lineam, qua vis illa im-<lb />primitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0105-03" corresp="note-0105-03a" place="margin">245.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando corpori moto alia ſuperadditur vis, ad illud mo-<lb />vendum in eadem directione, motus celerior fit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando nova impreſſio, motui corporis contraria eſt, <lb />retardatur motus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si obliquè agat nova impreſſio, viam ſuam mutat cor-<lb />pus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Et in genere omnes mutationes in motu fiunt ſecundum <lb />directiones &amp; </s>
          <s xml:space="preserve">pro magnitudinibus impreſſionum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit Corpus in A motum per AE celeritate, quam per <lb />
<ptr xml:id="note-0106-01a" corresp="note-0106-01" type="noteAnchor" />
hanc ipſam deſignamus lineam, agat in A impreſſio, juxta <lb />directionem <hi rend="small caps">A</hi>D, quæ corpori (ut diximus) agitato juxta <lb />hanc directionem communicat celeritatem <hi rend="small caps">A</hi>D. </s>
          <s xml:space="preserve">Corpus <lb />duobus nunc agitatur motibus, quibus lineæ <hi rend="small caps">A</hi>E &amp; </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>D eo-<lb />dem tempore percurruntur; </s>
          <s xml:space="preserve">hi duo motus ſeſe mutuo non <lb />turbant, ſed motu ex ambobus compoſito, ſecundum hanc <lb />legem, quæ ex Phænomenis fuit deducta, corpus fertur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0106-01" corresp="note-0106-01a" place="margin">TAB. X. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut motum hunc compoſitum determinemus, concipiamus <lb />lineam <hi rend="small caps">A</hi>D, dum in hac corpus movetur, motu parallelo <lb />moveri celeritate, qua corpus fertur per <hi rend="small caps">A</hi>E quam in hoc mo-<lb />tu punctum A percurrit. </s>
          <s xml:space="preserve">Translata jam ſit linea in ad, cor-<lb />pus erit in b, ita ut <hi rend="small caps">A</hi>E ſit ad <hi rend="small caps">A</hi>D, ut A a ad ab; </s>
          <s xml:space="preserve">quia &amp; </s>
          <s xml:space="preserve"><lb />motum lineæ, &amp; </s>
          <s xml:space="preserve">corporis, in hac æquabilem ponimus. </s>
          <s xml:space="preserve">Ab-<lb />ſoluto parallelogrammo <hi rend="small caps">A</hi><hi rend="small caps">DBe</hi>, &amp; </s>
          <s xml:space="preserve">ductâ diagonali <hi rend="small caps">A</hi>B, <lb />clare patet punctum b in hac diagonali dari,&amp; </s>
          <s xml:space="preserve">corpus dari <lb />in B, ubi linea <hi rend="small caps">A</hi>D motu ſuo pervenit ad <hi rend="small caps">E</hi>B: </s>
          <s xml:space="preserve">motu ergo <lb />
<ptr xml:id="note-0106-02a" corresp="note-0106-02" type="noteAnchor" />
compoſito corpus percurrit diagonalem parallelogrammi for-<lb />mati lineis, ſitu directiones, &amp; </s>
          <s xml:space="preserve">longitudinibus celeritates mo-<lb />tuum deſignantibus; </s>
          <s xml:space="preserve">diagonalis autem celeritatem motus com-<lb />poſiti exprimit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0106-02" corresp="note-0106-02a" place="margin">246.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſequentibus videbimus &amp; </s>
          <s xml:space="preserve">legem reſpectu vis inſitæ lo-<lb />cum habere, id eſt, vim inſitam corpori, per diagonalem <lb />AB moto, æqualem eſſe viribus primæ per <hi rend="small caps">A</hi>E, &amp; </s>
          <s xml:space="preserve">ſecun-<lb />dæ quæ corpori juxta <hi rend="small caps">A</hi>D communicatur. </s>
          <s xml:space="preserve">Si nempe vis <lb />ſecunda non pro parte cum prima contrarie agat, quod
</s>
          <pb facs="0107" n="59" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIS. I. CAP. XVI.</fw>
obtinet, quando Angulus <hi rend="small caps">Ea</hi>D eſt obtuſus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Lex</hi> III.</head>
        <p rend="italics">
          <s xml:space="preserve">Actioni contraria ſemper &amp; </s>
          <s xml:space="preserve">æqualis eſt reactio; </s>
          <s xml:space="preserve">ſive cor-<lb />
<ptr xml:id="note-0107-01a" corresp="note-0107-01" type="noteAnchor" />
porum duorum actiones in ſe mutuo ſemper ſunt æquales, &amp; </s>
          <s xml:space="preserve"><lb />in partes contrarias diriguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0107-01" corresp="note-0107-01a" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quomodocunque corpus in aliud agat, ipſum reactionem <lb />æqualem &amp; </s>
          <s xml:space="preserve">contrariam pati ſemper videmus. </s>
          <s xml:space="preserve">Digito lapi-<lb />dem premo, premitur æqualiter digitus a lapide. </s>
          <s xml:space="preserve">Currume-<lb />quus protrahit, à curru æqualiter retrotrahitur; </s>
          <s xml:space="preserve">lora enim <lb />æqualiter verſus utramque partem diſtenduntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus in aliud impingitur, quæcumque ſit impreſſio, <lb />utrumque æqualem patitur; </s>
          <s xml:space="preserve">impreſſiones vero contrariæ ſunt: <lb /></s>
          <s xml:space="preserve">illud pleniſſime confirmatur Experimentis circa colliſio-<lb />nes corporum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Magnes ferrum ad ſe trahit, trahitur æqualiter a ferro.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>.</head>
        <p>
          <s xml:space="preserve">Suſpenditur magnes M, ita ut facillime moveri poſſit, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0107-02a" corresp="note-0107-02" type="noteAnchor" />
ferro admoto ad certam diſtantiam, accedit magnes ad fer-<lb />
<ptr xml:id="note-0107-03a" corresp="note-0107-03" type="noteAnchor" />
rum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hoc retrahendo, antequam magnes ad hoc perve-<lb />nerit, magnes ferrum ſequitur; </s>
          <s xml:space="preserve">eodem omnino modo, ac <lb />ferrum ad magnetem accedit, &amp; </s>
          <s xml:space="preserve">hunc ſequitur, quando il-<lb />lud ſuſpenditur, &amp; </s>
          <s xml:space="preserve">magnes admovetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0107-02" corresp="note-0107-02a" place="margin">248.</note>
              <note xml:space="preserve" xml:id="note-0107-03" corresp="note-0107-03a" place="margin">TAB. X. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sedet quis in cymba, cymbam aliam æqualem, &amp; </s>
          <s xml:space="preserve">æqua-<lb />liter onuſtam, fune trahit; </s>
          <s xml:space="preserve">ambæ cymbæ æqualiter moven-<lb />tur, &amp; </s>
          <s xml:space="preserve">in medio diſtantiæ primæ concurrunt: </s>
          <s xml:space="preserve">ſi una cym-<lb />ba altera ſit major, aut magis onuſta, pro diverſis quanti-<lb />tatibus materiæ in ſingulis celeritates erunt diverſæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Et hæc eadem lex generaliter in omnibus corporum a-<lb />ctionibus in alia copora locum habet.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVII.</head>
        <head rend="italics" xml:space="preserve">De Acceleratione &amp; Retardatione Gravium.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">MOtus acceleratus, eſt cujus celeritas omnibus momentis <lb />
<ptr xml:id="note-0107-04a" corresp="note-0107-04" type="noteAnchor" />
major fit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0107-04" corresp="note-0107-04a" place="margin">249.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0108" n="60" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Motus retardatus, eſt cujus celeritas omnibus momentis mi-<lb />
<ptr xml:id="note-0108-01a" corresp="note-0108-01" type="noteAnchor" />
nuitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0108-01" corresp="note-0108-01a" place="margin">250.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis gravitatis in omnia corpora pro quantitate materiæ <lb />continuo agit <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">quæcunque fuerint, gravitate eodem
<ptr xml:id="note-0108-02a" corresp="note-0108-02" type="noteAnchor" />
modo moventur. </s>
          <s xml:space="preserve">Quando corpus liberè cadit, impreſſio <lb />primi momenti in ſecundo momento non deſtruitur; </s>
          <s xml:space="preserve">ergo ei <lb />ſuperadditur impreſſio ſecundi momenti, &amp; </s>
          <s xml:space="preserve">ſic de cæteris; <lb /></s>
          <s xml:space="preserve">motus igitur corporis libere cadentis eſt acceleratus, &amp; </s>
          <s xml:space="preserve">ex <lb />
<ptr xml:id="note-0108-03a" corresp="note-0108-03" type="noteAnchor" />
Phænomenis conſtat motum æquabiliter in temporibus æ-<lb />qualibus accelerari; </s>
          <s xml:space="preserve">quod deduci poteſt ex Exp. </s>
          <s xml:space="preserve">n. </s>
          <s xml:space="preserve">277.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0108-02" corresp="note-0108-02a" n="*" anchored="true" place="margin">124.</note>
              <note xml:space="preserve" xml:id="note-0108-03" corresp="note-0108-03a" place="margin">251.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde ſequitur gravitatem eodem modo agere in corpus mo-<lb />
<ptr xml:id="note-0108-04a" corresp="note-0108-04" type="noteAnchor" />
tum ac in corpus quieſcens; </s>
          <s xml:space="preserve">ideò celeritates æquales, in mo-<lb />mentis æqualibus, corpori communicat. </s>
          <s xml:space="preserve">Unde celeritas, <lb />
<ptr xml:id="note-0108-05a" corresp="note-0108-05" type="noteAnchor" />
inter cadendum acquiſita, eſt ut tempus, in quo corpus ce-<lb />cidit. </s>
          <s xml:space="preserve">Velocitas ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">in certo tempore acquiſita erit du-<lb />pla, ſi tempus fuerit duplum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tripla, ſi tempus triplum, <lb />&amp; </s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0108-04" corresp="note-0108-04a" place="margin">252.</note>
              <note xml:space="preserve" xml:id="note-0108-05" corresp="note-0108-05a" place="margin">253.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Deſignetur tempus per lineam AB, &amp; </s>
          <s xml:space="preserve">initium temporis ſit <lb />
<ptr xml:id="note-0108-06a" corresp="note-0108-06" type="noteAnchor" />
A. </s>
          <s xml:space="preserve">In triangulo ABE, lineæ 1f, 2g, 3h, quæ parallelæ ad <lb />
<ptr xml:id="note-0108-07a" corresp="note-0108-07" type="noteAnchor" />
baſin, per puncta 1,2,3, ducuntur, ſunt inter ſe ut illarum <lb />diſtantiæ ab A, A1, A2, A3; </s>
          <s xml:space="preserve">id eſt, ut tempora quæ per illas di-<lb />ſtantias deſignantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">velocitates corporis libere cadentis <lb />poſt illa tempora denotant. </s>
          <s xml:space="preserve">Si pro lineis Mathematicis aliæ <lb />adhibeantur cum minima latitudine, unicuique æquali, non <lb />eo mutatur proportio; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hæ minimæ ſuperficies æque præ-<lb />dictas velocitates denotant. </s>
          <s xml:space="preserve">In tempore minimo velocitas <lb />pro æquabili haberi poteſt, &amp; </s>
          <s xml:space="preserve">ideo ſpatium in eo tempore <lb />percurſum velocitati proportionale eſt <ptr type="noteAnchor" />, eædemque minimæ
<ptr xml:id="note-0108-08a" corresp="note-0108-08" type="noteAnchor" />
ſuperficies ſpatia minimis, ſed æqualibus, temporibus percur-<lb />ſa deſignare poterunt: </s>
          <s xml:space="preserve">Idcirco in unaquaque minima ſuperfi-<lb />cie memorata, ſi latitudo ſuperficiei pro tempore habeatur, <lb />ſuperficies ipſa ſpatium percurſum deſignabit. </s>
          <s xml:space="preserve">Totum tem-<lb />pus AB conſtat ex talibus temporibus minimis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">area tri-<lb />anguli <hi rend="small caps">A</hi>BE formatur ex ſumma omnium ſuperficierum mi-<lb />nimarum hiſce temporibus minimis reſpondentium: </s>
          <s xml:space="preserve">area er-
</s>
          <pb facs="0109" n="61" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XVII.</fw>
go hæc ſpatium tempore <hi rend="small caps">A</hi>B percurſum deſignat. </s>
          <s xml:space="preserve">Eodem <lb />modo area trianguli A1 f repræſentat ſpatium tempore A1. <lb /></s>
          <s xml:space="preserve">percurſum; </s>
          <s xml:space="preserve">triangula hæc ſunt ſimilia, &amp; </s>
          <s xml:space="preserve">areæ illorum ſunt <lb />inter ſe ut quadrata laterum <hi rend="small caps">A</hi>B, A1.</s>
          <s xml:space="preserve">, id eſt, ſpatia ab i-<lb />
<ptr xml:id="note-0109-01a" corresp="note-0109-01" type="noteAnchor" />
nitio caſus percurſa ſunt inter ſe, ut quadrata temporum <lb />per quæ corpus cecidit; </s>
          <s xml:space="preserve">aut ut quadrata velocitatum inter <lb />cadendum acquiſitarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0108-06" corresp="note-0108-06a" place="margin">254.</note>
              <note xml:space="preserve" xml:id="note-0108-07" corresp="note-0108-07a" place="margin">TAB. X. <lb />fig. 8.</note>
              <note xml:space="preserve" xml:id="note-0108-08" corresp="note-0108-08a" n="*" anchored="true" place="margin">94.</note>
              <note xml:space="preserve" xml:id="note-0109-01" corresp="note-0109-01a" place="margin">255.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diviſo tempore <hi rend="small caps">A</hi>B in partes æquales, A1, 12, 23, <lb />
<ptr xml:id="note-0109-02a" corresp="note-0109-02" type="noteAnchor" />
3B; </s>
          <s xml:space="preserve">ducantur per diviſiones lineæ ad baſin parallelæ ſpa-<lb />tia percurſa in illis partibus, id eſt, in primo, ſecundo, <lb />tertio, &amp; </s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">momento, poſitis momentis æqualibus, ſunt in-<lb />ter ſe ut areæ A1f, 1fg2, 2gh3, 3hEB; </s>
          <s xml:space="preserve">quæ areæ ut <lb />ex inſpectione figuræ patet, ſunt inter ſe ut numeri impares <lb />1. </s>
          <s xml:space="preserve">3, 5. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">9.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0109-02" corresp="note-0109-02a" place="margin">256.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpus, poſtquam cecidit per tempus <hi rend="small caps">A</hi>B, non ulte-<lb />rius acceleretur, ſed celeritate BE, eo caſu acquiſita, u-<lb />niformiter motum continuet, per tempus BC, æquale tem-<lb />pori caſus ſpatium eo motu percurſum deſignatur per aream <lb />BEDC, duplam areæ trianguli ABE; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò</s>
        </p>
        <p rend="italics">
          <s xml:space="preserve">Corpus ab altitudine quacunque libere cadens, eacum celeri-<lb />
<ptr xml:id="note-0109-03a" corresp="note-0109-03" type="noteAnchor" />
tate, quam cadendo acquiſivit in tempore æqualitempori caſus, <lb />motu æquabili, ſpatium duplum prædictæ altitudinis percurret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0109-03" corresp="note-0109-03a" place="margin">257.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quæ propoſitio in ſequentibus etiam Experimento con-<lb />firmatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Motus corporis in altum projecti eodem modo retardatur, <lb />quo corporis cadentis motus acceleratur, ut ſequitur ex lege <lb />
<ptr xml:id="note-0109-04a" corresp="note-0109-04" type="noteAnchor" />
2 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in hoc caſu vis gravitatis cum motu acquiſito conſpi-
rat, in illo contrarie agit; </s>
          <s xml:space="preserve">cum vero vis gravitatis omnibus <lb />momentis æqualibus, æquales corpori celeritates commu-<lb />
<ptr xml:id="note-0109-05a" corresp="note-0109-05" type="noteAnchor" />
nicet <ptr type="noteAnchor" />, celeritas corporis projecti in altum, æqualibus tempo-
<ptr xml:id="note-0109-06a" corresp="note-0109-06" type="noteAnchor" />
ribus, æqualiter minuitur, aut retardatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0109-04" corresp="note-0109-04a" n="*" anchored="true" place="margin">245.</note>
              <note xml:space="preserve" xml:id="note-0109-05" corresp="note-0109-05a" n="*" anchored="true" place="margin">251.</note>
              <note xml:space="preserve" xml:id="note-0109-06" corresp="note-0109-06a" place="margin">258.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis eadem gravitatis generat motum in corpore cadente, <lb />&amp; </s>
          <s xml:space="preserve">deſtruit in corpore adſcendente, agitque ſemper in corpus <lb />motum ut in corpus quieſcens<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">æqualibus ergo temporibus
<ptr xml:id="note-0109-07a" corresp="note-0109-07" type="noteAnchor" />
celeritates eædem generantur, &amp; </s>
          <s xml:space="preserve">deſtr uuntur. </s>
          <s xml:space="preserve">Corpus in <lb />
<ptr xml:id="note-0109-08a" corresp="note-0109-08" type="noteAnchor" />
altum projectum adſcendit, donec totum motum amiſerit;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0110" n="62" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ideo adſcendit per tempus, in quo corpus cadendo poteſt ac-<lb />quirere velocitatem, æqualem velocitati cum qua in altum <lb />projicitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0109-07" corresp="note-0109-07a" n="*" anchored="true" place="margin">252.</note>
              <note xml:space="preserve" xml:id="note-0109-08" corresp="note-0109-08a" place="margin">259.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si <hi rend="small caps">Ba</hi> repræſentet tempus, in quo corpus adſcendit, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0110-01a" corresp="note-0110-01" type="noteAnchor" />
BE celeritatem, cum qua in altum projicitur; </s>
          <s xml:space="preserve">adſcenſus <lb />ceſſat, ubi celeritas corporis nulla eſt, ideo lineæ paralle-<lb />læ ad baſin in triangulo <hi rend="small caps">A</hi>BE repræſentant celeritates in <lb />momentis temporis, quibus reſpondent <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">area triangu-
<ptr xml:id="note-0110-02a" corresp="note-0110-02" type="noteAnchor" />
li <hi rend="small caps">A</hi>BE ſpatium adſcendendo percurſum deſignat, ut ex de-<lb />monſtratione, circa corpora cadentia data <ptr type="noteAnchor" /> poteſt deduci.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0110-03a" corresp="note-0110-03" type="noteAnchor" />
Cum autem BE ſit velocitas, quam corpus cadendo per <lb />tempus <hi rend="small caps">A</hi>B poteſtacquirere<ptr type="noteAnchor" />, triangulum hoc <hi rend="small caps">A</hi>BE idem eſt,
<ptr xml:id="note-0110-04a" corresp="note-0110-04" type="noteAnchor" />
quod ſpatium cadendo percurſum repræſentat, dum cor-<lb />pus inter cadendum hanc ipſam celeritatem BE acquirit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0110-05a" corresp="note-0110-05" type="noteAnchor" />
Unde ſequitur, corpus in altum projectum adſcendere ad <lb />
<ptr xml:id="note-0110-06a" corresp="note-0110-06" type="noteAnchor" />
eandem altitudinem, à qua cadendo poteſt acquirere veloci-<lb />tatem, cum qua projicitur. </s>
          <s xml:space="preserve">Et altitudines, ad quas corpo-<lb />
<ptr xml:id="note-0110-07a" corresp="note-0110-07" type="noteAnchor" />
ra cum diverſis velocitatibus projecta poſſunt adſcendere, eſſe <lb />inter ſe ut quadrata illarum velocitatum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0110-08a" corresp="note-0110-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0110-01" corresp="note-0110-01a" place="margin">260.</note>
              <note xml:space="preserve" xml:id="note-0110-02" corresp="note-0110-02a" n="*" anchored="true" place="margin">258.</note>
              <note xml:space="preserve" xml:id="note-0110-03" corresp="note-0110-03a" n="*" anchored="true" place="margin">254.</note>
              <note xml:space="preserve" xml:id="note-0110-04" corresp="note-0110-04a" n="*" anchored="true" place="margin">259.</note>
              <note xml:space="preserve" xml:id="note-0110-05" corresp="note-0110-05a" n="*" anchored="true" place="margin">254.</note>
              <note xml:space="preserve" xml:id="note-0110-06" corresp="note-0110-06a" place="margin">261.</note>
              <note xml:space="preserve" xml:id="note-0110-07" corresp="note-0110-07a" place="margin">262.</note>
              <note xml:space="preserve" xml:id="note-0110-08" corresp="note-0110-08a" n="*" anchored="true" place="margin">255.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVIII.</head>
        <head rend="italics" xml:space="preserve">De deſcenſu Gravium ſuper plano inclinato.</head>
        <p>
          <s xml:space="preserve">Vis, qua corpus ſuper plano inclinato deſcendere cona-<lb />tur, ex gravitate oritur, &amp; </s>
          <s xml:space="preserve">ejuſdem eſt naturæ cum <lb />gravitate; </s>
          <s xml:space="preserve">ideo vis illa, omnibus momentis, &amp; </s>
          <s xml:space="preserve">in omnibus <lb />plani partibus, æqualis eſt <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">agit in corpus motum eo-
<ptr xml:id="note-0110-09a" corresp="note-0110-09" type="noteAnchor" />
dem modo ac in corpus quieſcens <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">eâdem de cauſa motus
<ptr xml:id="note-0110-10a" corresp="note-0110-10" type="noteAnchor" />
corporis, ſuper plano libere devolventis, ejuſdem eſt natur <lb />
<ptr xml:id="note-0110-11a" corresp="note-0110-11" type="noteAnchor" />
cum motu corporis libere cadentis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quæ de hoc dicta <lb />ſunt, de illo etiam affirmari poſſunt. </s>
          <s xml:space="preserve">Eſt igitur motus æ-<lb />quabiliter acceleratus in temporibus æqualibus <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">propo-
<ptr xml:id="note-0110-12a" corresp="note-0110-12" type="noteAnchor" />
ſitiones num. </s>
          <s xml:space="preserve">252. </s>
          <s xml:space="preserve">253, 255. </s>
          <s xml:space="preserve">256. </s>
          <s xml:space="preserve">257. </s>
          <s xml:space="preserve">258. </s>
          <s xml:space="preserve">259. </s>
          <s xml:space="preserve">261. </s>
          <s xml:space="preserve">262. </s>
          <s xml:space="preserve">ſi <lb />
<ptr xml:id="note-0110-13a" corresp="note-0110-13" type="noteAnchor" />
pro deſcenſu, &amp; </s>
          <s xml:space="preserve">adſcenſu directo, motus ſuper plano in-<lb />clinato ponatur, hìc etiam locum habent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0110-09" corresp="note-0110-09a" n="*" anchored="true" place="margin">116.</note>
              <note xml:space="preserve" xml:id="note-0110-10" corresp="note-0110-10a" n="*" anchored="true" place="margin">252.</note>
              <note xml:space="preserve" xml:id="note-0110-11" corresp="note-0110-11a" place="margin">263.</note>
              <note xml:space="preserve" xml:id="note-0110-12" corresp="note-0110-12a" n="*" anchored="true" place="margin">251.</note>
              <note xml:space="preserve" xml:id="note-0110-13" corresp="note-0110-13a" place="margin">264.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Celeritates, quibus corpora duo deſcendunt, quorum u-<lb />
<ptr xml:id="note-0110-14a" corresp="note-0110-14" type="noteAnchor" />
num libere cadit, &amp; </s>
          <s xml:space="preserve">alterum ſuper plano inclinato devolvi-
</s>
          <pb facs="0111" n="63" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XVIII.</fw>
tur, ſi eodem tempore cadere incipiant, ſunt ſemper in ea-<lb />dem ratione quam in principio caſus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo ſpatia eodem
<ptr xml:id="note-0111-01a" corresp="note-0111-01" type="noteAnchor" />
tempore percurrunt, quæ ſunt in ratione longitudinis plani <lb />ad illius altitudinem. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0111-02a" corresp="note-0111-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0110-14" corresp="note-0110-14a" place="margin">265.</note>
              <note xml:space="preserve" xml:id="note-0111-01" corresp="note-0111-01a" n="*" anchored="true" place="margin">251. 263.</note>
              <note xml:space="preserve" xml:id="note-0111-02" corresp="note-0111-02a" n="*" anchored="true" place="margin">237.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In plano <hi rend="small caps">A</hi>B ſpatium a corpore percurſum, dum aliud li-<lb />
<ptr xml:id="note-0111-03a" corresp="note-0111-03" type="noteAnchor" />
bere cadit per altitudinem plani <hi rend="small caps">A</hi>C, determinatur, du-<lb />
<ptr xml:id="note-0111-04a" corresp="note-0111-04" type="noteAnchor" />
cendo ad <hi rend="small caps">A</hi>B perpendicularem CG: </s>
          <s xml:space="preserve">tunc enim longitudo <lb />plani <hi rend="small caps">A</hi>B eſt ad illius altitudinem <hi rend="small caps">A</hi>C, ut <hi rend="small caps">A</hi>C ad <hi rend="small caps">A</hi>G<ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si
<ptr xml:id="note-0111-05a" corresp="note-0111-05" type="noteAnchor" />
circulus deſcribatur diametro <hi rend="small caps">A</hi>C, punctum G erit in pe-<lb />ripheria circuli; </s>
          <s xml:space="preserve">quia angulus in ſemicirculo, ut <hi rend="small caps">A</hi>GC, <lb />ſemper eſt rectus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideo punctum ut G, pro plano ut-
<ptr xml:id="note-0111-06a" corresp="note-0111-06" type="noteAnchor" />
cunque inclinato, ſemper eſt in eadem illa peripheria: </s>
          <s xml:space="preserve">un-<lb />de ſequitur, chordas omnes, ut <hi rend="small caps">A</hi>G eſſe inter ſe ut vires, <lb />quibus corpora ſuper his deſcendere conantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">has per-<lb />curri a corporibus devolventibus, in tempore in quo cor-<lb />pus, libere cadendo, poteſt percurrere diametrum <hi rend="small caps">A</hi>C; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita tempora devolutionum per illas chordasſunt æqualia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0111-03" corresp="note-0111-03a" place="margin">266.</note>
              <note xml:space="preserve" xml:id="note-0111-04" corresp="note-0111-04a" place="margin">TAB. X. <lb />fig. 9.</note>
              <note xml:space="preserve" xml:id="note-0111-05" corresp="note-0111-05a" n="*" anchored="true" place="margin">8 El. VI.</note>
              <note xml:space="preserve" xml:id="note-0111-06" corresp="note-0111-06a" n="*" anchored="true" place="margin">31 El. III.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Per punctum C nulla poteſt duci chorda ut HC, quin de-<lb />tur per <hi rend="small caps">A</hi> chorda ut <hi rend="small caps">A</hi>G ei parallela, id eſt, æqualiter in-<lb />clinata, &amp; </s>
          <s xml:space="preserve">æqualis; </s>
          <s xml:space="preserve">igitur in ſemicirculo, ut <hi rend="small caps">A</hi>HC, Vires <lb />
<ptr xml:id="note-0111-07a" corresp="note-0111-07" type="noteAnchor" />
quibus corpora juxta chordas, in puncto infimo terminatas <lb />deſcendere conantur, ſunt inter ſe ut hæ chordæ &amp; </s>
          <s xml:space="preserve">quando <lb />
<ptr xml:id="note-0111-08a" corresp="note-0111-08" type="noteAnchor" />
corpus ſibi permittitur eodem tempore, ad punctum infimum <lb />ſemicirculi perveniet, ſive libere cadat juxta diametrum, <lb />ſive deſcendat ſuper chorda HC quacunque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0111-07" corresp="note-0111-07a" place="margin">267.</note>
              <note xml:space="preserve" xml:id="note-0111-08" corresp="note-0111-08a" place="margin">268.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tempus devolutionis per totum planum <hi rend="small caps">A</hi>B poteſt confer-<lb />
<ptr xml:id="note-0111-09a" corresp="note-0111-09" type="noteAnchor" />
ri cum tempore deſcenſus per plani altitudinem <hi rend="small caps">A</hi>C; </s>
          <s xml:space="preserve">nam <lb />hocce tempus eſt æquale tempori devolutionis per <hi rend="small caps">A</hi>G; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />quadrata temporum ſunt inter ſe ut <hi rend="small caps">A</hi>B ad <hi rend="small caps">A</hi>G <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſed
<ptr xml:id="note-0111-10a" corresp="note-0111-10" type="noteAnchor" />
<hi rend="small caps">A</hi>B eſt ad <hi rend="small caps">A</hi>C ut <hi rend="small caps">A</hi>C ad <hi rend="small caps">A</hi>G: </s>
          <s xml:space="preserve">quadrata igitur linearum <hi rend="small caps">A</hi>B &amp; </s>
          <s xml:space="preserve"><lb /><hi rend="small caps">A</hi>C ſunt inter ſe, ut <hi rend="small caps">A</hi>B ad <hi rend="small caps">A</hi>G; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideo iſtæ lineæ <hi rend="small caps">A</hi>B <lb />&amp; </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>C ſunt inter ſe, ut tempora deſcenſus per <hi rend="small caps">A</hi>B, &amp; </s>
          <s xml:space="preserve"><lb /><hi rend="small caps">A</hi>G, aut <hi rend="small caps">A</hi>C, id eſt, tempora, in eo caſu, ſunt ut ſpa-<lb />tia percurſa.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0111-09" corresp="note-0111-09a" place="margin">269.</note>
              <note xml:space="preserve" xml:id="note-0111-10" corresp="note-0111-10a" n="*" anchored="true" place="margin">264 255.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In eodem caſu velocitates in fine deſcenſus ſunt æquales; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0111-11a" corresp="note-0111-11" type="noteAnchor" />
nam poſt tempora æqualia, quando corpora ſunt in G &amp; </s>
          <s xml:space="preserve">C,
</s>
          <pb facs="0112" n="64" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
velocitates ſunt in eadem ratione quam in principio caſus <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0112-01a" corresp="note-0112-01" type="noteAnchor" />
id eſt, ut AC ad <hi rend="small caps">A</hi>B <ptr type="noteAnchor" /> Quando corpus deſcendit a G ad B,
<ptr xml:id="note-0112-02a" corresp="note-0112-02" type="noteAnchor" />
creſcit velocitas ut tempus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">velocitas in G eſt ad velo-
<ptr xml:id="note-0112-03a" corresp="note-0112-03" type="noteAnchor" />
citatem in B, ut <hi rend="small caps">A</hi>C ad <hi rend="small caps">A</hi>B <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">velocitates ergo in B &amp; </s>
          <s xml:space="preserve">C
<ptr xml:id="note-0112-04a" corresp="note-0112-04" type="noteAnchor" />
eandem rationem habent ad velocitatem in G, &amp; </s>
          <s xml:space="preserve">ſunt æ-<lb />quales. </s>
          <s xml:space="preserve">Ex hiſce deducimus corpus eandem acquirere ve-<lb />
<ptr xml:id="note-0112-05a" corresp="note-0112-05" type="noteAnchor" />
locitatem, cadendo a certa altitudine, ſive directe cadat, <lb />ſive per planum inclinatum devolvatur. </s>
          <s xml:space="preserve">Et, cum angulus <lb />inclinationis nullam adferat mutationem, poteſt corpus de-<lb />volvi per plurima plana varie inclinata, &amp; </s>
          <s xml:space="preserve">etiam per cur-<lb />vam, (quæ ut ex innumeris planis diverſe inclinatis concinna-<lb />ta conſiderari poteſt) &amp; </s>
          <s xml:space="preserve">celeritas ſemper erit eadem, quando al-<lb />titudo eſt æqualis. </s>
          <s xml:space="preserve">Non enim intereſt, utrum Corpus de-<lb />
<ptr xml:id="note-0112-06a" corresp="note-0112-06" type="noteAnchor" />
ſcendat per <hi rend="small caps">A</hi>B an per <hi rend="small caps">Eb</hi>, in Beadem erit celeritas &amp; </s>
          <s xml:space="preserve">eo-<lb />dem modo corpus movebitur per BC; </s>
          <s xml:space="preserve">ideoque habebit in <lb />C velocitatem, quam devolvendo per <hi rend="small caps">Ec</hi> potuiſſet acqui-<lb />rere, &amp; </s>
          <s xml:space="preserve">in D velocitatem, quam cadendo per GD habuiſ-<lb />ſet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0111-11" corresp="note-0111-11a" place="margin">270.</note>
              <note xml:space="preserve" xml:id="note-0112-01" corresp="note-0112-01a" n="*" anchored="true" place="margin">251. 263.</note>
              <note xml:space="preserve" xml:id="note-0112-02" corresp="note-0112-02a" n="*" anchored="true" place="margin">237.</note>
              <note xml:space="preserve" xml:id="note-0112-03" corresp="note-0112-03a" n="*" anchored="true" place="margin">263.</note>
              <note xml:space="preserve" xml:id="note-0112-04" corresp="note-0112-04a" n="*" anchored="true" place="margin">269.</note>
              <note xml:space="preserve" xml:id="note-0112-05" corresp="note-0112-05a" place="margin">271</note>
              <note xml:space="preserve" xml:id="note-0112-06" corresp="note-0112-06a" place="margin">TAB. X. <lb />fig. 10.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">In hoc Experimento notandum, corpus filo ſuſpenſum, <lb />
<ptr xml:id="note-0112-07a" corresp="note-0112-07" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">cadendo curvam deſcribens, eodem modo cadere ac ſi <lb />eandem curvam, in plano excavatam, ſine attritu percur-<lb />reret. </s>
          <s xml:space="preserve">Corpus filo ſuſpenſum cadat ab altitudine <hi rend="small caps">A</hi>C, <lb />
<ptr xml:id="note-0112-08a" corresp="note-0112-08" type="noteAnchor" />
per curvam DC, &amp; </s>
          <s xml:space="preserve">per curvam EC, &amp; </s>
          <s xml:space="preserve">per curvam FGHC <lb />ex portionibus variorum circulorum formatam, &amp; </s>
          <s xml:space="preserve">in <lb />omni caſu, ad eandem altitudinem eandem percurrens curvam <lb />adſcendet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0112-07" corresp="note-0112-07a" place="margin">272</note>
              <note xml:space="preserve" xml:id="note-0112-08" corresp="note-0112-08a" place="margin">TAB. XI. <lb />fig 1.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Corpus ea cum celeritate, quam cadendo per ſuperficiem <lb />
<ptr xml:id="note-0112-09a" corresp="note-0112-09" type="noteAnchor" />
quamcunque, ſive planam, ſive curvam, acquiſivit, per a-<lb />liam ſuperficiem ſimilem ad eandem altitudinem, eodem tem-<lb />pore, adſcendere poteſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0112-10a" corresp="note-0112-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0112-09" corresp="note-0112-09a" place="margin">273.</note>
              <note xml:space="preserve" xml:id="note-0112-10" corresp="note-0112-10a" n="*" anchored="true" place="margin">259. 264. 271.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Corpus ea cum celeritate, quam cadendo a certa altitudi-<lb />
<ptr xml:id="note-0112-11a" corresp="note-0112-11" type="noteAnchor" />
ne acquiſivit, ad eandem altitudinem per curvam quamcun-<lb />que adſcendere poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0112-11" corresp="note-0112-11a" place="margin">274.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Corpus P filo ſuſpenſum cadat ab altitudine <hi rend="small caps">A</hi>C, per <lb />
<ptr xml:id="note-0112-12a" corresp="note-0112-12" type="noteAnchor" />
</s>
          <pb facs="0113" />
          <s xml:space="preserve">
<ptr xml:id="fig-0113-01a" corresp="fig-0113-01" type="figureAnchor" />
<pb facs="0113a" />
<ptr xml:id="fig-0113a-01a" corresp="fig-0113a-01" type="figureAnchor" />
<pb facs="0114" />
<pb facs="0115" n="65" /><fw type="head">MATHEMATICA. LIB. I. CAP. XVIII.</fw>
curvam quamcunque BC; </s>
          <s xml:space="preserve">celeritate eo acquiſita adſcendet <lb />
<ptr xml:id="note-0115-01a" corresp="note-0115-01" type="noteAnchor" />
ad eandem altitudinem aliam partem verſus per cur-<lb />vas CD, aut CE, aut C HGF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0112-12" corresp="note-0112-12a" place="margin">275. <lb />FAB. VIII. <lb />fig. 1.</note>
              <figure xml:id="fig-0113-01" corresp="fig-0113-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01" />
                <label>0113-01</label>
              </figure>
              <figure xml:id="fig-0113a-01" corresp="fig-0113a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113a-01" />
                <label>0113a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0115-01" corresp="note-0115-01a" place="margin">TAB. XI. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex demonſtratis in hoc capite <ptr type="noteAnchor" />, deducimus methodum
<ptr xml:id="note-0115-02a" corresp="note-0115-02" type="noteAnchor" />
confirmandi experimentis, quæ de velocitate Corporum <lb />cadentium antea ſunt demonſtrata <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0115-02" corresp="note-0115-02a" n="*" anchored="true" place="margin">71.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">2553</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi>, <lb />Qua corporum Cadentium velocitates conferuntur.</head>
        <p>
          <s xml:space="preserve">Ex ligno cujus craſſities AB eſt duorum pollicum, &amp; </s>
          <s xml:space="preserve">alti-<lb />
<ptr xml:id="note-0115-04a" corresp="note-0115-04" type="noteAnchor" />
tudo circiter pollicum novem, formatur machina hæc; </s>
          <s xml:space="preserve">ex-<lb />
<ptr xml:id="note-0115-05a" corresp="note-0115-05" type="noteAnchor" />
cavatur lignum juxta portionem cycloïdis à ſuperiori parte <lb />ligni ad F uſque, ubi curva terminatur in ipſius vertice; <lb /></s>
          <s xml:space="preserve">continuaturque lignum ab F ad G, juxta tangentem ad cur-<lb />vam in vertice F, cujus diſtantia a G eſt unius pedis. </s>
          <s xml:space="preserve">Ut <lb />lignum hoc exactiſſimè ſit elaboratum habeatque ſuperfi-<lb />ciem admodum politam deſideratur. </s>
          <s xml:space="preserve">Formationem autem <lb />cycloïdis in capite ſequenti explicamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0115-04" corresp="note-0115-04a" place="margin">276.</note>
              <note xml:space="preserve" xml:id="note-0115-05" corresp="note-0115-05a" place="margin">TAB. XII, <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lignum hoc circumdatur regulis ligneis HH, HI, II; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſpatium quod hiſce continetur in duos quaſi canales divi-<lb />ditur regulâ LL, cujus altitudo eſt quartæ partis unius pol-<lb />licis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Canali utroque movetur globus æneus diametri ſemi <lb />pollicis, in utroque etiam datur obex O, hi ope cochleæ <lb />lateralis ubi deſideraveris firmantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Machina tribus ſuſtinetur cochleis æneis, quarum duæ vi-<lb />dentur in C, C; </s>
          <s xml:space="preserve">harum ope ſuperficies FG in ſitu ponitur <lb />horizontali, cujus ſitus indicium dat perpendiculum NM.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Regula LL in ſuperiori parte dividitur, ab F ad G in <lb />partes æquales, ab F autem ſurſum inæquales ſunt; </s>
          <s xml:space="preserve">ſed de-<lb />monſtrant intervalla æqualia inter altitudines.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hujus Machinæ hæc eſt proprietas, ut globi ab altitudi-<lb />nibus, utcunque inæqualibus, dimiſſi, æqualibus tempo-<lb />ribus ad F perveniant, quod facile patebit ſi obices O, O, <lb />in F firmentur, &amp; </s>
          <s xml:space="preserve">globi eodem momento a diverſis altitu-<lb />dinibus dimittantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Qui hujus proprietatis Geometricam deſiderant demon-
</s>
          <pb facs="0116" n="66" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſtrationem caput ſequens adeant; </s>
          <s xml:space="preserve">ipſam in machina obſerva-<lb />re proprietatem in hoc loco ſufficit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Conſtitutâ machinâ, ut dictum, firmentur obices, appli-<lb />
<ptr xml:id="note-0116-01a" corresp="note-0116-01" type="noteAnchor" />
cato uno diviſioni quartæ ab F, altero diviſioni ſextæ. </s>
          <s xml:space="preserve">Si <lb />nunc globi dimittantur eodem momento ab altitudinibus, <lb />quæ ſunt, ut quatuor ad novem, dimiſſo nempe globo illo a mi-<lb />nori altitudine qui datur in canali, in quo obex minus ab F <lb />diſtat, eodem etiam momento quàm exactiſſime ad obices <lb />pervenient.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0116-01" corresp="note-0116-01a" place="margin">277.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globi hi eodem momento in F dantur, æqualibus ergo <lb />temporibus percurrunt lineas, quæ ſunt ut quatuor ad ſex, <lb />id eſt, ut duo ad tria, in qua ratione ſunt horum globorum <lb />velocitates <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">horum numerorum quadrata ſunt quatuor &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0116-02a" corresp="note-0116-02" type="noteAnchor" />
novem, id eſt in ratione altitudinum a quibus cadendocor-<lb />pora acquiſivere velocitates ſuas; </s>
          <s xml:space="preserve">quod Experimento confir-<lb />mandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0116-02" corresp="note-0116-02a" n="*" anchored="true" place="margin">94.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In conſtituendis obicibus ad globorum magnitudinem at-<lb />tendendum.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIX.</head>
        <head rend="italics" xml:space="preserve">De Oſcillatione pendulorum.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi></head>
        <p>
          <s xml:space="preserve">G Rave, filo tenuiſſimo ſuſpenſium, &amp; </s>
          <s xml:space="preserve">cum filo, circa fili <lb />
<ptr xml:id="note-0116-03a" corresp="note-0116-03" type="noteAnchor" />
punctum fixum, mobile, vocatur Pendulum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0116-03" corresp="note-0116-03a" place="margin">278.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus penduli eſt vibratorius, ſeu oſcillatorius.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando pondus, filo extenſo, ab una parte elevatur, <lb />gravitate deſcendit, &amp; </s>
          <s xml:space="preserve">celeritate acquiſita ad eandem alti-<lb />tudinem aliam partem verſus adſcendit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">gravitate deinde ite-
<ptr xml:id="note-0116-04a" corresp="note-0116-04" type="noteAnchor" />
rum redit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vibrationes continuat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0116-04" corresp="note-0116-04a" n="*" anchored="true" place="margin">273.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Rationem circa punctum ſuſpenſionis liberrimam hìc po-<lb />nimus, &amp; </s>
          <s xml:space="preserve">nullam dari aëris reſiſtentiam; </s>
          <s xml:space="preserve">quæ in majoribus <lb />pendulis admodum eſt exigua.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">TAB. XI. <lb />fig. 2.</note>
        <p>
          <s xml:space="preserve">In motu ſuo corpus P deſcribit portionem circuli PBF; <lb /></s>
          <s xml:space="preserve">ſi loco hujus motus corpus deſcendat per chordam PB; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">i-<lb />
<ptr xml:id="note-0116-06a" corresp="note-0116-06" type="noteAnchor" />
terum adſcendat per chordam BF; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vibrationes ſuas per <lb />chordas peragat; </s>
          <s xml:space="preserve">deſcenſus fiet in tempore, in quo corpus ca-
</s>
          <pb facs="0117" n="67" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XIX.</fw>
dendo poteſt percurrere diametrum AB <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, longitudi-
<ptr xml:id="note-0117-01a" corresp="note-0117-01" type="noteAnchor" />
nem duplam longitudinis penduli: </s>
          <s xml:space="preserve">in tempore æquali, ad-<lb />ſcendet per chordam BF <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in tempore ergo integræ vibr atio-
<ptr xml:id="note-0117-02a" corresp="note-0117-02" type="noteAnchor" />
nis, corpus cadendo poſſet percurrere quatuor diametros <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt,
<ptr xml:id="note-0117-03a" corresp="note-0117-03" type="noteAnchor" />
longitudinem octuplam longitudinis penduli. </s>
          <s xml:space="preserve">Cumque deſcen-<lb />ſus &amp; </s>
          <s xml:space="preserve">adſcenſus per omnes chordas fiat in tempore æquali, o-<lb />mnes vibrationes per chordas, ſive magnas, ſive exiguas, ſunt æ-<lb />què diuturnæ. </s>
          <s xml:space="preserve">In vibrationibus exiguis harum durationes, dum <lb />in circulo movetur corpus, cum durationibus vibrationum in <lb />chordis conſtantem rationem habent, nempe quæ datur inter <lb />circuli peripheriæ quadrantem &amp; </s>
          <s xml:space="preserve">diametrum; </s>
          <s xml:space="preserve">idcirco ejuſdem <lb />
<ptr xml:id="note-0117-04a" corresp="note-0117-04" type="noteAnchor" />
penduli vibrationes exiguæ, licet inæquales, ad ſenſum ſunt <lb />æque diuturnæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0116-06" corresp="note-0116-06a" place="margin">279.</note>
              <note xml:space="preserve" xml:id="note-0117-01" corresp="note-0117-01a" n="*" anchored="true" place="margin">268.</note>
              <note xml:space="preserve" xml:id="note-0117-02" corresp="note-0117-02a" n="*" anchored="true" place="margin">273.</note>
              <note xml:space="preserve" xml:id="note-0117-03" corresp="note-0117-03a" n="*" anchored="true" place="margin">255</note>
              <note xml:space="preserve" xml:id="note-0117-04" corresp="note-0117-04a" place="margin">280.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum i</hi>.</head>
        <p>
          <s xml:space="preserve">Pendula duo CP &amp; </s>
          <s xml:space="preserve">cp æqualia, ſi a punctis P &amp; </s>
          <s xml:space="preserve">p eo-<lb />
<ptr xml:id="note-0117-05a" corresp="note-0117-05" type="noteAnchor" />
dem temporis momento dimittantur, eodem tempore per-<lb />
<ptr xml:id="note-0117-06a" corresp="note-0117-06" type="noteAnchor" />
venient in B &amp; </s>
          <s xml:space="preserve">b, &amp; </s>
          <s xml:space="preserve">deinde in F &amp; </s>
          <s xml:space="preserve">f; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſic motum con-<lb />tinuabunt per arcus PBF &amp; </s>
          <s xml:space="preserve">pbf, ſemper eodem tem-<lb />pore.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0117-05" corresp="note-0117-05a" place="margin">281.</note>
              <note xml:space="preserve" xml:id="note-0117-06" corresp="note-0117-06a" place="margin">TAB. XI. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc autem æqualitas plenius explicanda eſt, &amp; </s>
          <s xml:space="preserve">quare vi-<lb />brationes in circulo ad vibrationem per chordas quam dixi <lb />rationem habeant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Rotetur circulus FEBſuper lineâ AD donec punctum B <lb />
<ptr xml:id="note-0117-07a" corresp="note-0117-07" type="noteAnchor" />
in A ad lineam hanc perveniat; </s>
          <s xml:space="preserve">hoc motu punctum B deſcri-<lb />
<ptr xml:id="note-0117-08a" corresp="note-0117-08" type="noteAnchor" />
bit curvæ portionem BPA: </s>
          <s xml:space="preserve">eodem modo ſimilis curvæ <lb />portio B| D deſcribitur, totaque curva ABD vocatur Cy-<lb />cloïs, circulus FEB generator dicitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0117-07" corresp="note-0117-07a" place="margin">282.</note>
              <note xml:space="preserve" xml:id="note-0117-08" corresp="note-0117-08a" place="margin">TAB. XI. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dividatur in duas partes æquales in B, portioneſque BA <lb />
<ptr xml:id="note-0117-09a" corresp="note-0117-09" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">BD diſponantur, ut puncta A &amp; </s>
          <s xml:space="preserve">D jungantur in C; </s>
          <s xml:space="preserve">pun-<lb />ctum vero B cum punctis A &amp; </s>
          <s xml:space="preserve">D lineæ AD coincidat. <lb /></s>
          <s xml:space="preserve">Juxta harum portionum curvaturam laminæ metallicæ in-<lb />flectantur, ita ut filum penduli in C ſuſpenſi, motu ſuo vi-<lb />bratorio, ab utraque parte ſeſe laminis iſtis applicet, &amp; </s>
          <s xml:space="preserve">ean-<lb />dem curvaturam cum iſtis adipiſcatur. </s>
          <s xml:space="preserve">Nunc poſita longi-<lb />tudine penduli CB, corpus P in vibrationibus ſuis deſcri-<lb />bet cycloïdem ABD, ut in ſequenti ſcholio 3° demonſtra-
</s>
          <pb facs="0118" n="68" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
mus, ita ut filum longitudinis BC æquale ſit curvæ <lb />CA; </s>
          <s xml:space="preserve">quare tota curva ABD dupla eſt lineæ CB; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0118-01a" corresp="note-0118-01" type="noteAnchor" />
quadrupla axis FB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0117-09" corresp="note-0117-09a" place="margin">283.</note>
              <note xml:space="preserve" xml:id="note-0118-01" corresp="note-0118-01a" place="margin">284.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In eodem ſcholio demonſtramus. </s>
          <s xml:space="preserve">Tangentem ad curvam <lb />
<ptr xml:id="note-0118-02a" corresp="note-0118-02" type="noteAnchor" />
in puncto, ut P, parallelam eſſe chordæ EB, in circulo <lb />FBE ductæ ad punctum infimum B ex puncto E, in quo cir-<lb />culus ſecatur à lineâ PE parrallela ad baſim AD &amp; </s>
          <s xml:space="preserve">per <lb />P tranſeunti: </s>
          <s xml:space="preserve">Ut &amp; </s>
          <s xml:space="preserve">portionem PB curvæ æqualem eſſe <lb />
<ptr xml:id="note-0118-03a" corresp="note-0118-03" type="noteAnchor" />
duplæ chordæ EB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0118-02" corresp="note-0118-02a" place="margin">285.</note>
              <note xml:space="preserve" xml:id="note-0118-03" corresp="note-0118-03a" place="margin">286.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum autem in ſingulis curvæ punctis corpus in curva de-<lb />ſcendat juxta directionem tangentis ad curvam, ſequi-<lb />tur corpus in puncto quocunque curvæ conari deſcendere <lb />
<ptr xml:id="note-0118-04a" corresp="note-0118-04" type="noteAnchor" />
cumvi, quæ proportionalis portioni curvæ inter hoccepun-<lb />ctum &amp; </s>
          <s xml:space="preserve">curvæ punctum infimum B <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Unde patet, ſi duo
<ptr xml:id="note-0118-05a" corresp="note-0118-05" type="noteAnchor" />
pendula ut CP ab altitudinibus diverſis, eodem momento, <lb />dimittantur, celeritates, quibus cadere incipiunt, eſſe in-<lb />ter ſe, ut ſpatia percurrenda, antequam ad B perveniant: <lb /></s>
          <s xml:space="preserve">ſi ergo iſtis celeritatibus ſolis, motu non accelerato, agita-<lb />rentur, eodem temporis momento ad B pervenirent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eo-
<ptr xml:id="note-0118-06a" corresp="note-0118-06" type="noteAnchor" />
dem modo velocitatibus ſecundo momento acquiſitis, et-<lb />iam ad B eodem momento pertingunt; </s>
          <s xml:space="preserve">idemque ratioci-<lb />nium pro momentis ſequentibus procedit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſemi vibra-<lb />tiones ex omnibus celeritatibus junctis utcunque inæquales, <lb />ut &amp; </s>
          <s xml:space="preserve">vibrationes integræ, iiſdem temporibus peraguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0118-04" corresp="note-0118-04a" place="margin">287.</note>
              <note xml:space="preserve" xml:id="note-0118-05" corresp="note-0118-05a" n="*" anchored="true" place="margin">267 285. <lb />286.</note>
              <note xml:space="preserve" xml:id="note-0118-06" corresp="note-0118-06a" n="*" anchored="true" place="margin">94.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ulterius in primo ſcholio demonſtramus. </s>
          <s xml:space="preserve">Tempus unius <lb />
<ptr xml:id="note-0118-07a" corresp="note-0118-07" type="noteAnchor" />
cujuſque vibrationis eſſe ad tempus caſus verticalis, per ſe-<lb />milongitudinem penduli, ut peripheria circuli, ad diame-<lb />trum. </s>
          <s xml:space="preserve">In hac curva pars infima cum circuli arcu exiguo ad <lb />ſenſum coincidit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hæc eſt vera ratio, quare in circulo <lb />tempora vibrationum exiguarum, utcunque inæqualium, <lb />ſint æqualia; </s>
          <s xml:space="preserve">ideo etiam duratio harum vibrationum ad du-<lb />rationem vibrationis per chordas, id eſt ad tempus caſus <lb />verticalis per longitudinem octuplam longitudinis penduli <ptr type="noteAnchor" />,
<ptr xml:id="note-0118-08a" corresp="note-0118-08" type="noteAnchor" />
aut ſedecuplam ſemi longitudinis penduli, illam habet ra-<lb />tionem, quæ datur inter peripheriam circuli &amp; </s>
          <s xml:space="preserve">quatuor diame-<lb />tros <ptr type="noteAnchor" />, id eſt circiter ut 785 ad 1000: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">celerius per arcum
<ptr xml:id="note-0118-09a" corresp="note-0118-09" type="noteAnchor" />
</s>
          <pb facs="0119" n="69" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XIX.</fw>
quam per chordas vibratur corpus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0118-07" corresp="note-0118-07a" place="margin">288.</note>
              <note xml:space="preserve" xml:id="note-0118-08" corresp="note-0118-08a" n="*" anchored="true" place="margin">279.</note>
              <note xml:space="preserve" xml:id="note-0118-09" corresp="note-0118-09a" n="*" anchored="true" place="margin">255. <lb />289.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Durationes vibrationum pendulorum inæqualium poſſunt <lb />
<ptr xml:id="note-0119-01a" corresp="note-0119-01" type="noteAnchor" />
inter ſe comparari. </s>
          <s xml:space="preserve">Quando arcus ſunt ſimiles, deviationes re-<lb />ſpectu chordarum ſunt etiam ſimiles &amp; </s>
          <s xml:space="preserve">tempora vibrationum <lb />per arcus ſunt ut tempora vibrationum per chordas; </s>
          <s xml:space="preserve">hæc vero <lb />ut tempora deſcenſus per longitudines octuplas longitudinum <lb />pendulorum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſic quadrata durationum ſunt ut iſtæ lon-
<ptr xml:id="note-0119-02a" corresp="note-0119-02" type="noteAnchor" />
gitudines octuplæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſive ut ipſæ longitudines pendulorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0119-01" corresp="note-0119-01a" place="margin">290.</note>
              <note xml:space="preserve" xml:id="note-0119-02" corresp="note-0119-02a" n="*" anchored="true" place="margin">279.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">225.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Duo pendula CP, cp, quorum longitudines ſunt ut 4. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0119-04a" corresp="note-0119-04" type="noteAnchor" />
ad 1.</s>
          <s xml:space="preserve">, eodem tempore dimittuntur a punctis P &amp; </s>
          <s xml:space="preserve">p, ita ut <lb />
<ptr xml:id="note-0119-05a" corresp="note-0119-05" type="noteAnchor" />
vibrationbius arcus ſimiles deſcribant; </s>
          <s xml:space="preserve">pendulum majus ſe-<lb />mel vibratur, dum minus duas peragit vibrationes; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita <lb />quadrata durationum vibrationum ſunt ut 4. </s>
          <s xml:space="preserve">ad 1.</s>
          <s xml:space="preserve">, nem-<lb />pe ut longitudines pendulorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0119-04" corresp="note-0119-04a" place="margin">291.</note>
              <note xml:space="preserve" xml:id="note-0119-05" corresp="note-0119-05a" place="margin">TAB XI. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando vibrationes ſunt exiguæ, hæc ratio etiam locum <lb />habet, licèt pendula non vibrentur per arcus ſimiles <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">280.</note>
        <p>
          <s xml:space="preserve">Velocitates pendulorum in puncto infimo, in vibrationibus <lb />
<ptr xml:id="note-0119-07a" corresp="note-0119-07" type="noteAnchor" />
inæqualibus, ſunt inter ſe, ut ſubtenſæ arcuum, quos corpus <lb />deſcendendo deſcribit. </s>
          <s xml:space="preserve">Sic velocitas corporis P, cadentis per <lb />
<ptr xml:id="note-0119-08a" corresp="note-0119-08" type="noteAnchor" />
arcum PB, eſt ad ejus velocitatem quando cadit per DB, <lb />ut chorda PB ad chordam DB. </s>
          <s xml:space="preserve">Nam ductis lineis hori-<lb />
<ptr xml:id="note-0119-09a" corresp="note-0119-09" type="noteAnchor" />
zonti parallelis P f, D d &amp; </s>
          <s xml:space="preserve">junctis P &amp; </s>
          <s xml:space="preserve">A, triangula P f B, <lb />BPA ſunt ſimilia <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">idèo B f, BP, BA ſunt in con-
<ptr xml:id="note-0119-10a" corresp="note-0119-10" type="noteAnchor" />
tinuâ proportione, &amp; </s>
          <s xml:space="preserve">quadratum chordæ BP valet produ-<lb />ctum diametri per B f: </s>
          <s xml:space="preserve">eodem modo quadratum chordæ <lb />B d æquale eſt producto diametri per BD: </s>
          <s xml:space="preserve">ergo quadrata <lb />chordarum ſunt inter ſe ut producta hæc, quæ ſunt ut li-<lb />neæ f B, dB. </s>
          <s xml:space="preserve">Quadrata prædictarum velocitatum ſunt et-<lb />
<ptr xml:id="note-0119-11a" corresp="note-0119-11" type="noteAnchor" />
iâm ut iſtæ lineæ f B, d B <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo velocitates ut chordæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0119-07" corresp="note-0119-07a" place="margin">292.</note>
              <note xml:space="preserve" xml:id="note-0119-08" corresp="note-0119-08a" place="margin">TAB. XI. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0119-09" corresp="note-0119-09a" place="margin">293.</note>
              <note xml:space="preserve" xml:id="note-0119-10" corresp="note-0119-10a" n="*" anchored="true" place="margin">31-El. III. <lb />8: El. VI.</note>
              <note xml:space="preserve" xml:id="note-0119-11" corresp="note-0119-11a" n="*" anchored="true" place="margin">271. 255. <lb />253.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa omnia, quæ hucuſque dependulis dicta ſunt, non in-<lb />tereſt quantum ponderet corpus quod agitatur, aut an corpora <lb />
<ptr xml:id="note-0119-12a" corresp="note-0119-12" type="noteAnchor" />
diver ſorum pendulorum inæqualiter ponderent, aut ex diverſa <lb />dentur materiæ. </s>
          <s xml:space="preserve">Cùm vis gravitatis proportionalis ſit quan-<lb />titati materiæ in omnibus corporibus <ptr type="noteAnchor" />, omnia corpora, in
<ptr xml:id="note-0119-13a" corresp="note-0119-13" type="noteAnchor" />
iiſdem circumſtantiis, gravitate æque celeriter moventur.</s>
          <s xml:space="preserve">
</s>
          <pb facs="0120" n="70" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
Quod etiam ſequenti Experimento confirmatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0119-12" corresp="note-0119-12a" place="margin">294.</note>
              <note xml:space="preserve" xml:id="note-0119-13" corresp="note-0119-13a" n="*" anchored="true" place="margin">121.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Dentur duo globi æquales, aut inæquales, unus ex plum-<lb />
<ptr xml:id="note-0120-01a" corresp="note-0120-01" type="noteAnchor" />
bo, alter ex ebore; </s>
          <s xml:space="preserve">filis ſuſpendantur, ut forment pendu-<lb />la æqualia; </s>
          <s xml:space="preserve">vibrationes æquales, atque exiguæ utcunque <lb />inæquales, ſunt æquè diuturnæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0120-01" corresp="note-0120-01a" place="margin">295.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sæpe loco fili virga ferrea tenuis ſed rigida adhibetur, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0120-02a" corresp="note-0120-02" type="noteAnchor" />
aliquan-do etiam pondera duo aut plura ei annectuntur, &amp; </s>
          <s xml:space="preserve"><lb />vocatur pendulum compoſitum; </s>
          <s xml:space="preserve">in eo caſu regulæ memora-<lb />tæ locum non habent; </s>
          <s xml:space="preserve">ſed iſta pendula ad ſimplicia revocan-<lb />tur, determinando in iis punctum, in quo ſi pondera forent <lb />juncta, vibrationes eſſent æquè diuturnæ cum vibrationibus <lb />penduli compoſiti, Hocce punctum vocatur centrum oſcil-<lb />lationis. </s>
          <s xml:space="preserve">In ſcholio 2°. </s>
          <s xml:space="preserve">methodum hujus determinandi ex-<lb />plicamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0120-02" corresp="note-0120-02a" place="margin">296.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus cujuſcunque figuræ poteſt ſuſpendi, &amp; </s>
          <s xml:space="preserve">circa pun-<lb />ctum, aut potius axem, vibrari; </s>
          <s xml:space="preserve">in eo etiam poteſt deter-<lb />minari centrum oſcillationis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando linea recta, qualis eſt filum ferreum, circa ex-<lb />
<ptr xml:id="note-0120-03a" corresp="note-0120-03" type="noteAnchor" />
tremitatum alteram vibratur, centrum oſcillationis diſtat a <lb />puncto ſuſpenſionis duabus partibus tertiis longitudinis fili. <lb /></s>
          <s xml:space="preserve">ut in eodem ſcholio demonſtramus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0120-03" corresp="note-0120-03a" place="margin">297.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Lamina ferrea AB ita ſuſpenditur, ut circa extremita-<lb />
<ptr xml:id="note-0120-04a" corresp="note-0120-04" type="noteAnchor" />
tem A vibretur; </s>
          <s xml:space="preserve">pendulum ſimplex CP, cujus longitudo eſt <lb />
<ptr xml:id="note-0120-05a" corresp="note-0120-05" type="noteAnchor" />
duarum partium tertiarum AB, eodem tempore cum iſta <lb />lamina dimittitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vibrationes penduli, &amp; </s>
          <s xml:space="preserve">laminæ, eo-<lb />dem tempore peraguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0120-04" corresp="note-0120-04a" place="margin">298.</note>
              <note xml:space="preserve" xml:id="note-0120-05" corresp="note-0120-05a" place="margin">TAB. VIII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vibrationes pendulorum, ut diximus, licet inæquales, <lb />ſunt æquè diuturnæ <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">hæc pendulorum proprietas ma-
<ptr xml:id="note-0120-06a" corresp="note-0120-06" type="noteAnchor" />
ximi uſus eſt in horologiis, quibus motus æquabilis, pen-<lb />dulo adjuncto, communicatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0120-06" corresp="note-0120-06a" n="*" anchored="true" place="margin">280</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Horologiis in diverſis locis tranſſatis vim gravitatis non <lb />
<ptr xml:id="note-0120-07a" corresp="note-0120-07" type="noteAnchor" />
ubique terrarum æqualem eſſe, enotuit ex eo, quod vibra-<lb />tiones ejuſdem penduli, in diverſis regionibus, reſpectu <lb />temporis, inæquales repertæ ſunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hæc gravitatis diver-<lb />ſitas per pendula menſuratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0120-07" corresp="note-0120-07a" place="margin">299.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0121" n="71" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XIX.</fw>
        <p>
          <s xml:space="preserve">Dentur duo pendula, CP, cp, quorum longitudines ſint in-<lb />
<ptr xml:id="note-0121-01a" corresp="note-0121-01" type="noteAnchor" />
terſe, ut vires gravitatis quibus agitantur; </s>
          <s xml:space="preserve">ſi arcus ſimiles <lb />
<ptr xml:id="note-0121-02a" corresp="note-0121-02" type="noteAnchor" />
excurrant, in punctis reſpondentibus gravitates eandem ſem-<lb />per habebunt rationem inter ſe, propter inclinationes æ-<lb />quales, &amp; </s>
          <s xml:space="preserve">quidem rationem arcuum percurrendorum, (quia <lb />arcus ſimiles ſunt ut pendulorum longitudines) qui ergo æ-<lb />qualibus temporibus percurrentur <ptr type="noteAnchor" />, id eſt, vibr ationes e-
<ptr xml:id="note-0121-03a" corresp="note-0121-03" type="noteAnchor" />
runt æ æquè diuturnæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0121-01" corresp="note-0121-01a" place="margin">300.</note>
              <note xml:space="preserve" xml:id="note-0121-02" corresp="note-0121-02a" place="margin">TAB. XII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0121-03" corresp="note-0121-03a" n="*" anchored="true" place="margin">94</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ad eandem longitudinem reducantur mutato pendulo <lb />c p cujus longitudo fiat cq, æqualis CP; </s>
          <s xml:space="preserve">quadratum dura-<lb />tionis vibrationis penduli cq eſt ad quadratum durationisvi-<lb />brationis penduli cp, aut CP, ut longitudo cq, aut CP, <lb />ad cp <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt ut gravitas quæ in pendulum CP agit ad
<ptr xml:id="note-0121-04a" corresp="note-0121-04" type="noteAnchor" />
gravitatem quæ pendulum cq agitat. </s>
          <s xml:space="preserve">Id circo ſunt qua-<lb />
<ptr xml:id="note-0121-05a" corresp="note-0121-05" type="noteAnchor" />
drata durationum vibrationum pendulorum æqualium, inver-<lb />sè ut gravitates in pendula agentes. </s>
          <s xml:space="preserve">Et in genere quadrata <lb />
<ptr xml:id="note-0121-06a" corresp="note-0121-06" type="noteAnchor" />
durationum vibrationum ſunt directè ut pendulorum longi-<lb />
<ptr xml:id="note-0121-07a" corresp="note-0121-07" type="noteAnchor" />
tudines <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">inversè ut gravitates quibus moventur <ptr type="noteAnchor" />, Et-
<ptr xml:id="note-0121-08a" corresp="note-0121-08" type="noteAnchor" />
iam gravitates hæ ſunt directè ut longitudines <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">inversè
<ptr xml:id="note-0121-09a" corresp="note-0121-09" type="noteAnchor" />
ut quadrata durationum vibrationum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0121-04" corresp="note-0121-04a" n="*" anchored="true" place="margin">290.</note>
              <note xml:space="preserve" xml:id="note-0121-05" corresp="note-0121-05a" place="margin">301.</note>
              <note xml:space="preserve" xml:id="note-0121-06" corresp="note-0121-06a" place="margin">302.</note>
              <note xml:space="preserve" xml:id="note-0121-07" corresp="note-0121-07a" n="*" anchored="true" place="margin">290.</note>
              <note xml:space="preserve" xml:id="note-0121-08" corresp="note-0121-08a" place="margin">303.</note>
              <note xml:space="preserve" xml:id="note-0121-09" corresp="note-0121-09a" n="*" anchored="true" place="margin">301. <lb />* 300.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">302.</note>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM I.</head>
        <head rend="italics" xml:space="preserve">De motu in Cycloide.</head>
        <p>
          <s xml:space="preserve">Concipiamus portionem cycloïdis aut integram cycloïdem, in linea recta <lb />extendi ABD, &amp; </s>
          <s xml:space="preserve">corpus in hac linea recta moveri juxta legem penduli o-<lb />
<ptr xml:id="note-0121-11a" corresp="note-0121-11" type="noteAnchor" />
<ptr xml:id="note-0121-12a" corresp="note-0121-12" type="noteAnchor" />
ſcillati in cycloïde, id eſt dari preſſionem in corpusagentem, quæ ſequatur ratio-<lb />nem diſtantiæ corporis a puncto medioB, &amp; </s>
          <s xml:space="preserve">quæ in corpus motum agat ut in cor-<lb />pus quieſcens; </s>
          <s xml:space="preserve">centro B, radio BA, deſcribatur Semicirculus ALD, quitempus <lb />repræſentat, in quo corpus movetur ab A ad D; </s>
          <s xml:space="preserve">tempora in quibus portiones <lb />quæcunque lineæ AD deſcribuntur, erectis ad hanc perpendicularibus, de-<lb />terminantur, arcus HI tempus in quo FG, &amp; </s>
          <s xml:space="preserve">arcus AH tempus in quo AF <lb />percurruntur, deſignant: </s>
          <s xml:space="preserve">celeritates autem in punctis F &amp; </s>
          <s xml:space="preserve">G proportionales <lb />ſunt ipſis perpendicularibus FH, GI.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0121-11" corresp="note-0121-11a" place="margin">304.</note>
              <note xml:space="preserve" xml:id="note-0121-12" corresp="note-0121-12a" place="margin">TAB. XI. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quæ ut demonſtrentur, concipiendum eſt corpus, quod in linea AD mo-<lb />
<ptr xml:id="note-0121-13a" corresp="note-0121-13" type="noteAnchor" />
vetur ita, ut temporibus, quæ ſunt ut arcus AH, HI, percurrat portiones <lb />AF, FG, &amp; </s>
          <s xml:space="preserve">ſic de cæteris: </s>
          <s xml:space="preserve">ita ut totum tempus repræſentetur per ſemicircu-<lb />lum ALD. </s>
          <s xml:space="preserve">Concipiamus ulterius ſemicirculum in partes minimas æqua-<lb />les diviſum, momenta minima æqualia temporis deſignantes, quales ſunt <lb />H b &amp; </s>
          <s xml:space="preserve">I i. </s>
          <s xml:space="preserve">Id circo poſitis fh &amp; </s>
          <s xml:space="preserve">g i etiam perpendicularibus lineæ AD, tem-<lb />poribus æqualibus lineæ F f &amp; </s>
          <s xml:space="preserve">G g percurruntur, quæ cum exiguæ ſunt percur-
</s>
          <pb facs="0122" n="72" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
runtur motu æquabili, momenta enim temporis adeo exigua coucipipo ſſunt, <lb />ut acceleratio aut retardatio inſenſibilis ſit; </s>
          <s xml:space="preserve">celeritates ergo in punctis F &amp; </s>
          <s xml:space="preserve"><lb />G ſunt, ut F f &amp; </s>
          <s xml:space="preserve">G g <ptr type="noteAnchor" />, quæ ſunt inter ſe ut FH ad GI; </s>
          <s xml:space="preserve">propter triangu-
<ptr xml:id="note-0122-01a" corresp="note-0122-01" type="noteAnchor" />
la ſimilia HBF, A h l, &amp; </s>
          <s xml:space="preserve">IGB, I mi, ductis lineis H l &amp; </s>
          <s xml:space="preserve">I m parallelis li-<lb />neæ AD; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">propter æquales Hypotenuſas HB, IB, &amp; </s>
          <s xml:space="preserve">H b, I i.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0121-13" corresp="note-0121-13a" place="margin">305.</note>
              <note xml:space="preserve" xml:id="note-0122-01" corresp="note-0122-01a" n="*" anchored="true" place="margin">94.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Incrementa celeritatum momentis æqualibus minimis in punctis F &amp; </s>
          <s xml:space="preserve">G, ide ſt <lb />
<ptr xml:id="note-0122-02a" corresp="note-0122-02" type="noteAnchor" />
prefſiones agentes in iſtis punctis <ptr type="noteAnchor" />, ſunt ut l h &amp; </s>
          <s xml:space="preserve">m i; </s>
          <s xml:space="preserve">ſunt enim differentiæ cele-
<ptr xml:id="note-0122-03a" corresp="note-0122-03" type="noteAnchor" />
ritatum in punctis F, f, &amp; </s>
          <s xml:space="preserve">G, g. </s>
          <s xml:space="preserve">Sed, propter triangula memorata ſimilia, l h <lb />&amp; </s>
          <s xml:space="preserve">m i ſunt inter ſe, ut FB ad GB; </s>
          <s xml:space="preserve">idcirco preſſiones, in punctis F &amp; </s>
          <s xml:space="preserve">G in <lb />corpus agentes ſunt inter ſe ut diſtantiæ a puncto medio B.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0122-02" corresp="note-0122-02a" place="margin">107. 252.</note>
              <note xml:space="preserve" xml:id="note-0122-03" corresp="note-0122-03a" n="*" anchored="true" place="margin">107.252.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quæ de incrementis celeritatum demonſtrantur in parte AB Hineæ AD, <lb />in parte BD de decrementis eodem modo demonſtrantur. </s>
          <s xml:space="preserve">Agitatur ergo cor-<lb />pus juxta legem corporis in cycloïde oſcillati.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Detur corpus motu æquabili ſemicir culum percurrens ALD, in tempore <lb />
<ptr xml:id="note-0122-04a" corresp="note-0122-04" type="noteAnchor" />
unius vibrationis in cycloide, id eſt in tempore, in quo corpus, in linea <lb />recta AD ut explicavimus motum, illam percurrit. </s>
          <s xml:space="preserve">Ex dictis patet H b, <lb />F f, &amp; </s>
          <s xml:space="preserve">I i, G g, æqualibus temporibus percurri; </s>
          <s xml:space="preserve">unde ſequitur, cum dire-<lb />ctiones ſint parallelæ in L &amp; </s>
          <s xml:space="preserve">B, celeritates in hiſce punctis eſſe æquales. </s>
          <s xml:space="preserve">Idcirco <lb />corpus celeritate quam corpus pendulum habet in B, in tempore unius vibrationis <lb />deſcribit ſemicirculum, cujus diameter eſt arcus cycloidis a corpore percurſus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0122-04" corresp="note-0122-04a" place="margin">306.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpus integram percurrat cycloidem ABD, diameter hæc erit quadru-<lb />
<ptr xml:id="note-0122-05a" corresp="note-0122-05" type="noteAnchor" />
pla diametri FB <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">velocitas in B erit, quam corpus cadendo ab altitudi-
<ptr xml:id="note-0122-06a" corresp="note-0122-06" type="noteAnchor" />
ne FB acquirit <ptr type="noteAnchor" />, qua celeritate motu æquabili corpus in tempore caſus po-
<ptr xml:id="note-0122-07a" corresp="note-0122-07" type="noteAnchor" />
teſt percurrere lineam duplam ipſius FB <ptr type="noteAnchor" /> Sed ſpatia æqualibus velocitatibus
<ptr xml:id="note-0122-08a" corresp="note-0122-08" type="noteAnchor" />
percurſa ſunt ut tempora <ptr type="noteAnchor" />, id circo tempus caſus per ſemilongitudinem
<ptr xml:id="note-0122-09a" corresp="note-0122-09" type="noteAnchor" />
penduli eſt ad tempus unius vibrationis per integram cycloidem, aut arcum <lb />
<ptr xml:id="note-0122-10a" corresp="note-0122-10" type="noteAnchor" />
quemcumque <ptr type="noteAnchor" />, ut dupla FB, ad ſemicircumferentiam circuli, cujus diame-
<ptr xml:id="note-0122-11a" corresp="note-0122-11" type="noteAnchor" />
ter eſt quadrupla lineæ FB, aut ad integram circumferentiam, cujus diame-<lb />ter eſt etiam dupla FB; </s>
          <s xml:space="preserve">ergo in genere ut diameter circuli ad hujus circum-<lb />ferentiam; </s>
          <s xml:space="preserve">ut monuimus in n. </s>
          <s xml:space="preserve">288.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0122-05" corresp="note-0122-05a" place="margin">307.</note>
              <note xml:space="preserve" xml:id="note-0122-06" corresp="note-0122-06a" place="margin">TAB. XI. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0122-07" corresp="note-0122-07a" n="*" anchored="true" place="margin">284.</note>
              <note xml:space="preserve" xml:id="note-0122-08" corresp="note-0122-08a" n="*" anchored="true" place="margin">271.</note>
              <note xml:space="preserve" xml:id="note-0122-09" corresp="note-0122-09a" n="*" anchored="true" place="margin">257.</note>
              <note xml:space="preserve" xml:id="note-0122-10" corresp="note-0122-10a" n="*" anchored="true" place="margin">95.</note>
              <note xml:space="preserve" xml:id="note-0122-11" corresp="note-0122-11a" n="*" anchored="true" place="margin">280.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">De Centro oſcillationis determinando.</head>
        <p>
          <s xml:space="preserve">Sit CA pendulum compoſitum; </s>
          <s xml:space="preserve">pondera P &amp; </s>
          <s xml:space="preserve">Q; </s>
          <s xml:space="preserve">inter bæc datur centrum oſcil-<lb />
<ptr xml:id="note-0122-12a" corresp="note-0122-12" type="noteAnchor" />
lationis O, cujus hæc eſt proprietas, poſitâ virgâ AC rigidâ &amp; </s>
          <s xml:space="preserve">ſine pon-<lb />
<ptr xml:id="note-0122-13a" corresp="note-0122-13" type="noteAnchor" />
dere, ut pondus Q, multiplicatum per BC, ad pondus P, multiplicatum per <lb />AC, ita AO ad OQ. </s>
          <s xml:space="preserve">Quod ut demonſtremus, conſiderandum eſt pondera Q <lb />&amp; </s>
          <s xml:space="preserve">A moveri directionibus parallelis inter ſe, id eſt æqualiter ad horizontem <lb />inclinatis; </s>
          <s xml:space="preserve">ideo agitari continuo impreſſionibus ex gravitate, quæ, niſi cor-<lb />pora virgâ rigidâ juncta forent, illis celeritates communicarent æquales <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0122-14a" corresp="note-0122-14" type="noteAnchor" />
Junctorum autem ponderum celeritates neceſſario ſunt inæquales, &amp; </s>
          <s xml:space="preserve">celeri-<lb />tas corporis P, actione ponderis Q, augetur, dum hocalterius actione retardatur; <lb /></s>
          <s xml:space="preserve">quæ actiones contrariæ æquales ſunt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Interea punctum intermedium quoddam
<ptr xml:id="note-0122-15a" corresp="note-0122-15" type="noteAnchor" />
O, centrum nempe oſcillationis, movetur celeritate ex actione gravitatis ori-<lb />unda.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0122-12" corresp="note-0122-12a" place="margin">308.</note>
              <note xml:space="preserve" xml:id="note-0122-13" corresp="note-0122-13a" place="margin">TAB XII. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0122-14" corresp="note-0122-14a" n="*" anchored="true" place="margin">118.265.</note>
              <note xml:space="preserve" xml:id="note-0122-15" corresp="note-0122-15a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit B b, O o, aut A a (has enim æquales ponimus lineas) ſpatium percur-<lb />ſum ex actione gravitatis juxta inclinationem quamcunque agentis in tem-<lb />pore quocunque minimo. </s>
          <s xml:space="preserve">Cum punctum O hoc ſpatium percurrit, tantum <lb />per BE transſertur Q, &amp; </s>
          <s xml:space="preserve">potentia quæ in Q agit minuitur quantitate, qua eo
</s>
          <pb facs="0123" />
          <s xml:space="preserve">
<ptr xml:id="fig-0123-01a" corresp="fig-0123-01" type="figureAnchor" />
<pb facs="0123a" />
<ptr xml:id="fig-0123a-01a" corresp="fig-0123a-01" type="figureAnchor" />
<pb facs="0124" />
<pb facs="0125" n="73" /><fw type="head">MATHEMATICA. LIB. I. CAP. XIX.</fw>
dem tempore corpus hoc percurreret Eb &amp; </s>
          <s xml:space="preserve">quæ exprimitur per Q x E b <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0125-01a" corresp="note-0125-01" type="noteAnchor" />
Potentia autem, quæ in P agit, augetur quantitate, qua P eodem tempore <lb />transfertur per aD, &amp; </s>
          <s xml:space="preserve">quæ exprimitur per P x a D <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ponimus enim pa-
<ptr xml:id="note-0125-02a" corresp="note-0125-02" type="noteAnchor" />
rallelas Bb, Oo, Aa; </s>
          <s xml:space="preserve">potentia ergo quæ retardat motum corporis Q, eſt ad <lb />potentiam, quæ accelerat motum corporis P, ut Q x E b ad P x a D: </s>
          <s xml:space="preserve">Sed po-<lb />tentiæ hæapplicantur vecti, cujusfulcrum eſt C; </s>
          <s xml:space="preserve">idcirco harum actiones, quas <lb />æquales demonſtravimus, ſunt ut CB x E b x Q ad CA x a D x P <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ideo CB x Q
<ptr xml:id="note-0125-03a" corresp="note-0125-03" type="noteAnchor" />
ad CA x P, ut aD ad Eb, aut AO ad OB. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">E. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">Patet etiam in pendu-<lb />lo tali compoſito producta fore æqualia, ſi unumquodque pondus multipli-<lb />cetur per ſuas diſtantias a centris ſuſpenſionis &amp; </s>
          <s xml:space="preserve">oſcillationis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0123-01" corresp="fig-0123-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123-01" />
                <label>0123-01</label>
              </figure>
              <figure xml:id="fig-0123a-01" corresp="fig-0123a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123a-01" />
                <label>0123a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0125-01" corresp="note-0125-01a" n="*" anchored="true" place="margin">108.</note>
              <note xml:space="preserve" xml:id="note-0125-02" corresp="note-0125-02a" n="*" anchored="true" place="margin">128.</note>
              <note xml:space="preserve" xml:id="note-0125-03" corresp="note-0125-03a" n="*" anchored="true" place="margin">175.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si plura pondera dentur &amp; </s>
          <s xml:space="preserve">unumquodque per ſuas diſtantias a centris ſuſpenſio-<lb />
<ptr xml:id="note-0125-04a" corresp="note-0125-04" type="noteAnchor" />
nis &amp; </s>
          <s xml:space="preserve">oſcillationis multiplicetur, ſummæ productorum ab utraque parte centri o-<lb />ſcillationis æquales ſunt. </s>
          <s xml:space="preserve">Quod demonſtratione ſimili evincitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0125-04" corresp="note-0125-04a" place="margin">309.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde deducimus Methodum computatione determinandi centrum oſcil-<lb />lationis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sint corpora quæcunque A, B, C, D, E, horum diſtantiæ a centro ſuſpen-<lb />
<ptr xml:id="note-0125-05a" corresp="note-0125-05" type="noteAnchor" />
ſionis reſpectivè litteris a, b, c, d, e, exprimuntur; </s>
          <s xml:space="preserve">ſit diſtantia centri oſcilla-<lb />tionis a centro ſufpenſionis x. </s>
          <s xml:space="preserve">Ponamus a, b, c, minores eſſe x, d &amp; </s>
          <s xml:space="preserve">e autern <lb />majores.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0125-05" corresp="note-0125-05a" place="margin">310.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corporum A, B, C, diſtantiæ a centro oſcillationis ſunt x-a, x-b, <lb />x-c, &amp; </s>
          <s xml:space="preserve">corporum reliquorum diſtantiæ ab eodem centro ſunt d-x, <lb />e-x, multiplicando corpora ſingula per ſuas diſtantias ab utroque cen-<lb />tro, habemus Aax - Aaa + Bbx - Bbb + Ccx - Ccc = Ddd - Ddx + Eee - Eex <ptr type="noteAnchor" /> unde de-
<ptr xml:id="note-0125-06a" corresp="note-0125-06" type="noteAnchor" />
ducimus x = {Aaa + Bbb + Ccc + Ddd + Eee/Aa + Bb + Cc + Dd + Ee}, quam eandem æquationem ha-<lb />bemus quæcunque ex diſtantiis a, b, c, d, e, ſuperent x; </s>
          <s xml:space="preserve">quare generalem hanc <lb />detegimus regulam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0125-06" corresp="note-0125-06a" n="*" anchored="true" place="margin">309.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſingula corpora multiplicentur per quadrata ſuarum diſtantiarum à centro ſu-<lb />
<ptr xml:id="note-0125-07a" corresp="note-0125-07" type="noteAnchor" />
ſpenſionis, &amp; </s>
          <s xml:space="preserve">ſumma productorum dividatur per ſummam productorum ſingulorum <lb />corporum raultiplicatorum per ſuas diſtantias ab eodem centro ſuſpenſionis, quotiens <lb />diviſionis dabit diſtantiam inter centra ſuſpenſionis &amp; </s>
          <s xml:space="preserve">oſcillationis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0125-07" corresp="note-0125-07a" place="margin">311.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si, continuato pendulo ultra centrum ſuſpenſionis, corpora quædam <lb />
<ptr xml:id="note-0125-08a" corresp="note-0125-08" type="noteAnchor" />
ſupra punctum ſuſpenſionis applicentur, horum diſtantia erit negativa; </s>
          <s xml:space="preserve">Si <lb />Ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">talia forent corpora A&amp;</s>
          <s xml:space="preserve">B, pro + a &amp; </s>
          <s xml:space="preserve">+ b computatio ineunda foret <lb />cum -a, -b, quorum quadrata cum etiam ſint + aa &amp; </s>
          <s xml:space="preserve">+ bb, diſtantia x in hoc ca-<lb />ſu erit {Aaa + Bbb + Ccc + Ddd + Eee/-Aa-Bb + Cc + Dd + Ee.</s>
          <s xml:space="preserve">}</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0125-08" corresp="note-0125-08a" place="margin">312.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut memoratam <ptr type="noteAnchor" /> regulam applicemus lineæ cujus extremitas eſt ſuſpen-
<ptr xml:id="note-0125-09a" corresp="note-0125-09" type="noteAnchor" />
fionis centrum, ſingula ipſius puncta, aut potius partes minimæ, multipli-<lb />
<ptr xml:id="note-0125-10a" corresp="note-0125-10" type="noteAnchor" />
candæ ſunt per quadrata diſtantiarum ſuarum ab extremitate, ſumma horum <lb />
<ptr xml:id="note-0125-11a" corresp="note-0125-11" type="noteAnchor" />
productorum eſt pyramis, cujus baſis eſt lineæ quadratum, &amp; </s>
          <s xml:space="preserve">altitudo ipſa <lb />linea, ſi linea dicatur a, pyramis hæc valet {1/3}a<hi rend="superscript">3</hi> <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Dividenda hæc eſt per
ſummam partium minimarum multiplicatarum per ſuas diſtantias ab extre-<lb />
<ptr xml:id="note-0125-12a" corresp="note-0125-12" type="noteAnchor" />
mitate, quorum productorum ſumma eſt area trianguli cujus baſis eſt a, &amp; </s>
          <s xml:space="preserve"><lb />altitudo etiam a; </s>
          <s xml:space="preserve">quæ area valet {1/2}aa <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Dividendo autem {1/3}a<hi rend="superscript">3</hi> per {1/2}a<hi rend="superscript">2</hi> quo-
tiens eſt {2/3}a diſtantia centri oſcillationis a centro ſuſpenſionis, ut ſuperius ex-<lb />perimento confirmavimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0125-09" corresp="note-0125-09a" place="margin">313.</note>
              <note xml:space="preserve" xml:id="note-0125-10" corresp="note-0125-10a" n="*" anchored="true" place="margin">311.</note>
              <note xml:space="preserve" xml:id="note-0125-11" corresp="note-0125-11a" n="*" anchored="true" place="margin">7.6. El. XII</note>
              <note xml:space="preserve" xml:id="note-0125-12" corresp="note-0125-12a" n="*" anchored="true" place="margin">34. El. I.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">298.</note>
        <pb facs="0126" n="74" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM. 3.</head>
        <head rend="italics" xml:space="preserve">In quo quædam in boc capite memoratæ Cycloidis <lb />proprietates demonſtrantur.</head>
        <p>
          <s xml:space="preserve">Poſitâ cycloidis memoratâ <ptr type="noteAnchor" /> formatione; </s>
          <s xml:space="preserve">ſit circulus generator BEF. </s>
          <s xml:space="preserve">Pona-
<ptr xml:id="note-0126-01a" corresp="note-0126-01" type="noteAnchor" />
mus hunc perveniſſe ad punctum Gbaſeos, punctum F erit in f, poſito arcu Gf <lb />
<ptr xml:id="note-0126-02a" corresp="note-0126-02" type="noteAnchor" />
lineæ GF æquali; </s>
          <s xml:space="preserve">Punctum deſcribens erit in b, &amp; </s>
          <s xml:space="preserve">erit hoc punctum Cycloïdis-</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0126-01" corresp="note-0126-01a" place="margin">34.</note>
              <note xml:space="preserve" xml:id="note-0126-02" corresp="note-0126-02a" n="*" anchored="true" place="margin"> 282.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XII. <lb />fig. 4.</note>
        <p>
          <s xml:space="preserve">Ducatur G c H diameter per punctum contactus, erit hæc ad baſin per-<lb />
<ptr xml:id="note-0126-04a" corresp="note-0126-04" type="noteAnchor" />
pendicularis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">parallela diametro BF. </s>
          <s xml:space="preserve">Ductâ nunc b L, per punctum
Cycloïdis b, baſi parallelâ, ſecante circulum FEB in E, &amp; </s>
          <s xml:space="preserve">GH in I; </s>
          <s xml:space="preserve">ma-<lb />nifeſtum eſt, propter æquales GI &amp; </s>
          <s xml:space="preserve">FL <ptr type="noteAnchor" />, in circulis æqualibus æquales
<ptr xml:id="note-0126-05a" corresp="note-0126-05" type="noteAnchor" />
eſſe b I, EL; </s>
          <s xml:space="preserve">additâ utrimque IE æquales erunt b E, IL, cui æqualis <lb />GF <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0126-04" corresp="note-0126-04a" n="*" anchored="true" place="margin">18. El. III.</note>
              <note xml:space="preserve" xml:id="note-0126-05" corresp="note-0126-05a" n="*" anchored="true" place="margin">34. El. I.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">34. El. I.</note>
        <p>
          <s xml:space="preserve">Facile etiam liquet arcus G f, b H, EB, æquales eſſe inter ſe &amp; </s>
          <s xml:space="preserve">lineæ <lb />GF; </s>
          <s xml:space="preserve">ideoque lineæ b E.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex quibus hanc curvæ deducimus proprietatem, Si ex puncto quocunque Cy-<lb />
<ptr xml:id="note-0126-07a" corresp="note-0126-07" type="noteAnchor" />
cloidis ad baſin ducatur parallela, quæ ſemicirculum ſecat ſuper axe deſcriptum <lb />ad partem curvæ, qualis linea hìc eſt b EL, erit hujus portio, inter Cycloi-<lb />dem &amp; </s>
          <s xml:space="preserve">ſemicirculum intercepta, æqualis arcui ſemicir culi inter lineam memora-<lb />tam &amp; </s>
          <s xml:space="preserve">verticem intercepto. </s>
          <s xml:space="preserve">id eſt b E arcui EB æqualis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0126-07" corresp="note-0126-07a" place="margin">315.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Cycloïs ADB; </s>
          <s xml:space="preserve">vertex B; </s>
          <s xml:space="preserve">baſis AF; </s>
          <s xml:space="preserve">axis BF, qui diameter eſt ſemi-<lb />
<ptr xml:id="note-0126-08a" corresp="note-0126-08" type="noteAnchor" />
circuli FMB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0126-08" corresp="note-0126-08a" place="margin">316.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XII. <lb />fig. 5.</note>
        <p>
          <s xml:space="preserve">Sumtâ D d portione quacunque infinitè exigua Cycloïdis, poterit hæc <lb />pro lineâ rectâ haberi, &amp; </s>
          <s xml:space="preserve">continuatâ formabit tangentem in puncto D aut d. <lb /></s>
          <s xml:space="preserve">Ducantur DL, dl, ad baſin parallelæ ſemicirculum ſecantes in E, e; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />ductâ B e continuetur hæc donec ſecet in b lineam DL; </s>
          <s xml:space="preserve">ſit etiam BO ad ba-<lb />ſin parallela, circulum tangens in B, &amp; </s>
          <s xml:space="preserve">quæ in O ſecatur lineâ eO, con-<lb />tinuatione lineæ E e.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Triangula b Ee &amp; </s>
          <s xml:space="preserve">e OB, propter Bo &amp; </s>
          <s xml:space="preserve">hE parallelas ſunt ſimilia. </s>
          <s xml:space="preserve">La-<lb />tera autem EO &amp; </s>
          <s xml:space="preserve">OB ſunt æqualia <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo &amp; </s>
          <s xml:space="preserve">æqualia e E, h E; </s>
          <s xml:space="preserve">eſt eE ar-
<ptr xml:id="note-0126-10a" corresp="note-0126-10" type="noteAnchor" />
cuum B e BE, aut linearum de, DE, differentia <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ eadem differen-
<ptr xml:id="note-0126-11a" corresp="note-0126-11" type="noteAnchor" />
tia eſt ideò etiam h E, quare ſunt æquales parallelæ D h, de; </s>
          <s xml:space="preserve">ſuntetiam id-<lb />circo æquales &amp; </s>
          <s xml:space="preserve">parallelæ D d, b e <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">id eſt tangens in d parallela chordæ e B,
<ptr xml:id="note-0126-12a" corresp="note-0126-12" type="noteAnchor" />
quam Cycloïdis proprietatem ſuperius indicavimus in n. </s>
          <s xml:space="preserve">285.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0126-10" corresp="note-0126-10a" n="*" anchored="true" place="margin">36. El III.</note>
              <note xml:space="preserve" xml:id="note-0126-11" corresp="note-0126-11a" n="*" anchored="true" place="margin">315</note>
              <note xml:space="preserve" xml:id="note-0126-12" corresp="note-0126-12a" n="*" anchored="true" place="margin">33. El I.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Iiſdem poſitis ducatur FE i; </s>
          <s xml:space="preserve">erit hæc ad BE aut B b (propter augulum <lb />
<ptr xml:id="note-0126-13a" corresp="note-0126-13" type="noteAnchor" />
infinite exiguum e BE) perpendicularis <ptr type="noteAnchor" />, dividetque baſin trianguli iſoce-
<ptr xml:id="note-0126-14a" corresp="note-0126-14" type="noteAnchor" />
les b E e in duas partes æquales ita, ut ei ſit dimidium ipſius eb aut d D. <lb /></s>
          <s xml:space="preserve">Eſt verò ei differentia inter chordas BE, Be; </s>
          <s xml:space="preserve">nam ſi centro B, radio BE, <lb />circulus deſcribatur coincidet hic cum Ei, quæ infinite exigua eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">D d <lb />eſt differentia arcuum Cycloidis DB, dB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0126-13" corresp="note-0126-13a" place="margin">317.</note>
              <note xml:space="preserve" xml:id="note-0126-14" corresp="note-0126-14a" n="*" anchored="true" place="margin">31. El. III,</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus nunc lineam ad baſim Cycloidis AF parallelam moveri à <lb />B ad F, aliamque lineam interea circa B ita rotari, ut continuo tranſeat <lb />per interſectionem primæ cum ſemicirculo. </s>
          <s xml:space="preserve">Ubi prima Ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">pervenit <lb />ad dl erit ſecunda in B e, translatâ primâ ad DL rotatur ſecunda ut ſit in <lb />BE. </s>
          <s xml:space="preserve">In hoc motu, commune initium habent, &amp; </s>
          <s xml:space="preserve">continuo augentur, arcus <lb />Cycloïdis DB &amp; </s>
          <s xml:space="preserve">chorda EB; </s>
          <s xml:space="preserve">ſed illius augmentum ſemper duplum eſt au-<lb />gmentihujus, quare &amp; </s>
          <s xml:space="preserve">integer arcus qui eſt ſumma augmentorum, erit du-<lb />plusintegræ chordæ, quæ etiam ſummam valet augmentorum ſuorum. </s>
          <s xml:space="preserve">Ha-
</s>
          <pb facs="0127" n="75" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XIX.</fw>
bemus ergo etiam demonſtratam propoſitionem in n, 386. </s>
          <s xml:space="preserve">memoratam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Supereſt ut, quæ de evolutione Cycloidis in n. </s>
          <s xml:space="preserve">283. </s>
          <s xml:space="preserve">dicta ſunt, de mon-<lb />ſtremus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Detur iterum eadem Cycloïs ADB; </s>
          <s xml:space="preserve">baſis AF; </s>
          <s xml:space="preserve">axis FB; </s>
          <s xml:space="preserve">FEB ſe-<lb />
<ptr xml:id="note-0127-01a" corresp="note-0127-01" type="noteAnchor" />
micirculus. </s>
          <s xml:space="preserve">Producatur BF ad Cita, ut BF &amp; </s>
          <s xml:space="preserve">FC ſint æquales; </s>
          <s xml:space="preserve">formato-<lb />que parallelogrammo AfCF; </s>
          <s xml:space="preserve">detur ſemicirculus A mf, qui ſemicirculo FEB, <lb />æqualis erit; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">ſemi cycloïs A qC, cujus axis eſt A f &amp; </s>
          <s xml:space="preserve">quæ æqualis <lb />eſt ſemi-cycloïdi ADB. </s>
          <s xml:space="preserve">Concipiamus etiam filum fixum in C &amp; </s>
          <s xml:space="preserve">cycloïdi <lb />C q A applicatum, evolvi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0127-01" corresp="note-0127-01a" place="margin">318.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus filum ad hunc perveniſſe ſitum, ut cum cycloïde tantum con-<lb />veniat à C ad q, &amp; </s>
          <s xml:space="preserve">ulterius protendi juxta tangentem ad curvam in q: </s>
          <s xml:space="preserve">ſi <lb />linea q Q æqualis ſit arcui q A, cui filum, nunc tenſum, fuit applicatum, e-<lb />rit Q fili extremitas.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ducatur q p ad baſin parallela ſemicirculum A m f ſecans in m, ex quo <lb />puncto ducatur linea m A ad A, ſunt m A &amp; </s>
          <s xml:space="preserve">q N parallelæ <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">æquales;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0127-02a" corresp="note-0127-02" type="noteAnchor" />
ſed q A, ideoque q Q dupla eſt m A aut qN; </s>
          <s xml:space="preserve">ſunt ergo æquales N q, NQ; <lb /></s>
          <s xml:space="preserve">idcirco ſi per Q ad AF &amp; </s>
          <s xml:space="preserve">p q detur parallela QP, erunt æquales PF, A p; </s>
          <s xml:space="preserve"><lb />ergo etiam erunt æquales arcus FM, A m; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">anguli MFA, m AF <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0127-03a" corresp="note-0127-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">eſt FM, parallela A m <ptr type="noteAnchor" />, ut &amp; </s>
          <s xml:space="preserve">Q q; </s>
          <s xml:space="preserve">unde ſequitur FMQN eſſe paral.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0127-04a" corresp="note-0127-04" type="noteAnchor" />
lelogrammum, &amp; </s>
          <s xml:space="preserve">æquales eſie FN, QM; </s>
          <s xml:space="preserve">ſunt etiam æquales qm, AN, <lb />in parallelogrammo m AN q.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0127-02" corresp="note-0127-02a" n="*" anchored="true" place="margin">285 316.</note>
              <note xml:space="preserve" xml:id="note-0127-03" corresp="note-0127-03a" n="*" anchored="true" place="margin">32 27 <lb />El. III.</note>
              <note xml:space="preserve" xml:id="note-0127-04" corresp="note-0127-04a" n="*" anchored="true" place="margin">27. El. I.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Linea mq, aut AN, æqualis eſt arcui A m <ptr type="noteAnchor" />, aut arcui FM; </s>
          <s xml:space="preserve">AF, æ-
<ptr xml:id="note-0127-05a" corresp="note-0127-05" type="noteAnchor" />
qualis eſt ſemicirculo FMB <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">idcirco NF, aut QM, æqualis eſt arcui
<ptr xml:id="note-0127-06a" corresp="note-0127-06" type="noteAnchor" />
MEB, &amp; </s>
          <s xml:space="preserve">punctum Q, ideſt fili extremitas datur in cycloïde ADB <ptr type="noteAnchor" />, quam
<ptr xml:id="note-0127-07a" corresp="note-0127-07" type="noteAnchor" />
integram extremitas hæc percurret dum totum filum evolvitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0127-05" corresp="note-0127-05a" n="*" anchored="true" place="margin">325.</note>
              <note xml:space="preserve" xml:id="note-0127-06" corresp="note-0127-06a" n="*" anchored="true" place="margin">282. 315.</note>
              <note xml:space="preserve" xml:id="note-0127-07" corresp="note-0127-07a" n="*" anchored="true" place="margin">315.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SHOLIUM 4.</head>
        <head rend="italics" xml:space="preserve">De linea celerrimi deſcenſus.</head>
        <p>
          <s xml:space="preserve">Monuimus ſuperius <ptr type="noteAnchor" />, quod ex deinde demonſtratis etiam patuit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">corpus
<ptr xml:id="note-0127-08a" corresp="note-0127-08" type="noteAnchor" />
per arcus circuli exiguos breviori tempore deſcendere, quàm per ho-<lb />
<ptr xml:id="note-0127-09a" corresp="note-0127-09" type="noteAnchor" />
rum arcuum chordas. </s>
          <s xml:space="preserve">Unde patet corpus quod à puncto ad punctum de-<lb />ſcendit, quando puncta ambo non in eadem verticali dantur, ut viam ſuam <lb />breviſſimo tempore peragat, non debere per lineam rectam incedere. </s>
          <s xml:space="preserve">Quam-<lb />nam autem lineam ſequi debeat, lubet hìc demonſtrate; </s>
          <s xml:space="preserve">quia ad hoc uſu ve-<lb />niunt quæ in ſuperiori ſcholio de Cycloïde demonſtrata ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0127-08" corresp="note-0127-08a" n="*" anchored="true" place="margin">289.</note>
              <note xml:space="preserve" xml:id="note-0127-09" corresp="note-0127-09a" n="*" anchored="true" place="margin">307.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint puncta duo A &amp; </s>
          <s xml:space="preserve">B, lineâ CD ſeparata; </s>
          <s xml:space="preserve">moveatur punctum &amp; </s>
          <s xml:space="preserve">ab A <lb />
<ptr xml:id="note-0127-10a" corresp="note-0127-10" type="noteAnchor" />
tendat ad B; </s>
          <s xml:space="preserve">ſed ea lege, ut antequam ad lineam CD perveniat, feratur velo-<lb />
<ptr xml:id="note-0127-11a" corresp="note-0127-11" type="noteAnchor" />
citate quam dicimus v, ubi autem tranſivit lineam hanc incedat celeritate <lb />majori quam vocamus c: </s>
          <s xml:space="preserve">Ponamus ulterius punctum velocitatibus ſingulis <lb />rectas vias percurrere; </s>
          <s xml:space="preserve">ideòque moveri per rectam AB, aut lineas AE, EB <lb />peragrare: </s>
          <s xml:space="preserve">determinandum, quomodo motum dirigere debeat, ut tempore <lb />omnium breviſſimo perveniat ex A in B,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0127-10" corresp="note-0127-10a" place="margin">319.</note>
              <note xml:space="preserve" xml:id="note-0127-11" corresp="note-0127-11a" place="margin">TAB. XII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus tempus quo corpus, velocitate v, lineam quamcunque percur-<lb />rit ipſâ lineâ percurfâ repræſentari; </s>
          <s xml:space="preserve">tempus quo linea percurritur, velocita-<lb />te aliâ majori, eo brevius eſt, quo velocitas major eſt, &amp; </s>
          <s xml:space="preserve">minuitur in ratio-<lb />ne in qua velocitas augetur; </s>
          <s xml:space="preserve">tempus ergo, in quo linea quæcunque, veloci-<lb />tate c percurritur, repræſentabitur lineâ minore ipſâ percurſâ, &amp; </s>
          <s xml:space="preserve">quæ ad percur-<lb />ſam habet rationem quæ datur inter v &amp; </s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si punctum eat per AE &amp; </s>
          <s xml:space="preserve">EB tempus motus per AE; </s>
          <s xml:space="preserve">quia velocitate v
</s>
          <pb facs="0128" n="76" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
percurritur linea hæc, hac ipſâ lineâ repræſentatur; </s>
          <s xml:space="preserve">tempus quo EB peragratur, <lb />repræſentatur lineâ EF, quæ ſe habet ad EB, ut v ad c. </s>
          <s xml:space="preserve">Punctum ve-<lb />ro F determinatur ſi ex B ad CD ducatur BD perpendicularis, fiatque c, v:</s>
          <s xml:space="preserve">: <lb />BD, LD &amp; </s>
          <s xml:space="preserve">per L ad DC ducatur parallela, ſecabit hæc BE in puncto F: <lb /></s>
          <s xml:space="preserve">nam propter parallelas ED, FL, habemus BD, LD :</s>
          <s xml:space="preserve">: BE, FE.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hac demoſiſtratione etiam ſequitur, ſi punctum per lineas alias AM, <lb />MB, progrediatur, quarum ultima ſecat LF in N, tempus motus repræ-<lb />ſentari lineis AM, MN, ita ut determinandum ſit per quod punctum lineæ <lb />CD punctum mobile tranſeat, quando ſumma talium linearum tempora repræ-<lb />ſentantium eſt omnium minima; </s>
          <s xml:space="preserve">quod ut fiat ad ſequentia attendendum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Summas ab utraque parte recedendo à puncto quæſito augeri continuo; <lb /></s>
          <s xml:space="preserve">ideoque in eo puncto ſolo ſummas vicinas eſſe æquales, idcirco ſi punctum <lb />hoc ſit E erunt æquales AE + EF &amp; </s>
          <s xml:space="preserve">Ae + ef ex qua æqualitate ſitus pun-<lb />
<ptr xml:id="note-0128-01a" corresp="note-0128-01" type="noteAnchor" />
cti E deducendus eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0128-01" corresp="note-0128-01a" place="margin">TAB XII. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Centro A, radio A e deſcribatur circuli arcus eb; </s>
          <s xml:space="preserve">Centro Bradiis Bf, &amp; </s>
          <s xml:space="preserve"><lb />BE deſcribantur arcus E i, fg, eruntque æquales Ab + Eg &amp; </s>
          <s xml:space="preserve">A e + i f ſubtra-<lb />ctis hiſce quantitatibus æqualibus ex AE + EF = Ae + ef, reſtanth E + gF = ei. <lb /></s>
          <s xml:space="preserve">Unde deducimus. </s>
          <s xml:space="preserve">hE = ei-gF. </s>
          <s xml:space="preserve">Propter triangula ſimilia eiE, fgF, &amp; </s>
          <s xml:space="preserve">Bfg, <lb />Bie ut &amp; </s>
          <s xml:space="preserve">BFL, BED,</s>
        </p>
        <p>
          <s xml:space="preserve">ei, g F :</s>
          <s xml:space="preserve">: Ei, fg, :</s>
          <s xml:space="preserve">: BE, Bf aut BF (difterentia enim eſt infi nite exigua) <lb />:</s>
          <s xml:space="preserve">: BD, BL. </s>
          <s xml:space="preserve">Dividendo</s>
        </p>
        <p>
          <s xml:space="preserve">ei, ei g F = bE:</s>
          <s xml:space="preserve">: BD, BD-BL = LD; </s>
          <s xml:space="preserve">id eſt ut velocitas infra lineam ad <lb />velocitatem ſupra lineam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Triangula eiE, ENO, ſunt ſimilia ut &amp; </s>
          <s xml:space="preserve">eb E &amp; </s>
          <s xml:space="preserve">e MP; </s>
          <s xml:space="preserve">ergo</s>
        </p>
        <p>
          <s xml:space="preserve">ei, Ee:</s>
          <s xml:space="preserve">: EO, EN</s>
        </p>
        <p>
          <s xml:space="preserve">bE, Ee:</s>
          <s xml:space="preserve">: EP, Me = EN nam ſunt radii ejuſdem circuli; </s>
          <s xml:space="preserve">E e c-<lb />nim eſt infinite exigua.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex æquo ei, bE:</s>
          <s xml:space="preserve">: EO, EP. </s>
          <s xml:space="preserve">Sunt autem hæ lineæ coſinus angulorum <lb />
<ptr xml:id="note-0128-02a" corresp="note-0128-02" type="noteAnchor" />
quos directiones motuum efficiunt cum linea CD quæ ſpatia ſeparat in quibus velo-<lb />eitates differunt: </s>
          <s xml:space="preserve">qui ergo coſinus directionum ſunt inter ut velocitates in ipſis <lb />iltis directionibus, quando tempus eſt omnium breviſſimum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0128-02" corresp="note-0128-02a" place="margin">320.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Moveatur iterum corpus ex A &amp; </s>
          <s xml:space="preserve">tendat ad B, ea conditioneut dum tranſ-<lb />
<ptr xml:id="note-0128-03a" corresp="note-0128-03" type="noteAnchor" />
it lineas CD, IL, MN, OP, ſingulis vicibus velocitatem mutet, quæ-<lb />
<ptr xml:id="note-0128-04a" corresp="note-0128-04" type="noteAnchor" />
ritur qua lege movetur, poſitis hiſce lineis parallelis, ut tempore breviſſimo <lb />ex A ad B perveniat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0128-03" corresp="note-0128-03a" place="margin">321.</note>
              <note xml:space="preserve" xml:id="note-0128-04" corresp="note-0128-04a" place="margin">TAB. XII. <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Requiritur ut corpus ex A ad F perveniat tempore breviſſimo poſſibili, <lb />ut &amp; </s>
          <s xml:space="preserve">ex E ad G, ex F ad H, &amp; </s>
          <s xml:space="preserve">ex G ad B, aliter enim in toto motu tem-<lb />pus brevius dari poteſt. </s>
          <s xml:space="preserve">Ideò coſinus angulorum quos motus directiones AE, <lb />
<ptr xml:id="note-0128-05a" corresp="note-0128-05" type="noteAnchor" />
EF, FG, GH, HB, efficiunt cum lineis, parallelis inter ſe, ſeparantibus ſpa-<lb />tia in quibus diverſa eſt velocitas, ſunt reſpectivè inter ſe ut velocitates quibus ſin-<lb />gu'a percurruntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0128-05" corresp="note-0128-05a" place="margin">322.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Conſideremus nunc corpus quod gravitate deſcendit. </s>
          <s xml:space="preserve">Celeritas continuo <lb />deſcendendo augetur, &amp; </s>
          <s xml:space="preserve">ad eandem profunditatem ubique eſt eadem <ptr type="noteAnchor" />, innu-
<ptr xml:id="note-0128-06a" corresp="note-0128-06" type="noteAnchor" />
meris ergo, &amp; </s>
          <s xml:space="preserve">inter ſe infinitè parum diſtantibus, planis horizontalibus divi-<lb />duntur ſpatia in quibus celeritas variat: </s>
          <s xml:space="preserve">Linea ergo celerrimi deſcenſus inter <lb />
<ptr xml:id="note-0128-07a" corresp="note-0128-07" type="noteAnchor" />
duo puncta eſt cujus tangens ubique cum borizonte eſſicit angulum, cujus coſinus <lb />velocitati cadendo acquiſitæ proportionalis eſt <ptr type="noteAnchor" />, id eſt radici quadratæ altitu-
<ptr xml:id="note-0128-08a" corresp="note-0128-08" type="noteAnchor" />
dinis per quam corpus cecidit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hanc autem eſſe Cycloïdis proprietatem de-
<ptr xml:id="note-0128-09a" corresp="note-0128-09" type="noteAnchor" />
monſtramus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0128-06" corresp="note-0128-06a" n="*" anchored="true" place="margin">271.</note>
              <note xml:space="preserve" xml:id="note-0128-07" corresp="note-0128-07a" place="margin">323.</note>
              <note xml:space="preserve" xml:id="note-0128-08" corresp="note-0128-08a" n="*" anchored="true" place="margin">322.</note>
              <note xml:space="preserve" xml:id="note-0128-09" corresp="note-0128-09a" n="*" anchored="true" place="margin">255-271.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0129" n="77" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XIX.</fw>
        <p>
          <s xml:space="preserve">Ponamus Cycloïdem ADB, inverſam, cujus axis ſit verticalis, &amp; </s>
          <s xml:space="preserve">corpus <lb />
<ptr xml:id="note-0129-01a" corresp="note-0129-01" type="noteAnchor" />
ex A deſcendere, demonſtrandum anguliut d DE, aut BEL <ptr type="noteAnchor" />, coſinum pro-
<ptr xml:id="note-0129-02a" corresp="note-0129-02" type="noteAnchor" />
portionalem eſſe radici quadratæ altitudinis FL <ptr type="noteAnchor" />, id eſt proportionem ſe-
<ptr xml:id="note-0129-03a" corresp="note-0129-03" type="noteAnchor" />
qui chordæ FE cujus quadratum ad inſtar altitudinis FL augetur &amp; </s>
          <s xml:space="preserve">minui-<lb />
<ptr xml:id="note-0129-04a" corresp="note-0129-04" type="noteAnchor" />
tur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Angulus BE l æqualis eſt angulo BFE <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">cujus coſinus ſi centrum
<ptr xml:id="note-0129-05a" corresp="note-0129-05" type="noteAnchor" />
circuli ſit F, &amp; </s>
          <s xml:space="preserve">radius FB, eſt FE; </s>
          <s xml:space="preserve">quod in omnibus punctis cycloïdis Io-<lb />
<ptr xml:id="note-0129-06a" corresp="note-0129-06" type="noteAnchor" />
cum habet, manente eodem radio FB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0129-01" corresp="note-0129-01a" place="margin">324.</note>
              <note xml:space="preserve" xml:id="note-0129-02" corresp="note-0129-02a" n="*" anchored="true" place="margin">285. 316.</note>
              <note xml:space="preserve" xml:id="note-0129-03" corresp="note-0129-03a" n="*" anchored="true" place="margin">323.</note>
              <note xml:space="preserve" xml:id="note-0129-04" corresp="note-0129-04a" place="margin">TAB. XII. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0129-05" corresp="note-0129-05a" n="*" anchored="true" place="margin">293.</note>
              <note xml:space="preserve" xml:id="note-0129-06" corresp="note-0129-06a" place="margin">8. El. VI.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Linea ergo celerrimi deſcenſus, à puncto ad punctum, eſt Cycloïs inverſa, cu-<lb />
<ptr xml:id="note-0129-07a" corresp="note-0129-07" type="noteAnchor" />
jus punctum extremum, ut A, cum ſuperiori puncto coincidit &amp; </s>
          <s xml:space="preserve">quæ per punctum <lb />alterum tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0129-07" corresp="note-0129-07a" place="margin">325.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XX.</head>
        <head rend="italics" xml:space="preserve">De Projectione Gravium.</head>
        <p>
          <s xml:space="preserve">SI in corpus motum potentia agat, mutatur motus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0129-08a" corresp="note-0129-08" type="noteAnchor" />
Corpus projiciatur per AB, in tempore, in quo poteſt <lb />
<ptr xml:id="note-0129-09a" corresp="note-0129-09" type="noteAnchor" />
percurrere AB, vi gravitatis, fertur terræ centrum verſus <lb />
<ptr xml:id="note-0129-10a" corresp="note-0129-10" type="noteAnchor" />
per BF, &amp; </s>
          <s xml:space="preserve">ita, motu compoſito ex iſtis duobus, movetur <lb />per AF <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hoc motu, ſecundo momento, percurreret <ptr type="noteAnchor" />
<ptr xml:id="note-0129-11a" corresp="note-0129-11" type="noteAnchor" />
FC, ipſi AF æqualem, niſi ſecundo momento eadem vi <lb />gravitatis translatum foret per CG, ita ut motus in ſecun-<lb />do momento ſit per FG; </s>
          <s xml:space="preserve">eodem modo, motus tertii mo-<lb />menti eſt per GH, &amp; </s>
          <s xml:space="preserve">quarti momenti per HI; </s>
          <s xml:space="preserve">cùm verò <lb />vis gravitatis continuò agat, illa temporis momenta mini-<lb />ma ſunt, &amp; </s>
          <s xml:space="preserve">ubique dabitur motus aliter compoſitus, id eſt, <lb />directionis inflexio; </s>
          <s xml:space="preserve">in eo caſu ergo corpus movetur in li-<lb />nea curva.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0129-08" corresp="note-0129-08a" place="margin">326.</note>
              <note xml:space="preserve" xml:id="note-0129-09" corresp="note-0129-09a" place="margin">TAB XIII. <lb />fig. I.</note>
              <note xml:space="preserve" xml:id="note-0129-10" corresp="note-0129-10a" n="*" anchored="true" place="margin">245</note>
              <note xml:space="preserve" xml:id="note-0129-11" corresp="note-0129-11a" n="*" anchored="true" place="margin">246.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hic motus corporis ex projectione magis ſimpliciter con-<lb />
<ptr xml:id="note-0129-12a" corresp="note-0129-12" type="noteAnchor" />
ſiderari poteſt in omnibus projectionibus, quæ a nobis fie-<lb />ri poſſunt; </s>
          <s xml:space="preserve">quia omnes lineæ, quæ ad terræ centrum ten-<lb />dunt, pro parallelis haberi poſſunt; </s>
          <s xml:space="preserve">quare directio motus <lb />ex gravitate ſemper eſt eadem; </s>
          <s xml:space="preserve">unde motus ex projectione <lb />ex duobus tantum motibus conſtat, primo æquabili per li-<lb />neam projectionis, ſecundo terram verſus accelerato <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0129-12" corresp="note-0129-12a" place="margin">327.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">251.</note>
        <p>
          <s xml:space="preserve">Projiciatur corpus per lineam AE, horizonti parallelam; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0129-14a" corresp="note-0129-14" type="noteAnchor" />
temporibus æqualibus, hoc motu, percurret partes æquales <lb />AB, BC, CD, DE: </s>
          <s xml:space="preserve">Ex gravitate fertur motu ad horizontem <lb />perpendiculari, directione BF, CG, DH, aut EI, quæ hìc <lb />parallelæ ponuntur; </s>
          <s xml:space="preserve">motus hic eſt acceleratus, &amp; </s>
          <s xml:space="preserve">ideò, ſi
</s>
          <pb facs="0130" n="78" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
poſt primum momentum corpus ſit in F, poſt ſecundum <lb />erit in G, poſt tertium in H, poſt quartum in I, ita quidem <lb />ut poſito BF unum, CG ſit quatuor, DH novem, &amp; </s>
          <s xml:space="preserve">EI <lb />ſedecim <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Corpus percurret curvam tranſeuntem per o-
<ptr xml:id="note-0130-01a" corresp="note-0130-01" type="noteAnchor" />
mnia puncta, quæ eodem modo ac F, G, H, I, determinari <lb />poſſunt, vocaturque Parabola.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0129-14" corresp="note-0129-14a" place="margin">TAB XIII. <lb />fig. 25</note>
              <note xml:space="preserve" xml:id="note-0130-01" corresp="note-0130-01a" n="*" anchored="true" place="margin">255.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head rend="italics" xml:space="preserve">Qua demonſtrata de corporum projectione confirmantur.</head>
        <p>
          <s xml:space="preserve">Conſtat hæc ex tribus partibus, quarum conſtructio ex <lb />
<ptr xml:id="note-0130-02a" corresp="note-0130-02" type="noteAnchor" />
figura ſatis patet. </s>
          <s xml:space="preserve">Ah eſt altitudinis ſex pollicum; </s>
          <s xml:space="preserve">DE eſt <lb />
<ptr xml:id="note-0130-03a" corresp="note-0130-03" type="noteAnchor" />
exacte ejuſdem altitudinis; </s>
          <s xml:space="preserve">longitudo b H eſt duodecim <lb />pollicum, poſito puncto H, ad diſtantiam unius pollicis ab <lb />extremitate cavitatis in qua punctum hocce ponitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0130-02" corresp="note-0130-02a" place="margin">328.</note>
              <note xml:space="preserve" xml:id="note-0130-03" corresp="note-0130-03a" place="margin">TAB. XIII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circulariter, aut juxta aliam curvam quamcunque, ex-<lb />cavatur EA; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">lamina ferri, ſtanno illiti, &amp; </s>
          <s xml:space="preserve">admodum <lb />politi, obtegitur; </s>
          <s xml:space="preserve">ut globus æneus libere juxta illam cur-<lb />vam devolvi poſſit; </s>
          <s xml:space="preserve">in qua devolutione obſervandum, ut <lb />curvæ directio in A ſit horizontalis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dividitur A h in novem partes æquales, quarum A f u-<lb />na eſt, A g quatuor.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando huic primæ parti Machinæ conjungitur ſecunda <lb />
<ptr xml:id="note-0130-04a" corresp="note-0130-04" type="noteAnchor" />
B, pertingit hæc ad g, &amp; </s>
          <s xml:space="preserve">g G eſt octo pollicum: </s>
          <s xml:space="preserve">ſi huic ſu-<lb />perimponatur pars tertia C, pertingit hæc ultima ad f, &amp; </s>
          <s xml:space="preserve"><lb />fF eſt quatuor pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0130-04" corresp="note-0130-04a" place="margin">TAB. XIII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Suſtinetur Machina hæc tribus cochleis, quarum ope li-<lb />nea A b ponitur in ſitu verticali, qui ſitus determinatur per-<lb />pendiculo ad partem machinæ poſticam; </s>
          <s xml:space="preserve">eodem omnino <lb />modo ac hæc in alia Machina exhibentur in fig. </s>
          <s xml:space="preserve">I. </s>
          <s xml:space="preserve">Tab XII. <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">explicantur in n. </s>
          <s xml:space="preserve">276.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Diameter globi P, qui in Experimentis dimittitur juxta <lb />curvam EA, eſt circiter ſemi-pollicis; </s>
          <s xml:space="preserve">nec minori globo, <lb />aut Machinâ, quàm quæ hìc deſcribitur, majori utendum: <lb /></s>
          <s xml:space="preserve">quo enim corpora ſunt minora &amp; </s>
          <s xml:space="preserve">motus celeriores, eo etiam <lb />magis, ſervatâ proportione, motus aëris reſiſtentiâ re-<lb />tardatur; </s>
          <s xml:space="preserve">ut ſuo loco dicetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando globus P ab E dimittitur, devolvendo per cur-<lb />vam EA certam acquirit velocitatem, quæ in repetitis de-
</s>
          <pb facs="0131" n="78" />
          <s xml:space="preserve">
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</s>
          <pb facs="0131a" />
          <s xml:space="preserve">
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</s>
          <pb facs="0132" />
          <s xml:space="preserve">
</s>
          <pb facs="0133" n="79" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XX.</fw>
volutionibus ſemper eſt eadem; </s>
          <s xml:space="preserve">eaque cum celeritate, &amp; </s>
          <s xml:space="preserve"><lb />directione horizontali, motum continuat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0131-01" corresp="fig-0131-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0131-01" />
                <label>0131-01</label>
              </figure>
              <figure xml:id="fig-0131a-01" corresp="fig-0131a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0131a-01" />
                <label>0131a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum.</hi></head>
        <p>
          <s xml:space="preserve">Junctis tribus Machinæ partibus; </s>
          <s xml:space="preserve">ut in fig. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve">, dimittatur <lb />
<ptr xml:id="note-0133-01a" corresp="note-0133-01" type="noteAnchor" />
globus P ab E, impinget in F. </s>
          <s xml:space="preserve">Sublata parte minori C, ite-<lb />rum dimittatur globus, impinget in G. </s>
          <s xml:space="preserve">Sublata tandem <lb />parte B, &amp; </s>
          <s xml:space="preserve">globo dimiſſo, impingit in H.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0133-01" corresp="note-0133-01a" place="margin">329.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si argilla mollis detur in H &amp; </s>
          <s xml:space="preserve">G, punctum impactus exa-<lb />ctiſſime notatur; </s>
          <s xml:space="preserve">in puncto F, propter directionem motus <lb />nimium obliquam, hæc methodus locum non habet; </s>
          <s xml:space="preserve">ſed <lb />repetitis Experimentis, ſolo viſu, punctum hocce ſatis de-<lb />terminatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propoſitio n. </s>
          <s xml:space="preserve">257, hac Machina Experimento confirma-<lb />
<ptr xml:id="note-0133-02a" corresp="note-0133-02" type="noteAnchor" />
tur; </s>
          <s xml:space="preserve">nam ut ſtatim dictum, globus devolvens per EA im-<lb />
<ptr xml:id="note-0133-03a" corresp="note-0133-03" type="noteAnchor" />
pingit in H. </s>
          <s xml:space="preserve">Devolvendo per EA acquirit celeritatem, <lb />quam cadendo per ED potuiſſet acquirere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ea cum celeri-
<ptr xml:id="note-0133-04a" corresp="note-0133-04" type="noteAnchor" />
tate, ex puncto A, horizontaliter projicitur, &amp; </s>
          <s xml:space="preserve">æquabili-<lb />ter ſecundum illam directionem movetur per b H, dum ca-<lb />dendo percurrit A b, ipſi ED æqualem; </s>
          <s xml:space="preserve">b H vero eſt i-<lb />pſius A b aut ED dupla.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0133-02" corresp="note-0133-02a" place="margin">330.</note>
              <note xml:space="preserve" xml:id="note-0133-03" corresp="note-0133-03a" place="margin">TAB XIII. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0133-04" corresp="note-0133-04a" n="*" anchored="true" place="margin">271.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quæ de curva a corpore horizontaliter projecto dicta ſunt, <lb />
<ptr xml:id="note-0133-05a" corresp="note-0133-05" type="noteAnchor" />
etiam pertinent ad projectionem quamcumque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0133-05" corresp="note-0133-05a" place="margin">331.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Projiciatur corpus per AE; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſint AB, BC, CD, DE, <lb />
<ptr xml:id="note-0133-06a" corresp="note-0133-06" type="noteAnchor" />
æquales; </s>
          <s xml:space="preserve">corpus percurret curvam AFGHI ita, ut ver-<lb />ticales lineæ BF, CG, DH, EI ſint inter ſe, ut I. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">9. <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">16.</s>
          <s xml:space="preserve">; in quo caſu etiam curva Parabola vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0133-06" corresp="note-0133-06a" place="margin">TAB. XIII. <lb />fig. 506.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi></head>
        <p>
          <s xml:space="preserve">Sit AI planum quod per A tranſit, ſi curva memorata <lb />
<ptr xml:id="note-0133-07a" corresp="note-0133-07" type="noteAnchor" />
hoc ſecet in I; </s>
          <s xml:space="preserve">AI vocatur amplitudo jactus</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0133-07" corresp="note-0133-07a" place="margin">332.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus corporum, quæ eadem celeritate projiciuntur, cum <lb />directionibus diverſe inclinatis, poſſunt inter ſe comparari:</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Poteſtque corpus celeritate data in plano dato ad diſtantiam <lb />
<ptr xml:id="note-0133-08a" corresp="note-0133-08" type="noteAnchor" />
quamcunque projici. </s>
          <s xml:space="preserve">Sit celeritas data illa, quam corpus acqui-<lb />rit cadendo ab altitudine LA, quam horizonti AT perpendi-<lb />cularem concipimus, &amp; </s>
          <s xml:space="preserve">corpus in plano AI in I projicien-<lb />dum ſit. </s>
          <s xml:space="preserve">Ductâ LN horizonti parallelâ, erigatur AN nor-
</s>
          <pb facs="0134" n="80" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
malis plano A I, ſecans L N in N; </s>
          <s xml:space="preserve">centro puncto medio li-<lb />neæ <hi rend="small caps">A</hi>N per <hi rend="small caps">A</hi> deſcribatur circulus, qui etiam per L tranſ-<lb />ibit; </s>
          <s xml:space="preserve">ſit <hi rend="small caps">A</hi>R pars quarta lineæ <hi rend="small caps">A</hi>I; </s>
          <s xml:space="preserve">per R ducatur, hori-<lb />zonti perpendicularis, id eſt parallela lineæ <hi rend="small caps">A</hi>L, linea R b, <lb />quæ circulum ſecat in B &amp; </s>
          <s xml:space="preserve">b; </s>
          <s xml:space="preserve">ſi corpus projiciatur per <hi rend="small caps">A</hi>B <lb />aut A b cadet in I. </s>
          <s xml:space="preserve">Qua methodo directio jactus determi-<lb />natur, ſi punctum ſit in linea horizontali per A tranſeunti <lb />(in quo caſu L &amp; </s>
          <s xml:space="preserve">N coincidunt), aut in plano quocunque <lb />inclinato ſive ſupra ſive infra lineam hanc horizontalem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0133-08" corresp="note-0133-08a" place="margin">333.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motu æ quabili celeritate, cum qua projectio fit, corpus <lb />
<ptr xml:id="note-0134-01a" corresp="note-0134-01" type="noteAnchor" />
poteſt percurrere <hi rend="small caps">A</hi>E, dum cadit per EI Quia corpus pro-<lb />jicitur velocitate per <hi rend="small caps">La</hi> cadendo acquiſita, eodem motu <lb />æ quabili poteſt percurrere duplam <hi rend="small caps">La</hi> in tempore in quo <lb />ab altitudine <hi rend="small caps">La</hi> cadit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Spatia, velocitate eâdem &amp; </s>
          <s xml:space="preserve">æ-
<ptr xml:id="note-0134-02a" corresp="note-0134-02" type="noteAnchor" />
quabili percurſa, ſunt ut tempora in quibus percurruntur<ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0134-03a" corresp="note-0134-03" type="noteAnchor" />
ergo tempus caſus per <hi rend="small caps">La</hi> ad tempus caſus per EI, ut <lb />dupla <hi rend="small caps">La</hi> ad <hi rend="small caps">A</hi>E. </s>
          <s xml:space="preserve">Ideo 2 <hi rend="small caps">La</hi><hi rend="superscript">9</hi> ad <hi rend="small caps">A</hi>E<hi rend="superscript">9</hi> ut, <hi rend="small caps">La</hi> ad <lb />EI <ptr type="noteAnchor" />, Quam ergo proportionem ſi demonſtremus dari in
<ptr xml:id="note-0134-04a" corresp="note-0134-04" type="noteAnchor" />
conſtructione præ cedenti, directionem benè fuiſſe determi-<lb />natam conſtabit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0134-01" corresp="note-0134-01a" place="margin">334.</note>
              <note xml:space="preserve" xml:id="note-0134-02" corresp="note-0134-02a" n="*" anchored="true" place="margin">257.</note>
              <note xml:space="preserve" xml:id="note-0134-03" corresp="note-0134-03a" n="*" anchored="true" place="margin">95.</note>
              <note xml:space="preserve" xml:id="note-0134-04" corresp="note-0134-04a" n="*" anchored="true" place="margin">255.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ducatur LB, &amp; </s>
          <s xml:space="preserve">habemus angulum <hi rend="small caps">Ba</hi>R a tangente <hi rend="small caps">A</hi>R, <lb />eſt enim perpendicularis radio <hi rend="small caps">A</hi>O, &amp; </s>
          <s xml:space="preserve">a linea circulum ſe-<lb />cante <hi rend="small caps">A</hi>B formatum æ qualem angulo <hi rend="small caps">A</hi>MB in ſegmento <lb />
<ptr xml:id="note-0134-05a" corresp="note-0134-05" type="noteAnchor" />
oppoſito <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">anguli etiam alterni <hi rend="small caps">RBa</hi>, <hi rend="small caps">La</hi>B, ſunt æ quales <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0134-06a" corresp="note-0134-06" type="noteAnchor" />
ergo ſunt ſimilia triangula <hi rend="small caps">A</hi>BR, <hi rend="small caps">A</hi>LB, &amp; </s>
          <s xml:space="preserve">lineæ <hi rend="small caps">La</hi>, <lb /><hi rend="small caps">A</hi>B, <hi rend="small caps">Br</hi>, proportionales; </s>
          <s xml:space="preserve">ergo <hi rend="small caps">La</hi><hi rend="superscript">9</hi> ad <hi rend="small caps">A</hi>B<hi rend="superscript">9</hi> ut <hi rend="small caps">La</hi> ad <lb />BR; </s>
          <s xml:space="preserve">ideo 2 <hi rend="small caps">La</hi><hi rend="superscript">9</hi> ad 2 <hi rend="small caps">A</hi>B<hi rend="superscript">9</hi>, aut <hi rend="small caps">A</hi>C<hi rend="superscript">9</hi> ut <hi rend="small caps">La</hi> ad BR: <lb /></s>
          <s xml:space="preserve">multiplicando conſequentia per quatuor, habemus 2 <hi rend="small caps">La</hi><hi rend="superscript">9</hi> <lb />ad <hi rend="small caps">A</hi>C<hi rend="superscript">9</hi> multiplicatum per quatuor, id eſt 2 <hi rend="small caps">A</hi>C<hi rend="superscript">9</hi>, aut <lb /><hi rend="small caps">A</hi>E<hi rend="superscript">9</hi>, ut <hi rend="small caps">La</hi> ad 4 BR, aut EI, quod demonſtrandum <lb />erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0134-05" corresp="note-0134-05a" n="*" anchored="true" place="margin">32 EI. III.</note>
              <note xml:space="preserve" xml:id="note-0134-06" corresp="note-0134-06a" n="*" anchored="true" place="margin">29. EI. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Demonſtratio ſimilis eſt, ſi corpus per A b projiciatur. </s>
          <s xml:space="preserve">Un-<lb />
<ptr xml:id="note-0134-07a" corresp="note-0134-07" type="noteAnchor" />
de ſequitur corpus per duas directiones poſſe projici ut in <lb />idem punctum cadat, ſi autem diſtantia ſit omnium maxima <lb />ad quam corpus, data velocitate, in plano dato, poteſt pro-<lb />jici, unica eſt directio per quam projiciendum eſt corpus,
</s>
          <pb facs="0135" n="81" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XX.</fw>
punctis B &amp; </s>
          <s xml:space="preserve">b coincidentibus in Q, puncto medio arcus <lb />LQA, a quo puncto ſemper æqualiter diſtant puncta B <lb />&amp; </s>
          <s xml:space="preserve">b.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0134-07" corresp="note-0134-07a" place="margin">335.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si AI ſit horizontalis arcus AQL, eſt ſemicirculus, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0135-01a" corresp="note-0135-01" type="noteAnchor" />
in hoc caſu amplitudo, manente celeritate, cum qua pro-<lb />jectio fit, eſt omnium maxima, quando directio projectionis <lb />cum borizonte efficit angulum ſemirectum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0135-01" corresp="note-0135-01a" place="margin">336.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si celeritas mutetur, &amp; </s>
          <s xml:space="preserve">corpus ſecundum eandem dire-<lb />ctionem projiciatur, amplitudo in eodem plano mutatur in ea-<lb />dem ratione cum altitudine A L; </s>
          <s xml:space="preserve">id eſt, amplitudines, manente <lb />
<ptr xml:id="note-0135-02a" corresp="note-0135-02" type="noteAnchor" />
eâdem directione, ſunt ut altitudines ad quas corpora, iiſ-<lb />dem celeritatibus, in altum projecta adſcendere poſſunt; <lb /></s>
          <s xml:space="preserve">ſunt ergo ut quadrata celeritatum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0135-02" corresp="note-0135-02a" place="margin">337.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">262.</note>
        <p>
          <s xml:space="preserve">Sit iterum <hi rend="small caps">La</hi> altitudo a qua cadendo corpus acquirit <lb />
<ptr xml:id="note-0135-04a" corresp="note-0135-04" type="noteAnchor" />
velocitatem cum qua projicitur per <hi rend="small caps">A</hi>B; </s>
          <s xml:space="preserve">punctum altiſſi-<lb />
<ptr xml:id="note-0135-05a" corresp="note-0135-05" type="noteAnchor" />
mum viæ percurſæ determinatur, ſi deſcripto ſemicirculo <lb />cujus diameter eſt AL, per punctum B in quo a directio-<lb />ne projectionis ſecatur ducatur horizontalis linea MBG, <lb />&amp; </s>
          <s xml:space="preserve">fiat BG æqualis BM; </s>
          <s xml:space="preserve">punctum quæſitum erit G.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0135-04" corresp="note-0135-04a" place="margin">338.</note>
              <note xml:space="preserve" xml:id="note-0135-05" corresp="note-0135-05a" place="margin">TAB XIII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hujus patebit demonſtratio ſi ad ſequentia attendamus; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0135-06a" corresp="note-0135-06" type="noteAnchor" />
ductâ AI horizontali, corpus ut dictum projectum cadet in <lb />I, poſitâ AI quadrupla MB aut AR <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0135-06" corresp="note-0135-06a" place="margin">339.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">134.</note>
        <p>
          <s xml:space="preserve">Dum corpus per AB projicitur motus hicce coincidit <lb />cum duplici motu horizontali uno &amp; </s>
          <s xml:space="preserve">æquabili, altero <lb />verticali <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ultimo motu corpus adſcendit &amp; </s>
          <s xml:space="preserve">deſcen-
<ptr xml:id="note-0135-08a" corresp="note-0135-08" type="noteAnchor" />
dit, tempuſque adſcenſus æquale eſt tempori deſcenſus; <lb /></s>
          <s xml:space="preserve">ideò aſcenſus terminatur ubi corpus motu horizontali dimi-<lb />dium AI, id eſt MG, percurrit; </s>
          <s xml:space="preserve">punctum ergo altiſſimum <lb />datur in verticali lineâ SC quæ per G tranſit. </s>
          <s xml:space="preserve">Dentur IE <lb />verticalis, AB continuatam ſecans in E, ut &amp; </s>
          <s xml:space="preserve">verticalis <lb />BR; </s>
          <s xml:space="preserve">quia MG dupla eſt MB, id eſt <hi rend="small caps">A</hi>S dupla <hi rend="small caps">A</hi>R; </s>
          <s xml:space="preserve"><lb />eſt etiam CS dupla BR, id eſt CG æqualis GS: </s>
          <s xml:space="preserve">Sed <lb />AI dupla eſt AS; </s>
          <s xml:space="preserve">ergo EI dupla CS, &amp; </s>
          <s xml:space="preserve">quadrupla CG; </s>
          <s xml:space="preserve"><lb />etiam AE dupla AC. </s>
          <s xml:space="preserve">Dum Corpus motu projectitio per-<lb />currit <hi rend="small caps">A</hi>E, cadit per EI; </s>
          <s xml:space="preserve">dum percurrit AC, cadendo quar-<lb />tam partem EI id eſt CG percurrit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">tranſit idcirco in
<ptr xml:id="note-0135-09a" corresp="note-0135-09" type="noteAnchor" />
</s>
          <pb facs="0136" n="82" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
motu ſuo per punctum G, quod eſt punctum altiſſimum <lb />cùm hoc detur in linea CS.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0135-08" corresp="note-0135-08a" n="*" anchored="true" place="margin">246.</note>
              <note xml:space="preserve" xml:id="note-0135-09" corresp="note-0135-09a" n="*" anchored="true" place="margin">255.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si detur curvâ à corpore percurſâ, velocitas quam habet <lb />
<ptr xml:id="note-0136-01a" corresp="note-0136-01" type="noteAnchor" />
corpus in puncto quocunque ut F, illa eſt, quam Corpus po-<lb />teſt acquirere cadendo à linea horizontali per L ducta ad <lb />punctum F. </s>
          <s xml:space="preserve">Nam Corpus per planum quodcunque ex A, <lb />velocitate qua projicitur, adſcendere poteſt ad horizontalem <lb />hanc lineam <ptr type="noteAnchor" />, ſi nunc planum detur ad F uſque cum ipſa
<ptr xml:id="note-0136-02a" corresp="note-0136-02" type="noteAnchor" />
corporis projecti via congruens, in F autem ſurſum defle-<lb />xum, corpus in F illam habebit velocitatem qua juxta pla-<lb />num hoc ad horizontalem memoratam pervenire poteſt, <lb />id eſt quam cadendo ab ipſa horizontali ad F uſque ac-<lb />quirere poteſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0136-01" corresp="note-0136-01a" place="margin">340.</note>
              <note xml:space="preserve" xml:id="note-0136-02" corresp="note-0136-02a" n="*" anchored="true" place="margin">274.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">274.</note>
        <p>
          <s xml:space="preserve">Sit corpus ex A projiciendum per punctum H in I, poſi-<lb />
<ptr xml:id="note-0136-04a" corresp="note-0136-04" type="noteAnchor" />
tis tribus hiſce punctis in eodem plano verticali, &amp; </s>
          <s xml:space="preserve">puncto <lb />
<ptr xml:id="note-0136-05a" corresp="note-0136-05" type="noteAnchor" />
medio ſupra lineam quæ reliqua duo jungit. </s>
          <s xml:space="preserve">Sit AI ho-<lb />rizontalis &amp; </s>
          <s xml:space="preserve">per tria puncta data ad hanc normales TE, FD, <lb />AL. </s>
          <s xml:space="preserve">Ex I per puncta A &amp; </s>
          <s xml:space="preserve">H ducantur lineæ IA, IH, <lb />quarum ultima ſecat AL in P; </s>
          <s xml:space="preserve">fiat GD æqualis <hi rend="small caps">A</hi>P, &amp; </s>
          <s xml:space="preserve"><lb />habetur <hi rend="small caps">A</hi>D directio jactus. </s>
          <s xml:space="preserve">Celeritas detegitur ſi ſumtâ <lb /><hi rend="small caps">A</hi>R quartâ parte <hi rend="small caps">A</hi>I; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ductâ verticali RB, quæ <hi rend="small caps">A</hi>D <lb />ſecat in B, ducatur BL ita, ut angulus <hi rend="small caps">A</hi>BL æqualis ſit <lb />angulo <hi rend="small caps">A</hi>RB, velocitas quæſita eſt quam corpus acquirit <lb />cadendo ex L in A,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0136-04" corresp="note-0136-04a" place="margin">341.</note>
              <note xml:space="preserve" xml:id="note-0136-05" corresp="note-0136-05a" place="margin">TAB. XIII. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus projectum æquabili percurrit velocitate <hi rend="small caps">A</hi>E &amp; </s>
          <s xml:space="preserve"><lb />AD, dum cadit per EI &amp; </s>
          <s xml:space="preserve">DH: </s>
          <s xml:space="preserve">ut ergo demonſtremus <lb />corpus per hæc puncta tranſire, demonſtrandum <lb /><hi rend="small caps">A</hi>E<hi rend="superscript">9</hi> ſe habere ad <hi rend="small caps">A</hi>D<hi rend="superscript">9</hi>, aut EI<hi rend="superscript">9</hi> ad DG<hi rend="superscript">9</hi>, ut EI ad <lb />DH <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">255.</note>
        <p>
          <s xml:space="preserve">In triangulis ſimilibus IHG, <hi rend="small caps">IPa</hi>, <hi rend="small caps">A</hi>I ad AG, ut <lb /><hi rend="small caps">A</hi>P, aut DG, ad DG minus GH, id eſt HD, Sed <lb />in triangulis ſimilibus <hi rend="small caps">A</hi>EI, <hi rend="small caps">A</hi>DG; </s>
          <s xml:space="preserve"><hi rend="small caps">A</hi>I ad <hi rend="small caps">A</hi>G, ut EI <lb />ad DG; </s>
          <s xml:space="preserve">ergo EI ad DG, ut DG ad HD; </s>
          <s xml:space="preserve">idcirco EI<hi rend="superscript">9</hi> <lb />ad DG<hi rend="superscript">9</hi>, ut EI ad HD. </s>
          <s xml:space="preserve">Quod demonſtrandum erat. </s>
          <s xml:space="preserve">Ve-<lb />locitatem autem rite eſſe determinatam conſtabit ex colla-<lb />tione fig. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">cum 6.</s>
          <s xml:space="preserve">; ſi ad puncta B, L, attendamus, quæ
</s>
          <pb facs="0137" n="82" />
          <s xml:space="preserve">
<ptr xml:id="fig-0137-01a" corresp="fig-0137-01" type="figureAnchor" />
</s>
          <pb facs="0137a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0137a-01a" corresp="fig-0137a-01" type="figureAnchor" />
</s>
          <pb facs="0138" />
          <s xml:space="preserve">
</s>
          <pb facs="0139" n="83" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
in utraque figura iiſdem literis deſignantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0137-01" corresp="fig-0137-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01" />
                <label>0137-01</label>
              </figure>
              <figure xml:id="fig-0137a-01" corresp="fig-0137a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137a-01" />
                <label>0137a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXI. <lb />De Viribus Centralibus.</head>
        <p>
          <s xml:space="preserve">COrpus in motu, motum in linea recta continuat <ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0139-01a" corresp="note-0139-01" type="noteAnchor" />
ab ea non recedit, niſi impulſu novo agitetur; </s>
          <s xml:space="preserve">poſt <lb />impulſum motus eſt compoſitus, ex duobus naſcitur tertius <lb />etiam in linea recta <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si ergo corpus movetur in curva,
<ptr xml:id="note-0139-02a" corresp="note-0139-02" type="noteAnchor" />
omnibus momentis novo impulſu agitatur; </s>
          <s xml:space="preserve">curva enim ad <lb />rectas lineas revocari non poteſt, niſi concipiatur diviſa in <lb />partes infinite exiguas. </s>
          <s xml:space="preserve">Exemplum talis motus habemus in <lb />projectione gravium <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">aliud habemus in omnibus motibus
<ptr xml:id="note-0139-03a" corresp="note-0139-03" type="noteAnchor" />
circa punctum quaſi centrum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0139-01" corresp="note-0139-01a" n="*" anchored="true" place="margin">140</note>
              <note xml:space="preserve" xml:id="note-0139-02" corresp="note-0139-02a" n="*" anchored="true" place="margin">148.</note>
              <note xml:space="preserve" xml:id="note-0139-03" corresp="note-0139-03a" n="*" anchored="true" place="margin">316.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus quod continuò centrum aliquod verſus pellitur, ſi <lb />
<ptr xml:id="note-0139-04a" corresp="note-0139-04" type="noteAnchor" />
projiciatur ſecundum lineam quæ per illud centrum non <lb />tranſit, curvam deſcrihit: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in omnibus punctis conatur ab <lb />
<ptr xml:id="note-0139-05a" corresp="note-0139-05" type="noteAnchor" />
illa curva recedere ſecundum directionem curvaturæ, id eſt, <lb />tangentis ad curvam; </s>
          <s xml:space="preserve">ita ut, ſi vis qua ad centrum trahitur, <lb />ſubito ab actione ceſſaret, corpus in recta linea per tangen-<lb />tem motum continuaret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0139-04" corresp="note-0139-04a" place="margin">342.</note>
              <note xml:space="preserve" xml:id="note-0139-05" corresp="note-0139-05a" place="margin">343.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lapis fundæ impoſitus, &amp; </s>
          <s xml:space="preserve">in gyrum agitatus, curvam <lb />deſcribit, quia funda manum verſus omnibus momen-<lb />tis quaſi retrotrahitur; </s>
          <s xml:space="preserve">ſi ſibi relinquatur per curvæ tangen-<lb />tem recedit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Vis qua corpus in caſu prædicto a centro recedere cona-<lb />
<ptr xml:id="note-0139-06a" corresp="note-0139-06" type="noteAnchor" />
tur, qualis eſt vis qua funda agitata diſtenditur, vocatur vis <lb />centrifuga.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0139-06" corresp="note-0139-06a" place="margin">344.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Vis autem qua corpus centrum verſus trabitur, aut pelli-<lb />
<ptr xml:id="note-0139-07a" corresp="note-0139-07" type="noteAnchor" />
tur, vocatur vis centripeta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0139-07" corresp="note-0139-07a" place="margin">345.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Nomine communi vires hæ vocantur vires centrales.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">346.</note>
        <p>
          <s xml:space="preserve">In omni caſu vis centrifuga &amp; </s>
          <s xml:space="preserve">vis centripeta ſunt a qua-<lb />
<ptr xml:id="note-0139-09a" corresp="note-0139-09" type="noteAnchor" />
les inter ſe; </s>
          <s xml:space="preserve">nam agunt contrarie &amp; </s>
          <s xml:space="preserve">ſeſe mutuo deſtruunt.</s>
          <s xml:space="preserve">
</s>
          <pb facs="0140" n="84" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
Vicentripetâ corpus retinetur in curvâ, &amp; </s>
          <s xml:space="preserve">centrifugâ cona-<lb />tur ex hac recedere. </s>
          <s xml:space="preserve">Funda agitata æqualiter utramque <lb />partem verſus diſtenditur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">lapis eacum vi a manu co-
<ptr xml:id="note-0140-01a" corresp="note-0140-01" type="noteAnchor" />
natur recedere, cum qua retinetur, id eſt, manum verſus <lb />trahitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0139-09" corresp="note-0139-09a" place="margin">347.</note>
              <note xml:space="preserve" xml:id="note-0140-01" corresp="note-0140-01a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Virium centralium maximus uſus eſt in Philoſophia Na-<lb />turali; </s>
          <s xml:space="preserve">Planetæ omnes in gyros moventur, &amp; </s>
          <s xml:space="preserve">plerique, ſi <lb />non omnes, circa axes rotantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propoſitiones præcipuas circa haſce vires ſeligam &amp; </s>
          <s xml:space="preserve">ex-<lb />plicabo, hasque Experimentis confirmabo, &amp; </s>
          <s xml:space="preserve">in ſcholiis huic <lb />capiti adjectis ipſas demonſtrabo.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Præmittenda vero eſt Machinarum deſcriptio; </s>
          <s xml:space="preserve">quibus hæc <lb />Experimenta peraguntur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <p rend="italics">
          <s xml:space="preserve">Qua Experimenta de viribus centralibus inſtituuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">A eſt orbis ligneus diametri circiter duorum pedum cum <lb />
<ptr xml:id="note-0140-02a" corresp="note-0140-02" type="noteAnchor" />
ſemiſſe; </s>
          <s xml:space="preserve">hujus fectio verticalis datur in Fig. </s>
          <s xml:space="preserve">2.</s>
          <s xml:space="preserve">, in qua a a i-<lb />
<ptr xml:id="note-0140-03a" corresp="note-0140-03" type="noteAnchor" />
pſius orbis ſectionem repræſentat, g h ſectionem ſuſtentacu-<lb />li tornati, orbi perpendiculariter in centro adjuncti; </s>
          <s xml:space="preserve">conſtat <lb />hoc ex duabus partibus ſeparatis in D, quæ junguntur qua-<lb />tuor cylindris ferreis tenuibus, quorum extremitates annu-<lb />lis ex eodem metallo cohærent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0140-02" corresp="note-0140-02a" place="margin">348.</note>
              <note xml:space="preserve" xml:id="note-0140-03" corresp="note-0140-03a" place="margin">TAB. XIV. <lb />fig 1. &amp; 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pars ſuperior ſuſtentaculi ſulco circumdatur cc; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cylin-<lb />drice excavatur in f g, cujus foraminis diameter eſt trium <lb />partium quartarum unius pollicis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Totius Machinæ pes datur in C, eſt ſolidiſſimus: </s>
          <s xml:space="preserve">ab u-<lb />na parte ei applicatur orbis A, ubi quadrum ſuperius pe-<lb />dis C excavatur, ut recipiat ſuſtentaculum orbis. </s>
          <s xml:space="preserve">Cum hoc <lb />quadro firmiter connectitur caput ligneum F, (Fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">cu-<lb />jus angulus G, in g (fig. </s>
          <s xml:space="preserve">1.) </s>
          <s xml:space="preserve">videri poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Capiti huic ſuperimponitur lamina ferrea R quæ ipſi li-<lb />gno inſeritur &amp; </s>
          <s xml:space="preserve">cum hoc, ope cochlearum, quales in s, s, <lb />delineatæ dantur, firmiter connectitur, Cum lamina R <lb />cohæret alia r circa verticulum mobilem, ita ut laminæ <lb />ambæ inter ſe recipiant ſuſtentaculum tabulæ dum ipſæ ſul-<lb />co c c (fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">inſeruntur, in quo caſu cuſpis Z foramina Z, Z, <lb />trajicit.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0141" n="85" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
        <p>
          <s xml:space="preserve">Orbis cum ſuſtentaculo ſuſtinetur ligno ED, in quo da-<lb />tur lamina ferrea, cui cuſpis æneus b (fig 2.) </s>
          <s xml:space="preserve">inſeritur. </s>
          <s xml:space="preserve">Ita <lb />cum pede Machinæ lignum hocce conjungitur, ut altitudo <lb />ſulci c c cum altitudine laminarum R r congruat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hiſce ita diſpoſitis, liberrime cirea centrum horizonta-<lb />liter orbis movetur, &amp; </s>
          <s xml:space="preserve">ut commode circumvolvatur, ei ad-<lb />ditur, inter orbem &amp; </s>
          <s xml:space="preserve">ſulcum c e, rota minor, cujus ſectio <lb />videtur in b b; </s>
          <s xml:space="preserve">in eo loco ſuſtentaculum eſt polygonum, &amp; </s>
          <s xml:space="preserve"><lb />congruit cum foramine in ipſa rota, quæ ope cochlearum <lb />el, el; </s>
          <s xml:space="preserve">firmatur. </s>
          <s xml:space="preserve">Variæ tales rotæ minores requiruntur, <lb />quarum peripheriæ, in fundo ſulci quo circumdantur, ſunt <lb />inter ſe ut duo, tria, quatuor &amp;</s>
          <s xml:space="preserve">c; </s>
          <s xml:space="preserve">rotæ omnium minimæ <lb />diameter eſt circiter quinque pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Orbis B, priori ſimilis, eodem modo, in parte oppoſita <lb />pedis C circa centrum rotatur. </s>
          <s xml:space="preserve">Parva tamen inter ambos <lb />datur differentia; </s>
          <s xml:space="preserve">hujus orbis ſuſtentaculi pars inferior et-<lb />iam eſt perforata, ut i b (Fig. </s>
          <s xml:space="preserve">4.)</s>
          <s xml:space="preserve">; </s>
          <s xml:space="preserve">commode nihilominus <lb />circumvolvitur, in h applicatur lamina metallica perforata, <lb />cui inſeritur tubus inhærens laminæ aliæ M, cujus ſectio <lb />verticalis videtur in L, &amp; </s>
          <s xml:space="preserve">quæ in ligno <hi rend="small caps">E</hi>D pedis C hæret <lb />in m. </s>
          <s xml:space="preserve">Perforatur etiam lignum ED, in loco reſpondenti <lb />foramini ſuſtentaculi, ita ut filum a ſuperficie orbis per to-<lb />tum ſuſtentaculum &amp; </s>
          <s xml:space="preserve">lignum ED trajiciatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Rota ut b b, quæ huic orbi B additur, cum eo cohæret, <lb />&amp; </s>
          <s xml:space="preserve">eſt æqualis minimæ illarum quæ orbi A ſeparatim anne-<lb />ctuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Orbes A &amp; </s>
          <s xml:space="preserve">B, aut conjunctim, autſeparatim, celeriter <lb />circumvolvuntur, ope rotæ majoris &amp; </s>
          <s xml:space="preserve">verticalis Q, cujus <lb />pars ſuperior in eodem datur plano horizontali cum rotis <lb />minoribus ut b b. </s>
          <s xml:space="preserve">Cum pede C conjungitur machina quæ <lb />in fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">repræſentatur; </s>
          <s xml:space="preserve">conſtat hæc ex plano ligneo, cui <lb />perpendiculariter inhæret parallelopipedum, in cujus ſuperfi-<lb />ciei ſuperioris extremitatibus verticaliter inſeruntur tro-<lb />chleæ v, v, &amp; </s>
          <s xml:space="preserve">a latere in extremitate altera datur trochlea <lb />tertia horizontalis t, cæteris pollice fere magis elevata. </s>
          <s xml:space="preserve">Superfi-<lb />cies ſuperior Machinæ, eſt in eodem plano horizontali cum ſu-
</s>
          <pb facs="0142" n="86" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
perficiebus inferioribus rotarum minorum orbibus con-<lb />junctarum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit Orbis B ſolus circumvolvendus; </s>
          <s xml:space="preserve">Machina Fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">pedi C <lb />connectitur, ope duarum cochlearum tranſeuntium per fora-<lb />mina ut x, in plano inferiori Machinæ, quæ diſponitur ut illius <lb />ſuperficies ſuperior, erga rotam minorem Orbi adhærentem, fi-<lb />tum habeat, qui in Fig. </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">videtur, in qua b rotam illam minorem <lb />deſignat: </s>
          <s xml:space="preserve">funis circumit rotam majorem Q, &amp; </s>
          <s xml:space="preserve">ab inſeriori hu-<lb />jus parte tendit a d verſus v, circumponitur rotæ b, &amp; </s>
          <s xml:space="preserve">juxta <lb />t trochleam, c verſus, ad partem ſuperiorem rotæ Q pervenit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Fig. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">ſitus Machinæ Fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">repræ ſentatur, quando <lb />ambo Orbes ſimul circumrotandi ſunt; </s>
          <s xml:space="preserve">ſunis diſpoſitio ex <lb />inſpectione figuræ liquet, ab v tendit verſus d, ad rotæ ma-<lb />joris Q partem inferiorem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In multis Experimentis ulterius requiruntur pyxides oblon-<lb />gæ P, P, quæ orbibus imponuntur, &amp; </s>
          <s xml:space="preserve">cochleis ibi firmantur; <lb /></s>
          <s xml:space="preserve">in unaquaque centrum Orbis cum medio pyxidis congruit, &amp; </s>
          <s xml:space="preserve"><lb />ibi datur foramen æquale foramini g f (Fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">huic reſpon-<lb />dens, cui inſeritur cylindrus ligneus N (Fig. </s>
          <s xml:space="preserve">2.)</s>
          <s xml:space="preserve">, ut videtur in L, L: </s>
          <s xml:space="preserve"><lb />hunc trajicit, &amp; </s>
          <s xml:space="preserve">in eo hæret tubulus vitreus, diametri circiter <lb />quartæ partis unius pollicis, cujus extremitates lampadis flam-<lb />mâ fuſæ anguſtum in medio foramen habent; </s>
          <s xml:space="preserve">ita ut per tu-<lb />bum filum, aut funis tenuis, ſine attritu ſenſibili, moveatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In pyxide, ad exiguam ab L diſtantiam, lamina lignea <lb />ſuſpenditur v, quæ cum pyxidis lateribus angulos efficit re-<lb />ctos, &amp; </s>
          <s xml:space="preserve">in V ſeparatim repræſentatur; </s>
          <s xml:space="preserve">circa latus ſuperius <lb />liberrimè volubilis eſt; </s>
          <s xml:space="preserve">in inferiori parte ſciſſura datur, <lb />ad cujus latus paxillus P laminæ inſeritur, infra quem <lb />foramen datur, per quod filum trajicit, quod cum paxillo <lb />cohæret.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum latere pyxidis lamina lignea elaſtica s conjungitur <lb />ope cochlearum q, q; </s>
          <s xml:space="preserve">ſeparatim in ſitu inverſo videri po-<lb />teſt in S; </s>
          <s xml:space="preserve">in k cum hac cohæret ſphæræ ſegmentum ex li-<lb />gno duriori, aut ebore. </s>
          <s xml:space="preserve">Cochlearum q, q, figura datur in <lb />Q. </s>
          <s xml:space="preserve">Pars oppoſita pyxidis in partes æquales, recedendo a <lb />centro, in fundo dividitur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0143" n="87" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
        <p>
          <s xml:space="preserve">Pyxis Globum continet, qui ſeparatim in G (fig. </s>
          <s xml:space="preserve">12.) </s>
          <s xml:space="preserve">vi-<lb />detur. </s>
          <s xml:space="preserve">Habet hic prominentiam in quo foramen datur ad <lb />centrum globi tendens, &amp; </s>
          <s xml:space="preserve">quod terminatur in foramine <lb />transverſo; </s>
          <s xml:space="preserve">filum foramen primum trajicit, &amp; </s>
          <s xml:space="preserve">ex forami-<lb />ne transverſo exit; </s>
          <s xml:space="preserve">hoc cuſpide ligneo c exacte repletur ita, <lb />ut filum firmiter hæreat. </s>
          <s xml:space="preserve">Filum per tubum memoratum im-<lb />mittitur, &amp; </s>
          <s xml:space="preserve">in ſeparatione D ſuſtentaculi Orbis cum ponde-<lb />re O (Fig. </s>
          <s xml:space="preserve">9) connectitur. </s>
          <s xml:space="preserve">Pondus parti inferiori ſuſten-<lb />taculi imponitur, &amp; </s>
          <s xml:space="preserve">receſſu Globi a centro elevatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pondus hocce eſt Orbis plumbeus, diametri circiter duo-<lb />rum pollicum; </s>
          <s xml:space="preserve">in centro perpendiculariter ei inhæret cy-<lb />lindrus æneus, cum cujus extremitate ſuperiori filum con-<lb />jungitur. </s>
          <s xml:space="preserve">Ponderat Orbis cum cylindro ſemi-libram, duo <lb />talia pondera dantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dantur varia alia pondera, quædam ſemi-libræ, alia qua-<lb />drantis, quorum figura datur in P (Fig. </s>
          <s xml:space="preserve">9.)</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">quæ præ-<lb />dicto ponderi O ſuperimponuntur, ut ſic ad libitum pondus <lb />cum Globo conjunctum variari poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quando corpus plano impoſitum, cum iſto plano, æquali in <lb />
<ptr xml:id="note-0143-01a" corresp="note-0143-01" type="noteAnchor" />
tempore, circa commune centrum revolvitur, &amp; </s>
          <s xml:space="preserve">circulum <lb />deſcribit; </s>
          <s xml:space="preserve">ſi vis centripeta, qua corpus, omnibus momentis <lb />centrum verſus trabitur aut pellitur, agere ceſſet, &amp; </s>
          <s xml:space="preserve">pla-<lb />num eadem celeritate movere continuet; </s>
          <s xml:space="preserve">corpus a centro re-<lb />cedere incipit, reſpectu plani, per lineam quæ per centrum <lb />tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0143-01" corresp="note-0143-01a" place="margin">349.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Detur Globus funi tenui cohærens, extremitaſque altera <lb />
<ptr xml:id="note-0143-02a" corresp="note-0143-02" type="noteAnchor" />
fixa ſit in centro Orbis unius <hi rend="small caps">A</hi> aut B, &amp; </s>
          <s xml:space="preserve">ſolus circumvol-<lb />vatur, donec Globus ei impoſitus eodem tempore cum illo <lb />circumrotetur; </s>
          <s xml:space="preserve">reſpectu Orbis quieſcit Globus, &amp; </s>
          <s xml:space="preserve">in eo ſitu, <lb />ſolo fune centro Orbis alligato, retinetur; </s>
          <s xml:space="preserve">nullam ergo im-<lb />preſſionem in illo plano patitur, nifi qua funis diſtenditur <lb />id eſt, cujus directio per centrum Orbis tranſit, &amp; </s>
          <s xml:space="preserve">ſic, ſi <lb />ſibi relinquatur, non poteſt in illo plano, in primo momen-<lb />to, ſecundum aliam directionem moveri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0143-02" corresp="note-0143-02a" place="margin">350.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quando corpus circa centrum movetur, ſi inter movendum <lb />
<ptr xml:id="note-0143-03a" corresp="note-0143-03" type="noteAnchor" />
</s>
          <pb facs="0144" n="88" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
magis ad centrum accedat, acceleratur illius motus; </s>
          <s xml:space="preserve">retar-<lb />datur contra, ſi a centro recedat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0143-03" corresp="note-0143-03a" place="margin">351.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Orbi B cohæret pyxis P, per cujus medium Orbi inſeri-<lb />
<ptr xml:id="note-0144-01a" corresp="note-0144-01" type="noteAnchor" />
tur cylindrus L, cum ſuo tubo vitreo, ut in deſcriptione <lb />Machinæ dictum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0144-01" corresp="note-0144-01a" place="margin">352.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus t filo alligatus, pyxidi imponitur; </s>
          <s xml:space="preserve">filum tranſmit-<lb />titur per tubum ſtatim memoratum, ut &amp; </s>
          <s xml:space="preserve">per integrum <lb />Orbis ſuſtentaculum, &amp; </s>
          <s xml:space="preserve">infra lignum ED pervenit, cui et-<lb />iam in inferiori parte inſeritur tubus ut N cum tubo vitreo <lb />quem funis etiam trajicit. </s>
          <s xml:space="preserve">Manu extremitas fili retine-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Orbis circumrotatur; </s>
          <s xml:space="preserve">in motu lateri pyxidis Globus ſe <lb />applicat, &amp; </s>
          <s xml:space="preserve">circumfertur ita, ut æquali celeritate cum py-<lb />xide moveatur. </s>
          <s xml:space="preserve">Trahatur filum, ut Globus magis ad centrum <lb />accedat, ſtatim in latus oppoſitum pyxidis impinget, quia <lb />celerius quam ipſa pyxis movetur. </s>
          <s xml:space="preserve">Nunc ſi manus admo-<lb />veatur, Globus a centro recedit, &amp; </s>
          <s xml:space="preserve">in latus primum py-<lb />xidis impingit, quia tardius quam pyxis movetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hanc accelerationem in acceſſu corporis ad centrum, &amp; </s>
          <s xml:space="preserve"><lb />retardationem ex receſſu, in ſcholio primo ſequenti deter-<lb />minamus; </s>
          <s xml:space="preserve">moveatur ex gr. </s>
          <s xml:space="preserve">corpus, quod fertur centrum <lb />
<ptr xml:id="note-0144-02a" corresp="note-0144-02" type="noteAnchor" />
C verſus, in curva AE, dabitur curva hæc in eodem plano <lb />
<ptr xml:id="note-0144-03a" corresp="note-0144-03" type="noteAnchor" />
cum centro C; </s>
          <s xml:space="preserve">celerius autem movebitur in E, tardius in <lb />A: </s>
          <s xml:space="preserve">ducantur lineæ AC, BC, &amp; </s>
          <s xml:space="preserve">EC, DC, ita ut areæ ABC <lb />&amp; </s>
          <s xml:space="preserve">DEC ſint æquales inter ſe, portiones curvæ AB, DE, <lb />in temporibus æqualibus, a corpore deſcribuntur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideo, <lb />corpus, quod vi verſus centrum tendente in curva retinetur, <lb />
<ptr xml:id="note-0144-04a" corresp="note-0144-04" type="noteAnchor" />
dicitur deſcribere areas circa illud centrum temporibus pro-<lb />portionales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0144-02" corresp="note-0144-02a" place="margin">353.</note>
              <note xml:space="preserve" xml:id="note-0144-03" corresp="note-0144-03a" place="margin">TAB XIV. <lb />flg. 11.</note>
              <note xml:space="preserve" xml:id="note-0144-04" corresp="note-0144-04a" place="margin">354.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Hujus propoſitionis inverſam etiam demonſtramus, cor-<lb />
<ptr xml:id="note-0144-05a" corresp="note-0144-05" type="noteAnchor" />
pus, quod movetur in linea aliquâ curvâ in plano, &amp; </s>
          <s xml:space="preserve">deſcri-<lb />bit areas circa punctum quoddam temporibus proportionales, <lb />à recta linea detorqueri &amp; </s>
          <s xml:space="preserve">urgeri vitendente ad idem pun-<lb />ctum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0144-05" corresp="note-0144-05a" place="margin">355.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quo major eſt quantitas materia in corpore, eomajor eſt, <lb />
<ptr xml:id="note-0144-06a" corresp="note-0144-06" type="noteAnchor" />
</s>
          <pb facs="0145" n="89" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
cæteris paribus, bujus vis centrifuga; </s>
          <s xml:space="preserve">quod oritur exma-<lb />jori vi inſitâ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0144-06" corresp="note-0144-06a" place="margin">356.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſluida variæ denſitatis in ſpatio determinato includan-<lb />
<ptr xml:id="note-0145-01a" corresp="note-0145-01" type="noteAnchor" />
tur, ita ut graviora a centro non poſſint recedere, quin le-<lb />viora ad illud accedant, &amp; </s>
          <s xml:space="preserve">diſpoſita ſint, ut pondere ſuo <lb />graviora ad centrum accedant, in motu circa illud centrum <lb />leviora verſus hoc feruntur, &amp; </s>
          <s xml:space="preserve">graviora centrum fugiunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0145-01" corresp="note-0145-01a" place="margin">357.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſolidum cum fluido ſpatio determinato includatur, ad <lb />centrum accedit, ſi fluido levius fuerit; </s>
          <s xml:space="preserve">ſi gravius ab eo re-<lb />cedit. </s>
          <s xml:space="preserve">Quæ omnia oriuntur ex majori vi centriſuga in gra-<lb />viori corpore.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Quatuor tubi vitrei, diametri circiter unius pollicis, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0145-02a" corresp="note-0145-02" type="noteAnchor" />
longitudinis unius pedis, plano inclinato firmiter alligantur, <lb />
<ptr xml:id="note-0145-03a" corresp="note-0145-03" type="noteAnchor" />
hermetice ab utraque parte clauſi. </s>
          <s xml:space="preserve">In primo datur mercu-<lb />rius cum aqua; </s>
          <s xml:space="preserve">in ſecundo oleum tartari per deliquium cum <lb />ſpiritu vini; </s>
          <s xml:space="preserve">in tertio aqua cum globo plumbeo; </s>
          <s xml:space="preserve">in quarto <lb />tandem aqua cum fruſto ſuberis, omnes pro dimidia parte <lb />vacui relinquuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0145-02" corresp="note-0145-02a" place="margin">358.</note>
              <note xml:space="preserve" xml:id="note-0145-03" corresp="note-0145-03a" place="margin">TAB. XIV. <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planum hocce inclinatum Orbi A aut B imponitur ita, <lb />
<ptr xml:id="note-0145-04a" corresp="note-0145-04" type="noteAnchor" />
ut pars inſerior plani fere ad Orbis centrum pertingat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />ope duarum cochlearum, quarum una tranſit per x (Fig. </s>
          <s xml:space="preserve">8.)</s>
          <s xml:space="preserve">, <lb />Orbi annectitur. </s>
          <s xml:space="preserve">Circumvolvatur Orbis, ſtatim pars infe-<lb />rior tuborum vacua remanebit, &amp; </s>
          <s xml:space="preserve">corpora graviora locum <lb />a centro maxime remotum occupabunt; </s>
          <s xml:space="preserve">ſuber deſcendit <lb />&amp; </s>
          <s xml:space="preserve">hæret in inferiori aquæ parte, dum globus plumbeus ad <lb />extremitatem uſque tubi adſcendit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0145-04" corresp="note-0145-04a" place="margin">TAB. XIV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires centrales non modo reſpectu quantitatis materiæ <lb />
<ptr xml:id="note-0145-05a" corresp="note-0145-05" type="noteAnchor" />
differunt, ſed etiam diſtantia à centro mutationem aſſert, <lb />ut &amp; </s>
          <s xml:space="preserve">celeritas cum qua circumvolvitur corpus; </s>
          <s xml:space="preserve">præter hæc <lb />nihil in iſtis viribus datur ex quo differentia inter illas oriri <lb />poſht, &amp; </s>
          <s xml:space="preserve">in comparandis iſtis viribus hæc ſola conſideran-<lb />da ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0145-05" corresp="note-0145-05a" place="margin">359.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p>
          <s xml:space="preserve">Tempus periodicum, eſt tempus in quo corpus circa cen-<lb />
<ptr xml:id="note-0145-06a" corresp="note-0145-06" type="noteAnchor" />
trum revolvens integram revolutionem peragit; </s>
          <s xml:space="preserve">id eſt, ſi
</s>
          <pb facs="0146" n="90" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
curvam deſcribat quæ in ſe redit, tempus elapſum inter re-<lb />ceſſum a puncto &amp; </s>
          <s xml:space="preserve">acceſſum ad idem punctum: </s>
          <s xml:space="preserve">ſi curva in <lb />ſe non redeat, pro puncto linea per centrum tranſiens ſu-<lb />menda eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0145-06" corresp="note-0145-06a" place="margin">360.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tempus periodicum pendet a corporis celeritate, &amp; </s>
          <s xml:space="preserve">ideò <lb />in comparandis viribus centralibus tempus hocce loco cele-<lb />ritatis conſiderari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando tempora periodica ſunt aqualia &amp; </s>
          <s xml:space="preserve">diſtantia æqua-<lb />
<ptr xml:id="note-0146-01a" corresp="note-0146-01" type="noteAnchor" />
les a centro, vires centrales ſunt ut quantitates materiæ in <lb />corporibus quæ revolvuntur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Temporibus enim æquali-
<ptr xml:id="note-0146-02a" corresp="note-0146-02" type="noteAnchor" />
bus eodem modo viribus centralibus moventur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0146-01" corresp="note-0146-01a" place="margin">361.</note>
              <note xml:space="preserve" xml:id="note-0146-02" corresp="note-0146-02a" n="*" anchored="true" place="margin">106.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Applicatur Orbi A, rota omnium minima, ex tribus ro-<lb />
<ptr xml:id="note-0146-03a" corresp="note-0146-03" type="noteAnchor" />
tis ut b b, de quibus in deſcriptione Machinæ; </s>
          <s xml:space="preserve">ita ut ſi am-<lb />
<ptr xml:id="note-0146-04a" corresp="note-0146-04" type="noteAnchor" />
bo Orbes A &amp; </s>
          <s xml:space="preserve">B ſimul agitentur motu rotæ Q in tempore <lb />æquali circumvolvantur; </s>
          <s xml:space="preserve">ſingulis applicantur pyxides oblon-<lb />gæ P, P; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cylindri cum tubulis vitreis L, L, per <lb />foramina in medio pyxidum, ſuſtentaculis Orbium inſerun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0146-03" corresp="note-0146-03a" place="margin">362.</note>
              <note xml:space="preserve" xml:id="note-0146-04" corresp="note-0146-04a" place="margin">TAB XIV. <lb />fig. 1.2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus t ponderis ſemi-libræ pyxidi Orbis B imponitur, <lb />&amp; </s>
          <s xml:space="preserve">globus t ponderis unius libræ pyxidi Orbis A; </s>
          <s xml:space="preserve">filis per <lb />tubulos L, L, tranſeuntibus &amp; </s>
          <s xml:space="preserve">cum ponderibus, in ſepa-<lb />rationibus ſuſtentaculorum Orbium poſitis, cohærentibus, <lb />globi annectuntur ita, ut diſtantiæ globorum a centro, <lb />quando fila extenduntur, &amp; </s>
          <s xml:space="preserve">non elevantur pondera, ſint <lb />æquales. </s>
          <s xml:space="preserve">Inutraque pyxide Elaſterii s extremitas inſeritur ſciſ-<lb />ſuræ laminæ v (V) &amp; </s>
          <s xml:space="preserve">filum paxillo p annexum globo etiam <lb />conjungitur, dum per idem foramen in prominentiâ globi <lb />tranſit cum filo primo. </s>
          <s xml:space="preserve">Ope paxilli p ita fili ſecundi longitudo <lb />determinatur, ut ad altitudinem octavæ partis pollicis pondus <lb />in ſuſtentaculo, receſſu globi a centro, elevari poſſit quieſcente <lb />lamina v; </s>
          <s xml:space="preserve">ſi autem magis a centro recedat globus, trahitur la-<lb />mina hæc, relaxatur elaſterium, &amp; </s>
          <s xml:space="preserve">ſegmentum k in latus pyxidis <lb />impingit, ſtrepituſque auditur, qui magis erit intenſus ſi la-<lb />tus pyxidis etiam ſegmento ſphæræ ex ligno duriore aut e-<lb />bore muniatur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0147" n="91" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
        <p>
          <s xml:space="preserve">Nunc ſit pondus in ſeparatione ſuſtentaculi Orbis A uni-<lb />us libræ, in ſeparatione ſuſtentaculi Orbis B ſemi-libræ; <lb /></s>
          <s xml:space="preserve">aut ſit hoc unius libræ, &amp; </s>
          <s xml:space="preserve">illud duarum librarum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Moveatur rota Q celerius atque celerius, donec globo-<lb />rum vi centrifuga pondera ſtatim memorata eleventur; </s>
          <s xml:space="preserve">am-<lb />bo eodem exactè temporis momento in altum ferentur, <lb />quod ex ſtrepitu memorato manifeſtum fit. </s>
          <s xml:space="preserve">Pondera ergo <lb />quæ ſunt ut corpora, cæteris paribus, vi centrifuga ſupe-<lb />rantur.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quando quantitates materiæ in corporibus circumrotatis <lb />
<ptr xml:id="note-0147-01a" corresp="note-0147-01" type="noteAnchor" />
ſunt æquales, &amp; </s>
          <s xml:space="preserve">tempora periodica æqualia, vires centrales <lb />ſunt ut diſtantiæ a centro.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0147-01" corresp="note-0147-01a" place="margin">363.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Hocce Experimentum eodem modo ac præcedens pera <lb />
<ptr xml:id="note-0147-02a" corresp="note-0147-02" type="noteAnchor" />
gitur; </s>
          <s xml:space="preserve">pro globo ſemi-libræ, pyxidi Orbis B globus alteri <lb />
<ptr xml:id="note-0147-03a" corresp="note-0147-03" type="noteAnchor" />
æqualis, id eſt, unius libræ, imponitur. </s>
          <s xml:space="preserve">Diſtantiæ globo-<lb />rum a centro ſint in quacunque ratione, ſi pondera cum <lb />quibus globi conjunguntur eandem inter ſe habeant propor-<lb />tionem, &amp; </s>
          <s xml:space="preserve">rota Q motu continuo accelerato circumagatur, <lb />eodem exacte temporis momento pondera elevantur. </s>
          <s xml:space="preserve">Sit <lb />ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">diſtantia globi Orbis A partium viginti quatuor, &amp; </s>
          <s xml:space="preserve"><lb />pondus ei annexum unius libræ cum ſemiſſe; </s>
          <s xml:space="preserve">diſtantia al-<lb />terius globi ſedecim partium, &amp; </s>
          <s xml:space="preserve">pondus annexum unius li-<lb />bræ; </s>
          <s xml:space="preserve">Experimentum procedet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0147-02" corresp="note-0147-02a" place="margin">364.</note>
              <note xml:space="preserve" xml:id="note-0147-03" corresp="note-0147-03a" place="margin">TAB. XIV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando tempora periodica ſunt æqualia, ſed diſtantiæ à <lb />
<ptr xml:id="note-0147-04a" corresp="note-0147-04" type="noteAnchor" />
centro &amp; </s>
          <s xml:space="preserve">quantitates materiæ in corporibus revolutis diffe-<lb />runt, vires centrales ſunt in ratione compoſita, quantitatum <lb />materiæ, &amp; </s>
          <s xml:space="preserve">diſtantiarum; </s>
          <s xml:space="preserve">quod ex duabus ultimis propo-<lb />ſitionibus ſequitur. </s>
          <s xml:space="preserve">Ratio hæc compoſita determinatur, ſi <lb />quantitas materiæ in unoquoque corpore per ſuam diſtan-<lb />tiam a centro multiplicetur, &amp; </s>
          <s xml:space="preserve">producta quæſitam inter ſe <lb />rationem habent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0147-04" corresp="note-0147-04a" place="margin">365.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Si in Experimento ultimo globus Orbi B impoſitus mu-<lb />
<ptr xml:id="note-0147-05a" corresp="note-0147-05" type="noteAnchor" />
tetur, &amp; </s>
          <s xml:space="preserve">globus ſemi-libræ ad eandem diſtantiam partium <lb />
<ptr xml:id="note-0147-06a" corresp="note-0147-06" type="noteAnchor" />
ſedecim a centro pyxidi imponatur, mutetur etiam pondus
</s>
          <pb facs="0148" n="92" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ei annexum, &amp; </s>
          <s xml:space="preserve">pro una libra, ſemi - libra adhibeatur, Ex-<lb />perimentum procedet, &amp; </s>
          <s xml:space="preserve">pondera eodem tempore adſcen-<lb />dere incipient. </s>
          <s xml:space="preserve">Multiplicando globum ſemi-libræ per di-<lb />ſtantiam a centro ſedecim, productum eſt octo; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">mul-<lb />tiplicando globum unius libræ per diſtantiam viginti quatuor <lb />a centro, productum eſt viginti quatuor, quæ producta <lb />ſunt inter ſe ut unum ad tria, id eſt, ut pondera ſemi-libræ, <lb />&amp; </s>
          <s xml:space="preserve">unius libræ cum ſemiſſe, quæ in hoc Experimento ſimul <lb />elevantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0147-05" corresp="note-0147-05a" place="margin">366.</note>
              <note xml:space="preserve" xml:id="note-0147-06" corresp="note-0147-06a" place="margin">TAB. XIV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Differentiæ virium centralium, ex differentiis diſtantia-<lb />rum a centro &amp; </s>
          <s xml:space="preserve">quantitatum materiæ oriundæ, ſeſe mu-<lb />tuo poſſunt compenſare; </s>
          <s xml:space="preserve">nam poſitis quantit atibus materiæ <lb />
<ptr xml:id="note-0148-01a" corresp="note-0148-01" type="noteAnchor" />
in corporibus circumactis in ratione inverſa diſtantiarum a <lb />centro, vires centrales erunt æquales; </s>
          <s xml:space="preserve">quantum vis una al-<lb />teri major eſt reſpectu quantitatis materiæ, tantum hæc il-<lb />lam ſuperat propter majorem diſtantiam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0148-01" corresp="note-0148-01a" place="margin">367.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Sit globus ſemi libræ ad diſtantiam a centro viginti qua-<lb />
<ptr xml:id="note-0148-02a" corresp="note-0148-02" type="noteAnchor" />
tuor partium; </s>
          <s xml:space="preserve">globus unius libræ ad diſtantiam duodecim <lb />partium; </s>
          <s xml:space="preserve">cæteris manentibus ut in Experimento præceden-<lb />ti, ſi pondera in ſuſten aculis Orbium fuerint æqualia, eo-<lb />dem momento adſcendent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0148-02" corresp="note-0148-02a" place="margin">368.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Caſus hujus propoſitionis exſtat, quando duo corpora fi-<lb />
<ptr xml:id="note-0148-03a" corresp="note-0148-03" type="noteAnchor" />
lo juncta circa commune centrum gravitatis revolvuntur. </s>
          <s xml:space="preserve">Di-<lb />ſtantiæ enim ab illo centro ſu nt in ratione inverſa ponde-<lb />rum corporum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ergo vires centrales æquales. </s>
          <s xml:space="preserve">Viqua
<ptr xml:id="note-0148-04a" corresp="note-0148-04" type="noteAnchor" />
corpus unum a centro conatur recedere, alterum ad cen-<lb />trum trahitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">propter virium æqualitatem ſeſe mutuo <lb />netinent &amp; </s>
          <s xml:space="preserve">motum continuant; </s>
          <s xml:space="preserve">ſi circa aliud punctum revol-<lb />vantur, motum non continuant, &amp; </s>
          <s xml:space="preserve">corpus, cujus vis <lb />centrifuga præpollet, a centro recedit, &amp; </s>
          <s xml:space="preserve">corpus aliud ſe-<lb />cum fert.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0148-03" corresp="note-0148-03a" place="margin">369.</note>
              <note xml:space="preserve" xml:id="note-0148-04" corresp="note-0148-04a" n="*" anchored="true" place="margin">143. 134.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Corpora duo inæqualia P &amp; </s>
          <s xml:space="preserve">Q, filo junguntur, &amp; </s>
          <s xml:space="preserve">in <lb />
<ptr xml:id="note-0148-05a" corresp="note-0148-05" type="noteAnchor" />
hoc notatur punctum C, centrum commune gravitatis il-<lb />
<ptr xml:id="note-0148-06a" corresp="note-0148-06" type="noteAnchor" />
lorum corporum quando filum diſtenditur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0148-05" corresp="note-0148-05a" place="margin">370.</note>
              <note xml:space="preserve" xml:id="note-0148-06" corresp="note-0148-06a" place="margin">TAB. XIV. <lb />fig. 10.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0149" n="93" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
        <p>
          <s xml:space="preserve">In hoc Experimento unicus adhibetur Orbis, ei imponi-<lb />tur pyxis oblonga ab utraque parte Orbem excedens, &amp; </s>
          <s xml:space="preserve"><lb />cujus medium cum centro Orbis congruat. </s>
          <s xml:space="preserve">Pyxidi huic <lb />corpora ſtatim memorata imponuntur, &amp; </s>
          <s xml:space="preserve">filo quo jungun-<lb />tur manente extenſo, punctum C puncto medio pyxidis ad-<lb />movetur. </s>
          <s xml:space="preserve">Circumrotatur Orbis, corpora cum pyxide cir-<lb />cumferuntur, &amp; </s>
          <s xml:space="preserve">in hac quieta manent. </s>
          <s xml:space="preserve">Removeatur pun-<lb />ctum C a medio pyxidis, in circumvolutione corpora am-<lb />bo ferentur ad illam pyxidis extremitatem cui punctum C <lb />magis acceſlit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Etne in hoc caſu ambo corpora ex pyxidi ejiciantur, cum <lb />periculo ſpectatorum, pyxidis extremitates obteguntur tabel-<lb />lis ligneis, ſex poll. </s>
          <s xml:space="preserve">longis, infra quas dum corpora in py-<lb />xidis extrema impingunt ex hac ejici nequeunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Differentia virium centralium ex differentia temporis pe-<lb />riodici etiam determinatur.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quando quantitates materiæ in corporibus circumrotatis, <lb />
<ptr xml:id="note-0149-01a" corresp="note-0149-01" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">diſtantiæ a centro ſunt æquales, vires centrales ſunt in <lb />ratione inverſa quadratorum temporum periodicorum, id eſt, <lb />directe ut quadrata revolutionum eodem tempore peracta-<lb />rum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0149-01" corresp="note-0149-01a" place="margin">371.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Orbi A applicatur rota ut b b, (Fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">cujus circumfe-<lb />
<ptr xml:id="note-0149-02a" corresp="note-0149-02" type="noteAnchor" />
rentia ſe habeat ad circumferentiam rotæ illius quæ cum Orbe <lb />
<ptr xml:id="note-0149-03a" corresp="note-0149-03" type="noteAnchor" />
B cohæret, ut tria ad duo; </s>
          <s xml:space="preserve">ita ut B, quando Orbes ſimul <lb />moventur, ter revolvatur dum A bis circumagitur, id eſt, <lb />hujus tempus periodicum eſt alterius tempus periodicum <lb />feſquiplicatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0149-02" corresp="note-0149-02a" place="margin">372.</note>
              <note xml:space="preserve" xml:id="note-0149-03" corresp="note-0149-03a" place="margin">TAB. XIV. <lb />fig. 1.2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In utraque pyxide P, P, globus unius libræ imponitur, <lb />ad diſtantias æquales a centro. </s>
          <s xml:space="preserve">In Orbe B, conjungitur glo-<lb />bus cum pondere duarum librarum cum quadrante in ſu-<lb />ſtentaculo, &amp; </s>
          <s xml:space="preserve">alter globus cum pondere unius libræ in ſu-<lb />ſtentaculo Orbis A. </s>
          <s xml:space="preserve">Circumrotantur Orbes, &amp; </s>
          <s xml:space="preserve">pondera <lb />ſimul adſcendunt. </s>
          <s xml:space="preserve">Pondera hic ſunt ut 9. </s>
          <s xml:space="preserve">ad 4. </s>
          <s xml:space="preserve">dum tem-<lb />pora periodica ut 2. </s>
          <s xml:space="preserve">ad 3. </s>
          <s xml:space="preserve">quorum quadrata ſunt reciproce <lb />ut 9. </s>
          <s xml:space="preserve">ad 4.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0150" n="94" />
        <fw type="head">PHYSCES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Quomodocunque inter ſe vires centrales differant, ex <lb />
<ptr xml:id="note-0150-01a" corresp="note-0150-01" type="noteAnchor" />
jam dictis inter ſe poſſunt comparari; </s>
          <s xml:space="preserve">nam ſunt ſemper in <lb />ratione compoſita, ex ratione quantitatum materiæ in cor-<lb />poribus revolutis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ratione diſtantiarum a centro <ptr type="noteAnchor" />, ut
<ptr xml:id="note-0150-02a" corresp="note-0150-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">ratione inverſa quadratorum temporum periodicorum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0150-03a" corresp="note-0150-03" type="noteAnchor" />
Multiplicando quantitatem materiæ in unoquoque corpore <lb />per ſuam diſtantiam a centro, &amp; </s>
          <s xml:space="preserve">dividendo productum per <lb />quadratum temporis periodici, quotientes diviſionum erunt <lb />in dicta ratione compoſita, id eſt, ut vires centrales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0150-01" corresp="note-0150-01a" place="margin">373.</note>
              <note xml:space="preserve" xml:id="note-0150-02" corresp="note-0150-02a" n="*" anchored="true" place="margin">361. <lb />363.</note>
              <note xml:space="preserve" xml:id="note-0150-03" corresp="note-0150-03a" n="*" anchored="true" place="margin">371.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 10.</head>
        <p>
          <s xml:space="preserve">Obſervatis iiſdem quæ in Experimento præcedenti, de-<lb />
<ptr xml:id="note-0150-04a" corresp="note-0150-04" type="noteAnchor" />
tur globus ſemi-libræ, ad diſtantiam ſedecim a centro Or-<lb />bis B, &amp; </s>
          <s xml:space="preserve">cum pondere {3/4} unius libræ in ſuſtentaculo con-<lb />jungatur; </s>
          <s xml:space="preserve">globus alter ſit unius libræ, ad diſtantiam vigin-<lb />ti quatuor a centro Orbis A, &amp; </s>
          <s xml:space="preserve">conjungatur cum pondere <lb />unius libræ; </s>
          <s xml:space="preserve">circumagantur Orbes, eodem momento pon-<lb />dera elevantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0150-04" corresp="note-0150-04a" place="margin">374.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpora hic ſunt ut {1/2} ad 1.</s>
          <s xml:space="preserve">; diſtantiæ ut 16. </s>
          <s xml:space="preserve">ad 24.</s>
          <s xml:space="preserve">; qua-<lb />drata temporum periodicorum ut 4. </s>
          <s xml:space="preserve">ad 9.</s>
          <s xml:space="preserve">; multiplicando <lb />{1/2} per 16.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">dividendo productum per 4.</s>
          <s xml:space="preserve">, quotiens eſt 2. <lb /></s>
          <s xml:space="preserve">multiplicando 1. </s>
          <s xml:space="preserve">per 24.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">dividendo productum per 9.</s>
          <s xml:space="preserve">, <lb />quotiens diviſionis eſt 2 {2/3}. </s>
          <s xml:space="preserve">Vires ergo centrales ſunt inter <lb />ſe ut 2. </s>
          <s xml:space="preserve">ad 2 {2/3}, aut ut 3. </s>
          <s xml:space="preserve">ad 4. </s>
          <s xml:space="preserve">quam rationem pondera in <lb />ſuſtentaculis etiam inter ſe habent.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quando quantitates materiæ ſunt æquales, diſtantiæ ipſæ <lb />
<ptr xml:id="note-0150-05a" corresp="note-0150-05" type="noteAnchor" />
per quadrata temporum periodicorum dividuntur ad deter-<lb />minandam proportionem inter vires centrales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0150-05" corresp="note-0150-05a" place="margin">375.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc caſu ſi quadratatemporum periodicorum fuerint in-<lb />
<ptr xml:id="note-0150-06a" corresp="note-0150-06" type="noteAnchor" />
ter ſe ut cubi diſtantiarum, quotientes diviſionum erunt in <lb />ratione inverſa quadratorum diſtantiarum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in hac ratio-<lb />ne etiam vires centrales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0150-06" corresp="note-0150-06a" place="margin">376.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> II.</head>
        <p>
          <s xml:space="preserve">Sint tempora periodica Orbis B &amp; </s>
          <s xml:space="preserve">A, ut 1. </s>
          <s xml:space="preserve">ad 2.</s>
          <s xml:space="preserve">; den-<lb />
<ptr xml:id="note-0150-07a" corresp="note-0150-07" type="noteAnchor" />
tur globi æquales, &amp; </s>
          <s xml:space="preserve">diſtantia a centro in orbe B ſit decem <lb />alterius globi diſtantia a centro ſit ſedecim, pondus primo <lb />annexum ſit unius libræ cum quadrante, &amp; </s>
          <s xml:space="preserve">pondus in ſu-
</s>
          <pb facs="0151" />
          <s xml:space="preserve">
<ptr xml:id="fig-0151-01a" corresp="fig-0151-01" type="figureAnchor" />
<pb facs="0151a" />
<ptr xml:id="fig-0151a-01a" corresp="fig-0151a-01" type="figureAnchor" />
<pb facs="0152" />
<pb facs="0153" n="95" /><fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
ſtentaculo alterius Orbis A ſit ſemi-libræ; </s>
          <s xml:space="preserve">in agitatione Or-<lb />bium pondera eodem momento adſcendunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0150-07" corresp="note-0150-07a" place="margin">377.</note>
              <figure xml:id="fig-0151-01" corresp="fig-0151-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0151-01" />
                <label>0151-01</label>
              </figure>
              <figure xml:id="fig-0151a-01" corresp="fig-0151a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0151a-01" />
                <label>0151a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hocce Experimento vires centrales ſunt ut 5. </s>
          <s xml:space="preserve">ad 2. </s>
          <s xml:space="preserve">quod <lb />etiam computatione detegitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hæc ratio paululum admo-*
<ptr xml:id="note-0153-01a" corresp="note-0153-01" type="noteAnchor" />
dum differt a ratione inverſa quadratorum diſtantiarum, <lb />quæ ſunt inter ſe ut 200. </s>
          <s xml:space="preserve">ad 512.</s>
          <s xml:space="preserve">: cubi etiam diſtantiarum, <lb />ſunt fere ut quadrata temporum periodicorum; </s>
          <s xml:space="preserve">hæc ſunt ut <lb />1. </s>
          <s xml:space="preserve">ad 4.</s>
          <s xml:space="preserve">, illi ut 125. </s>
          <s xml:space="preserve">ad 512. </s>
          <s xml:space="preserve">quæ rationes non admodum dif-<lb />ferunt. </s>
          <s xml:space="preserve">Aliis adhibitis numeris hæ rationes exacte eædem <lb />erunt, &amp; </s>
          <s xml:space="preserve">Experimentum eodem modo procedet; </s>
          <s xml:space="preserve">ſed non <lb />commodètempora periodica, aut pondera, ſecundum quam-<lb />libet rationem variari poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0153-01" corresp="note-0153-01a" n="*" anchored="true" place="margin">375</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si corpora ſint inæqualia, ſed in bæc agant vires centra-<lb />
<ptr xml:id="note-0153-02a" corresp="note-0153-02" type="noteAnchor" />
les, quæ, ut gravitas, æqualiter in ſingulas materiæ particu-<lb />las agant, non intereſt quæcunque ſint maſſæ corporum, &amp; </s>
          <s xml:space="preserve"><lb />propoſitio ultima etiam in corporibus inæqualibus obti-<lb />net.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0153-02" corresp="note-0153-02a" place="margin">378.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ellipſin vocant Geometræ lineam ovalem cujus hæc eſt <lb />
<ptr xml:id="note-0153-03a" corresp="note-0153-03" type="noteAnchor" />
deſcriptio. </s>
          <s xml:space="preserve">Sit A a recta; </s>
          <s xml:space="preserve">C punctum hujus medium; </s>
          <s xml:space="preserve">F, f, <lb />
<ptr xml:id="note-0153-04a" corresp="note-0153-04" type="noteAnchor" />
puncta à C æqualiter diſtantia; </s>
          <s xml:space="preserve">F G f filum, cujus extremi-<lb />tates in F &amp; </s>
          <s xml:space="preserve">f fixæ ſunt, quod æquale eſt lineæ A a. </s>
          <s xml:space="preserve">Ten-<lb />ſo filo clavo G, in plano in quo datur A a Ellipſis deſcribi-<lb />tur. </s>
          <s xml:space="preserve">Puncta F, f, vocantur foci; </s>
          <s xml:space="preserve">C centrum; </s>
          <s xml:space="preserve">A a axis major; <lb /></s>
          <s xml:space="preserve">minor axis per centrum tranſit, cum majori angulos effici-<lb />ens rectos, &amp; </s>
          <s xml:space="preserve">ab utraque parte curvâ terminatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0153-03" corresp="note-0153-03a" place="margin">379.</note>
              <note xml:space="preserve" xml:id="note-0153-04" corresp="note-0153-04a" place="margin">TAB. XV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando vis, qua corpus punctum verſus fertur, non u-<lb />
<ptr xml:id="note-0153-05a" corresp="note-0153-05" type="noteAnchor" />
bique eſt eadem, ſed cum diſtantia à centro creſcit, aut <lb />minuitur, ſecundum certam proportionem, variæ inde <lb />oriuntur curvæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0153-05" corresp="note-0153-05a" place="margin">380.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus vim quæ in corpora mota agit ut in quieſcentia, <lb />
<ptr xml:id="note-0153-06a" corresp="note-0153-06" type="noteAnchor" />
quæ ad diſtantias æquales à centro æqualis ſit, adinæquales de-<lb />creſcat, in ratione inverſa quadratorum diſtantiarum ab hoc <lb />puncto, deſcribet corpus Ellipſin cujus focorum alter cum cen-<lb />tro virium coincidit; </s>
          <s xml:space="preserve">ita ut in unaquaque revolutione ſemel ad <lb />hoc accedat corpus, &amp; </s>
          <s xml:space="preserve">iterum ab hoc recedat. </s>
          <s xml:space="preserve">In receſſu <lb />minuitur corporis celeritas <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">quidem ita, ut vis centralis, li-
<ptr xml:id="note-0153-07a" corresp="note-0153-07" type="noteAnchor" />
</s>
          <pb facs="0154" n="96" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cet ipſa minuatur, viam corporis flectat, &amp; </s>
          <s xml:space="preserve">hoc ad <lb />centrum accedere cogat: </s>
          <s xml:space="preserve">acceſſu augetur velocitas ita, ut, <lb />licet vis augeatur, corpus iterum a centro recedat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0153-06" corresp="note-0153-06a" place="margin">381.</note>
              <note xml:space="preserve" xml:id="note-0153-07" corresp="note-0153-07a" n="*" anchored="true" place="margin">3526</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circulus ad hoc genus curvarum pertinet, &amp; </s>
          <s xml:space="preserve">in hoc ca-<lb />
<ptr xml:id="note-0154-01a" corresp="note-0154-01" type="noteAnchor" />
ſu corpus etiam circulum poteſt deſcribere, qui, ſi bujus <lb />diameter æqualis ſit aximajori Ellipſeos cujuſcunque, eodem <lb />tempore cum bac deſcribitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0154-01" corresp="note-0154-01a" place="margin">382.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus poteſt tali celeritate projici, ut in receſſu a cen-<lb />
<ptr xml:id="note-0154-02a" corresp="note-0154-02" type="noteAnchor" />
tro vis, quæ auctâ diſtantiâ minuitur, non valeat ad viam <lb />ita inflectendam, ut corpus redeat; </s>
          <s xml:space="preserve">percurrit in hoc caſu <lb />corpus curvam aliam Parabolam aut Hyperbolam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0154-02" corresp="note-0154-02a" place="margin">383.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si vis centralis juxta alvam proportionem quamcunque <lb />
<ptr xml:id="note-0154-03a" corresp="note-0154-03" type="noteAnchor" />
in receſſu a centro decreſcat, non poterit corpus lineam in <lb />ſe redeuntem, &amp; </s>
          <s xml:space="preserve">a circulo parum aberrantem, deſcribere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0154-03" corresp="note-0154-03a" place="margin">384.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sed ſi vis decreſcat juxta proportionem parum ab bac ab-<lb />
<ptr xml:id="note-0154-04a" corresp="note-0154-04" type="noteAnchor" />
errantem, aut curva à circulo non multum differat; </s>
          <s xml:space="preserve">poterit <lb />curva a corpore deſcripta referri ad Ellipſin mobilem, cu-<lb />jus nempe axis, in plano, in quo corpus revolvitur, mo-<lb />vetur motu angulari, manente foco in centro virium. </s>
          <s xml:space="preserve">Mo-<lb />
<ptr xml:id="note-0154-05a" corresp="note-0154-05" type="noteAnchor" />
tus autem axeos in eandem partem dirigitur cum motu cor-<lb />poris, ſi vis celerius decreſcat auctâ diſtantiâ quam prora-<lb />tione inverſa quadrati diſtantiæ: </s>
          <s xml:space="preserve">Si vero vis tardius, id eſt <lb />
<ptr xml:id="note-0154-06a" corresp="note-0154-06" type="noteAnchor" />
minus, decreſcat in reseſſu a centro, motus Ellipſeos in <lb />contrariam partem dirigitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0154-04" corresp="note-0154-04a" place="margin">385.</note>
              <note xml:space="preserve" xml:id="note-0154-05" corresp="note-0154-05a" place="margin">386.</note>
              <note xml:space="preserve" xml:id="note-0154-06" corresp="note-0154-06a" place="margin">387.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Corpus etiam Ellipſin deſcribit, ſi vis centralis, in re-<lb />
<ptr xml:id="note-0154-07a" corresp="note-0154-07" type="noteAnchor" />
ceſſu a centro, creſcat, &amp; </s>
          <s xml:space="preserve">ſit ubique in ratione diſtantiæ a <lb />centro, quod in boc caſu cum centro Ellipſeos coincidit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0154-07" corresp="note-0154-07a" place="margin">388.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 12</head>
        <p>
          <s xml:space="preserve">Longiori filo ſuſpendatur globus plumbeus; </s>
          <s xml:space="preserve">ſi a puncto <lb />
<ptr xml:id="note-0154-08a" corresp="note-0154-08" type="noteAnchor" />
in quo quieſcit retrahatur, gravitate ſua ſemper hoc verſus <lb />fertur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ab omni parte, ſi diſtantia fuerit æqualis æqua-<lb />li cum vi. </s>
          <s xml:space="preserve">In motu ſuo a puncto memorato globus circu-<lb />lum deſcribit, partem quamcunque verſus retrahatur: </s>
          <s xml:space="preserve">ſi <lb />portiones circuli nonfuerint admodum magnæ, cum cycloï-<lb />de coïncidunt, &amp; </s>
          <s xml:space="preserve">vis cum qua globus, in quocumque pun-<lb />cto, fertur punctum inſimum verſus, eſt ut illius diſtantia
</s>
          <pb facs="0155" n="97" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB I. CAP. XXI.</fw>
ab hocce puncto <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">vis ergo illa creſcit in ratione diſtan-
<ptr xml:id="note-0155-01a" corresp="note-0155-01" type="noteAnchor" />
tiæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0154-08" corresp="note-0154-08a" place="margin">389.</note>
              <note xml:space="preserve" xml:id="note-0155-01" corresp="note-0155-01a" n="*" anchored="true" place="margin">2@7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Retrahatur globus a puncto infimo, &amp; </s>
          <s xml:space="preserve">oblique projicia-<lb />tur, figuram ovalem circa hocce punctum deſcribet, quæ, <lb />quando globus per ſpatium magnum non excurrit, ab Elli-<lb />pſi fere nihil differt, propter virium proportionem, &amp; </s>
          <s xml:space="preserve">quia <lb />in eo caſu ad ſenſum in eodem plano movetur globus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Centrum Ellipſis eſt punctum in quo globus quando non <lb />projicitur quieſcit, in unaquaque revolutione bis ad illud <lb />globus accedit, &amp; </s>
          <s xml:space="preserve">bis ab illo recedit. </s>
          <s xml:space="preserve">Si ſupra menſam <lb />globus ſuſpendatur ita, ut fere menſam quando quieſcit tangat, <lb />&amp; </s>
          <s xml:space="preserve">punctum cui tunc reſpondet in menſa notetur, Experi-<lb />mentum multo ſit magis ſenſibile; </s>
          <s xml:space="preserve">inſequendo globum hujus <lb />via cum creta in menſa notari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si vis juxta aliam rationem creſcat, curva in ſe non re-<lb />
<ptr xml:id="note-0155-02a" corresp="note-0155-02" type="noteAnchor" />
dit; </s>
          <s xml:space="preserve">Sed poteſt ſæpe ad Ellipſin in plano mobilem referri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0155-02" corresp="note-0155-02a" place="margin">390.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 13.</head>
        <p>
          <s xml:space="preserve">Iiſdem poſitis quæ in Experimento præcedenti, projiciatur <lb />
<ptr xml:id="note-0155-03a" corresp="note-0155-03" type="noteAnchor" />
globus ut ad diſtantiam majorem excurrat; </s>
          <s xml:space="preserve">curvam deſcri-<lb />bit quæ ad Ovalem mobilem referri poteſt; </s>
          <s xml:space="preserve">bis in unaqua-<lb />que revolutione quidem accedit ad centrum, &amp; </s>
          <s xml:space="preserve">bis ab eo <lb />recedit; </s>
          <s xml:space="preserve">ſed ſitus punctorum, in quibus minime aut maxi-<lb />me diſtat, in ſingulis revolutionibus mutatur, &amp; </s>
          <s xml:space="preserve">ſempere-<lb />andem partem verſus hæc puncta feruntur, horumque motus <lb />cum globi motu conſpirat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0155-03" corresp="note-0155-03a" place="margin">391.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hac ultima propoſitione, ſi ad n. </s>
          <s xml:space="preserve">384. </s>
          <s xml:space="preserve">attendamus, ſe-<lb />
<ptr xml:id="note-0155-04a" corresp="note-0155-04" type="noteAnchor" />
quitur, nullâ vi centrali, ad æquales diſtantias æqualiter <lb />agenti, curvam poſſe deſcribi in ſe redeuntem &amp; </s>
          <s xml:space="preserve">excentri-<lb />cam, id eſt cujus centrum cum centro virium non coincidit, <lb />præter Ellipſin, in cujus focorum altero centrum virium da-<lb />tur; </s>
          <s xml:space="preserve">vimque centralem, in hoc caſu, ſequi rationem in-<lb />verſam quadrati diſtantiæ</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0155-04" corresp="note-0155-04a" place="margin">392.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">393.</note>
        <p>
          <s xml:space="preserve">Circulum autem, cujus centrum cum centro virium coin-<lb />cidit, poſſe deſcribi vi juxta rationem quamcunque creſcen-<lb />tem aut decreſcentem, ſi modo ad diſtantias æquales æqua-<lb />liter agat, facile patet.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0156" n="98" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 1.</head>
        <head rend="italics" xml:space="preserve">Generalia de viribus centralibus.</head>
        <p>
          <s xml:space="preserve">Concipiamus dari vim, qua corpus, ubicunque detur, pellatur centrum <lb />
<ptr xml:id="note-0156-01a" corresp="note-0156-01" type="noteAnchor" />
C verſus, non intereſt quomodocunque in punctis diverſis varietur vis <lb />
<ptr xml:id="note-0156-02a" corresp="note-0156-02" type="noteAnchor" />
hæc; </s>
          <s xml:space="preserve">concipiamus vim hanc non eſſe continuam, ſed illam ictibus in cor-<lb />pus agere, &amp; </s>
          <s xml:space="preserve">momenta temporis inter ictus eſſe æqualia. </s>
          <s xml:space="preserve">Ponamus etiam cor <lb />pus projectum per AB hanc percurrere lineam in momento tali; </s>
          <s xml:space="preserve">motum <lb />per BL, æqualem AB, in momento ſequenti continuaret, niſi in B ictu <lb />in corpus pelleretur hoc ad C; </s>
          <s xml:space="preserve">ponamus celeritatem, ex hoc ictu oriundam <lb />in corpore jam agitato, talem eſſe, ut hac corpus poſſit, in intervallo tem-<lb />poris inter duos ictus, percurrere lineam LD; </s>
          <s xml:space="preserve">ſi LD ſit parallela BC, <lb />corpus duobus motibus agitatum pecurrit BD <ptr type="noteAnchor" />, daturque in D, in momento in
<ptr xml:id="note-0156-03a" corresp="note-0156-03" type="noteAnchor" />
quo ictu ſequenti iterum ad centrum pellitur. </s>
          <s xml:space="preserve">Si ictus hic non daretur, in mo-<lb />mento ſequenti percurreret DE, poſitis DE &amp; </s>
          <s xml:space="preserve">BD æqualibus, ſed eodem <lb />tempore centrum verſus fertur, id eſt per DC pellitur, ſi juxta hanc dire-<lb />ctionem percurrat lineam æqualem lineæ EF in tempore in quo percurre-<lb />ret DE, motu compoſito corpus movetur per DF, poſitis EF &amp; </s>
          <s xml:space="preserve">DC pa-<lb />rallelis. </s>
          <s xml:space="preserve">Eodem modo demonſtramus in momento ſequenti corpus percur-<lb />rere FH, ſi GH ſit æqualis ſpatio in hoc momento, ex ictu C verſus per-<lb />currendo, poſitiſque FG &amp; </s>
          <s xml:space="preserve">DF æqualibus, ut &amp; </s>
          <s xml:space="preserve">GH &amp; </s>
          <s xml:space="preserve">FC parallelis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0156-01" corresp="note-0156-01a" place="margin">394.</note>
              <note xml:space="preserve" xml:id="note-0156-02" corresp="note-0156-02a" place="margin">TAB. XV. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0156-03" corresp="note-0156-03a" n="*" anchored="true" place="margin">146.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Triangula ABC, BLC, habent baſes æquales AB, BL in eadem li-<lb />nea, &amp; </s>
          <s xml:space="preserve">verticem communem C; </s>
          <s xml:space="preserve">ſunt ergo æqualia <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Triangula BLC,
<ptr xml:id="note-0156-04a" corresp="note-0156-04" type="noteAnchor" />
BDC baſinhabent communem BC&amp; </s>
          <s xml:space="preserve">conſtituuntur inter parallelas BC, LD, <lb />ſunt ergo æqualia <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Idcirco etiam æqualia ſunt triangula ABC, BDC.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0156-05a" corresp="note-0156-05" type="noteAnchor" />
Eodem modo demonſtramus æqualia triangula BDC, DFC &amp; </s>
          <s xml:space="preserve">in gene-<lb />re æqualia eſſe inter ſe triangula quæcunque ut ABC, BDC, DFC; <lb /></s>
          <s xml:space="preserve">FHC, quorum baſes momentis æqualibus a corpore projecto percurrun-<lb />tur. </s>
          <s xml:space="preserve">Ex qua demonſtratione deducitur propoſitio n. </s>
          <s xml:space="preserve">351.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0156-04" corresp="note-0156-04a" n="*" anchored="true" place="margin">38. El. 1.</note>
              <note xml:space="preserve" xml:id="note-0156-05" corresp="note-0156-05a" n="*" anchored="true" place="margin">37. El. 1.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Etiam patet corpus projectum &amp; </s>
          <s xml:space="preserve">vi centrum verſus tendenti agitatum, move-<lb />
<ptr xml:id="note-0156-06a" corresp="note-0156-06" type="noteAnchor" />
ri in plano, quod tranſit per lineam juxta quam corpus projicitur &amp; </s>
          <s xml:space="preserve">per centrum <lb />virium, ut monuimus in n. </s>
          <s xml:space="preserve">353.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0156-06" corresp="note-0156-06a" place="margin">395.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus nunc momenta inter duos ictus minui, ut &amp; </s>
          <s xml:space="preserve">ipſos ictus, ma-<lb />
<ptr xml:id="note-0156-07a" corresp="note-0156-07" type="noteAnchor" />
nentibus nihilominus illis æqualibus inter ſe, poſitis hiſce utcunque inæ-<lb />qualibus, demonſtratio eadem locum habebit. </s>
          <s xml:space="preserve">Si diminutio ſit in infinitum <lb />mutantur ictus in preſſionem continuam, &amp; </s>
          <s xml:space="preserve">corpus in ſingulis punctis a via <lb />recta deflectitur; </s>
          <s xml:space="preserve">ſubjicitur tamen legi in demonſtratione præcedenti deter-<lb />minata. </s>
          <s xml:space="preserve">Si ergo corpus moveatur in curva ABDE, &amp; </s>
          <s xml:space="preserve">tempus concipia-<lb />
<ptr xml:id="note-0156-08a" corresp="note-0156-08" type="noteAnchor" />
tur diviſum in momenta infinite exigua, &amp; </s>
          <s xml:space="preserve">æqualiainter ſe, area trianguli mixti <lb />ACB continebit tot triangula exigua æqualia inter ſe, quot dantur momen-<lb />ta in tempore, in quo percurritur AB, &amp; </s>
          <s xml:space="preserve">area trianguli mixti DCE eo-<lb />dem modo continebit tot triangula æqualia inter ſe &amp; </s>
          <s xml:space="preserve">prioribus, quot dan-<lb />tur momenta in tempore in quo percurritur DE; </s>
          <s xml:space="preserve">ideoque @empora in quibus <lb />corpus AB &amp; </s>
          <s xml:space="preserve">DE, percurrit, ſunt inter ſe ut numeri triangulorum æqua-<lb />lium areis ACB, DCE, contentorum, id eſt ut ipſæ areæ. </s>
          <s xml:space="preserve">Unde genera-<lb />lem deducimus propoſitionem in n. </s>
          <s xml:space="preserve">354. </s>
          <s xml:space="preserve">memoratam</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0156-07" corresp="note-0156-07a" place="margin">396.</note>
              <note xml:space="preserve" xml:id="note-0156-08" corresp="note-0156-08a" place="margin">TAB. XIV-<lb />fig. 11.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cujus propoſitionis inverſa, quæ continentur in n. </s>
          <s xml:space="preserve">355. </s>
          <s xml:space="preserve">etiam demonſtratur. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0156-09a" corresp="note-0156-09" type="noteAnchor" />
Si corpus motum per AB in momento ſequenti, &amp; </s>
          <s xml:space="preserve">æquali, percurrat BD, quia <lb />
<ptr xml:id="note-0156-10a" corresp="note-0156-10" type="noteAnchor" />
</s>
          <pb facs="0157" n="99" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
motu primo, in momento hoc, per BL æqualem AB motum continuaſſet, <lb />neceſſario juxta directionem L Da via ſua remotum fuit <ptr type="noteAnchor" />, ſi autem trian-
<ptr xml:id="note-0157-01a" corresp="note-0157-01" type="noteAnchor" />
gula ABC, BDC ſint æqualia, etiam æqualia erunt BDC, BLC; </s>
          <s xml:space="preserve">i-<lb />deoque linea LD parallela BC<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt directio vis quæ corpus a linea re-
<ptr xml:id="note-0157-02a" corresp="note-0157-02" type="noteAnchor" />
cta detorquet centrum C verſus dirigitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0156-09" corresp="note-0156-09a" place="margin">397.</note>
              <note xml:space="preserve" xml:id="note-0156-10" corresp="note-0156-10a" place="margin">TAB. XV. <lb />fig 2.</note>
              <note xml:space="preserve" xml:id="note-0157-01" corresp="note-0157-01a" n="*" anchored="true" place="margin">246.</note>
              <note xml:space="preserve" xml:id="note-0157-02" corresp="note-0157-02a" n="*" anchored="true" place="margin">39.21.1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc concipiamus curvam quamcunque dividi, lineis ad centrum viri-<lb />um ductis, in triangula minima æqualia, horum baſes, temporibus æqua-<lb />libus a corpore quod in curva vi centrali retinetur, percurruntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſunt ideo
<ptr xml:id="note-0157-03a" corresp="note-0157-03" type="noteAnchor" />
<ptr xml:id="note-0157-04a" corresp="note-0157-04" type="noteAnchor" />
corporis velocitates in variis curvæ punctis, ut baſes hæ <ptr type="noteAnchor" />, quæ ſunt inversè ut
<ptr xml:id="note-0157-05a" corresp="note-0157-05" type="noteAnchor" />
perpendiculares à centro virium in baſes continuatas <ptr type="noteAnchor" />, id eſt in tangentes adcur-
<ptr xml:id="note-0157-06a" corresp="note-0157-06" type="noteAnchor" />
vam in punctis de quibus agitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-03" corresp="note-0157-03a" place="margin">398.</note>
              <note xml:space="preserve" xml:id="note-0157-04" corresp="note-0157-04a" n="*" anchored="true" place="margin">394.</note>
              <note xml:space="preserve" xml:id="note-0157-05" corresp="note-0157-05a" n="*" anchored="true" place="margin">94.</note>
              <note xml:space="preserve" xml:id="note-0157-06" corresp="note-0157-06a" n="*" anchored="true" place="margin">1@. El. VI. <lb />38. El 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Maxime generalia ſunt huc uſque in ſcholio hoc demonſtrata, quæ nunc <lb />
<ptr xml:id="note-0157-07a" corresp="note-0157-07" type="noteAnchor" />
addam tantum obtinent, ſi vis in hoc cum gravitate congruat, ut agat in cor-<lb />poramota ut in quieſcentia, corpora autem ponimus æqualia; </s>
          <s xml:space="preserve">ſi verò vis &amp; </s>
          <s xml:space="preserve">in <lb />hoc cum gravitate congruat, ut eodem modo agat in ſingulas materiæ parti-<lb />culas, non intereſt utrum corpora ſint æqualia nec ne.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-07" corresp="note-0157-07a" place="margin">399.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lineæ infinitæ exiguæ, viribus æqualibus, a@cedendo adcentrum, percurſæ ſunt, <lb />
<ptr xml:id="note-0157-08a" corresp="note-0157-08" type="noteAnchor" />
ut quadrata temporum quibus percurruntur. </s>
          <s xml:space="preserve">Vis enim pro uniformi in ſpatio <lb />infinitè exiguo haberi poteſt, &amp; </s>
          <s xml:space="preserve">quæ de corporibus cadentibus demonſtrata <lb />ſunt <ptr type="noteAnchor" />, hìc referri poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-08" corresp="note-0157-08a" place="margin">400.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">235.</note>
        <p rend="italics">
          <s xml:space="preserve">Si vires differant, ſed tempora fuerint æqualia, ſpatia percurſa ſunt ut vi-<lb />
<ptr xml:id="note-0157-10a" corresp="note-0157-10" type="noteAnchor" />
res <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-10" corresp="note-0157-10a" place="margin">401.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">107</note>
        <p>
          <s xml:space="preserve">Ergo ſpatia infinite exigua, viribus centralibus percurſa, ſunt, ut viresipſæ, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0157-12a" corresp="note-0157-12" type="noteAnchor" />
ut quadrata temporum; </s>
          <s xml:space="preserve">in ratione nempe compoſita ex hiſce ambabus ratio-<lb />nibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-12" corresp="note-0157-12a" place="margin">402.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce deducimus, corpus, quod vi centrali in curva retinetur, in ſingu-<lb />
<ptr xml:id="note-0157-13a" corresp="note-0157-13" type="noteAnchor" />
lis momentis infinitè exiguis moveri juxta leges explicatas <ptr type="noteAnchor" /> de corporibus pro-
<ptr xml:id="note-0157-14a" corresp="note-0157-14" type="noteAnchor" />
jectis. </s>
          <s xml:space="preserve">Nam, licet corpus tendat ad centrum, ſi ſpatium percurſum ſit in-<lb />finitè exiguum reſpectu diſtantiæ a centro, lineæ ad centrum ductæ pro pa-<lb />rallelis haberi poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-13" corresp="note-0157-13a" place="margin">403.</note>
              <note xml:space="preserve" xml:id="note-0157-14" corresp="note-0157-14a" n="*" anchored="true" place="margin">327. 331.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Curva AFGE in qua corpus movetur; </s>
          <s xml:space="preserve">C centrum virium; </s>
          <s xml:space="preserve">AD <lb />
<ptr xml:id="note-0157-15a" corresp="note-0157-15" type="noteAnchor" />
tangens ad curvam in puncto A; </s>
          <s xml:space="preserve">ponamus AD infinitè exiguam, lineas-<lb />que BF &amp; </s>
          <s xml:space="preserve">DG ad AC dari parallelas, erunt hæ ut quadrata linearum <lb />AB, AD <ptr type="noteAnchor" />, quæ ſunt ut tempora quibus AF, AG percurruntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-15" corresp="note-0157-15a" place="margin">TAB. XV. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">331. 327.</note>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">De Motu in Circulo.</head>
        <p>
          <s xml:space="preserve">Vis quæcunque qua corpus in circulo retinetur, ſi ad circuli centrum dirigatur, <lb />
<ptr xml:id="note-0157-17a" corresp="note-0157-17" type="noteAnchor" />
agit ſemper perpendiculariter ad motus directionem; </s>
          <s xml:space="preserve">tangens enim ad ra-<lb />dium perpendicularis eſt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Idcirco actio hujus vis nunquam cum motu
<ptr xml:id="note-0157-18a" corresp="note-0157-18" type="noteAnchor" />
corporis conſpiràt, aut contrarie agit, quare agit eodem modo ac in corpus qui-<lb />eſcens ageret; </s>
          <s xml:space="preserve">hac de cauſa non intereſt utrum vis in omni caſu eodem modo <lb />poſſit agere in corpus motum ac in quieſcens ut gravitas, an non.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-17" corresp="note-0157-17a" place="margin">404.</note>
              <note xml:space="preserve" xml:id="note-0157-18" corresp="note-0157-18a" n="*" anchored="true" place="margin">18. El. 114.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Moveatur corpus in circulo cujus Diameter eſt GL; </s>
          <s xml:space="preserve">C centrum circuli <lb />
<ptr xml:id="note-0157-19a" corresp="note-0157-19" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">virium. </s>
          <s xml:space="preserve">Detur corpus æquale per AD projectum, velocitate qua cor-<lb />
<ptr xml:id="note-0157-20a" corresp="note-0157-20" type="noteAnchor" />
pus in circulo movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0157-19" corresp="note-0157-19a" place="margin">405.</note>
              <note xml:space="preserve" xml:id="note-0157-20" corresp="note-0157-20a" place="margin">TAB XV. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpora hæc æqualibus temporibus percurrunt lineas æquales, infinitè
</s>
          <pb facs="0158" n="100" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
exiguas, AB, GH; </s>
          <s xml:space="preserve">æqualibus etiam temporibus percurrunt lineolas BE, <lb />HI, primum pondere ſuo, ſecundum vi centrali, poſitâ BE verticali, <lb />&amp; </s>
          <s xml:space="preserve">HI ad GC parallelâ; </s>
          <s xml:space="preserve">quæ lineolæ ſunt inter ſe, ut corporis pondus ad vim <lb />centralem quæ corpus in circulo retinet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">107.</note>
        <p>
          <s xml:space="preserve">Sit DF altitudo à qua cadendo corpus acquirit velocitatem cum qua pro-<lb />jectio fit, corpus ſpatium hoc cadendo percurrit dum motu uniformi proje-<lb />
<ptr xml:id="note-0158-02a" corresp="note-0158-02" type="noteAnchor" />
ctitio lineam duplam percurrit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi ergo DF ſit verticalis &amp; </s>
          <s xml:space="preserve">AD dupla i-
<ptr xml:id="note-0158-03a" corresp="note-0158-03" type="noteAnchor" />
pſius DF corpus projectum per F tranſibit <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Idcirco AB<hi rend="superscript">q</hi> aut GH<hi rend="superscript">q</hi>, ad
<ptr xml:id="note-0158-04a" corresp="note-0158-04" type="noteAnchor" />
AD<hi rend="superscript">q</hi>, aut 4 x DF<hi rend="superscript">q</hi>, ut BE ad DF<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0158-02" corresp="note-0158-02a" n="*" anchored="true" place="margin">257.</note>
              <note xml:space="preserve" xml:id="note-0158-03" corresp="note-0158-03a" n="*" anchored="true" place="margin">327.</note>
              <note xml:space="preserve" xml:id="note-0158-04" corresp="note-0158-04a" n="*" anchored="true" place="margin">95. 255.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In circulo ducta I i parallela GH, id eſt perpendiculari ad diametrum, <ptr type="noteAnchor" />
<ptr xml:id="note-0158-05a" corresp="note-0158-05" type="noteAnchor" />
erunt Gi aut <hi rend="small caps">Hi</hi>, GI aut GH, &amp; </s>
          <s xml:space="preserve">GL, in continuâ proportione <ptr type="noteAnchor" />, quare
<ptr xml:id="note-0158-06a" corresp="note-0158-06" type="noteAnchor" />
GH<hi rend="superscript">q</hi> = HI x GL.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0158-05" corresp="note-0158-05a" n="*" anchored="true" place="margin">18. El 111.</note>
              <note xml:space="preserve" xml:id="note-0158-06" corresp="note-0158-06a" n="*" anchored="true" place="margin">31. El 111, <lb />@. 4. El VI.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Memorata proportio mutatur ergo in hanc <lb />HI x GL, 4 x DF<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: BE, DF:</s>
          <s xml:space="preserve">: BE x GL, DF x GL. </s>
          <s xml:space="preserve">Alternando <lb />HI x GL, BE x GL:</s>
          <s xml:space="preserve">: 4 x DF<hi rend="superscript">q</hi>, DF x GL. </s>
          <s xml:space="preserve">Unde deducimus <lb />HI, BE:</s>
          <s xml:space="preserve">: DF, {1/4} GL.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Id eſt vis qua corpus in circulo retinetur eſt ad corporis pondus, ut altitudo à <lb />
<ptr xml:id="note-0158-07a" corresp="note-0158-07" type="noteAnchor" />
qua corpus cadendo acquirit velocitatem cum quæ projectio fit ad quartam partem <lb />diametri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0158-07" corresp="note-0158-07a" place="margin">406.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si idem corpus in eodem circulo aliâ velocitate feratur, conſequentia propor-<lb />
<ptr xml:id="note-0158-08a" corresp="note-0158-08" type="noteAnchor" />
tionis manent; </s>
          <s xml:space="preserve">mutantur ideo antecedentia in eadem ratione, id eſt viscen-<lb />tralis variat, ut altitudo à qua cadendo corpus acquirit velocitatem cum qua <lb />movetur, quæ altitudo ſequitur proportionem quadrati velociatatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0158-08" corresp="note-0158-08a" place="margin">407.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">255.</note>
        <p>
          <s xml:space="preserve">Quamdiu autem de eodem circulo agitur tempus periodicum eo minus eſt, <lb />
<ptr xml:id="note-0158-10a" corresp="note-0158-10" type="noteAnchor" />
quo velocitas eſt major, &amp; </s>
          <s xml:space="preserve">vice verſa, eſtque tempus hoc inverſè ut velo-<lb />citas, unde patet demonſtratio n. </s>
          <s xml:space="preserve">371. </s>
          <s xml:space="preserve">vires cæteris paribus eſſe inverſè ut <lb />quadrata temporum periodicorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0158-10" corresp="note-0158-10a" place="margin">408.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In n. </s>
          <s xml:space="preserve">363. </s>
          <s xml:space="preserve">diximus, vires centrales, poſitis corporibus, ut &amp; </s>
          <s xml:space="preserve">temporibus <lb />
<ptr xml:id="note-0158-11a" corresp="note-0158-11" type="noteAnchor" />
periodicis æqualibus, eſſe ut diſtantias a centro, quod ut demonſtremus po-<lb />
<ptr xml:id="note-0158-12a" corresp="note-0158-12" type="noteAnchor" />
nimus duo corpora æqualia, circulos concentricos BIL, AFM æquali-<lb />bus temporibus deſcribere; </s>
          <s xml:space="preserve">momentis minimis æqualibus arcus ſimiles BI, <lb />AF percurrunt. </s>
          <s xml:space="preserve">Corpora autem momentis iiſdem per tangentes BH, AD, <lb />moverentur, ſi nulla daretur vis centralis; </s>
          <s xml:space="preserve">nam propter arcus exiguos ſunt <lb />hi tangentibus æquales; </s>
          <s xml:space="preserve">Corpora ergo, æqualibus momentis, viribus centra-<lb />libus, transferuntur per lineas HI, DF, in quorum ratione ſunt vires cen-<lb />trales; </s>
          <s xml:space="preserve">has autem lineas eſſe ut diſtantiæ a centro BC, AC, facile pa-<lb />tet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0158-11" corresp="note-0158-11a" place="margin">409.</note>
              <note xml:space="preserve" xml:id="note-0158-12" corresp="note-0158-12a" place="margin">TAB. XV. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Supereſt circa motum in circulo ut demonſſremus propoſitionem n. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0158-13a" corresp="note-0158-13" type="noteAnchor" />
ſint diſtantiæ à centro D &amp; </s>
          <s xml:space="preserve">d; </s>
          <s xml:space="preserve">tempora periodica T, t, vires centrales V, v; <lb /></s>
          <s xml:space="preserve">ponamus T<hi rend="superscript">q</hi>, t<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: D<hi rend="superscript">c</hi> d<hi rend="superscript">c</hi>; </s>
          <s xml:space="preserve">erg<hi rend="superscript">o</hi> {D/T<hi rend="superscript">q</hi>}, {d/t<hi rend="superscript">q</hi>}:</s>
          <s xml:space="preserve">: {D/D<hi rend="superscript">c</hi>}, {d/d<hi rend="superscript">c</hi>}:</s>
          <s xml:space="preserve">: {1/D<hi rend="superscript">q</hi>}, {1/d<hi rend="superscript">q</hi>}. </s>
          <s xml:space="preserve">Sed V, v:</s>
          <s xml:space="preserve">: {D/T<hi rend="superscript">q</hi>}, {d<ptr type="noteAnchor" />/t<hi rend="superscript">q</hi>};</s>
          <s xml:space="preserve">
ergo V, v:</s>
          <s xml:space="preserve">: {1/D<hi rend="superscript">q</hi>}, {1/d<hi rend="superscript">q</hi>}. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">D, E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0158-13" corresp="note-0158-13a" place="margin">376.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0159" n="101" />
        <fw type="head">MATHEMATICA. LIB. I. CAP XXI</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SHOLIUM 3.</head>
        <head rend="italics" xml:space="preserve">De Motu in Ellipſi.</head>
        <p>
          <s xml:space="preserve">In hoc, &amp; </s>
          <s xml:space="preserve">ſequentibus ſcholiis, ponimus agi de vi quæ in corpora mota ut <lb />in quieſcentia agit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit Ellipſis DAE; </s>
          <s xml:space="preserve">centrum C; </s>
          <s xml:space="preserve">moveatur corpus in Ellipſi, in quare-<lb />tinetur vi, quæ ad centrum dirigitur; </s>
          <s xml:space="preserve">vis hæc determinanda eſt.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">410.</note>
        <p>
          <s xml:space="preserve">Detur Corpus in A, &amp; </s>
          <s xml:space="preserve">ſit AI tangens ad Ellipſin; </s>
          <s xml:space="preserve">AB diameter; </s>
          <s xml:space="preserve">ED <lb />
<ptr xml:id="note-0159-02a" corresp="note-0159-02" type="noteAnchor" />
diameter ipſi conjugata tangenti parallela <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">AL arcus momento exiguo
<ptr xml:id="note-0159-03a" corresp="note-0159-03" type="noteAnchor" />
conſtanti deſcriptus; </s>
          <s xml:space="preserve">IL, parallela AC, ſpatium eodem momento vi cen-<lb />trali percurſum, quod ſpatium ipſius vis centralis rationem ſequitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-02" corresp="note-0159-02a" place="margin">TAB. XV. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0159-03" corresp="note-0159-03a" n="*" anchored="true" place="margin">La Hire <lb />ſect. con. <lb />Lib. 2. <lb />pro. 10.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">401.</note>
        <p>
          <s xml:space="preserve">Ducantur LG parallela IA, &amp; </s>
          <s xml:space="preserve">LH ad AC perpendicularis; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">AF <lb />ad ED normalis; </s>
          <s xml:space="preserve">jungantur etiam C &amp; </s>
          <s xml:space="preserve">L.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Triangula rectangula LHG, AFC, ſunt ſimilia propter angulos æqua-<lb />les LGH, ACF <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ergo LH, LG :</s>
          <s xml:space="preserve">: AF, AC; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">LH x AC = LG x
AF. </s>
          <s xml:space="preserve"> <lb />
<ptr xml:id="note-0159-05a" corresp="note-0159-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-05" corresp="note-0159-05a" n="*" anchored="true" place="margin">29. El. 1</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Conſtans autem eſt quantitas LH x AC; </s>
          <s xml:space="preserve">eſt enim duplum areæ triangu-<lb />li ALC <ptr type="noteAnchor" />, quæ momento conſtanti quo AL deſcribitur proportionalis
eſt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">
<ptr xml:id="note-0159-06a" corresp="note-0159-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-06" corresp="note-0159-06a" n="*" anchored="true" place="margin">34. El 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Ellipſi etiam eſt conſtans quantitas ED x AF <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Ergo ED x AF,
<ptr xml:id="note-0159-07a" corresp="note-0159-07" type="noteAnchor" />
eſt ad LH x AC aut LG x AF, id eſt, ED ad LG, ſemper in eadem <lb />
<ptr xml:id="note-0159-08a" corresp="note-0159-08" type="noteAnchor" />
ratione ubicunque punctum ut A in Ellipſi ſumatur; </s>
          <s xml:space="preserve">conſtans id circo etiam <lb />eſt ratio inter ED<hi rend="superscript">q</hi> &amp; </s>
          <s xml:space="preserve">LG<hi rend="superscript">q</hi>. </s>
          <s xml:space="preserve">In Ellipſi autem ED<hi rend="superscript">q</hi>, LG<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: AB<hi rend="superscript">q</hi>, AG x <lb />GB <ptr type="noteAnchor" />, aut LI x AB, propter æquales AG &amp; </s>
          <s xml:space="preserve">LI, &amp; </s>
          <s xml:space="preserve">differentiam infini-
<ptr xml:id="note-0159-09a" corresp="note-0159-09" type="noteAnchor" />
tè exiguam inter GB &amp; </s>
          <s xml:space="preserve">AB; </s>
          <s xml:space="preserve">conſtans idcirco etiam eſt ratio inter AB<hi rend="superscript">q</hi> &amp; </s>
          <s xml:space="preserve"><lb />LI x AB, id eſt, inter AB &amp; </s>
          <s xml:space="preserve">LI, augetur ideò LI, id eſt, vis centra-<lb />lis in eadem ratione in qua augetur &amp; </s>
          <s xml:space="preserve">minuitur AB, aut ipſius dimidium <lb />AC, quod æquale eſt diſtantiæ corporis à centro; </s>
          <s xml:space="preserve">ut notavimus in n. </s>
          <s xml:space="preserve">388.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-07" corresp="note-0159-07a" n="*" anchored="true" place="margin">354. 396.</note>
              <note xml:space="preserve" xml:id="note-0159-08" corresp="note-0159-08a" n="*" anchored="true" place="margin">La Hire <lb />ſect. con. <lb />lib. 5. <lb />prop. 21.</note>
              <note xml:space="preserve" xml:id="note-0159-09" corresp="note-0159-09a" n="*" anchored="true" place="margin">ibid. <lb />Lib. 3. <lb />prop 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si vero dum corpus in Ellipſi movetur vis ad focum dirigatur, hæc rece-<lb />
<ptr xml:id="note-0159-10a" corresp="note-0159-10" type="noteAnchor" />
dendo a centro virium decreſcit in ratione inverſa quadrati diſtantiæ, ut <lb />habetur in n. </s>
          <s xml:space="preserve">381. </s>
          <s xml:space="preserve">cujus propoſitionis hîc dabimus demonſtrationem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-10" corresp="note-0159-10a" place="margin">411.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit DAB ſemi Ellipſis; </s>
          <s xml:space="preserve">BD axis; </s>
          <s xml:space="preserve">C centrum; </s>
          <s xml:space="preserve">F focus ad quem vis diſigi-<lb />
<ptr xml:id="note-0159-11a" corresp="note-0159-11" type="noteAnchor" />
tur; </s>
          <s xml:space="preserve">AI tangens ad Ellipſin in puncto quocunque A; </s>
          <s xml:space="preserve">AL arcus infinitè <lb />exiguus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-11" corresp="note-0159-11a" place="margin">TAB XV <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ductis AC, AF, ſint LG &amp; </s>
          <s xml:space="preserve">CE parallelæ tangenti AI; </s>
          <s xml:space="preserve">LI paral-<lb />lela AC; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">L i æqui diſtans AF; </s>
          <s xml:space="preserve">erunt æquales LI &amp; </s>
          <s xml:space="preserve">AG, ut &amp; </s>
          <s xml:space="preserve">L i <lb />&amp; </s>
          <s xml:space="preserve">A g <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">AE autem erit æqualis CD ſemi axi majori; </s>
          <s xml:space="preserve">ductis enim A f ad
<ptr xml:id="note-0159-12a" corresp="note-0159-12" type="noteAnchor" />
focum alium &amp; </s>
          <s xml:space="preserve">f M etiam ad AI parallelam, erunt anguli AMf, AfM <lb />æquales <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">latera AM, Af, æqualia <ptr type="noteAnchor" />, ſunt etiam æqualia EM, EF <ptr type="noteAnchor" />
<ptr xml:id="note-0159-13a" corresp="note-0159-13" type="noteAnchor" />
<ptr xml:id="note-0159-14a" corresp="note-0159-14" type="noteAnchor" />
<ptr xml:id="note-0159-15a" corresp="note-0159-15" type="noteAnchor" />
propter æquales CF, Cf<ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Ergo EM + M Aid eſt EA valet FE + Af, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0159-16a" corresp="note-0159-16" type="noteAnchor" />
eſt EA dimidium ſummæ linearum FA, Af, quæ ſimul ſumtæ æquales <lb />ſunt axi BD <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-12" corresp="note-0159-12a" n="*" anchored="true" place="margin">34. El 1.</note>
              <note xml:space="preserve" xml:id="note-0159-13" corresp="note-0159-13a" n="*" anchored="true" place="margin">La Hire <lb />ſect. con. <lb />Lib. 8. <lb />prop. 8.</note>
              <note xml:space="preserve" xml:id="note-0159-14" corresp="note-0159-14a" n="*" anchored="true" place="margin">5. El. 1.</note>
              <note xml:space="preserve" xml:id="note-0159-15" corresp="note-0159-15a" n="*" anchored="true" place="margin">2 El. VI.</note>
              <note xml:space="preserve" xml:id="note-0159-16" corresp="note-0159-16a" n="*" anchored="true" place="margin">379.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">379.</note>
        <p>
          <s xml:space="preserve">Ducantur ulterius LH ad AC normalis, &amp; </s>
          <s xml:space="preserve">Lb cum AF angulos effi-<lb />ciens rectos; </s>
          <s xml:space="preserve">junganturque puncta H, b.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propter angulos rectos ALb, LHA, puncta H, b, ſunt in circumfe-<lb />rentia ſemi circuli cujus diameter A eſt L <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">idcirco anguli bLH, bAH,
<ptr xml:id="note-0159-18a" corresp="note-0159-18" type="noteAnchor" />
ſunt in eodem ſegmento &amp; </s>
          <s xml:space="preserve">ideò æquales <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ſunt etiam in eodem ſegmento,
<ptr xml:id="note-0159-19a" corresp="note-0159-19" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">æquales anguli LHb &amp; </s>
          <s xml:space="preserve">LAb; </s>
          <s xml:space="preserve">hic autem quia AL eſt inſinitè exigua
</s>
          <pb facs="0160" n="102" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cum angulo IAb coincidit &amp; </s>
          <s xml:space="preserve">angulo AEC æqualis eſt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare ſimilia
<ptr xml:id="note-0160-01a" corresp="note-0160-01" type="noteAnchor" />
ſunt triangula LbH, AEC, &amp; </s>
          <s xml:space="preserve">#  <lb /># Lb, LH:</s>
          <s xml:space="preserve">: AC, AE aut CD.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0159-18" corresp="note-0159-18a" n="*" anchored="true" place="margin">31 El. 117.</note>
              <note xml:space="preserve" xml:id="note-0159-19" corresp="note-0159-19a" n="*" anchored="true" place="margin">21. El. 111.</note>
              <note xml:space="preserve" xml:id="note-0160-01" corresp="note-0160-01a" n="*" anchored="true" place="margin">29 El 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Etiam propter triangula ſimilia AgG, AEC, AG eſt ad Ag, aut LI, <lb />ad Li, ut AC ad AE, aut CD.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hiſce poſitis concipiamus duo corpora Ellipſin hanc percurrentia, eodem <lb />tempore, quorum unum retineatur vi, quæ ad centrum Ellipſeos C dirigitur, <lb />alterum vi ad focorum alterum F tendente.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dum corpora ambo arcum exiguum percurrunt AL, primum vi centrali <lb />movetur per IL, ſecundum vi centrali percurrit iL, tempora autem quibus <lb />corpora has lineolas percurrunt, ſuntinter ſe ut areæ LAC, LAF <ptr type="noteAnchor" />, ponimus
<ptr xml:id="note-0160-02a" corresp="note-0160-02" type="noteAnchor" />
enim integram Ellipſin æqualibus temporibus a ſingulis corporibus percurri; <lb /></s>
          <s xml:space="preserve">ideoque in utroque caſu idem tempus periodicum per integram aream repræ-<lb />ſentari. </s>
          <s xml:space="preserve">Areæ vero illæ ſunt inter ſe ut harum dupla AC x LH, AF x <lb />Lb; </s>
          <s xml:space="preserve">hæc autem producta quia LH, Lb:</s>
          <s xml:space="preserve">: CD, AC, ſunt ut AC x CD ad <lb />AF x AC, id eſt ut CD, ad AF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0160-02" corresp="note-0160-02a" n="*" anchored="true" place="margin">354. 396.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Spatia IL, iL, viribus centralibus percurſa, quæ ut vidimus ſunt ad AC ad <lb />CD, ſunt etiam in ratione compoſita virium, &amp; </s>
          <s xml:space="preserve">quadratorum temporum <ptr type="noteAnchor" />, aut li-
<ptr xml:id="note-0160-03a" corresp="note-0160-03" type="noteAnchor" />
nearum CD, AF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0160-03" corresp="note-0160-03a" n="*" anchored="true" place="margin">402.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis per AC huic lineæ proportionalis eſt, ut demonſtravimus <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">hac
<ptr xml:id="note-0160-04a" corresp="note-0160-04" type="noteAnchor" />
ipſâ lineâ deſignari poteſt; </s>
          <s xml:space="preserve">vim per AF dicimus V: </s>
          <s xml:space="preserve">ergo <lb />AC, CD :</s>
          <s xml:space="preserve">: AC x CD<hi rend="superscript">q</hi>, V x AF<hi rend="superscript">q</hi> <lb />Unde deducimus V = {CD<hi rend="superscript">c</hi>/AF<hi rend="superscript">q</hi>}; </s>
          <s xml:space="preserve">patet igitur propter conſtantem CD<hi rend="superscript">c</hi>, mutato <lb />puncto A, vim V mutari in ratione inverſa quadrati diſtantiæ AF. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0160-04" corresp="note-0160-04a" n="*" anchored="true" place="margin">410.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">412.</note>
        <p>
          <s xml:space="preserve">Circa motum in Ellipſi ulterius notavimus <ptr type="noteAnchor" />, quod nunc demonſtrabimus, ſi
<ptr xml:id="note-0160-06a" corresp="note-0160-06" type="noteAnchor" />
vis decreſcat in ratione inverſa quadrati diſtantiæ, circulum cujus diameter <lb />axi majori Ellipſeos æqualis eſt, eo tempore a corpore percurri in quo hoc <lb />Ellpiſim ipſam deſcribere poſſet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0160-06" corresp="note-0160-06a" place="margin">382.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit ſemi Ellipſis BAD; </s>
          <s xml:space="preserve">axis major BD; </s>
          <s xml:space="preserve">ſemi axis minor CA; </s>
          <s xml:space="preserve">F focus <lb />
<ptr xml:id="note-0160-07a" corresp="note-0160-07" type="noteAnchor" />
centrum virium. </s>
          <s xml:space="preserve">Centro F, &amp; </s>
          <s xml:space="preserve">radio FA circulus deſcribatur AP, de-<lb />monſtrandum tempus periodicum in circulo æquale eſſe tempori periodico <lb />in Ellipſi; </s>
          <s xml:space="preserve">radius enim FA æqualis eſt ſemi axi majori Ellipſeos, ut ex <lb />hujus deſcriptione ſequitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0160-07" corresp="note-0160-07a" place="margin">TAB. XV. <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">379.</note>
        <p>
          <s xml:space="preserve">Dentur duo corpora in A, quorum unum in circulo, alterum in Ellipſi <lb />moveatur, ſintque AL, AM arcus minimi codem tempore deſcripti; </s>
          <s xml:space="preserve">ſpa-<lb />tia vicentrali percurſaerunt æqualia; </s>
          <s xml:space="preserve">quia ambo corpora ad eandem diſtanti-<lb />am AF a centro dantur: </s>
          <s xml:space="preserve">ſpatia autem hæc ſunt iL, NM, poſitis Ai ad <lb />Ellipſin &amp; </s>
          <s xml:space="preserve">IN ad circulum, tangentibus, ut &amp; </s>
          <s xml:space="preserve">NM, &amp; </s>
          <s xml:space="preserve">iL, ad AF pa-<lb />rallelis. </s>
          <s xml:space="preserve">Sint etiam IL ad AC, OM ad NA, GL ad AI parallelæ, &amp; </s>
          <s xml:space="preserve">du-<lb />cantur LC, LF, MF.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In circulo OM<hi rend="superscript">q</hi> æquale eſt <hi rend="superscript">2</hi>MN x AF<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam AF &amp; </s>
          <s xml:space="preserve">OF pro æqua-
<ptr xml:id="note-0160-09a" corresp="note-0160-09" type="noteAnchor" />
libus habentur &amp; </s>
          <s xml:space="preserve">AO, MN ſunt æquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0160-09" corresp="note-0160-09a" n="*" anchored="true" place="margin">32. El. 111. <lb />3. 4 El. VI.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Ellipſi AC<hi rend="superscript">q</hi>, BC<hi rend="superscript">q</hi> aut AF<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: <hi rend="superscript">2</hi>IL x AC, GL<hi rend="superscript">q</hi> = {<hi rend="superscript">2</hi>IL x AF<hi rend="superscript">q</hi>/AC} ſunt <lb />
<ptr xml:id="note-0160-10a" corresp="note-0160-10" type="noteAnchor" />
enim æquales AG, IL, &amp; </s>
          <s xml:space="preserve">AC, GC tantum quantitate infinite exigua <lb />differunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0160-10" corresp="note-0160-10a" n="*" anchored="true" place="margin">La Hire <lb />ſect. com. <lb />lib. 3. <lb />prop 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Triangula IiL, ACF, ſunt ſimilia quia latera ſunt reſpectivè parallela; </s>
          <s xml:space="preserve">ideò
</s>
          <pb facs="0161" n="103" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA, LIB I. CAP. XXI.</fw>
FA, AC:</s>
          <s xml:space="preserve">: iL, aut MN, IL = {MN x AC/FA}</s>
        </p>
        <p>
          <s xml:space="preserve">Subſtituendo pro IL valorem in hac æquatione GL<hi rend="superscript">q</hi> = {<hi rend="superscript">2</hi>IL x AF<hi rend="superscript">q</hi>/AC} habe-<lb />mus GL<hi rend="superscript">q</hi> = <hi rend="superscript">2</hi>MN x AF, cui quantitati etiam æquale eſt OM<hi rend="superscript">q</hi>, ſunt ergo <lb />
<ptr xml:id="note-0161-01a" corresp="note-0161-01" type="noteAnchor" />
æquales GL &amp; </s>
          <s xml:space="preserve">OM, unde patet in Ellipſi corpus in extremitate axeos mino-<lb />ris eadem velocitate moveri qua aliud fertur in circulo cujus diameter æqualis eſt axi <lb />Ellipſeos majori, ſi eadem vi centrali quæ ad ſocum Ellipſeos dirigitur, ambo in <lb />curvis retineantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0161-01" corresp="note-0161-01a" place="margin">413.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quia curva in A parallela eſt ipſi Axi BD, ſunt æqualia triangula CAL, <lb />
<ptr xml:id="note-0161-02a" corresp="note-0161-02" type="noteAnchor" />
FAL <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">triangula rectangula CAL, FAM, quorum baſes ſunt æqua-
les ſunt inter ſe ut altitudines AC, AF aut CD; </s>
          <s xml:space="preserve">In hac eadem ratione <lb />ſunt inter ſe areæ Ellipſeos, &amp; </s>
          <s xml:space="preserve">circuli. </s>
          <s xml:space="preserve">Idcirco alternando area trianguli <lb />CAL, aut FAL, ad aream Ellipſeos, ut area trianguli FAM ad aream <lb />circuli: </s>
          <s xml:space="preserve">ergo tempus in quo corpus movetur per AL ad tempus periodicum <lb />in Ellipſi, ut tempus in quo percurritur AM ad tempus periodicum in cir-<lb />
<ptr xml:id="note-0161-03a" corresp="note-0161-03" type="noteAnchor" />
culo <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">antecedentia ſunt æqualia ideò &amp; </s>
          <s xml:space="preserve">conſequentia Q. </s>
          <s xml:space="preserve">D.</s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0161-02" corresp="note-0161-02a" n="*" anchored="true" place="margin">37. El. 1.</note>
              <note xml:space="preserve" xml:id="note-0161-03" corresp="note-0161-03a" n="*" anchored="true" place="margin">354. 396.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 4.</head>
        <head rend="italics" xml:space="preserve">De Motu in orbitâ agitatâ</head>
        <p>
          <s xml:space="preserve">Detur curva quæcunque a corpore vi centrali deſcripta, AF; </s>
          <s xml:space="preserve">centrum vi-<lb />
<ptr xml:id="note-0161-04a" corresp="note-0161-04" type="noteAnchor" />
rium C. </s>
          <s xml:space="preserve">Dividatur curva hæc ductis radiis ex centro C, CA, CB, <lb />
<ptr xml:id="note-0161-05a" corresp="note-0161-05" type="noteAnchor" />
CD &amp; </s>
          <s xml:space="preserve">c, angulos æquales infinitè exiguos inter ſe continentibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0161-04" corresp="note-0161-04a" place="margin">414</note>
              <note xml:space="preserve" xml:id="note-0161-05" corresp="note-0161-05a" place="margin">TAB. XV. <lb />fig. 9.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus ſingulos angulos ſervarâ radiorum longitudine æqualiterau-<lb />geri aut minui, novamque curvam dari a f per radiorum extrema tranſeuntem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Triangula ACB, acb propter baſes æquales CA, ca, ſunt inter ſe utaltitu-<lb />dines <ptr type="noteAnchor" />, quæ ſunt ut anguli ACB, acb; </s>
          <s xml:space="preserve">ſinguli autem anguli in unâ cur-
<ptr xml:id="note-0161-06a" corresp="note-0161-06" type="noteAnchor" />
vâ ſunt ad reſpondentes in aliâ in eâdem ratione; </s>
          <s xml:space="preserve">in ſingulis enim curvis <lb />ſunt omnes æquales inter ſe; </s>
          <s xml:space="preserve">ideo triangula quæcunque reſpondentia ut <lb />ACB acb; </s>
          <s xml:space="preserve">BCD, bcd, ſunt in eadem ratione, &amp; </s>
          <s xml:space="preserve">ſummæ quæcunque <lb />triangulorum reſpondentium etiam in eadem ratione; </s>
          <s xml:space="preserve">idcirco triangula hæc <lb />mixta ſunt proportionalia ACE, ace:</s>
          <s xml:space="preserve">: ECF, ecf; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">alternando <lb />ACE, ECF:</s>
          <s xml:space="preserve">: ace, ecf.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0161-06" corresp="note-0161-06a" n="*" anchored="true" place="margin">1. El. VI</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus nunc corpus in curva af moveri, dum corpus quod vi centrali <lb />ad C tendenti curvam AF percurrit; </s>
          <s xml:space="preserve">concipiamus ulterius, dum corpus unum <lb />percurrit AB, alterum per ab transferri, dum primum ad D pertingit, alterum da-<lb />ri in d, &amp; </s>
          <s xml:space="preserve">ſic ulterius; </s>
          <s xml:space="preserve">eodem tempore ergo percurruntur AF, ae, &amp; </s>
          <s xml:space="preserve">tem-<lb />pore etiam eodem percurruntur EF &amp; </s>
          <s xml:space="preserve">ef. </s>
          <s xml:space="preserve">idcirco tempora quibus AE, EF <lb />percurruntur ſunt ut illa quibus per ae, ef corpus movetur. </s>
          <s xml:space="preserve">Tempora autem <lb />illa ſunt ut areæ ACE; </s>
          <s xml:space="preserve">ECF <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ ſunt ut areæ ace, ecf; </s>
          <s xml:space="preserve">in qua ergo
<ptr xml:id="note-0161-07a" corresp="note-0161-07" type="noteAnchor" />
ratione ſunt tempora quibus per ae, &amp; </s>
          <s xml:space="preserve">ef, corpus transfertur; </s>
          <s xml:space="preserve">quæ eadem de-<lb />monſtratio cumlocum habeat, ſumtis arcubus quibuſcunque; </s>
          <s xml:space="preserve">ſequitur corpus <lb />in curva af translatum deſcribere areas lineis ad centrum c ductis tempori-<lb />bus proportionales, &amp; </s>
          <s xml:space="preserve">retineri in curvâ vi centrali ad c tendenti <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0161-07" corresp="note-0161-07a" n="*" anchored="true" place="margin">354. 396.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">355. 397.</note>
        <p>
          <s xml:space="preserve">Concipiamus nunc curvam AC circa centrum C moveri ita, ut motus <lb />
<ptr xml:id="note-0161-09a" corresp="note-0161-09" type="noteAnchor" />
angularis curvæ ſequatur proportionem motus angularis corporis in hac <lb />curva agitati: </s>
          <s xml:space="preserve">dum corpus in curva ab A ad F movetur ipſius motus an-<lb />gularis eſt ACF, ponamus curvam interea transferri motu angulari, lineam-
</s>
          <pb facs="0162" n="104" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
que a Cad ſitum AC perveniſſe, anguloſque ACF, ACa dum augentur eandem <lb />ſemper inter ſe rationem habere; </s>
          <s xml:space="preserve">quare erunt etiam in ratione conſtanti an-<lb />guli aCF, ACF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0161-09" corresp="note-0161-09a" place="margin">TAB. XV. <lb />fig. 10.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc hæc ratio illa ſit quæ in figura præcedenti datur interangulos acf, <lb />ACF, &amp; </s>
          <s xml:space="preserve">moveatur corpus, retineaturque vi centrali in curva quieſcente <lb />
<ptr xml:id="note-0162-01a" corresp="note-0162-01" type="noteAnchor" />
AEF, aliudque corpus eodem modo percurrat curvam ſimilem &amp; </s>
          <s xml:space="preserve">æqualem, <lb />ut dictum, agitatam, hoc ultimum, ut facile, patet, revera movebitur in cur-<lb />vâ aef quieſcente.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0162-01" corresp="note-0162-01a" place="margin">Fig. 9.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Hinc deducimus corpus omne quod vi centrali curvam quamcunque deſcribit, <lb />
<ptr xml:id="note-0162-02a" corresp="note-0162-02" type="noteAnchor" />
eandem curvam, circa centrum virium mobilem, vi aliâ centrali deſcribere <lb />poſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0162-02" corresp="note-0162-02a" place="margin">415.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De differentia inter vires has centrales nunc agendum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sint A, B, D, tria parum admodum a ſe invicem diſtantia puncta curvæ <lb />
<ptr xml:id="note-0162-03a" corresp="note-0162-03" type="noteAnchor" />
cujuſcunque a corpore, vicentrali ad C tendenti percurſæ detur GBH tan-<lb />
<ptr xml:id="note-0162-04a" corresp="note-0162-04" type="noteAnchor" />
gens ad curvam in puncto B; </s>
          <s xml:space="preserve">ſintque GD, HA, ad BC parallelæ poni-<lb />mus GB, BH æquales inter ſe, ideoque AB, BD æqualibus temporibus <lb />percurri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0162-03" corresp="note-0162-03a" place="margin">416.</note>
              <note xml:space="preserve" xml:id="note-0162-04" corresp="note-0162-04a" place="margin">TAB. XV. <lb />fig. 11.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propter diſtantiam inter puncta A, B, D, infinitè exiguam, vis <lb />centralis in motu per hæc puncta non mutatur, ideò temporibus æqualibus <lb />quibus AB, BD percurruntur, æqualiter vi centrali a recta deflectitur cor-<lb />pus, id eſt hujus via æqualiter incurvatur, ex qua æquali deflectione ſequi-<lb />tur æquales eſſe inter ſe HA, GD.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Angulus quem curva quæcunque cum tangenti efficit eſt infinitè exiguus <lb />
<ptr xml:id="note-0162-05a" corresp="note-0162-05" type="noteAnchor" />
ideoque HA &amp; </s>
          <s xml:space="preserve">DG ſunt inſinite exiguæ reſpectu HB, HG; </s>
          <s xml:space="preserve">quare cum <lb />hæ ſint æquales, &amp; </s>
          <s xml:space="preserve">infinitè exiguæ, ſunt æquales anguli BCA, BCD.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0162-05" corresp="note-0162-05a" place="margin">417.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint ulterius anguli ACa, DCd, æquales inter ſe; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">centro C deſcri-<lb />pti arcus circulorum Aa, Dd. </s>
          <s xml:space="preserve">Evidentiſſime patet puncta a, B, d, eſſe pun-<lb />cta curvæ in qua corpus movetur, ſi in curva ABD mobili feratur, poſito mo-<lb />tu angulari curvæ ad motum angularem corporis, ut angulus aCA ad an-<lb />gulum ACB <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in hoc motu corpus ab a ad B fertur eodem tempore, in
<ptr xml:id="note-0162-06a" corresp="note-0162-06" type="noteAnchor" />
quo in curvâ quieſcente ab A ad B pergit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0162-06" corresp="note-0162-06a" n="*" anchored="true" place="margin">434.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus FBI, in puncto B, tangere curvam aBd, &amp; </s>
          <s xml:space="preserve">ad BC paralle-<lb />las dari I a, F d; </s>
          <s xml:space="preserve">quia æqualibus temporibus percurruntur a B, Bd, ſuntæ-<lb />quales IB, BF, quæ iiſdem temporibus ſublatâ vi centrali poſſet percurri; <lb /></s>
          <s xml:space="preserve">ſuntque etiam æquales Fd, Ia; </s>
          <s xml:space="preserve">quod eâdem demonſtratione evincitur qua <lb />probavimus æquales HA, GD <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">416.</note>
        <p>
          <s xml:space="preserve">Jungantur F, G ut &amp; </s>
          <s xml:space="preserve">H, I; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ducantur DE parallela FG, &amp; </s>
          <s xml:space="preserve">AL paral-<lb />lela HI; </s>
          <s xml:space="preserve">producatur ED ad O ſecans BC in N.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propter æquales BH, BG, &amp; </s>
          <s xml:space="preserve">BI, BF, ut &amp; </s>
          <s xml:space="preserve">æquales angulos HBI, <lb />FBG, ſunt æquiangula &amp; </s>
          <s xml:space="preserve">congrua triangula FBG, BHI <ptr type="noteAnchor" />, quare ſunt
<ptr xml:id="note-0162-08a" corresp="note-0162-08" type="noteAnchor" />
æquales FG, HI quæ etiam parallelæ ſunt <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">quare etiam æquales &amp; </s>
          <s xml:space="preserve">pa-
<ptr xml:id="note-0162-09a" corresp="note-0162-09" type="noteAnchor" />
rallelæ AL, ED <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Sunt quoque æquales La, Ed, cum ſint quantitatum
<ptr xml:id="note-0162-10a" corresp="note-0162-10" type="noteAnchor" />
reſpective æqualium differentiæ A a &amp; </s>
          <s xml:space="preserve">D d, angulorum æqualium menſuræ, <lb />in circulis, quorum radii infinitè parum differunt, ſunt etiam æquales; </s>
          <s xml:space="preserve">ideò <lb />æquiangula ſunt triangula A La, DEd <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">æquales anguli AL a, DE d;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0162-11a" corresp="note-0162-11" type="noteAnchor" />
hic autem æqualis eſt angulo ONC, &amp; </s>
          <s xml:space="preserve">ille angulo DNC <ptr type="noteAnchor" />, propter cru-
<ptr xml:id="note-0162-12a" corresp="note-0162-12" type="noteAnchor" />
ta parallela; </s>
          <s xml:space="preserve">quare ſunt æquales &amp; </s>
          <s xml:space="preserve">recti anguli ONC, DNC.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0162-08" corresp="note-0162-08a" n="*" anchored="true" place="margin">4. El. 1.</note>
              <note xml:space="preserve" xml:id="note-0162-09" corresp="note-0162-09a" n="*" anchored="true" place="margin">27. El. 1.</note>
              <note xml:space="preserve" xml:id="note-0162-10" corresp="note-0162-10a" n="*" anchored="true" place="margin">30. 34. <lb />El. 1.</note>
              <note xml:space="preserve" xml:id="note-0162-11" corresp="note-0162-11a" n="*" anchored="true" place="margin">8. El. 1.</note>
              <note xml:space="preserve" xml:id="note-0162-12" corresp="note-0162-12a" n="*" anchored="true" place="margin">29. El. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eo tempore quo, vi centrali, in curvâ mobili percurritur Fd, in curva <lb />
<ptr xml:id="note-0162-13a" corresp="note-0162-13" type="noteAnchor" />
quieſcente, vi centrali, percurritur GD, quæ æqualis eſt FE; </s>
          <s xml:space="preserve">ideò ſpa-<lb />tium differentiâ virium eodem tempore percurſum eſt Ed. </s>
          <s xml:space="preserve">Punctum au-
</s>
          <pb facs="0163" n="105" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XXI.</fw>
tem E in hac figura determinatur ductâ per D perpendiculari ad BC.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0162-13" corresp="note-0162-13a" place="margin">418.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hiſce poſitis, ſit centrum virium C, &amp; </s>
          <s xml:space="preserve">moveatur corpus in curvâ AEG <lb />
<ptr xml:id="note-0163-01a" corresp="note-0163-01" type="noteAnchor" />
ita circa centruin C agitatâ, ut motus angularis curvæ ſe habeat ad motum an-<lb />
<ptr xml:id="note-0163-02a" corresp="note-0163-02" type="noteAnchor" />
gularem corporis in curva circa idem centrum C, ut angulus a CA ad an-<lb />gulum ACE. </s>
          <s xml:space="preserve">Sit EG continuatio curvæ AE; </s>
          <s xml:space="preserve">centro C radio CG de-<lb />ſcribatur arcus FG g; </s>
          <s xml:space="preserve">ductiſque EC, GC, fiat angulus GCF ad ECG, <lb />ut angulus a CA ad ACE. </s>
          <s xml:space="preserve">Dum corpus percurrit EG in curva AE, mo-<lb />tu curvæ punctum G ad F transfertur &amp; </s>
          <s xml:space="preserve">corpus percurrit EF, tempore quo <lb />potuiſſet percurrere EG in curva quieſcente Per G ad EC ducatur per-<lb />pendicularis GH, quæ utrimque continuata ſecat EC in H &amp; </s>
          <s xml:space="preserve">CF conti-<lb />nuatam in f; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">erit fF ſpatium differentiâ virium percurſum, poſitis angu-<lb />lis FCG &amp; </s>
          <s xml:space="preserve">GCE infinite exiguis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0163-01" corresp="note-0163-01a" place="margin">419.</note>
              <note xml:space="preserve" xml:id="note-0163-02" corresp="note-0163-02a" place="margin">TAB XV. <lb />fig. 12.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">418.</note>
        <p>
          <s xml:space="preserve">Si, ſumpto puncto E alio quocunque, EG &amp; </s>
          <s xml:space="preserve">EF ita determinentur, ut æ-<lb />quali tempore deſcribantur ubicunque detur punctum E; </s>
          <s xml:space="preserve">id eſt, areæ EGC, <lb />EFC, determinatam habeant magnitudinem <ptr type="noteAnchor" />, lineola f F differentiæ viri-
<ptr xml:id="note-0163-04a" corresp="note-0163-04" type="noteAnchor" />
um proportionalis erit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0163-04" corresp="note-0163-04a" n="*" anchored="true" place="margin">354. 396.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">401.</note>
        <p>
          <s xml:space="preserve">Area EGC dicatur N; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">M area EFC; </s>
          <s xml:space="preserve">poſitis N &amp; </s>
          <s xml:space="preserve">M quantitatibus <lb />determinatis. </s>
          <s xml:space="preserve">Habemus EC x GH = <hi rend="superscript">2</hi>N &amp; </s>
          <s xml:space="preserve">EC x f H = <hi rend="superscript">2</hi>M; </s>
          <s xml:space="preserve">unde dedu-<lb />cimus GH = {<hi rend="superscript">2</hi>N/EC} &amp; </s>
          <s xml:space="preserve">fH = {<hi rend="superscript">2</hi>M/EC}; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">f H + GH, id eſt f g = {<hi rend="superscript">2</hi>M + <hi rend="superscript">2</hi>N/EC}, <lb />&amp; </s>
          <s xml:space="preserve">f H - GH, id eſt f G, = {<hi rend="superscript">2</hi>M - <hi rend="superscript">2</hi>N/EC}. </s>
          <s xml:space="preserve">Ex proprietate circuli eſt f G x fg <lb />= f F x f @ ſumtis FC &amp; </s>
          <s xml:space="preserve">CI æqualibus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">36. El. 213.</note>
        <p>
          <s xml:space="preserve">Æquatio hæc, ſubſtituendo pro f G &amp; </s>
          <s xml:space="preserve">fg valores, mutatur in hanc <lb />{<hi rend="superscript">4</hi>M<hi rend="superscript">q</hi> - <hi rend="superscript">4</hi>N<hi rend="superscript">q</hi>/EC<hi rend="superscript">q</hi>} = fF x fI; </s>
          <s xml:space="preserve">ſed, propter f F infinitè exiguam, f I valet <hi rend="superscript">2</hi>FC, <lb />&amp; </s>
          <s xml:space="preserve">quia infinitè parum differunt CF, EC, una pro aliâ uſurpari poteſt: </s>
          <s xml:space="preserve">er-<lb />go iterum mutatur æquatio in hanc {<hi rend="superscript">4</hi>M<hi rend="superscript">q</hi> - <hi rend="superscript">4</hi>N<hi rend="superscript">q</hi>/CF<hi rend="superscript">q</hi>} = <hi rend="superscript">2</hi>f F x CF: </s>
          <s xml:space="preserve">idcirco <lb />f F = {<hi rend="superscript">2</hi>M<hi rend="superscript">q</hi> - <hi rend="superscript">2</hi>N<hi rend="superscript">q</hi>/CF<hi rend="superscript">c</hi>}. </s>
          <s xml:space="preserve">Numerator hujus fractionis eſt conſtans quantitas ſe-<lb />quitur ergo f F, id eſt differentia virium, rationem inverſam denominatoris, <lb />nempe, cubi diſtantiæ a centro.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vis hæc eſt exceſſus qua vis centralis in curva mobili ſuperat vim in curva <lb />quieſcente &amp; </s>
          <s xml:space="preserve">motus curvæ cum motu corporis conſpirat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando punctum f cadit inter G &amp; </s>
          <s xml:space="preserve">H, eadem demonſtratio locum habet, <lb />ſed vis centralis in curvâ quieſcente excedit aliam, &amp; </s>
          <s xml:space="preserve">curvæ motus in con-<lb />trariam partem dirigitur. </s>
          <s xml:space="preserve">Si autem punctum f inter H &amp; </s>
          <s xml:space="preserve">g, aut ultra g ca-<lb />dat, agitur de motu corporis in contrariam partem ex E ad A.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ex hiſce omnibus deducimus. </s>
          <s xml:space="preserve">Si corpus vi centrali quacunque curvam deſcri-<lb />
<ptr xml:id="note-0163-07a" corresp="note-0163-07" type="noteAnchor" />
bat, ſuperadditâ, aut detractâ, vi quæ ſequatur rationem inverſam cubi diſtan-<lb />tiæ, eandem curvam, circa centrum virium mobilem, corpus deſcribere. </s>
          <s xml:space="preserve">Si vis ſu-<lb />
<ptr xml:id="note-0163-08a" corresp="note-0163-08" type="noteAnchor" />
peradditur motus curvæ cum motu corporis ad eandem partem tendunt. </s>
          <s xml:space="preserve">In con-<lb />
<ptr xml:id="note-0163-09a" corresp="note-0163-09" type="noteAnchor" />
trarias partes diriguntur ſi vis detrabatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0163-07" corresp="note-0163-07a" place="margin">420.</note>
              <note xml:space="preserve" xml:id="note-0163-08" corresp="note-0163-08a" place="margin">421.</note>
              <note xml:space="preserve" xml:id="note-0163-09" corresp="note-0163-09a" place="margin">422.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0164" n="106" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 5.</head>
        <head rend="italics" xml:space="preserve">De Motu in Ellipſi agitatâ.</head>
        <p>
          <s xml:space="preserve">Corpus in Ellipſi retinetur vi centrali ad focum tendente &amp; </s>
          <s xml:space="preserve">juxtarationem <lb />
<ptr xml:id="note-0164-01a" corresp="note-0164-01" type="noteAnchor" />
inverſam quadrati diſtantiæ decreſcente <ptr type="noteAnchor" />, ſi ſuperaddatur vis quæ decre-
<ptr xml:id="note-0164-02a" corresp="note-0164-02" type="noteAnchor" />
ſcat in ratione inverſa cubi diſtantiæ, eandem corpus deſcribit Ellipſim trans-<lb />latam ita, ut eandem partem verſus motus ipſius cum motu corporis diri-<lb />gatur <ptr type="noteAnchor" /> Vis ultima magis decreſcit, auctâ diſtantiâ, quam prima; </s>
          <s xml:space="preserve">idcirco ſum-
<ptr xml:id="note-0164-03a" corresp="note-0164-03" type="noteAnchor" />
ma virium, celerius decreſcit quam juxta rationem inverſam quadrati diſtan-<lb />tiæ, unde conſtat propoſitio n. </s>
          <s xml:space="preserve">386.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0164-01" corresp="note-0164-01a" place="margin">423.</note>
              <note xml:space="preserve" xml:id="note-0164-02" corresp="note-0164-02a" n="*" anchored="true" place="margin">381. 411.</note>
              <note xml:space="preserve" xml:id="note-0164-03" corresp="note-0164-03a" n="*" anchored="true" place="margin">420. 421.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simili demonſtratione conſtat n. </s>
          <s xml:space="preserve">387. </s>
          <s xml:space="preserve">nam ſi ex vi quæ ſequitur rationem <lb />
<ptr xml:id="note-0164-04a" corresp="note-0164-04" type="noteAnchor" />
inverſam quadrati diſtantiæ tollatur vis, quæ ſequatur rationem inverſam cubi <lb />diſtantiæ, id eſt primâ celerius decreſcens, quæ ſupereſt lentius quàm juxta <lb />rationem inverſam quadrati diſtantiæ, auctâ hac, minuitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0164-04" corresp="note-0164-04a" place="margin">424.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In n. </s>
          <s xml:space="preserve">385, 386, 387. </s>
          <s xml:space="preserve">egimus de viribus, juxta rationem, a ratione dupli-<lb />
<ptr xml:id="note-0164-05a" corresp="note-0164-05" type="noteAnchor" />
catâ inverſa diſtantiæ parum aberrante, decreſcentibus, aut de curvis circulis fini-<lb />timis; </s>
          <s xml:space="preserve">quia in hiſce caſibus in propoſitionibus error ſenſibilis non datur, licet vires <lb />ſequantur rationem aliûs poteſtatis cujuſdam diſtantiæ; </s>
          <s xml:space="preserve">in quo caſu Mathe-<lb />maticè loquendo curva non eſt Ellipſis mota juxta leges explicatas, ad quod <lb />requiritur vis, quæ eſt ſumma aut differentia virium, quarum una ſequitur ra-<lb />tionem inverſam duplicatam <ptr type="noteAnchor" />, alia inverſam triplicatam, diſtantiæ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0164-05" corresp="note-0164-05a" place="margin">425.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">331. 411.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">420.</note>
        <p>
          <s xml:space="preserve">Ut autem ex dato motu angulari Ellipſeos vim addendam aut detrahen-<lb />dam, &amp; </s>
          <s xml:space="preserve">vice verſa ex data hac, motum curvæ determinemus, <lb />
<ptr xml:id="note-0164-08a" corresp="note-0164-08" type="noteAnchor" />
ſit A extremitas axeos majoris; </s>
          <s xml:space="preserve">F focus centrum virium; </s>
          <s xml:space="preserve">a A portio circuli <lb />
<ptr xml:id="note-0164-09a" corresp="note-0164-09" type="noteAnchor" />
centro F, radio F A deſcripti; </s>
          <s xml:space="preserve">A L Ellipſeos portio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0164-08" corresp="note-0164-08a" place="margin">426.</note>
              <note xml:space="preserve" xml:id="note-0164-09" corresp="note-0164-09a" place="margin">TAB. XV. <lb />fig, 13.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus dum corpus in Ellipſi fertur per AL, ipſam curvam motu an-<lb />gulari a FA transferri; </s>
          <s xml:space="preserve">anguloſque a FL, AFL eſſe inter ſe ut M ad N. <lb /></s>
          <s xml:space="preserve">Ponimus etiam angulos hos eſſe infinite exiguos.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In a &amp; </s>
          <s xml:space="preserve">A ad circulum a A ducantur tangentes a i, EAI, ſibi mutuo oc-<lb />currentes in E, &amp; </s>
          <s xml:space="preserve">quarum ultima etiam Ellipſin tangit in A; </s>
          <s xml:space="preserve">ducantur et-<lb />iam AB, LI, ad a F parallelæ, ultima propter infinite exiguos arcus a A, <lb />AL, pro parallela haberi poteſt ipſi AF; </s>
          <s xml:space="preserve">tandem ſint AC ad a B, &amp; </s>
          <s xml:space="preserve">LG ad <lb />AI parallelæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sunt æquales E a, EA <ptr type="noteAnchor" />, ideoque a E &amp; </s>
          <s xml:space="preserve">EB, quæ EA æqualis eſt. </s>
          <s xml:space="preserve">Pro-
<ptr xml:id="note-0164-10a" corresp="note-0164-10" type="noteAnchor" />
pter triangula ſimilia EBA, EiI, eſt #  <lb /># EB aut {1/2} a B, E i aut a i-{1/2} a B:</s>
          <s xml:space="preserve">: BA, i I; <lb /></s>
          <s xml:space="preserve">a B autem ſe habet ad a i, ut angulus a F A ad a FL, id eſt, ut M-N ad M: </s>
          <s xml:space="preserve"><lb />ergo <lb />BA, i I:</s>
          <s xml:space="preserve">:{1/2} M-{1/2}N, {1/2}M + {1/2}N:</s>
          <s xml:space="preserve">:M-N, M + N.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0164-10" corresp="note-0164-10a" n="*" anchored="true" place="margin">36. El. III.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex circuli proprietate a C aut BA, a A aut a B, &amp; </s>
          <s xml:space="preserve">diameter, ſunt <lb />in continua proportione <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo BA = {a B<hi rend="superscript">q</hi>/2AF}. </s>
          <s xml:space="preserve">Ellipſis in extremitate a-
<ptr xml:id="note-0164-11a" corresp="note-0164-11" type="noteAnchor" />
xeos majoris coincidit cum circulo cujus diameter eſt axeos parameter <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id-
<ptr xml:id="note-0164-12a" corresp="note-0164-12" type="noteAnchor" />
</s>
          <pb facs="0165" n="107" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXI.</fw>
eo ſi hæc dicatur 2R, erit IL = {AI<hi rend="superscript">q</hi>/2R} = {Bi<hi rend="superscript">q</hi>/2R}:</s>
          <s xml:space="preserve">ſed{aB<hi rend="superscript">q</hi>/2AF} ſe habet ad {Bi<hi rend="superscript">q</hi>/2R}, <lb />ut {<hi rend="overline">M-N</hi><hi rend="superscript">q</hi>/AF} ad{N<hi rend="superscript">q</hi>/R}; </s>
          <s xml:space="preserve">idcirco <lb />IL, AB:</s>
          <s xml:space="preserve">: {N<hi rend="superscript">q</hi>/R} {<hi rend="overline">M-N</hi><hi rend="superscript">q</hi>/AF}</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0164-11" corresp="note-0164-11a" n="*" anchored="true" place="margin">31. El. 111. <lb />8. El <hi rend="small caps">VI.</hi></note>
              <note xml:space="preserve" xml:id="note-0164-12" corresp="note-0164-12a" n="*" anchored="true" place="margin">La Hire <lb />ſect. con. <lb />lib. 7. cot. <lb />prop. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sed ut vidimus AB, I i:</s>
          <s xml:space="preserve">: M-N, M + N; </s>
          <s xml:space="preserve">ergo ex compoſitione rationis <lb />IL, I i:</s>
          <s xml:space="preserve">: {N<hi rend="superscript">q</hi> x <hi rend="overline">M-N</hi>/R}, {<hi rend="overline">M-N</hi><hi rend="superscript">q</hi> x <hi rend="overline">M + N</hi>/AF} = {<hi rend="overline">M<hi rend="superscript">q</hi>-N<hi rend="superscript">q</hi></hi> x <hi rend="overline">M-N</hi>/AF} :</s>
          <s xml:space="preserve">: {N<hi rend="superscript">q</hi>/R}, {M<hi rend="superscript">q</hi>-N<hi rend="superscript">q</hi>/AF} <lb />Eodem tempore percurruntur IL &amp; </s>
          <s xml:space="preserve">i I, prima vi qua corpus retinetur in <lb />Ellipſi quieſcente, ſecunda difterentiâ vis hujus cum vi qua corpus in El-<lb />lipſi mobili retinetur, ergo vis in Ellipſi ad differentiam hanc, ut {N<hi rend="superscript">q</hi>/R} <lb />ad {M<hi rend="superscript">q</hi>-N<hi rend="superscript">q</hi>/AF} <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">401.</note>
        <p>
          <s xml:space="preserve">Dicatur {N<hi rend="superscript">q</hi>/AF<hi rend="superscript">q</hi>} vis qua corpus in Ellipſi retinetur in puncto A, &amp; </s>
          <s xml:space="preserve">fiat <lb />{N<hi rend="superscript">q</hi>/R}, {M<hi rend="superscript">q</hi>-N<hi rend="superscript">q</hi>/AF} :</s>
          <s xml:space="preserve">: {N<hi rend="superscript">q</hi>/AF<hi rend="superscript">q</hi>}, ad differentiam virium {RMM-RNN/AF<hi rend="superscript">c</hi>}</s>
        </p>
        <p>
          <s xml:space="preserve">Si agatur de diſtantia alia quæcunque quæ dicatur D, vis qua corpus reti-<lb />netur in Ellipſi hac analogia detegitur <ptr type="noteAnchor" />,
<ptr xml:id="note-0165-02a" corresp="note-0165-02" type="noteAnchor" />
{I/AF<hi rend="superscript">q</hi>}, {I/D<hi rend="superscript">q</hi>} :</s>
          <s xml:space="preserve">: {N<hi rend="superscript">q</hi>/AF<hi rend="superscript">q</hi>} ad vim quæſitam {NN/DD}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0165-02" corresp="note-0165-02a" n="*" anchored="true" place="margin">381. 411.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Difterentia virium detegitur hac regulâ <ptr type="noteAnchor" />,
<ptr xml:id="note-0165-03a" corresp="note-0165-03" type="noteAnchor" />
{I/AF<hi rend="superscript">c</hi>}, {I/D<hi rend="superscript">c</hi>} :</s>
          <s xml:space="preserve">: {RMM-RNN/AF<hi rend="superscript">c</hi>} ad differentiam quæſitam <lb />{RMM-RNN/D<hi rend="superscript">c</hi>}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0165-03" corresp="note-0165-03a" n="*" anchored="true" place="margin">410.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Idcirco vis integra qua corpus in Ellipſi mobili retinetur ſequitur propor-<lb />
<ptr xml:id="note-0165-04a" corresp="note-0165-04" type="noteAnchor" />
tionem {NN/D<hi rend="superscript">q</hi>} + {RMM-RNN/D<hi rend="superscript">c</hi>}, quando corpus &amp; </s>
          <s xml:space="preserve">Ellipſis ad eandem <lb />partem tendunt. </s>
          <s xml:space="preserve">Si motus hi fuerint contrarii vis proportionalis eſt <lb />{NN/D<hi rend="superscript">q</hi>}-{RMM - RNN/D<hi rend="superscript">c</hi>}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0165-04" corresp="note-0165-04a" place="margin">427.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0166" n="108" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM. 6</head>
        <head xml:space="preserve">De Computatione motuum Apſidum in curvis parum <lb />cum circulo differentibus.</head>
        <p>
          <s xml:space="preserve">Apſides dicuntur extremitates axeos majoris Ellipſeos in qua movetur cor-<lb />pus, quod vi ad focum tendente retinetur. </s>
          <s xml:space="preserve">Agitur hìc de motus Apſidum <lb />determinatione, id eſt de motu angulari Ellipſeos, poſitâ vi, quæ ſequatur <lb />rationem poteſtatis cujuſcunque diſtantiæ, in quo caſu motus ad Elliptin <lb />mobilem referri non poterit, niſi agatur de curvâ à circulo parum diffe-<lb />rente <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">425.</note>
        <p>
          <s xml:space="preserve">Lemmatica autem propoſitio præmittenda eſt. </s>
          <s xml:space="preserve">Quadratum hujus quanti-<lb />
<ptr xml:id="note-0166-02a" corresp="note-0166-02" type="noteAnchor" />
tatis a-b eſt aa-2ab + bb, ut cubus formetur ſingulæ quanti-<lb />tates hujus quadrati per a-b multiplicari debent, productum duarum prima-<lb />rum per has eſt a<hi rend="superscript">3</hi> - 3aab + 2abb &amp; </s>
          <s xml:space="preserve">in reliqua parte producti adſcendit b <lb />ad majorem quàm ad primam poteſtatem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0166-02" corresp="note-0166-02a" place="margin">428.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut ex cubo formetur quarta poteſtas, ſingulæ cubi quantitates per a-b <lb />multiplicari debent; </s>
          <s xml:space="preserve">multiplicatis duabus primis, habemus a<hi rend="superscript">4</hi> - 4a<hi rend="superscript">3</hi>b + 3aabb <lb />&amp; </s>
          <s xml:space="preserve">in reliquis quantitatibus totius poteſtatis elevatur b ultra primam poteſta-<lb />tem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Siccontinuando clarè patet: </s>
          <s xml:space="preserve">Siagatur de poteſtate quantitatis a-b, cujus index ſit <lb />
<ptr xml:id="note-0166-03a" corresp="note-0166-03" type="noteAnchor" />
n, primos terminos eſſe a<hi rend="superscript">n</hi> - na<hi rend="superscript">n-1</hi>b, &amp; </s>
          <s xml:space="preserve">in reliquis omnibus dabitur b ad poteſta-<lb />tem magis elevatam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0166-03" corresp="note-0166-03a" place="margin">429.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitis nunc quæ in Scholio præcedenti ſunt demonſtrata; </s>
          <s xml:space="preserve">dicatur H di-<lb />
<ptr xml:id="note-0166-04a" corresp="note-0166-04" type="noteAnchor" />
ſtantia omnium maxima AF; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">X difterentia indeterminata inter H &amp; </s>
          <s xml:space="preserve">D; <lb /></s>
          <s xml:space="preserve">reducendo duas fractiones {NN/D<hi rend="superscript">q</hi>} + {RMM-RNN/D<hi rend="superscript">c</hi>} ad unicam habemus <lb />{DNN + RMM - RNN/D<hi rend="superscript">c</hi>}, ſubſtituendo in numeratore pro D valorem <lb />H-X, vis in Ellipſi mobili proportionalis eſt {RMM-RNN - HNN-NNX/D<hi rend="superscript">c</hi>}. </s>
          <s xml:space="preserve"><lb />Detur nunc vis quæ ſequatur rationem cujuſcunque poteſtatis diſtantiæ, cu-<lb />jus poteſtatis index ſit n-3, id eſt vis eſt ut D<hi rend="superscript">n-3</hi> = {D<hi rend="superscript">n</hi>/D<hi rend="superscript">c</hi>} = {<hi rend="overline">H-X</hi><hi rend="superscript">n</hi>/D<hi rend="superscript">c</hi>} = <lb />{H<hi rend="superscript">n</hi>-nH<hi rend="superscript">n-1</hi>X + &amp;</s>
          <s xml:space="preserve">c<ptr type="noteAnchor" />/D<hi rend="superscript">c</hi>} in reliquis terminis numeratoris ultra primam poteſtatem
<ptr xml:id="note-0166-05a" corresp="note-0166-05" type="noteAnchor" />
adſcendit X; </s>
          <s xml:space="preserve">ideò hi omnes exigui ſunt reſpectu illorumqui hìc ponuntur, quia X <lb />exigua eſt reſpectu H: </s>
          <s xml:space="preserve">ponimus enim curvam cum circulo parum differrre. <lb /></s>
          <s xml:space="preserve">Si nunc motus corporis quod vi hac in curva retinetur referri debeat ad mo-<lb />tum in Ellipſi mobili, vis hæc analoga ponenda eſt cum vi qua corpus <lb />in tali Ellipſi revera retinetur, ſunt ergo analogæ quantitates hæ
</s>
          <pb facs="0167" n="109" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XXI.</fw>
{RMM - RNN + HNN - NNX/D<hi rend="superscript">c</hi>} &amp; </s>
          <s xml:space="preserve">{H<hi rend="superscript">n</hi>-nH<hi rend="superscript">n-1</hi>X/D<hi rend="superscript">c</hi>} id eſt propter <lb />communem denominatorem, ſunt analogi numeratores.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0166-04" corresp="note-0166-04a" place="margin">430.</note>
              <note xml:space="preserve" xml:id="note-0166-05" corresp="note-0166-05a" n="*" anchored="true" place="margin">429.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Ellipſi a circulo parum differenti, H cum ſemi parametro R vix dif-<lb />fert, ut ex generatione Ellipſeos <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">parametri definitione ſequitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">er-
<ptr xml:id="note-0167-01a" corresp="note-0167-01" type="noteAnchor" />
go -RNN HNN ſeſe mutuo deſtruunt &amp; </s>
          <s xml:space="preserve">RMM fit HMM; </s>
          <s xml:space="preserve">quanti-<lb />
<ptr xml:id="note-0167-02a" corresp="note-0167-02" type="noteAnchor" />
tatesque analogæ ſunt HMM-NNX &amp; </s>
          <s xml:space="preserve">H<hi rend="superscript">n</hi>-nH<hi rend="superscript">n-1</hi>X, id eſt partes con-<lb />ſtantes ſunt inter ſe ut indeterminatæ quæ per X multiplicantur; </s>
          <s xml:space="preserve">ergo HMM, <lb />NNX :</s>
          <s xml:space="preserve">: H<hi rend="superscript">n</hi>, nH<hi rend="superscript">n-1</hi>X: </s>
          <s xml:space="preserve">dividendo antecedentia per H, conſequentia per X, &amp; </s>
          <s xml:space="preserve"><lb />dividendo terminos ſecundæ rationis per H<hi rend="superscript">n-1</hi> habemus <lb />MM, NN :</s>
          <s xml:space="preserve">: I, n. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />M, N :</s>
          <s xml:space="preserve">: I, I n</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0167-01" corresp="note-0167-01a" n="*" anchored="true" place="margin">397.</note>
              <note xml:space="preserve" xml:id="note-0167-02" corresp="note-0167-02a" n="*" anchored="true" place="margin">La Hire <lb />ſect. con. <lb />det. poſt. <lb />pro. 3. lib <lb />3.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Id eſt, motus angularis corporis in Ellipſi translatd ſe habet ad ipſius motum <lb />
<ptr xml:id="note-0167-03a" corresp="note-0167-03" type="noteAnchor" />
angularem in eadem Ellipſi quieſcente, ut unitas ad radicem quadratam numeri, <lb />qui tribus excedit indicem poteſtatis, cujus rationem vis ſequitur</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0167-03" corresp="note-0167-03a" place="margin">431.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex dato igitur motu angulari curvæ, poteſtas quam ſequitur vis detegitur <lb />&amp; </s>
          <s xml:space="preserve">vice verſa ex datâ poteſtate detegitur motus curvæ angularis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Exemplum unicum dabo, quod uſum ſuum habet in Aſtronomicis Detur cor-<lb />
<ptr xml:id="note-0167-04a" corresp="note-0167-04" type="noteAnchor" />
pus quod movetur in Ellipſi quæ ſingulis revolutionibus tribus gradibus progre-<lb />diatur, id eſt motus ipſius in curva translata eſt 363 grad dum m orbe qui-<lb />eſcente foret 360. </s>
          <s xml:space="preserve">grad.</s>
          <s xml:space="preserve">; M ergo ad N, ut 363. </s>
          <s xml:space="preserve">ad 360. </s>
          <s xml:space="preserve">aut ut 121 ad 120; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">MM ad NN ut 14641, ad 14400: </s>
          <s xml:space="preserve">ergo n = {14400/14641}, &amp; </s>
          <s xml:space="preserve">poteſtas diſtantiæ <lb />cujus proportionem ſequitur vis eſt {14400/14641} - 3 = -{29523/14641} quare vis eſt reci-<lb />procè ut D<hi rend="superscript">2</hi>{9523/14641} = D<hi rend="superscript">2</hi>{241/14641} = D<hi rend="superscript">2</hi>{4/243} proximè.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0167-04" corresp="note-0167-04a" place="margin">432.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">LIBRI I. PARS IV.</head>
        <head xml:space="preserve">De Viribus inſitis, &amp; Colliſione <lb />corporum.</head>
        <head xml:space="preserve">CAPUT XXII.</head>
        <head xml:space="preserve">De Viribus corporibus motis inſitis.</head>
        <p>
          <s xml:space="preserve">Vi inſitâ corpus de loco in locum transferri diximus <ptr type="noteAnchor" />,
<ptr xml:id="note-0167-05a" corresp="note-0167-05" type="noteAnchor" />
de virium comparatione nunc agendum; </s>
          <s xml:space="preserve">quod ut or-<lb />dine fiat, de harum geneſi quædam præmittenda erunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0167-05" corresp="note-0167-05a" n="*" anchored="true" place="margin">12.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vidimus antea corpus ex loco moveri, ſi preſſio, con-<lb />traria preſſione non deſtructa, in illud agat <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod ergo
<ptr xml:id="note-0167-06a" corresp="note-0167-06" type="noteAnchor" />
obtinebit, ſi corpus nullo obſtaculo retineatur: </s>
          <s xml:space="preserve">quacunque <lb />
<ptr xml:id="note-0167-07a" corresp="note-0167-07" type="noteAnchor" />
celeritate corpus cedit hanc in perpetuum ſervabit quamdiu
</s>
          <pb facs="0168" n="110" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
causâ extraneâ non deſtruitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si continuetur preſſio in
<ptr xml:id="note-0168-01a" corresp="note-0168-01" type="noteAnchor" />
corpus, augetur celeritas jam acquiſita, illudque quam diu <lb />corpus premitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0167-06" corresp="note-0167-06a" n="*" anchored="true" place="margin">101.</note>
              <note xml:space="preserve" xml:id="note-0167-07" corresp="note-0167-07a" place="margin">433.</note>
              <note xml:space="preserve" xml:id="note-0168-01" corresp="note-0168-01a" n="*" anchored="true" place="margin">2432</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nulla unquam datur preſſio ſine reactione ipſi preſſioni <lb />
<ptr xml:id="note-0168-02a" corresp="note-0168-02" type="noteAnchor" />
æquali <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">uhi non contraria preſſione deſtruitur, ſed ob-
<ptr xml:id="note-0168-03a" corresp="note-0168-03" type="noteAnchor" />
ſtaculum movet preſſio, vimque generat, ex obſtaculi in-<lb />ertiâ oritur reſiſtentia, aut reactio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0168-02" corresp="note-0168-02a" place="margin">434.</note>
              <note xml:space="preserve" xml:id="note-0168-03" corresp="note-0168-03a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pro parte ſæpe contrariâ preſſione deſtruitur preſſio, quod <lb />ſupereſt in hoc caſu movet obſtaculum, &amp; </s>
          <s xml:space="preserve">vim generat; </s>
          <s xml:space="preserve">ſic <lb />navis quæ fune trahitur, ab aquâ patitur reſiſtentiam, quam-<lb />diu hæc minor eſt preſſione illâ, qua funis trahitur, auge-<lb />tur navis celeritas, &amp; </s>
          <s xml:space="preserve">reactio, quæ actioni æqualis eſt, cum <lb />utramque partem verſus funis æqualiter diſtentatur, pro <lb />parte inertiæ navis tribuenda eſt. </s>
          <s xml:space="preserve">Ubi, auctâ celeritate, <lb />eo uſque reſiſtentia aquæ crevit, ut ſola actionem deſtruat, <lb />qua navis protrahitur, motu æquabili, viinſitâ, progredi-<lb />tur hæc; </s>
          <s xml:space="preserve">duabus preſſionibus in hanc agentibus ſeſe mutuo <lb />deſtruentibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In omni caſu in quo preſſione obſtaculum movetur, aut hu-<lb />
<ptr xml:id="note-0168-04a" corresp="note-0168-04" type="noteAnchor" />
jus motus mutatur, non contrariâ preſſione in totum de-<lb />ſtruitur preſſio, &amp; </s>
          <s xml:space="preserve">vis generatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0168-04" corresp="note-0168-04a" place="margin">435.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Clare etiam patet preſſionem minuere poſſe corporis cele-<lb />
<ptr xml:id="note-0168-05a" corresp="note-0168-05" type="noteAnchor" />
ritatem, ideoque vim; </s>
          <s xml:space="preserve">eodem modo ac auget celeritatem <lb />&amp; </s>
          <s xml:space="preserve">vim.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0168-05" corresp="note-0168-05a" place="margin">436.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Videmus, vim eſſe effectum integrum preſſionis, quæ <lb />per tempus finitum in corpus egit, preſſio autem ipſa, ſingulis <lb />momentis infinite exiguis deſtruitur. </s>
          <s xml:space="preserve">Ergo preſſio omnis <lb />
<ptr xml:id="note-0168-06a" corresp="note-0168-06" type="noteAnchor" />
reſpectu vis inſitœ eſt infinite exigua. </s>
          <s xml:space="preserve">Id circo vis minima <lb />
<ptr xml:id="note-0168-07a" corresp="note-0168-07" type="noteAnchor" />
maximam poteſt ſuper are preſſionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0168-06" corresp="note-0168-06a" place="margin">437.</note>
              <note xml:space="preserve" xml:id="note-0168-07" corresp="note-0168-07a" place="margin">438.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Qui conati ſunt experimentis preſſionem cum vi inſitâ <lb />conferre effectum preſſionis conſiderarunt in quo corpus <lb />fuit confractum, aut partes intropreſſæ, quod ſine motu <lb />locali, ideoque geneſi vis inſitæ <ptr type="noteAnchor" />, fieri non potuit, cujus
<ptr xml:id="note-0168-08a" corresp="note-0168-08" type="noteAnchor" />
vis inſitæ effectus, cum effectu alîus vis fuit collatus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0168-08" corresp="note-0168-08a" n="*" anchored="true" place="margin">435.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In his omnibus non agitur de preſſione infinite magna, <lb />quæ tempore finito vim generat infinite magnam. </s>
          <s xml:space="preserve">Quan-
</s>
          <pb facs="0169" />
          <s xml:space="preserve">
<ptr xml:id="fig-0169-01a" corresp="fig-0169-01" type="figureAnchor" />
</s>
          <pb facs="0169a" />
          <s xml:space="preserve">
<pb facs="0170" />
<pb facs="0171" n="111" /><fw type="head">MATHEMATICA. LIB. I. CAP. XXII.</fw>
do preſſio vim generat non in acceleratione æquales gradus <lb />velocitatis æquali actione communicantur; </s>
          <s xml:space="preserve">ut enim æquales <lb />
<ptr xml:id="note-0171-01a" corresp="note-0171-01" type="noteAnchor" />
gradus velocitatis corporibus æqualibus, quorum unum quie-<lb />ſcit, alterum movetur, æqualibus actionibus communicentur; <lb /></s>
          <s xml:space="preserve">requiritur ut illud quod in corpora agit reſpectu utriuſque <lb />eandem habeat relationem; </s>
          <s xml:space="preserve">id eſt, deſideratur ut cauſa mo-<lb />vens eadem velocitate cum corpore moto feratur, in quod <lb />tunc poterit agere ut in corpus quieſcens: </s>
          <s xml:space="preserve">actio autem qua <lb />cauſa movens transfertur ſuper addenda eſt actioni hujus <lb />ipſius, ut habeamus actionem integram qua corpus move-<lb />tur. </s>
          <s xml:space="preserve">Unde deducimus difficilius corpus acceler ari quam mo-<lb />
<ptr xml:id="note-0171-02a" corresp="note-0171-02" type="noteAnchor" />
veri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0169-01" corresp="fig-0169-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0169-01" />
                <label>0169-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0171-01" corresp="note-0171-01a" place="margin">439.</note>
              <note xml:space="preserve" xml:id="note-0171-02" corresp="note-0171-02a" place="margin">440.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint elaſtra infinite parva e, e, e, e, &amp;</s>
          <s xml:space="preserve">c, juncta inter ſe, <lb />
<ptr xml:id="note-0171-03a" corresp="note-0171-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">flexa, quæ, ſi ad priſtinam redeant figuram, illam ac <lb />
<ptr xml:id="note-0171-04a" corresp="note-0171-04" type="noteAnchor" />
quirant, quæ in E repræſentatur, &amp; </s>
          <s xml:space="preserve">per ſpatium infinite <lb />exiguum ſeſe expandant. </s>
          <s xml:space="preserve">Elaſtrorum hæc eſt proprietas, <lb />ut, ſi, dum ſe expandunt, in corpus ſibi relictum premant, <lb />huic vim integram, cum qua ſe expandunt, communicent, <lb />ſi ad partem oppoſitam obſtaculo immobili inſiſtant. </s>
          <s xml:space="preserve">Ela-<lb />ſtrum E communicat corpori P gradum velocitatis infinitè <lb />exiguum. </s>
          <s xml:space="preserve">Ut elaſtrum ſequens corpori æqualem gradum <lb />velocitatis communicet, requiritur ut elaſtrum, dum ſeſe <lb />expandit, ea velocitate feratur, quam corpus jam acqui-<lb />ſivit, aliter non ageret in corpus motum, ut E in corpus <lb />quieſcens egit; </s>
          <s xml:space="preserve">præterea requiritur, ut in hoc motu inſi-<lb />ſtat Elaſtrum translatum obſtaculo, quod verſus partem op-<lb />poſitam cedere nequeat; </s>
          <s xml:space="preserve">id eſt propellendum eſt ea vi, <lb />qua hoc propellit corpus; </s>
          <s xml:space="preserve">quod obtinebit, ſi elaſtro ſimili <lb />ſeſe expandente propellatur. </s>
          <s xml:space="preserve">Duo ergo elaſtra eodem mo-<lb />mento ſeſe expandentia requiruntur, ut ſecundus gradus <lb />celeritatis corpori communicetur, id eſt vis deſidera-<lb />tur dupla illius, qua primus gradus corpori communicatur. <lb /></s>
          <s xml:space="preserve">Simili demonſtratione patebit, tria elaſtra, eodem momen-<lb />to ſeſe expandentia, aut vim triplam requiri, ut communi-<lb />cetur tertius velocitatis gradus &amp; </s>
          <s xml:space="preserve">ſic de cæteris. </s>
          <s xml:space="preserve">Poſitis <lb />nempe gradibus velocitatis infinitè exiguis ne in ſingulis
</s>
          <pb facs="0172" n="112" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
gradibus varii gradus dentur, &amp; </s>
          <s xml:space="preserve">poſitis elaſtris ſine inertiâ, <lb />ne ad hæc transferenda vis quædam conſumatur, quæ ut <lb />Mathematica ſit demonftratio ponenda ſunt. </s>
          <s xml:space="preserve">Patet ergo <lb />vim, qua gradu infinite exiguo corporis celeritas augetur, <lb />eo majorem deſiderari, quo corpus majorem jam acquiſivit <lb />celeritatem, vimque hanc in ratione celeritatis jam acquiſi-<lb />tæ augeri; </s>
          <s xml:space="preserve">unde ſequitur corpus accelerationi reſiſtere in ra-<lb />
<ptr xml:id="note-0172-01a" corresp="note-0172-01" type="noteAnchor" />
tione velocitatis ſuæ. </s>
          <s xml:space="preserve">Eademque actione gradum quemcun-<lb />que velocitatis tolli qua communicari potuit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0171-03" corresp="note-0171-03a" place="margin">441.</note>
              <note xml:space="preserve" xml:id="note-0171-04" corresp="note-0171-04a" place="margin"><hi rend="small caps">TAB. XVI.</hi> <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0172-01" corresp="note-0172-01a" place="margin">442.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde ſequitur difficilius corpus accelerari quam retarda-<lb />
<ptr xml:id="note-0172-02a" corresp="note-0172-02" type="noteAnchor" />
ri. </s>
          <s xml:space="preserve">Si Ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">corpus decem habeat gradus velocitatis, mi-<lb />nori impetu tollitur decimus, quàm communicatur unde-<lb />cimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0172-02" corresp="note-0172-02a" place="margin">443.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Etiam patet, corporis, quod velocitate finita fertur, id <lb />
<ptr xml:id="note-0172-03a" corresp="note-0172-03" type="noteAnchor" />
eſt quod habet gradus velocitatis infinitè exiguos infinito nu-<lb />mero, velocitatem gradu infinitè exiguo non poſſe augeri, <lb />niſi actione in infinitum ſuperante actionem, qua æqualis gra-<lb />dus infinite exiguus communicari poſſet corpori quieſcen-<lb />ti <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0172-03" corresp="note-0172-03a" place="margin">444.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">442.</note>
        <p>
          <s xml:space="preserve">Et ne quis objiciat demonftrationem locum non habere, <lb />
<ptr xml:id="note-0172-05a" corresp="note-0172-05" type="noteAnchor" />
ſi ſucceſſiva non detur, qualem poſuimus, Elaſtrorum re-<lb />laxatio; </s>
          <s xml:space="preserve">ſed velocitatem communicari corpori quieſcenti pro-<lb />portionalem numero illorum quæ ſimul relaxantur. </s>
          <s xml:space="preserve">Reſp. <lb /></s>
          <s xml:space="preserve">Talem quidem eſſe velocitatem Elaſterii primi ſepoſitâ, ut <lb />fecimus, horum inertiâ, &amp; </s>
          <s xml:space="preserve">ſepoſitâ omni actione in corpus; </s>
          <s xml:space="preserve"><lb />poſitâ autem hac negamus velocitate tali moveri elaſterium <lb />primum, quod non corpore celerius moveri poteſt; </s>
          <s xml:space="preserve">hujus <lb />autem celeritatem ex præcedenti demonſtratione deduci de-<lb />bere liquet, quia relaxatis ſimul elaſteriis, corpus tamen <lb />ſucceſſivè omnes gradus velocitatis ſuæ acquirit ita, ut de-<lb />monſtrata de diverſis elaſteriis referri debeant in hoc caſu <lb />ad ſucceſſivam partium relaxionem in Elaſtris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0172-05" corresp="note-0172-05a" place="margin">445.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex præcedenti demonſtratione <ptr type="noteAnchor" /> etiam deducimus, juxta
<ptr xml:id="note-0172-06a" corresp="note-0172-06" type="noteAnchor" />
quam rationem, auctâ corporis velocitate, augeatur vis cor-<lb />
<ptr xml:id="note-0172-07a" corresp="note-0172-07" type="noteAnchor" />
pori inſita. </s>
          <s xml:space="preserve">Elaſteria ſeſe expandentia agunt in corpus, cui <lb />nullum reſiſtit obſtaculum; </s>
          <s xml:space="preserve">ideo integram qua ſe expandunt
</s>
          <pb facs="0173" n="113" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAR. XXII.</fw>
vim corpori communicant; </s>
          <s xml:space="preserve">cûm autem elaſteria ſint æqua-<lb />lia, vires ſunt ut numeri Elaſteriorum, quorum expanſione <lb />communicantur. </s>
          <s xml:space="preserve">Corpus verò expanſione Elaſteriorum non <lb />poteſt celeritatem acquirere, miſi motu accelerato, ita ut <lb />per ſingulos gradus minores velocitatis tranſeat. </s>
          <s xml:space="preserve">Sit A F <lb />
<ptr xml:id="note-0173-01a" corresp="note-0173-01" type="noteAnchor" />
celeritas corporis; </s>
          <s xml:space="preserve">A b, bc, cd, &amp; </s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">gradus infinitè exi-<lb />gui celeritatis, A b primus, bc ſecundus, &amp; </s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">per quos o-<lb />mnes tranſit corpus antequam acquirat celeritatem AF. <lb /></s>
          <s xml:space="preserve">Parallelogramma A bhe, bcif, cdlg, &amp; </s>
          <s xml:space="preserve">c ſunt in-<lb />ter ſe reſpectivè, ut numeri Elaſteriorum, quibus gradus <lb />velocitatis primus, ſecundus, tertius, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">acquiruntur; </s>
          <s xml:space="preserve"><lb />ideoque areæ A dle, AFG e, ſunt inter ſe ut numerie-<lb />laſteriorum, quibus velocitates A d, AF acquiruntur, id <lb />eſt ſunt hæ areæ inter ſe ut Vires ejuſdem corporis, aut <lb />
<ptr xml:id="note-0173-02a" corresp="note-0173-02" type="noteAnchor" />
duorum corporum æqualium, hiſce velocitatibus motorum; <lb /></s>
          <s xml:space="preserve">eùm autem lineæ A e, eh, bf, fi, &amp; </s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">ſint infinitè exi-<lb />guæ; </s>
          <s xml:space="preserve">areæ A dle, AFG e à triangulis ſimilibus adl, afg, <lb />non differunt, &amp; </s>
          <s xml:space="preserve">ſunt inter ſe ut quadrata laterum homolo-<lb />gorum <ptr type="noteAnchor" />, aut velocitatum A d, AF, quod confirmabimus
<ptr xml:id="note-0173-03a" corresp="note-0173-03" type="noteAnchor" />
experimentis; </s>
          <s xml:space="preserve">ſed pauca antea præmittenda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0172-06" corresp="note-0172-06a" place="margin">446.</note>
              <note xml:space="preserve" xml:id="note-0172-07" corresp="note-0172-07a" n="*" anchored="true" place="margin">441.</note>
              <note xml:space="preserve" xml:id="note-0173-01" corresp="note-0173-01a" place="margin"><hi rend="small caps">TAB. XVL.</hi> <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0173-02" corresp="note-0173-02a" place="margin">447.</note>
              <note xml:space="preserve" xml:id="note-0173-03" corresp="note-0173-03a" n="*" anchored="true" place="margin">19. El. <lb /><hi rend="small caps">VI</hi>.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires eſſe inter ſe ut quadrata velocitatum, aliis demon-<lb />ſtrationibus, quæ ex principiis quæ nil inter ſe, neque cum <lb />his quæ hìc ponuntur commune habent, deductis, in ſequenti-<lb />bus etiam demonſtrabo, ubi de viribus obliquis, &amp; </s>
          <s xml:space="preserve">de reſiſten-<lb />tia fluidorum, agam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vires, quas corpus cadendo acquirit, ſunt ut altitudines, <lb />
<ptr xml:id="note-0173-04a" corresp="note-0173-04" type="noteAnchor" />
quas cadendo percurrit, ab initio caſits; </s>
          <s xml:space="preserve">ſunt enim hæ ut <lb />quadrata velocitatum in fine deſcenſus <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Cum propoſitio
<ptr xml:id="note-0173-05a" corresp="note-0173-05" type="noteAnchor" />
hæc ſequentibus Experimentis immediatè demonſtretur, <lb />patet gravitatem, quæ æqualibus temporibus æquales corpo-<lb />
<ptr xml:id="note-0173-06a" corresp="note-0173-06" type="noteAnchor" />
ri communicat gradus celeritatis, <ptr type="noteAnchor" /> non iidem æquales gradus
<ptr xml:id="note-0173-07a" corresp="note-0173-07" type="noteAnchor" />
vis communicare, <ptr type="noteAnchor" /> ſed illud, quo corpus ad Tellurem ten-
<ptr xml:id="note-0173-08a" corresp="note-0173-08" type="noteAnchor" />
dit, cum ipſo corpore moveri <ptr type="noteAnchor" />, dum in corpus motum
<ptr xml:id="note-0173-09a" corresp="note-0173-09" type="noteAnchor" />
agit, ut in quieſcens.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0173-04" corresp="note-0173-04a" place="margin">448.</note>
              <note xml:space="preserve" xml:id="note-0173-05" corresp="note-0173-05a" n="*" anchored="true" place="margin">255.</note>
              <note xml:space="preserve" xml:id="note-0173-06" corresp="note-0173-06a" place="margin">419.</note>
              <note xml:space="preserve" xml:id="note-0173-07" corresp="note-0173-07a" n="*" anchored="true" place="margin">251.</note>
              <note xml:space="preserve" xml:id="note-0173-08" corresp="note-0173-08a" n="*" anchored="true" place="margin">442.</note>
              <note xml:space="preserve" xml:id="note-0173-09" corresp="note-0173-09a" n="*" anchored="true" place="margin">439.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpora fuerint inæqualia, æqualibus velocitatibus <lb />
<ptr xml:id="note-0173-10a" corresp="note-0173-10" type="noteAnchor" />
mota, vires inſitæ ſunt inter ſe ut quantitates materiæ in
</s>
          <pb facs="0174" n="114" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſingulis; </s>
          <s xml:space="preserve">Vis enim corporis eſt ſumma virium omnium par-<lb />ticularum ex quibus conſtat, &amp; </s>
          <s xml:space="preserve">ſingulæ particulæ minimæ <lb />æquales vires habent æquales, ſivelocitate eâdem ferantur; <lb /></s>
          <s xml:space="preserve">idcirco in corporibus æque velocibus ſunt vires, ut nume-<lb />ri particularum æqualium materiæ in ſingulis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0173-10" corresp="note-0173-10a" place="margin">450.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina.</hi></head>
        <head xml:space="preserve">Qua corporum motorum vires conferuntur.</head>
        <p>
          <s xml:space="preserve">Aſſeris AB longitudo eſt unius pedis, latitudo decem <lb />
<ptr xml:id="note-0174-01a" corresp="note-0174-01" type="noteAnchor" />
pollicum, craſſities pollicum duorum. </s>
          <s xml:space="preserve">Excavatur hic in <lb />
<ptr xml:id="note-0174-02a" corresp="note-0174-02" type="noteAnchor" />
a b c d ad profunditatem unius pollicis cum ſemiſſe, &amp; </s>
          <s xml:space="preserve"><lb />cum pedibus EE, EE, quibus ſuſtinetur firmiter conne-<lb />ctitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0174-01" corresp="note-0174-01a" place="margin">451.</note>
              <note xml:space="preserve" xml:id="note-0174-02" corresp="note-0174-02a" place="margin"><hi rend="small caps">TAB XVI.</hi> <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pedibus hiſce etiam quatuor ſuſtinentur columnæ ligneæ <lb />CD, CD, CD, CD, ad angulos ipſius aſſeris. </s>
          <s xml:space="preserve">Colu-<lb />mnarum altitudo excedit paululum pedestres. </s>
          <s xml:space="preserve">Duæ quæ pede <lb />eodem, juxta latitudinem aſſeris poſito, inhærent, regulis <lb />minoribus ee, ee, f, f, g, g, b, b, junguntur ita, ut <lb />regula RR, tranſiens inter minores reſpondentes, parallela <lb />ſit ſuperficiei aſſeris.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tres globi (fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">æquales, diametri ſesquipollicis, ex <lb />ære formantur; </s>
          <s xml:space="preserve">ſolidus unus eſt C, reliqui duo cavi; </s>
          <s xml:space="preserve">conſtant <lb />hi ſinguli ex hemiſphæriis duobus A, a, &amp; </s>
          <s xml:space="preserve">B, b, quæ co-<lb />ehleâ junguntur. </s>
          <s xml:space="preserve">Globorum pondera ſunt inter ſe ut u-<lb />num, duo, tria.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ubi Experimenta inſtituenda ſunt, argillâ molli, &amp; </s>
          <s xml:space="preserve">homo-<lb />geneâ, exacte repletur cavitas a b c d, &amp; </s>
          <s xml:space="preserve">cultro ligneo, <lb />quod ex argillâ prominet, abraditur, ut hujus ſuperficies <lb />non modo exacte plana ſit, ſed &amp; </s>
          <s xml:space="preserve">idem formet planum cum <lb />illo quod ex aſſeris ſuperficie ſupereſt, cavitatiſque oras <lb />format.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Regula memorata RR inferius paululum juxta longitudi-<lb />nem, excavata eſt, ut globum quemcunque ex memoratis <lb />recipiat, qui in G videtur, dum manu M tenetur. </s>
          <s xml:space="preserve">In <lb />hoc ſitu inferius globi punctum ab argillæ ſuperficie diſtat <lb />pollicibus novem. </s>
          <s xml:space="preserve">Diſtantia hæc dupla eſt, ſiregula RR tranſ-<lb />eat inter regulas f, f, f, f, ſi inter regulas g, g, tripla;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0175" n="115" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXII.</fw>
quadrupla verò ſi ponatur RR inter regulas b, b.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimenta i<hi rend="superscript">2</hi></hi></head>
        <p>
          <s xml:space="preserve">Poſitâ regulâ RR, inter regulas e, e ſucceſſive dimittantur <lb />
<ptr xml:id="note-0175-01a" corresp="note-0175-01" type="noteAnchor" />
globi ænei tres, hiſce oleo antea illinitis; </s>
          <s xml:space="preserve">hi argillâ pro parte <lb />
<ptr xml:id="note-0175-02a" corresp="note-0175-02" type="noteAnchor" />
immerguntur cavitateſque formant, eo majoresquo globi gra-<lb />viores ſunt. </s>
          <s xml:space="preserve">Cavitates tres A, B, C, repræſentantur in fig. </s>
          <s xml:space="preserve">5.</s>
          <s xml:space="preserve">; <lb />punctis notatæ lineæ cavitatum profunditates demonſtrant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0175-01" corresp="note-0175-01a" place="margin">452.</note>
              <note xml:space="preserve" xml:id="note-0175-02" corresp="note-0175-02a" place="margin"><hi rend="small caps">TAB. XVI.</hi> <lb />ſig. 3. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Leviori globo cavitas A formata eſt, globum hunc voca-<lb />mus primum; </s>
          <s xml:space="preserve">ſecundum dicimus illum cujus pondus du-<lb />plum eſt, &amp; </s>
          <s xml:space="preserve">qui cavitatem formavit B; </s>
          <s xml:space="preserve">tandem tertium vo-<lb />camus globum ſolidum, cujus pondus eſt primi triplum, &amp; </s>
          <s xml:space="preserve"><lb />qui cadendo ab altitudine novem pollicum cavitatem forma-<lb />vit C.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si regula RR poſita ſit inter regulas f, f, &amp; </s>
          <s xml:space="preserve">globi dimit-<lb />
<ptr xml:id="note-0175-03a" corresp="note-0175-03" type="noteAnchor" />
tantur, cavitates formantur, quæ infig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">notantur litteris B, <lb />D, E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0175-03" corresp="note-0175-03a" place="margin">453.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si RR detur inter g, g, &amp; </s>
          <s xml:space="preserve">globi primus &amp; </s>
          <s xml:space="preserve">ſecundus di-<lb />
<ptr xml:id="note-0175-04a" corresp="note-0175-04" type="noteAnchor" />
mittantur, cavitates formantur C, E. </s>
          <s xml:space="preserve">(fig. </s>
          <s xml:space="preserve">5.)</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0175-04" corresp="note-0175-04a" place="margin">454.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tandem dimiſſo ab altitudine maximâ, poſitâ RR inter <lb />
<ptr xml:id="note-0175-05a" corresp="note-0175-05" type="noteAnchor" />
b, b, globo primo cavitas formatur D. </s>
          <s xml:space="preserve">(fig. </s>
          <s xml:space="preserve">5.)</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0175-05" corresp="note-0175-05a" place="margin">455.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ipſæ autem cavitates ſunt ſphæræ ſegmenta quæ ſunt in-<lb />
<ptr xml:id="note-0175-06a" corresp="note-0175-06" type="noteAnchor" />
ter ſe ut numeri in ipſis poſiti 1. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">6.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0175-06" corresp="note-0175-06a" place="margin">456.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut pateat, his Experimentis, quæ de viribus ſunt demon-<lb />ſtrata, confirmari, conſiderandum, vim inſitam illud eſſe <lb />
<ptr xml:id="note-0175-07a" corresp="note-0175-07" type="noteAnchor" />
(quodcunque hoc fuerit) quod datur in corpore moto, &amp; </s>
          <s xml:space="preserve"><lb />non datur in corpore quieſcente, id eſt, illud quo corpus <lb />motum, in obſtaculum incurrens, in hoc agit; </s>
          <s xml:space="preserve">Corpus autem <lb />ipſum dumagit, nullam patitur actionem, exceptâ reactione <lb />ex obſtaculi reſiſtentiâ, quæ reactio cum actioni æqualis ſit <ptr type="noteAnchor" />,
<ptr xml:id="note-0175-08a" corresp="note-0175-08" type="noteAnchor" />
ſequitur corpus pati quantum agit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">actionis effectum in <lb />
<ptr xml:id="note-0175-09a" corresp="note-0175-09" type="noteAnchor" />
obſtaculum ſequi rationem ipſius vis amiſſæ, diminutio <lb />enim ipſius vis eſt effectus reactionis; </s>
          <s xml:space="preserve">unde deducimus, vi-<lb />res integras proportionales eſſe effectibus quibus conſumun-<lb />tur, quod etiam aliâ conſideratione evidens eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0175-07" corresp="note-0175-07a" place="margin">457.</note>
              <note xml:space="preserve" xml:id="note-0175-08" corresp="note-0175-08a" n="*" anchored="true" place="margin">247.</note>
              <note xml:space="preserve" xml:id="note-0175-09" corresp="note-0175-09a" place="margin">458.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quo major eſt reſiſtentia quam patitur corpus, quo ipſi-<lb />us actio inſtantanea major eſt, &amp; </s>
          <s xml:space="preserve">eo citius integram amittit
</s>
          <pb facs="0176" n="116" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
vim, effectum tamen æqualem edit; </s>
          <s xml:space="preserve">nam vis quæ reſiſten-<lb />tiâ deſtruitur, proportionem ſequitur ipſius reſiſtentiæ, &amp; </s>
          <s xml:space="preserve"><lb />temporis per quod egit, id eſt vis amiſſa ſequitur rationem <lb />compoſitam reſiſtentiæ &amp; </s>
          <s xml:space="preserve">temporis; </s>
          <s xml:space="preserve">quam eandem ratio-<lb />nem ſequitur actio corporis, &amp; </s>
          <s xml:space="preserve">effectus quem edit;</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ita ut iterum pateat vim amiſſam effectui, quem edit dum de-<lb />
<ptr xml:id="note-0176-01a" corresp="note-0176-01" type="noteAnchor" />
ſtruitur, proportionalem eſſe, ſive breviori ſive longiori tem-<lb />pore deſtruatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0176-01" corresp="note-0176-01a" place="margin">459.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Actio preſſionis eſt indeterminata, &amp; </s>
          <s xml:space="preserve">manente intenſitate <lb />
<ptr xml:id="note-0176-02a" corresp="note-0176-02" type="noteAnchor" />
ſequitur rationem temporis per quodegit. </s>
          <s xml:space="preserve">Vis autem corpo-<lb />ri inſita, datis ipſius maſſâ, &amp; </s>
          <s xml:space="preserve">velocitate, determinata eſt, <lb />&amp; </s>
          <s xml:space="preserve">determinatum tantum edere poteſt effectum, quod brevio-<lb />ri aut longiori præſtatur tempore; </s>
          <s xml:space="preserve">pro majori aut minori, quam <lb />patitur, reſiſtentia <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0176-02" corresp="note-0176-02a" place="margin">460.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">459.</note>
        <p>
          <s xml:space="preserve">Quando corpus cavitatem formando in argillâ, mo-<lb />
<ptr xml:id="note-0176-04a" corresp="note-0176-04" type="noteAnchor" />
tum cadendo acquiſitum amittit, ſuperat preſſionem qua <lb />partes argillæ inter ſe cohærent, &amp; </s>
          <s xml:space="preserve">reſiſtentiâ, quam hanc <lb />ſuperando preſſionem patitur, vis ipſa minuitur, &amp; </s>
          <s xml:space="preserve">tandem <lb />in totum deſtruitur; </s>
          <s xml:space="preserve">effectus ergo vis, in hoc caſu dum cor-<lb />pus amittit motum, eſt ſeparatio partium argillæ dum juxta <lb />ſe invicem hæ moventur, qui effectus proportionem ſequitur <lb />numeri particularum mot arum, &amp; </s>
          <s xml:space="preserve">ſpatiiab his in motu juxta <lb />ſe invicem percurſi, &amp; </s>
          <s xml:space="preserve">ſive hoc lentius ſive celerius fiat, <lb />cohæſio fuperanda eadem eſt, &amp; </s>
          <s xml:space="preserve">evidentiſſimum eſt in du-<lb />bium minime vocari poſſe, Vires eſſe æquales quæ forman-<lb />
<ptr xml:id="note-0176-05a" corresp="note-0176-05" type="noteAnchor" />
do in eâdem argillâ cavitates æquales, &amp; </s>
          <s xml:space="preserve">ſimiles, conſumun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0176-04" corresp="note-0176-04a" place="margin">461.</note>
              <note xml:space="preserve" xml:id="note-0176-05" corresp="note-0176-05a" place="margin">462.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dimiſſis globis tribus ab altitudine novem pollicum vires <lb />
<ptr xml:id="note-0176-06a" corresp="note-0176-06" type="noteAnchor" />
<ptr xml:id="note-0176-07a" corresp="note-0176-07" type="noteAnchor" />
ſunt ut 1. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> cavitates formantur A, B, C <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">cavitates
<ptr xml:id="note-0176-08a" corresp="note-0176-08" type="noteAnchor" />
<ptr xml:id="note-0176-09a" corresp="note-0176-09" type="noteAnchor" />
hiſce æquales habemus ſi globus primus ſucceſſivè dimitta-<lb />tur ab altitudinibus novem <ptr type="noteAnchor" />, octodecim <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">viginti ſeptem
<ptr xml:id="note-0176-10a" corresp="note-0176-10" type="noteAnchor" />
<ptr xml:id="note-0176-11a" corresp="note-0176-11" type="noteAnchor" />
pollicum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in hoc ergo caſu vires ſunt ut altitudines, id eſt
<ptr xml:id="note-0176-12a" corresp="note-0176-12" type="noteAnchor" />
ut quadrata velocitatum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0176-06" corresp="note-0176-06a" place="margin">463.</note>
              <note xml:space="preserve" xml:id="note-0176-07" corresp="note-0176-07a" place="margin"><hi rend="small caps">TAB. XVI.</hi> <lb />ſig. 5.</note>
              <note xml:space="preserve" xml:id="note-0176-08" corresp="note-0176-08a" n="*" anchored="true" place="margin">450.</note>
              <note xml:space="preserve" xml:id="note-0176-09" corresp="note-0176-09a" n="*" anchored="true" place="margin">452.</note>
              <note xml:space="preserve" xml:id="note-0176-10" corresp="note-0176-10a" n="*" anchored="true" place="margin">452.</note>
              <note xml:space="preserve" xml:id="note-0176-11" corresp="note-0176-11a" n="*" anchored="true" place="margin">553.</note>
              <note xml:space="preserve" xml:id="note-0176-12" corresp="note-0176-12a" n="*" anchored="true" place="margin">454.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">255.</note>
        <p>
          <s xml:space="preserve">Si globus primus &amp; </s>
          <s xml:space="preserve">ſecundus dimittantur ab altitudine <lb />octodecim pollicum vires ſunt ut 1, 2 <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">cavitates forman-
<ptr xml:id="note-0176-14a" corresp="note-0176-14" type="noteAnchor" />
tur B &amp; </s>
          <s xml:space="preserve">D <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hiſce æquales habemus ſi globus primus di-
<ptr xml:id="note-0176-15a" corresp="note-0176-15" type="noteAnchor" />
</s>
          <pb facs="0177" />
          <s xml:space="preserve">
<ptr xml:id="fig-0177-01a" corresp="fig-0177-01" type="figureAnchor" />
<pb facs="0177a" />
<pb facs="0178" />
<pb facs="0179" n="117" /><fw type="head">MATHEMATICA. LIB. I. CAP. XXII.</fw>
mittatur ſucceſſive ab altitudine octodecim pollicum <ptr type="noteAnchor" /> &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0179-01a" corresp="note-0179-01" type="noteAnchor" />
ab altitudine trium pedum <ptr type="noteAnchor" />, ita ut iterum pateat vires eſſe
<ptr xml:id="note-0179-02a" corresp="note-0179-02" type="noteAnchor" />
ut altitudines. </s>
          <s xml:space="preserve">Concluſiones ſimiles ex aliis experimentis <lb />deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0176-14" corresp="note-0176-14a" n="*" anchored="true" place="margin">450.</note>
              <note xml:space="preserve" xml:id="note-0176-15" corresp="note-0176-15a" n="*" anchored="true" place="margin">453.</note>
              <figure xml:id="fig-0177-01" corresp="fig-0177-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-01" />
                <label>0177-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0179-01" corresp="note-0179-01a" n="*" anchored="true" place="margin">453.</note>
              <note xml:space="preserve" xml:id="note-0179-02" corresp="note-0179-02a" n="*" anchored="true" place="margin">455.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum cavitas formatur ſingula augmenta minora ſunt &amp; </s>
          <s xml:space="preserve"><lb />inter ſe ut numeri particularum quæ cedunt, &amp; </s>
          <s xml:space="preserve">ut ſpatia <lb />per quæ inter alias moventur, id eſt augmenta hæc ſunt ut <lb />vires quas corpus hæc augmenta formando amittit <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ideo-
<ptr xml:id="note-0179-03a" corresp="note-0179-03" type="noteAnchor" />
que augmentorum ſumma, id eſt integra cavitas, ſequitur <lb />
<ptr xml:id="note-0179-04a" corresp="note-0179-04" type="noteAnchor" />
proportionem ſummæ virium amiſſarum, id eſt, vis amiſſæ in <lb />formatione integræ cavitatis. </s>
          <s xml:space="preserve">Quod cum memoratis <lb />Experimentis congruit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0179-03" corresp="note-0179-03a" place="margin">* 461.</note>
              <note xml:space="preserve" xml:id="note-0179-04" corresp="note-0179-04a" place="margin">464.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">456.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimenta</hi> 2<hi rend="superscript">R</hi>.</head>
        <p>
          <s xml:space="preserve">Ex Ebore formantur cylindri duo AB, DC, diametri <lb />
<ptr xml:id="note-0179-06a" corresp="note-0179-06" type="noteAnchor" />
ſeſquipollicis, hemiſphericæ ſunt extremitates A, D, co-<lb />
<ptr xml:id="note-0179-07a" corresp="note-0179-07" type="noteAnchor" />
nicæ reliquæ B, C. </s>
          <s xml:space="preserve">Minoris longitudo eſt fere duorum pol-<lb />licum cum ſemiſſe; </s>
          <s xml:space="preserve">alter duobus pollicibus longior eſt, <lb />&amp; </s>
          <s xml:space="preserve">hujus pondus duplum exacte eſt ponderis alterius. </s>
          <s xml:space="preserve">Cum <lb />his cohærent fila in extremitatibus conicis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0179-06" corresp="note-0179-06a" place="margin">465.</note>
              <note xml:space="preserve" xml:id="note-0179-07" corresp="note-0179-07a" place="margin"><hi rend="small caps">TAB. XVL</hi> <lb />ſig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Deſideratur ut in extremitatibus A &amp; </s>
          <s xml:space="preserve">D axium eandem <lb />habeat ebur elaſticitatem, quod facilius obtinetur quàm <lb />quis forte crederet; </s>
          <s xml:space="preserve">ſi ad illud attendamus ut puncta illa <lb />coincidant cum axe ipſius dentis, quamvis in hoc pun-<lb />cto elaſticitas omnium minima ſit, ad quod hîc non atten-<lb />dimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Scrupulus omnis circa æqualitatem hanc elaſticitatis tol-<lb />li poteſt, ſi duo cylindri conſtruantur æquales, &amp; </s>
          <s xml:space="preserve">ſimiles cy-<lb />lindro DC; </s>
          <s xml:space="preserve">dimittantur hi a diverſis, ſed ſemper pro am-<lb />bobus æqualibus, altitudinibus, quod ut fiat filis ſuis ut C c <lb />retinentur, quibus relaxatis impingunt cylindrorum partes <lb />ut D in planum horizontale, quod ex ceruleo marmore <lb />deſideratur, &amp; </s>
          <s xml:space="preserve">probe admodum firmatum, paululum etiam <lb />madefactum, ut color magis ſit intenſus. </s>
          <s xml:space="preserve">In impactu par-<lb />tes elaſticæ intropremuntur maculamque notabilem admo-<lb />dum &amp; </s>
          <s xml:space="preserve">circinnatam cylindri in marmore, aut potius in hu-<lb />mido vapore quo obtegitur, relinquunt; </s>
          <s xml:space="preserve">ſi amborum cy-
</s>
          <pb facs="0180" n="118" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA.</fw>
lindrorum maculæ, ubi ab æqualibus altitudinibus deſcen-<lb />dunt, in omni caſu ſint æquales, eandem cylindrosin locis <lb />ut D elaſticitatem habere extra dubium erit. </s>
          <s xml:space="preserve">His expertis <lb />unus ex cylindris a parte C minuendus eſt, ut magnitudi-<lb />nem habeat AB, id eſt dimidium ponderis ſui amittat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si nunc cylindrus CD dimittatur ab altitudine novem <lb />
<ptr xml:id="note-0180-01a" corresp="note-0180-01" type="noteAnchor" />
pollicum, &amp; </s>
          <s xml:space="preserve">AB ab altitudine octodecim pollicum maculæ <lb />in marmore erunt quam exactiſſime æquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0180-01" corresp="note-0180-01a" place="margin">466</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si AB ab altitudine trium pedum, id eſt prioris quadru-<lb />
<ptr xml:id="note-0180-02a" corresp="note-0180-02" type="noteAnchor" />
plâ, dimittatur, macula major erit &amp; </s>
          <s xml:space="preserve">diametri erunt ut 5 ad <lb />6 proximè,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0180-02" corresp="note-0180-02a" place="margin">467.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Elaſteria æqualia, &amp; </s>
          <s xml:space="preserve">ſimilia, viribus æqualibus æqualiter <lb />
<ptr xml:id="note-0180-03a" corresp="note-0180-03" type="noteAnchor" />
flecti quis in dubium vocavit? </s>
          <s xml:space="preserve">dum enim relaxantur vires <lb />exerunt æquales illis quibus fuere flexa: </s>
          <s xml:space="preserve">æqualem autem, dum <lb />relaxatur elaſterium, ſemper exerit vim, ubi inflexio eſt ea-<lb />dem, ſive lentius ſive celerius fuerit inflexum, clarum ergo eſt <lb />vires æquales habuiſſe cylindros AB &amp; </s>
          <s xml:space="preserve">CD ubi hoc cecidit <lb />ab altitudine novem illud ab altitudine octodecim pollicum. <lb /></s>
          <s xml:space="preserve">Si ambo ab altitudine cecidiſſent novem pollicum vis cy-<lb />lindri CD dupla fuiſſet <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">duplicata ergo fuit vis cylindri
<ptr xml:id="note-0180-04a" corresp="note-0180-04" type="noteAnchor" />
AB, duplicatâ altitudine, id eſt vis ut altitudo aucta fuit; <lb /></s>
          <s xml:space="preserve">id eſt ut quadratum velocitatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0180-03" corresp="note-0180-03a" place="margin">468.</note>
              <note xml:space="preserve" xml:id="note-0180-04" corresp="note-0180-04a" n="*" anchored="true" place="margin">450.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">255.</note>
        <p>
          <s xml:space="preserve">Si autem vis creſceret ut velocitas juxta magis receptam <lb />ſententiam, duplicanda fuiſſet velocitas ad duplicandam vim, <lb />hanc autem in hoc caſu magis fuiſſe auctam experimento <lb />patuit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">467.</note>
        <p>
          <s xml:space="preserve">Licet abunde ſatisfactum mihi videatur illis, qui vires <lb />non ſtatuunt proportionales effectibus quibus conſumuntur, <lb />hìc experimenta quædam nihilominus addam, quibus con-<lb />ſtabit æqualibus edendo effectus vires conſumi æquales, licet <lb />inæqualibus temporibus effectus edantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Formatur ex ebore (potuiſſet ex ligno duriori &amp; </s>
          <s xml:space="preserve">gravio-<lb />
<ptr xml:id="note-0180-07a" corresp="note-0180-07" type="noteAnchor" />
ri formari) cylindrus cujus ſectio per axem in AB repræſen-<lb />
<ptr xml:id="note-0180-08a" corresp="note-0180-08" type="noteAnchor" />
tatur, Angulus in hac ſectione CAD eſt 120. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">angulus <lb />EBF eſt 54 gr. </s>
          <s xml:space="preserve">20′ BG æqualis eſt tribus partibus quar-
</s>
          <pb facs="0181" n="119" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXII.</fw>
tis unius pollicis. </s>
          <s xml:space="preserve">Ut cylindrus hicce ſuſpendatur, lamel-<lb />læ æneæ perforatæ dantur H &amp; </s>
          <s xml:space="preserve">I, ut &amp; </s>
          <s xml:space="preserve">duplicatus uncus <lb />in medio in L, cui fila connectuntur quæ per lamellarum H, <lb />I, foramina tranſmittuntur. </s>
          <s xml:space="preserve">Lamella H ita ponitur ut di-<lb />miſſa perpendiculari ad axem, A h ſit trium partium quarta-<lb />rum unius pollicis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0180-07" corresp="note-0180-07a" place="margin">469.</note>
              <note xml:space="preserve" xml:id="note-0180-08" corresp="note-0180-08a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Applicatur cylindrus hic machinæ, cujus ope Experi-<lb />menta circa colliſionem corporum inſtituuntur, &amp; </s>
          <s xml:space="preserve">cujus de-<lb />ſcriptio in capite ſequenti habetur <ptr type="noteAnchor" /> dum eidem machinæ
<ptr xml:id="note-0181-01a" corresp="note-0181-01" type="noteAnchor" />
firmiter jungitur pixis, in eâdem deſcriptione memoranda, <lb />argillam mollem cujus ſuperficies plana eſt, continens.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0181-01" corresp="note-0181-01a" n="*" anchored="true" place="margin">491.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In argillam dimittatur cylindrus velocitate quacumque, <lb />&amp; </s>
          <s xml:space="preserve">motum amittat cavitatem formando, extremitate A in <lb />argillam incurrente. </s>
          <s xml:space="preserve">Si, mutato paululum pixidis ſitu, eâ-<lb />dem velocitate cylindrus in argillam impingat, extremitate <lb />B in hanc penetrante; </s>
          <s xml:space="preserve">quæcunque fuerit velocitas qua cor-<lb />pus in utroque caſu movetur, ſi in utroque eandem habeat <lb />velocitatem, id eſt impactione eandem vim amittat; </s>
          <s xml:space="preserve">cavita-<lb />tum diametri erunt ut 2 ad 3.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cavitatum baſes, quæ ſunt ut quadrata diametrorum <ptr type="noteAnchor" />,
<ptr xml:id="note-0181-02a" corresp="note-0181-02" type="noteAnchor" />
funt ut 4 ad 9, &amp; </s>
          <s xml:space="preserve">cavitatum profunditates ut 9 ad 4, (hoc <lb />enim ex conorum forma ſequitur) id eſt baſes ſunt inversè <lb />ut altitudines, quare cavitates ſunt æquales <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideoque effectus
<ptr xml:id="note-0181-03a" corresp="note-0181-03" type="noteAnchor" />
virium æquales <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">inæqualibus tamen temporibus vires
<ptr xml:id="note-0181-04a" corresp="note-0181-04" type="noteAnchor" />
conſumuntur cum ad inæquales profunditates in argillam pe-<lb />netrent coni.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0181-02" corresp="note-0181-02a" n="*" anchored="true" place="margin">1 El. <hi rend="small caps">XII</hi></note>
              <note xml:space="preserve" xml:id="note-0181-03" corresp="note-0181-03a" n="*" anchored="true" place="margin">15. El, <lb /><hi rend="small caps">XII</hi>.</note>
              <note xml:space="preserve" xml:id="note-0181-04" corresp="note-0181-04a" n="*" anchored="true" place="margin">461.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires corporibus inſitæ, inter ſe differre non poſſunt niſi <lb />
<ptr xml:id="note-0181-05a" corresp="note-0181-05" type="noteAnchor" />
reſpectu velocitatis, aut quantitatis materiæ in corporibus: <lb /></s>
          <s xml:space="preserve">ergo vires quæeunque, ex dictis <ptr type="noteAnchor" /> conferuntur inter ſe, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0181-06a" corresp="note-0181-06" type="noteAnchor" />
ſunt in ratione compoſita quantitatum materiæ, &amp; </s>
          <s xml:space="preserve">quadra-<lb />torum velocitatum. </s>
          <s xml:space="preserve">Si igitur ſingulorum corporum maſſæ <lb />per quadrata ſuarum velocitatum multiplicentur, producta <lb />virium rationem exprimunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0181-05" corresp="note-0181-05a" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0181-06" corresp="note-0181-06a" n="*" anchored="true" place="margin">447. 450.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex his facillime deducimus corpora cadendo vires æqua-<lb />
<ptr xml:id="note-0181-07a" corresp="note-0181-07" type="noteAnchor" />
les acquirere, ſi altitudines, quas deſcendendo percurrunt, <lb />ſint inter ſe in ratione inverſa maſſarum. </s>
          <s xml:space="preserve">In Experimentis
</s>
          <pb facs="0182" n="120" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
hujus capitis primi cavitates, &amp; </s>
          <s xml:space="preserve">in ſecundis partium elaſti-<lb />carum introceſſiones fuere æquales, ubi corpora cecidere <lb />ab altitudinibus quæ erant inversè ut maſſæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0181-07" corresp="note-0181-07a" place="margin">471.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires vero ipſas eſſe in hac ratione inverſa maſſarum ſi <lb />
<ptr xml:id="note-0182-01a" corresp="note-0182-01" type="noteAnchor" />
velocitates fuerint reciprocè ut maſſæ, facile etiam liquet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0182-01" corresp="note-0182-01a" place="margin">472.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint maſſa corporis cujuſcunque M &amp; </s>
          <s xml:space="preserve">velocitas V; <lb /></s>
          <s xml:space="preserve">alterius corporis maſſa m &amp; </s>
          <s xml:space="preserve">hujus velocitas v: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">po-<lb />namus m, M:</s>
          <s xml:space="preserve">: V, v, id eſt M x V = m x v; </s>
          <s xml:space="preserve">hinc deduci-<lb />mus, V, v:</s>
          <s xml:space="preserve">: M x V<hi rend="superscript">q</hi>, m x v<hi rend="superscript">q</hi>, multiplicando V &amp; </s>
          <s xml:space="preserve">v per <lb />æquales quantitates: </s>
          <s xml:space="preserve">Sed M x V<hi rend="superscript">q</hi>, m x v<hi rend="superscript">q</hi> ſunt ut vires <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0182-02a" corresp="note-0182-02" type="noteAnchor" />
quæ ergo ſunt ut velocitates, id eſt inversè ut maſſæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0182-02" corresp="note-0182-02a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXIII.</head>
        <head xml:space="preserve">De Colliſione corporum.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> I.</head>
        <p rend="italics">
          <s xml:space="preserve">CEleritas qua duo corpora, ad ſe mutuo accedunt, aut <lb />
<ptr xml:id="note-0182-03a" corresp="note-0182-03" type="noteAnchor" />
ſeparantur, vocatur celeritas reſpectiva.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0182-03" corresp="note-0182-03a" place="margin">473.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quando corpora ambo ad eandem partem tendunt, ad ſe <lb />
<ptr xml:id="note-0182-04a" corresp="note-0182-04" type="noteAnchor" />
invicem accedunt, aut ſeparantur, velocitate, quæ æqualis eſt <lb />diſſerentiæ velocitatum abſolutarum. </s>
          <s xml:space="preserve">Velocitas autem re-<lb />
<ptr xml:id="note-0182-05a" corresp="note-0182-05" type="noteAnchor" />
ſpectiva eſt ſumma velocitatum abſolutarum, ſi motuum di-<lb />rectiones ſint contrariæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0182-04" corresp="note-0182-04a" place="margin">474.</note>
              <note xml:space="preserve" xml:id="note-0182-05" corresp="note-0182-05a" place="margin">475.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Impactio duorum corporum dicitur directa, ſi directio <lb />
<ptr xml:id="note-0182-06a" corresp="note-0182-06" type="noteAnchor" />
motus, aut motuum, quando ambo moventur, tranſeat per <lb />ſingulorum gravitatis centra; </s>
          <s xml:space="preserve">ſibæc eadem linea, quœ per <lb />ambo centra gravitatis tranſit, ſecet partes ſuperficierum quæ <lb />in ſe mutuo incurrunt; </s>
          <s xml:space="preserve">tandem ſi bæ ſuperficies quæ in ſemu-<lb />tuo incurrunt ad lineam, quæ per centra gravitatis tranſit, <lb />ſint perpendiculares.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0182-06" corresp="note-0182-06a" place="margin">476.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">In omni alio caſu ictus dicitur obliquus.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">477.</note>
        <p>
          <s xml:space="preserve">Quando corpus motum in aliud incurrit, in hoc agit, a-<lb />
<ptr xml:id="note-0182-08a" corresp="note-0182-08" type="noteAnchor" />
ctioque rationem ſequitur reſiſtentiæ quam patitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0182-09a" corresp="note-0182-09" type="noteAnchor" />
quantum agit tantum ex vi inſitâ amittit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0182-08" corresp="note-0182-08a" place="margin">478.</note>
              <note xml:space="preserve" xml:id="note-0182-09" corresp="note-0182-09a" n="*" anchored="true" place="margin">458.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0183" n="121" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
        <p>
          <s xml:space="preserve">Non hic agam de corporibus perfectè duris, talia nulla <lb />
<ptr xml:id="note-0183-01a" corresp="note-0183-01" type="noteAnchor" />
novimus, &amp; </s>
          <s xml:space="preserve">inutile foret in hiſce colliſionum leges deter-<lb />minare, quod an ſine errore factum eſſet experimentis de-<lb />terminari non poſſet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-01" corresp="note-0183-01a" place="margin">479.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omnia autem corpora nobis nota conſtant ex partibus in-<lb />
<ptr xml:id="note-0183-02a" corresp="note-0183-02" type="noteAnchor" />
ter ſe cobærentibus, vi cujus effectum novimus, &amp; </s>
          <s xml:space="preserve">cujus <lb />cauſa nos latet: </s>
          <s xml:space="preserve">Sed verâ preſſione partes inter ſe cohærere, <lb />cuicunque cauſæ hanc tribuamus, in dubium nemo voca-<lb />bit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-02" corresp="note-0183-02a" place="margin">480.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nulla datur preſſio, quæ minimâ inſitâ vi ſuperari non <lb />poteſt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo nulla datur corporum colliſio ſine quadampar-
<ptr xml:id="note-0183-03a" corresp="note-0183-03" type="noteAnchor" />
<ptr xml:id="note-0183-04a" corresp="note-0183-04" type="noteAnchor" />
tium introceſſione.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-03" corresp="note-0183-03a" n="*" anchored="true" place="margin">438.</note>
              <note xml:space="preserve" xml:id="note-0183-04" corresp="note-0183-04a" place="margin">481.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De colliſione corporum in genere hoc capite agam; </s>
          <s xml:space="preserve">ex-<lb />plicandum ideo quid obtineat in corporibus non ebaſticis; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0183-05a" corresp="note-0183-05" type="noteAnchor" />
nam &amp; </s>
          <s xml:space="preserve">hoc ipſum in elaſticis locum babet, in momento in <lb />quo corpora concurrunt, antequam partes intropreſſæ ad pri-<lb />ſtinam figuram redeant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-05" corresp="note-0183-05a" place="margin">482.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hac figuræ inſtauratione corpora elaſtica ſeſe mutuo re-<lb />
<ptr xml:id="note-0183-06a" corresp="note-0183-06" type="noteAnchor" />
pellunt; </s>
          <s xml:space="preserve">idcirco poſt ictum ſeparantur. </s>
          <s xml:space="preserve">Nulla autem talis <lb />datur actio ſi omnielaſterio deſtituantur; </s>
          <s xml:space="preserve">ergo poſt impactum <lb />
<ptr xml:id="note-0183-07a" corresp="note-0183-07" type="noteAnchor" />
directum non ſeparantur; </s>
          <s xml:space="preserve">nam in impactione hac, directio <lb />mutari non poteſt, &amp; </s>
          <s xml:space="preserve">ideo in eâdem lineâ ambo motum <lb />contiuuant, in qua ante ictum movebantur, &amp; </s>
          <s xml:space="preserve">in qua a ſe <lb />invicem non repelluntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-06" corresp="note-0183-06a" place="margin">483.</note>
              <note xml:space="preserve" xml:id="note-0183-07" corresp="note-0183-07a" place="margin">484.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum partes corporum intropremuntur deſtruitur vis <ptr type="noteAnchor" /> quæ
<ptr xml:id="note-0183-08a" corresp="note-0183-08" type="noteAnchor" />
preſſionem qua cohærent <ptr type="noteAnchor" /> ſuperat; </s>
          <s xml:space="preserve">Ergo corpus in aliud
<ptr xml:id="note-0183-09a" corresp="note-0183-09" type="noteAnchor" />
incurrere non poteſt, aut duo in ſemutuo, ſine diminutione ſum-<lb />
<ptr xml:id="note-0183-10a" corresp="note-0183-10" type="noteAnchor" />
mæ virium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-08" corresp="note-0183-08a" n="*" anchored="true" place="margin">436.</note>
              <note xml:space="preserve" xml:id="note-0183-09" corresp="note-0183-09a" n="*" anchored="true" place="margin">480.</note>
              <note xml:space="preserve" xml:id="note-0183-10" corresp="note-0183-10a" place="margin">485.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In corporibus elaſticis partes ictæ ad priſtinam re-<lb />deunt figuram, &amp; </s>
          <s xml:space="preserve">redeuntes premunt in corpus, cujus <lb />actione introceſſere, hac preſſione nova generatur vis, ſed <lb />de hac nondum agimus, in ipſis corporibus elaſticis datur, <lb />
<ptr xml:id="note-0183-11a" corresp="note-0183-11" type="noteAnchor" />
ante figuram inſtauratam, diminutio virium, de qua bic <lb />agimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-11" corresp="note-0183-11a" place="margin">486.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quando corpus, nonictu alius corporis, ſed preſſione movetur, <lb />
<ptr xml:id="note-0183-12a" corresp="note-0183-12" type="noteAnchor" />
ſi hæc minor ſit illa quapartes cobærent, ſine partium introceſſio-<lb />ne corporimotus communicatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0183-12" corresp="note-0183-12a" place="margin">487.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0184" n="122" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Nulla in corporum colliſione vis deſtruitur, niſi quæ ad <lb />
<ptr xml:id="note-0184-01a" corresp="note-0184-01" type="noteAnchor" />
partes intro premendas requiritur. </s>
          <s xml:space="preserve">Ponamus primo cor-<lb />pora ad eandem partem tendere, antecedens neceſſario tar-<lb />dius alio movetur, &amp; </s>
          <s xml:space="preserve">ictu acceleratur, conſequens ve-<lb />ro quia in aliud agit ex vi ſua amittit. </s>
          <s xml:space="preserve">Effectus vis a-<lb />miſſæ eſt augmentum vis in antecedente, &amp; </s>
          <s xml:space="preserve">introceſſio <lb />partium, &amp; </s>
          <s xml:space="preserve">effectus hic valet vim amiſſam à con-<lb />ſequente <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sed illa, quam acquiſivit antecedens, non
<ptr xml:id="note-0184-02a" corresp="note-0184-02" type="noteAnchor" />
eſt vis deſtructa, ergo ſola hæc deſtruitur, qua partes in-<lb />trocedunt. </s>
          <s xml:space="preserve">Secundo, tendant corpora in partes contrari-<lb />as, in hoc caſu corpora ambo ſibi mutuo reſiſtunt, non mo-<lb />do inertiâ, ſed etiam viribus inſitis, quo vero major eſt re-<lb />ſiſtentia, eo magis partes comprimuntur, eoque major par-<lb />tium introceſſio, ita ut vires impropriè dicantur ſeſe mu-<lb />tuo deſtruere, vi ſua corpus corpori reſiſtit, quâ natâ reſi-<lb />ſtentiâ vis corporis alîus deſtruitur, ſuperando preſſionem <lb />qua partes cohærent. </s>
          <s xml:space="preserve">Paradoxa hæc propoſitio, vim nun-<lb />
<ptr xml:id="note-0184-03a" corresp="note-0184-03" type="noteAnchor" />
quam immediate vim deſtruere, experimentis extra dubium <lb />eſt, quibus conſtat introceſſiones in corporibus ejuſdem ge-<lb />neris, (nempe quorum partes æqualiter cohærent,) eſſe æ-<lb />quales, ſi vires æquales ictibus deſtruantur, ſive corpora <lb />tendant ad eandem partem; </s>
          <s xml:space="preserve">ſive directionibus contrariis <lb />ferantur, viribus æqualibus, aut utcumque inæqualibus; </s>
          <s xml:space="preserve">ſive <lb />in obicem firmum impingat corpus; </s>
          <s xml:space="preserve">ut, præmifsâ machinarum <lb />deſcriptione, exponam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0184-01" corresp="note-0184-01a" place="margin">488.</note>
              <note xml:space="preserve" xml:id="note-0184-02" corresp="note-0184-02a" n="*" anchored="true" place="margin">478</note>
              <note xml:space="preserve" xml:id="note-0184-03" corresp="note-0184-03a" place="margin">489.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head xml:space="preserve">Qua experimenta circa colliſiones corporum <lb />inſtituuntur.</head>
        <p>
          <s xml:space="preserve">Tabula lignea ABC, fere triangularis, &amp; </s>
          <s xml:space="preserve">verticalis, <lb />
<ptr xml:id="note-0184-04a" corresp="note-0184-04" type="noteAnchor" />
altitudinis circiter quatuor pedum cum ſemiſſe, &amp; </s>
          <s xml:space="preserve">latitudi-<lb />
<ptr xml:id="note-0184-05a" corresp="note-0184-05" type="noteAnchor" />
nis, circa baſin trianguli, trium pedum, verticaliter diſponitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0184-04" corresp="note-0184-04a" place="margin">490.</note>
              <note xml:space="preserve" xml:id="note-0184-05" corresp="note-0184-05a" place="margin"><hi rend="small caps">TAB. XVII</hi>.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſuperiori parte datur ad horizontem parallela ſciſſura st, <lb />in qua duo clavi quadrati, aliquando plures, moventur; </s>
          <s xml:space="preserve">qui <lb />ubique cochleis, ad poſteriorem tabulæ partem applicantis <lb />firmantur; </s>
          <s xml:space="preserve">ut ex figura clavorum in V patet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Super unoquoque clavo movetur tubulus quadratus X,
</s>
          <pb facs="0185" n="123" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
poteſtque per totam clavi longitudinem firmiter cum eo <lb />connecti cochlea e in ſuperiori parte. </s>
          <s xml:space="preserve">In parte inferiori tubulis <lb />his unci minimi junguntur; </s>
          <s xml:space="preserve">quos fila tenuiſſima (aut potius <lb />chordæ citharæ) i h, i h trajiciunt, quæ globos veluti P&amp; </s>
          <s xml:space="preserve">Q ſu-<lb />ſtinent. </s>
          <s xml:space="preserve">Fila illa annectuntur paxillis l, l; </s>
          <s xml:space="preserve">quostorquendo ele-<lb />vantur, aut deprimuntur, globi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Clavus, quo globus quicunque ſuſtinetur, ita in ſcif-<lb />ſura st ſiſtitur, ut illius centri a linea AD, quæ tabulam <lb />in duas partes æquales verticaliter dividit, diſtantia æqualis ſit <lb />ſemidiametro globi; </s>
          <s xml:space="preserve">illudque pro omnibus globis fit, ductis <lb />notis in tabulæ ſuperficie.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tubulus cum unco, quo globus ſuſpenditur, in ea parte <lb />clavi firmatur, ut fili a tabulæ ſuperficie diſtantia paululum <lb />excedat ſemidiametrum globi; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">dantur in clavis diviſio-<lb />nes, quibus, pro magnitudine globi, ſitus tubuli determi-<lb />natur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando duo globi adhibentur, linea AD hos ſeparat; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in hoc caſu, ut &amp; </s>
          <s xml:space="preserve">quando plures adhibentur, ſi diverſæ <lb />fuerint magnitudinis, globus maximus minoris diſtantiam a <lb />tabula determinat, &amp; </s>
          <s xml:space="preserve">tubuli reſpondentibus clavorum divi-<lb />ſionibus admoventur, ut globorum omnium centra æque di-<lb />ſtent a tabula. </s>
          <s xml:space="preserve">Centra illa paxillorum l converſione ad ean-<lb />dem altitudinem reducuntur; </s>
          <s xml:space="preserve">quod in omnibus Experimen-<lb />tis obſervandum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Regulæ duæ æneæ EG, EG, ad horizontem parallelæ diſ-<lb />ponuntur; </s>
          <s xml:space="preserve">ſuperficies tabulæ ad illas recipiendas paululum <lb />excavatur, ut illarum ſuperficies cum tabulæ ſuperficie con-<lb />gruat A poſteriori utriuſque regulæ parte datur in tabula <lb />ſciſſura, longitudinis circiter quinque pollicum, per quam <lb />tranſit cochlea regulæ cohærens, &amp; </s>
          <s xml:space="preserve">cujus ope regula retine-<lb />tur, &amp; </s>
          <s xml:space="preserve">transfertur per longitudinem ſciſſuræ. </s>
          <s xml:space="preserve">In Experi-<lb />mentis diſtantia extremitatis G, utriuſque regulæ, a linea <lb />AD, æqualis eſt ſemidiametro globi, ad eandem partem <lb />hujus lineæ ſuſpenſi, quod ut fiat diſtantiæ pro ſingulis glo-<lb />bis notis indicandæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Diviſiones regularum tales ſunt, ut denotent angulos æ-
</s>
          <pb facs="0186" n="124" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
quales, a filis, quibus globi ſuſpenduntur, percurſos.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Uthos angulos in Experimentis menſuremus, dantur <lb />indices quatuor, duo majores M, M, &amp; </s>
          <s xml:space="preserve">duo minores N, <lb />N.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Moventur indices iſti per ſciſſuras or, or; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cochleis à <lb />poſteriori parte tabulæ, proarbitrio agentis, conſtituuntur. <lb /></s>
          <s xml:space="preserve">Tabulæ ſuperficies juxta ſciſſuras paululum excavatur, ad <lb />motum indicum dirigendum; </s>
          <s xml:space="preserve">majores ad tabulæ extremita-<lb />tem pertingunt, licet ſciſſuræ extremitas ab ea fere tribus <lb />pollicibus diſtet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Delineatio majorum indicum datur in figura ſeparata M; <lb /></s>
          <s xml:space="preserve">in qua a b eſt lamina, quæ in cavitate in tabulæ ſuperficie <lb />movetur; </s>
          <s xml:space="preserve">c d eſt index, ad illam laminam normalis, &amp; </s>
          <s xml:space="preserve">lon-<lb />gitudinis circiter trium pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Datur etiam in N figura ſeparata indicum minorum; </s>
          <s xml:space="preserve">ho-<lb />rum longitudo æqualis eſt ſemidiametro minimorum globo-<lb />rum, qui Machinæ applicantur, &amp; </s>
          <s xml:space="preserve">quorum diameter commode <lb />ſtatuitur unius pollicis cum ſemiſſe; </s>
          <s xml:space="preserve">indices hi inter majores po-<lb />nuntur, quia illis motus globorum non impeditur; </s>
          <s xml:space="preserve">aliquan-<lb />do ambo minores in eadem ſciſſura firmantur, quando tres <lb />anguli ab una parte menſurandi ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hoc caſu globus ut Q elevatur, aut poſt caſum adſcendit, <lb />B verſus. </s>
          <s xml:space="preserve">Ad diſponendum indicem ut menſuretur angu-<lb />lus ille, regulæ EG, quæ eſt a parte B, extremitas G con-<lb />jungi debet cum extremitate G alterius regulæ, poſitæ ut <lb />ante dictum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cochleæ tres ferreæ F, F, F, inſerviunt ad tabulam ex-<lb />acte in ſitu verticali diſponendam ita, ut linea AD ſit ad ho-<lb />rizontem perpendicularis; </s>
          <s xml:space="preserve">quod facillime præſtatur, ſuſpen-<lb />dendo globo quocunque, &amp; </s>
          <s xml:space="preserve">ponendo indice majori ita, ut <lb />filum tranſiens juxta notam in illo indice ſit parallelum li-<lb />neæ AD.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Experimentis circa colliſiones corporum non elaſtico-<lb />rum, utimur globis, in forma lignea L, ex argilla molli du-<lb />ctis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Forma hæc L quinque partibus conſtat; </s>
          <s xml:space="preserve">quarum quatuor
</s>
          <pb facs="0187" n="125" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
in H, H, H, H, videntur; </s>
          <s xml:space="preserve">hæ junctæ cavitatem ſphæricam <lb />continent, diametri unius pollicis &amp; </s>
          <s xml:space="preserve">ſemiſſis, cum apertura <lb />in inferiori parte: </s>
          <s xml:space="preserve">circumdantur cochlea ita, ut firmiter in-<lb />ter ſe connectantur ope annuli I, in interiori parte cochleam <lb />ſimilem continentis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Partes omnes conjunctæ in L repræſentantur; </s>
          <s xml:space="preserve">datur fora-<lb />men in v, communicationem habens cum cavitate interiori; <lb /></s>
          <s xml:space="preserve">per hocce tranſmittitur filum, &amp; </s>
          <s xml:space="preserve">cavitas oleo illinitur, &amp; </s>
          <s xml:space="preserve">ar-<lb />gilla impletur; </s>
          <s xml:space="preserve">filum memoratum in argillam penetrat, &amp; </s>
          <s xml:space="preserve">in <lb />hac irregulariter diſponitur. </s>
          <s xml:space="preserve">Sublato annulo I, quatuor re-<lb />liquæ partes facillime ſeparantur, &amp; </s>
          <s xml:space="preserve">globum in medio relin-<lb />quunt, qui filo ſtatim memorato alteri filo connectitur, quo <lb />Machinæ applicatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Experimenta circa corpora elaſtica inftituuntur adhibitis <lb />globis eburneis. </s>
          <s xml:space="preserve">Sex minores deſiderantur, diametri unius <lb />pollicis cum femiſſe; </s>
          <s xml:space="preserve">præter hos unus ponderis dupli, al-<lb />ter ponderis tripli, &amp; </s>
          <s xml:space="preserve">tandem unus ponderis quadrupli.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Experimento undecimo capitis ſequentis, ſex memora-<lb />ti globi æquales Machinæ applicantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita ſuſpenduntur, ut <lb />ſeſe mutuo tangant. </s>
          <s xml:space="preserve">Præſtamus hoc (vide fig. </s>
          <s xml:space="preserve">L.) </s>
          <s xml:space="preserve">ope laminæ <lb />m n, quæ cochleis q, q, per ſciſſuram st tranſeuntes, Ma-<lb />chinæ connectitur. </s>
          <s xml:space="preserve">Lamina hæc continet clavos quatuor <lb />p, p, p, p; </s>
          <s xml:space="preserve">in quorum extremitatibus dantur foramina, per quæ <lb />fila, quibus globi ſuſpenduntur, tranſmittuntur. </s>
          <s xml:space="preserve">Paxillis l, l, l, l <lb />fila illa annectuntur. </s>
          <s xml:space="preserve">Globi reliqui duo clavis memoratis V <lb />ſuſpenduntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hac Machina percuſſio globorum in loco infimo ſem-<lb />per eſt directa: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">globi, licet a diverſis altitudinibus, ſive <lb />ad eandem partem, ſive ad partes contrarias, dimittantur, <lb />eodem momento ad locum infimum perveniunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita,
<ptr xml:id="note-0187-01a" corresp="note-0187-01" type="noteAnchor" />
in eo caſu, percuſſio ſemper eſt directa; </s>
          <s xml:space="preserve">celeritates vero <lb />in loco infimo denotantur diviſionibus regularum EG, <lb />EG <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam pro arcubus non majoribus, quam quos glo-
<ptr xml:id="note-0187-02a" corresp="note-0187-02" type="noteAnchor" />
bi in hac Machina excurrunt, ratio inter arcus &amp; </s>
          <s xml:space="preserve">chordas <lb />fenſibiliter non differt. </s>
          <s xml:space="preserve">Altitudines, a quibus globi di-<lb />mittuntur, determinant celeritates ante impactum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">al-
</s>
          <pb facs="0188" n="126" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
titudines, ad quas globi adſcendunt, celeritates poſt impa-<lb />ctionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0187-01" corresp="note-0187-01a" n="*" anchored="true" place="margin">280.</note>
              <note xml:space="preserve" xml:id="note-0187-02" corresp="note-0187-02a" n="*" anchored="true" place="margin">222.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head xml:space="preserve">Alia, cujus ope eadem Experimenta circa colliſio-<lb />nes inſtituuntur.</head>
        <p>
          <s xml:space="preserve">Hîc &amp; </s>
          <s xml:space="preserve">aliam, quam eodem fundamento cum præceden-<lb />
<ptr xml:id="note-0188-01a" corresp="note-0188-01" type="noteAnchor" />
ti nixam conſtrui curavi machinam, etiam exponam. </s>
          <s xml:space="preserve">Varia <lb />huic addidi, quæ &amp; </s>
          <s xml:space="preserve">præcedenti applicari poſſunt, ita ut <lb />omnia experimenta, quibus hæc inſervit, &amp; </s>
          <s xml:space="preserve">primâ in-<lb />ſtitui poſſint, magis tamen commodè adhibitâ hac ſecun-<lb />da.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0188-01" corresp="note-0188-01a" place="margin">491.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Conſtat hæc ex aſſere verticali ABDC, cujus longitu-<lb />
<ptr xml:id="note-0188-02a" corresp="note-0188-02" type="noteAnchor" />
do BC eſt trium pedum; </s>
          <s xml:space="preserve">altitudo AD circiter decem pol-<lb />licum, craſſities fere ſeſqui pollicis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0188-02" corresp="note-0188-02a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Huic aſſeri, aut Tabulæ, applicantur, eodem modo ac <lb />in præcedenti machina, regulæ æneæ diviſæ EG, EG, <lb />ut &amp; </s>
          <s xml:space="preserve">indices majores, M, M, &amp; </s>
          <s xml:space="preserve">minores, qui hìc non de-<lb />lineantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pede ſuſtinetur Tabula ita, ut D ad altitudinem circiter <lb />duorum pedum cum ſemiſſe elevetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Columna H pedis poſt tabulam, quæ ipſi applicatur, <lb />continuatur, &amp; </s>
          <s xml:space="preserve">ſuſtinet tenuiorem columnam L, quæ ta-<lb />men pro parte ipſi tabulæ ſuperimponitur ita, ut ſuperſi-<lb />cies anterior ligni ſuperioris k ſit in eodem plano cum ſu-<lb />perficie ABDC.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Columna H in ſuperiori parte, ubi huic columna L ſu-<lb />perimponitur, excavatur, ut recipiat prominentiam in in-<lb />feriori parte columnæ L, quæ prominentia poligona eſt &amp; </s>
          <s xml:space="preserve"><lb />exacte cum cavitate congruit, in qua firmatur cochleâ. <lb /></s>
          <s xml:space="preserve">Cum columnâ L cohæret tabula lignea II, cujus craſſities <lb />eſt ſemi pollicis &amp; </s>
          <s xml:space="preserve">cujus uſus eſt, ut columnam in tali ſitu <lb />firmet, in quo hujus axis lineæ DA continuatæ, parallelus <lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pars columnæ ſuperior ſeparatim in R exhibetur, parti <lb />
<ptr xml:id="note-0188-03a" corresp="note-0188-03" type="noteAnchor" />
huic applicatur regula ænea quadrata SS, longitudinis cir-<lb />citer octo pollicum, latitudo &amp; </s>
          <s xml:space="preserve">altitudo quartæ parti
</s>
          <pb facs="0189" />
          <s xml:space="preserve">
<ptr xml:id="fig-0189-01a" corresp="fig-0189-01" type="figureAnchor" />
<pb facs="0189a" />
<pb facs="0190" />
<pb facs="0191" n="127" /><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
pollicis æquales ſunt. </s>
          <s xml:space="preserve">Horizonti regula hæc parallela eſt ut <lb />&amp; </s>
          <s xml:space="preserve">ſuperſiciei ligni R, à quo diſtat tribus partibus quartis <lb />unius pollicis. </s>
          <s xml:space="preserve">Ut firmetur cohæret cum prominentiis t, t <lb />quæ cochleis ad partem poſticam ligni K retinentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0188-03" corresp="note-0188-03a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 2.</note>
              <figure xml:id="fig-0189-01" corresp="fig-0189-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0189-01" />
                <label>0189-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Regulæ huic unci junguntur quatuor Y, V, V, Y, di-<lb />ſtantia inter medios V, V, eſt ſeſqui pollicis, hujuſque di-<lb />ſtantiæ punctum medium datur in plano, quod concipitur per-<lb />pendiculare ad ſuperficiem K &amp; </s>
          <s xml:space="preserve">per axem columnæ l tranſ-<lb />it; </s>
          <s xml:space="preserve">diſtantia Y Y eſt trium pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Juxta regulam hanc SS tubuli duo quadrati moventur, qui <lb />ad libitum cochleis firmantur, &amp; </s>
          <s xml:space="preserve">cum quibus unci exigui, <lb />ftatim memoratis ſimiles, cohærent. </s>
          <s xml:space="preserve">Tand em in medio &amp; </s>
          <s xml:space="preserve"><lb />in extremitatibus regulæ foramina dantur f, f, f, æqualiter a <lb />ſe in vicem diſtantia, poſitis extremis a ſe mutuo remotis ſe-<lb />ptem pollicibus cum ſemiſſe,</s>
        </p>
        <p>
          <s xml:space="preserve">Ut in præcedentis machinæ deſcriptione monui, ſex de <lb />
<ptr xml:id="note-0191-01a" corresp="note-0191-01" type="noteAnchor" />
ſiderantur globi eburnei diametri ſeſqui pollicis ut A. </s>
          <s xml:space="preserve">Loco <lb />majorum globorum utimur tribus cylindris eburneis quorum <lb />diametri globorum diametris æquales ſunt. </s>
          <s xml:space="preserve">Duorum ſectio <lb />per axem repræſentatur in C; </s>
          <s xml:space="preserve">tertii ſectio datur in B; </s>
          <s xml:space="preserve">cy-<lb />lindri B pondus duplum eſt ponderis globi A ejuſdem dia-<lb />metri cum cylindro; </s>
          <s xml:space="preserve">cylindrorum ſingulorum ut Cpondera <lb />tripla ſunt ponderum globorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0191-01" corresp="note-0191-01a" place="margin"><hi rend="small caps">TAB. XVIII</hi> <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In his cylindris cavendum ut axis dentis eburnei, ex <lb />quo formantur, perpendiculariter ſecet axem cylindri cir-<lb />citer in hujus medio. </s>
          <s xml:space="preserve">Ubi globus cum cylindro, aut duo <lb />cylindri, ſimul machinæ applicantur cavendum ut convexi-<lb />tas unius alterius planam ſuperficiem tangat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex ebore, aut ligno duriore &amp; </s>
          <s xml:space="preserve">graviore, ulterius quatuor <lb />
<ptr xml:id="note-0191-02a" corresp="note-0191-02" type="noteAnchor" />
formantur cylindri, quorum duorum minorum ſectiones per <lb />axem exhibentur in D, reliquorum in E, &amp; </s>
          <s xml:space="preserve">F.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0191-02" corresp="note-0191-02a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ex ebore formentur ad ſitum axeos dentis non atten-<lb />dimus, quia elaſticitate ſua in Experimentis non a-<lb />gunt</s>
        </p>
        <p>
          <s xml:space="preserve">Horum cylindrorum diametri ſunt etiam ſeſqui pollicis,
</s>
          <pb facs="0192" n="128" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
in extremo uno ad formam hemiſphærii formantur, ex-<lb />tremum alterum coni formam habet anguluſque m l n eſt <lb />centum graduum: </s>
          <s xml:space="preserve">angulos centum &amp; </s>
          <s xml:space="preserve">viginti graduum, ut <lb />&amp; </s>
          <s xml:space="preserve">nonaginta graduum, in experimentis adhibui, ſed antepo-<lb />nendum vidi angulum centum graduum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pondera cylindrorum ſunt inter ſe ut duo, tria, &amp; </s>
          <s xml:space="preserve">quatuor.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cylindri etiam duo cavi formantur ex ligno; </s>
          <s xml:space="preserve">quorum <lb />
<ptr xml:id="note-0192-01a" corresp="note-0192-01" type="noteAnchor" />
diametri externæ ſeſqui pollicis ſunt, minor longitudinis eſt <lb />trium poll.</s>
          <s xml:space="preserve">, major quinque poll.</s>
          <s xml:space="preserve">; repræſentatur ille in g, &amp; </s>
          <s xml:space="preserve">am-<lb />borum ſectiones per axem videntur in G &amp; </s>
          <s xml:space="preserve">H. </s>
          <s xml:space="preserve">Separatio in <lb />cavitate utriuſque datur ad diſtantiam unius pollicis ab ex-<lb />tremitate unâ; </s>
          <s xml:space="preserve">videntur hæ in a a, a a, &amp; </s>
          <s xml:space="preserve">ab eſt unius <lb />pollicis, craſſities ligni in b eſt octavæ partis pollicis. </s>
          <s xml:space="preserve">Majo-<lb />rem lignum habet craſſitiem in reliqua cylindri parte, ubi <lb />nempe cavitatem majorem circumdat. </s>
          <s xml:space="preserve">Cavitas minor, ubi <lb />experimenta inſtituenda ſunt, argillâ repletur, &amp; </s>
          <s xml:space="preserve">quæ pro-<lb />minet cultro ligneo abraditur, ut unita ſit ſuperficies in <lb />quam cylindri, ultimum memorati, in experimentis incur-<lb />runt; </s>
          <s xml:space="preserve">in majorem cavitatem, minori aut majori copiâ ar-<lb />gilla intruditur pro diverſo pondere cylindro communican-<lb />do.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0192-01" corresp="note-0192-01a" place="margin"><hi rend="small caps">TAB XVIII</hi>. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cylindri omnes eburnei &amp; </s>
          <s xml:space="preserve">lignei ſequenti methodo ſu-<lb />ſpenduntur. </s>
          <s xml:space="preserve">Ductâ lineâ in ſuperficie cylindri cujuſcunque ut <lb />g ad axem parallelâ, in hac duæ tenues lamellæ perforatæ, aut <lb />exigui annuli, o, o, firmantur ut &amp; </s>
          <s xml:space="preserve">duplex uncus v in me-<lb />dio. </s>
          <s xml:space="preserve">Foramina in lamellis o, o, non majora ſunt, niſi ut <lb />per hæc duplicatæ chordæ citharæ tranſmittantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lamellæ hæ omnes ita ponuntur, ut ductis ad cylindri <lb />axes perpendicularibus à centris foraminum; </s>
          <s xml:space="preserve">quales in <lb />cylindro D. </s>
          <s xml:space="preserve">(fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">o h, o h, perpendiculares hæ axem ſe-<lb />cent in h, h, ad diſtantiam trium partium quartarum poll. <lb /></s>
          <s xml:space="preserve">ab extremitatibus p, l. </s>
          <s xml:space="preserve">Notandum tamen reſpectu cylin-<lb />drorum cavorum, ſatis eſſe ſi hæc tantum obſerventur re-<lb />ſpectu lamellarum, quæ ad partem cavitatum minorum dan-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum globis ſingulis, ut A (Fig. </s>
          <s xml:space="preserve">3), etiam lamella exi-
</s>
          <pb facs="0193" n="129" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
gua perforata o jungitur in eo loco ubi dentis axis tranſit, &amp; </s>
          <s xml:space="preserve"><lb />uncus exiguus c ad exiguam â lamella diſtantiam ponitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Globi &amp; </s>
          <s xml:space="preserve">cylindri filis tenuibus, aut chordis citharæ, ſu-<lb />
<ptr xml:id="note-0193-01a" corresp="note-0193-01" type="noteAnchor" />
ſpenduntur, fila hæc cum paxillis p, p, p, p, cohærent, &amp; </s>
          <s xml:space="preserve">tranſ-<lb />eunt ſuper uncis v, v, z, z; </s>
          <s xml:space="preserve">in extremitatibus oppoſitis fila <lb />duplicantur formato nodo ad diſtantiam aliquot pollicum <lb />ab extremitate, &amp; </s>
          <s xml:space="preserve">per foramina lamellarum exiguarum tranſ-<lb />mittuntur, &amp; </s>
          <s xml:space="preserve">unco duplici connectuntur. </s>
          <s xml:space="preserve">Hac methodo cy-<lb />lindri P &amp; </s>
          <s xml:space="preserve">Q ſuſpenduntur, quàm facillimè etiam tollun-<lb />tur, manentibus filis, quibus cylindri alii annectuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0193-01" corresp="note-0193-01a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hac ſuſpenſione diſtantia inter uncum ut z, &amp; </s>
          <s xml:space="preserve">vicinum <lb />v, requiritur, quæ in cylindro datur inter lamellas per quas <lb />fila transmittuntur, quod admoto cylindro facillime men-<lb />ſuratur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Eadem diſtantia deſideratur inter extremitatem G regu-<lb />læ EG &amp; </s>
          <s xml:space="preserve">notam n, quæ ad eandem partem cum regula da-<lb />tur, &amp; </s>
          <s xml:space="preserve">a linea AD diſtat tribus partibus quartis unius polli-<lb />cis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cochleis ferreis F, F, F, ita diſponitur Machina ut cy-<lb />lindrorum ſeparatio lineæ AD reſpondeat, &amp; </s>
          <s xml:space="preserve">ut hi pa-<lb />rum admodum diſtent a plano ABDC.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando globus ſuſpenditur, connectitur filo tranſeunti <lb />ſuper unco v, &amp; </s>
          <s xml:space="preserve">extremitas G regulæ EG notæ n admo-<lb />vetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando cylindrus cavus ſuſpenditur minor cavitas line-<lb />am AD verſus datur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpora ad eandem altitudinem ſuſpendenda ſunt, &amp; </s>
          <s xml:space="preserve">ut <lb />cylindrorum axes horizonti paralleli ſint cavendum; </s>
          <s xml:space="preserve">his in-<lb />ſervit linea h h horizonti parallela in ſuperficie tabulæ du-<lb />cta, cui lineæ partes cylindrorum inferiores reſpondere de-<lb />bent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propter filorum amborum, quibus cylindrus quicunque <lb />ſuſpenditur, paralleliſmum, &amp; </s>
          <s xml:space="preserve">æqualitatem, axis in motu <lb />ſuo paralleliſmum ſervat &amp; </s>
          <s xml:space="preserve">ſingula corporis puncta æquali-<lb />ter deſcendunt, eâdemque velocitate moventur, ubi in
</s>
          <pb facs="0194" n="130" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
loco infimo ad quem pervenire poteſt cylindrus in aliud <lb />corpus directe incurrit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Velocitates corporum ante &amp; </s>
          <s xml:space="preserve">poſt impactum, ut de præ-<lb />cedenti machinâ dictum, menſurantur, attendendo ad fila ex-<lb />terna quamdiu agitur de motu corporum ad illam partem <lb />lineæ AD ad quam ſuſpenduntur; </s>
          <s xml:space="preserve">ſi autem agatur de mo-<lb />tu corporis ut P ultra AD, verſus C, interius filum adhi-<lb />bendum, &amp; </s>
          <s xml:space="preserve">regulæ EG, qua ad partem C datur, extremitas <lb />G admovenda eſt notæ n, quæ ad partem B datur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lignum N in quibuſdam experimentis applicatur tabulæ <lb />
<ptr xml:id="note-0194-01a" corresp="note-0194-01" type="noteAnchor" />
ABDC ita ut hujus latus c e cum linea AD congruat, <lb />firmaturque cochleis per foramina i, i, in tabula, &amp; </s>
          <s xml:space="preserve">ſciſſu-<lb />ras dg, dg, in ligno, tranſeuntibus. </s>
          <s xml:space="preserve">Cochleæ hæ in T re-<lb />præſentantur, horum capita ſuperficiei averſæ tabulæ <lb />ABDC applicantur, poteſtque lignum hoc ad varias altitu-<lb />dines firmari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0194-01" corresp="note-0194-01a" place="margin"><hi rend="small caps">TAB. XVIII.</hi> <lb />fig 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Excavatur lignum hocce in R ad profunditatem pollicis <lb />unius, cavitatis hujus altitudo c e eſt quatuor pollicum, la-<lb />titudo duorum pollicum, lignique craſſities in c e octavæ par-<lb />tis pollicis tantum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ubi Experimentis lignum hocce inſervit cavitas argillâ re-<lb />pletur, cultroque ligneo prominentem argillam abradimus, ut <lb />ſuperficies unita ſit. </s>
          <s xml:space="preserve">In hanc argillam cylindri incurrunt, ubi <lb />corpora in obicem firmum impingenda ſunt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentumi</hi>.</head>
        <p>
          <s xml:space="preserve">Lignum N (Fig. </s>
          <s xml:space="preserve">6.)</s>
          <s xml:space="preserve">, repletâ hujus cavitate argillâ molli, <lb />
<ptr xml:id="note-0194-02a" corresp="note-0194-02" type="noteAnchor" />
applicandum eſt tabulæ ABCD, ibique firmandum, ſub-<lb />
<ptr xml:id="note-0194-03a" corresp="note-0194-03" type="noteAnchor" />
lato nempe corpore Q, &amp; </s>
          <s xml:space="preserve">in loco corporis P cylindrus F <lb />(Fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">ſuſpendendus eſt ita, ut conus, qui oleo illiniri de-<lb />bet, argillam verſus dirigatur, &amp; </s>
          <s xml:space="preserve">ut inferior ſuperficies <lb />cylindri lineæ hh reſpondeat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0194-02" corresp="note-0194-02a" place="margin">492.</note>
              <note xml:space="preserve" xml:id="note-0194-03" corresp="note-0194-03a" place="margin"><hi rend="small caps">TAB. XVIII.</hi> <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dimittatur cylindrus ab altitudine quinque graduum &amp; </s>
          <s xml:space="preserve"><lb />impingendo in argillam vim ſuam amitter, formando cavi-<lb />tatem: </s>
          <s xml:space="preserve">partes enim argillæ ſolæ cedunt, cùm hujus partes <lb />multo minus cohæreant, quàm partes eboris aut ligni, &amp; </s>
          <s xml:space="preserve">ma-<lb />jor preſſio minorem vincat.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0195" n="131" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
        <p>
          <s xml:space="preserve">Cavitas hæc menſuranda eſt &amp; </s>
          <s xml:space="preserve">tollendum lignum N. <lb /></s>
          <s xml:space="preserve">Maſſa corporis eſt quatuor, velocitas quinque; </s>
          <s xml:space="preserve">ergo vis <lb />centum <ptr type="noteAnchor" /> deſtructa fuit formando cavitatem.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0195-01a" corresp="note-0195-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0195-01" corresp="note-0195-01a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cavitas minor cylindri G (Fig. </s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">argillâ replenda eſt, <lb />ſuperficieſque abradenda cultro ligneo, ut unita ſit; </s>
          <s xml:space="preserve">dein-<lb />de ponderandus eſt cylindrus, tantumque argillæ adjicien-<lb />dum, ut cum cylindro D (Fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">æqualiter ponderet, quæ ar-<lb />gilla majori cavitati intrudi debet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Suſpenſis nunc cylindris ita, ut pars conica cylindri D(Fig. </s>
          <s xml:space="preserve">4.)</s>
          <s xml:space="preserve">, <lb />oleo illinita, alium verſus dirigatur; </s>
          <s xml:space="preserve">à partibus oppoſitis ſingu-<lb />li a diviſione quinta dimittendi ſunt, in ſe mutuo incur-<lb />runt, poſt ictum quieſcunt, &amp; </s>
          <s xml:space="preserve">cavitas in argilla formatur. <lb /></s>
          <s xml:space="preserve">Menſuranda eſt hæc; </s>
          <s xml:space="preserve">ſingulorum corporum maſſæ valent duo, <lb />velocitates ſunt quinque, ergo ſingulorum vires quinqua-<lb />ginta <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">vis tota in colliſione deſtructa valet etiam cen-
<ptr xml:id="note-0195-02a" corresp="note-0195-02" type="noteAnchor" />
tum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0195-02" corresp="note-0195-02a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Iiſdem manentibus, unitâ iterum ſuperficie argillæ in ca-<lb />vitate minori cylindri, dimittendi ſunt ambo ab eadem par-<lb />te, unus ab altitudine quinque, alter ab altitudine quindecim; <lb /></s>
          <s xml:space="preserve">poſt ictum non ſeparantur &amp; </s>
          <s xml:space="preserve">ſimul ad diviſionem decimam <lb />adſcendunt; </s>
          <s xml:space="preserve">ſi enim huic diviſioni index applicetur ad ipſum <lb />pertingit filum, non autem ad illum pertingit hoc, ſi magis <lb />index removeatur. </s>
          <s xml:space="preserve">Et hìc cavitas formatur, quæ menſuran-<lb />da eſt. </s>
          <s xml:space="preserve">Unius corporis maſſa eſt duo, velocitas quindecim; </s>
          <s xml:space="preserve"><lb />ergo vis quadringenta &amp; </s>
          <s xml:space="preserve">quinquaginta, alterius vis eſt quin-<lb />quaginta, &amp; </s>
          <s xml:space="preserve">ſumma virium ante ictum quingenta. </s>
          <s xml:space="preserve">Poſt ictum <lb />maſſa eſt quatuor &amp; </s>
          <s xml:space="preserve">velocitas decem; </s>
          <s xml:space="preserve">ergo vis quadringen-<lb />ta: </s>
          <s xml:space="preserve">vis ergo ictu deſtructa etiam eſt centum ut in duobus præ-<lb />cedentibus experimentis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In tribus hiſce caſibus cavitates quâm exactiſſimè ſunt <lb />æquales, quod Experimentis confirmandum erat. </s>
          <s xml:space="preserve">In primo <lb />&amp; </s>
          <s xml:space="preserve">tertio caſu vires non fuere contrariæ, &amp; </s>
          <s xml:space="preserve">niſi ſuperando <lb />partium cohæſionem potuiſſe vim quandam deſtrui clare <lb />patet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Experimenta potuiſſent eodem modo inſtitui, partibus <lb />
<ptr xml:id="note-0195-03a" corresp="note-0195-03" type="noteAnchor" />
cylindrorum hemiſphæricis in argillam incurrentibus, ſed ca-
</s>
          <pb facs="0196" n="132" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
vitates conicæ exactius poſſunt conferri, quod ad Experi-<lb />menta ſequentia etiam debet referri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0195-03" corresp="note-0195-03a" place="margin">493.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motu duobus corporibus communi corpora hæc in ſe mu-<lb />tuo agere non poſſunt; </s>
          <s xml:space="preserve">pendet ergo ictus a velocitatereſpe-<lb />
<ptr xml:id="note-0196-01a" corresp="note-0196-01" type="noteAnchor" />
ctivâ, qua manente, intenſitas impactionis eadem erit, quomo-<lb />docunque celeritates abſolutæ varient; </s>
          <s xml:space="preserve">ab intenſitate hac pen-<lb />det partium introceſſio, quæ ergo ſemper eadem erit, ſi <lb />
<ptr xml:id="note-0196-02a" corresp="note-0196-02" type="noteAnchor" />
duo corpora eâdem velocitate reſpectivâ in ſe mutuo incur-<lb />rant, quibuſcunque velocitatibus moveantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0196-01" corresp="note-0196-01a" place="margin">494.</note>
              <note xml:space="preserve" xml:id="note-0196-02" corresp="note-0196-02a" place="margin">495.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Suſpenſo cylindro quocunque ex tribus qui in Fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">de-<lb />
<ptr xml:id="note-0196-03a" corresp="note-0196-03" type="noteAnchor" />
lineantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quolibet ex cylindris cavis, Fig. </s>
          <s xml:space="preserve">5. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0196-04a" corresp="note-0196-04" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0196-03" corresp="note-0196-03a" place="margin">496.</note>
              <note xml:space="preserve" xml:id="note-0196-04" corresp="note-0196-04a" place="margin"><hi rend="small caps">TAB XVIII</hi> <lb />fig. 4. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hujus minor cavitas argillâ repleatur, ut in deſcriptione <lb />machinæ &amp; </s>
          <s xml:space="preserve">experimento 1°. </s>
          <s xml:space="preserve">dictum, &amp; </s>
          <s xml:space="preserve">in majorem cavita-<lb />tem argillæ quantitas quæcunque intrudatur; </s>
          <s xml:space="preserve">dimittantur <lb />hi, unus à decimâ quintâ, alter à quintâ diviſione, ad ean-<lb />dem partem, &amp; </s>
          <s xml:space="preserve">menſuretur cavitatis diameter.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Unitâ iterum argillæ ſuperficie incurrat cylindrus unus <lb />velocitate decem in alium quieſcentem, &amp; </s>
          <s xml:space="preserve">iterum menſu-<lb />retur cavitatis diameter.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tandem, iterum unitâ argillæ ſuperficie, cylindrus unus <lb />dimittatur ab altitudine quartæ diviſionis, alter a ſexta di-<lb />viſione, &amp; </s>
          <s xml:space="preserve">in partes contrarias tendant, menſureturque ite-<lb />rum cavitatis diameter.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hiſce tribus caſibus velocitates reſpectivæ ſunt æquales <ptr type="noteAnchor" />,
<ptr xml:id="note-0196-05a" corresp="note-0196-05" type="noteAnchor" />
cavitates etiam minimè differunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0196-05" corresp="note-0196-05a" n="*" anchored="true" place="margin">474. 47;.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires æquales conſumuntur in formandis cavitatibus æ-<lb />qualibus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nulla vis perit niſi quæ in cavitatibus forman-
<ptr xml:id="note-0196-06a" corresp="note-0196-06" type="noteAnchor" />
dis conſumitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo quomodocunque duo corpora movean-
<ptr xml:id="note-0196-07a" corresp="note-0196-07" type="noteAnchor" />
tur, ſi eadem fuerit velocitas reſpectiva, eadem vis ictu <lb />
<ptr xml:id="note-0196-08a" corresp="note-0196-08" type="noteAnchor" />
deſtructa erit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hanc idcirco determinabimus in omni
<ptr xml:id="note-0196-09a" corresp="note-0196-09" type="noteAnchor" />
concurſu duorum corporum, manente velocitate reſpectivâ, <lb />ſi hoc fiat in uno caſu.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0196-06" corresp="note-0196-06a" n="*" anchored="true" place="margin">464</note>
              <note xml:space="preserve" xml:id="note-0196-07" corresp="note-0196-07a" n="*" anchored="true" place="margin">488</note>
              <note xml:space="preserve" xml:id="note-0196-08" corresp="note-0196-08a" place="margin">497</note>
              <note xml:space="preserve" xml:id="note-0196-09" corresp="note-0196-09a" n="*" anchored="true" place="margin">495</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sicorpora duo, ſive æqualia, ſive utcunque inæqualia in con-<lb />
<ptr xml:id="note-0196-10a" corresp="note-0196-10" type="noteAnchor" />
trarias partes lata, in ſe mutuo incurrant, poteſt, datâ <lb />velocitate reſpectivâ, ita componi horum motus, ut quod
</s>
          <pb facs="0197" />
          <s xml:space="preserve">
<ptr xml:id="fig-0197-01a" corresp="fig-0197-01" type="figureAnchor" />
<pb facs="0197a" />
<pb facs="0198" />
<pb facs="0199" n="133" /><fw type="head">MATHEMATICA, LIB. I. CAP. XXIII.</fw>
libuerit alium poſt ictum ſecum ferat, unde ſequitur, caſum <lb />dari, in quo poſt ictum quieſcunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0196-10" corresp="note-0196-10a" place="margin">498.</note>
              <figure xml:id="fig-0197-01" corresp="fig-0197-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0197-01" />
                <label>0197-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc caſu ſumma virium abſolutarum valet vim in <lb />omni caſu, poſitâ eadem velocitate reſpectivâ, deſtructam <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0199-01a" corresp="note-0199-01" type="noteAnchor" />
In hoc eodem caſu ſumma hæc eſt, ſervatâ velocitate re-<lb />ſpectivâ omnium minima: </s>
          <s xml:space="preserve">ſi enim ſumma minor daretur, mi-<lb />nor vis ictu periret, quod impoſſibile <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0199-02a" corresp="note-0199-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0199-01" corresp="note-0199-01a" n="*" anchored="true" place="margin">497.</note>
              <note xml:space="preserve" xml:id="note-0199-02" corresp="note-0199-02a" n="*" anchored="true" place="margin">497.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Summam autem hanc eſſe omnium minimam, ſi poſitis diro-<lb />
<ptr xml:id="note-0199-03a" corresp="note-0199-03" type="noteAnchor" />
ctionibus contrariis, celeritates fuerint inverſe ut maſſæ, <lb />&amp; </s>
          <s xml:space="preserve">in hoc caſu ſolo eſſe minimam, in ſcholio ſequenti 1. <lb /></s>
          <s xml:space="preserve">demonſtramus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0199-03" corresp="note-0199-03a" place="margin">499.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde ergo ſequitur in eo ſolo caſu corpora in contrarias <lb />
<ptr xml:id="note-0199-04a" corresp="note-0199-04" type="noteAnchor" />
partes lata, &amp; </s>
          <s xml:space="preserve">in ſe mutuo incurrentia, poſt ictum quieſce-<lb />re, ſi velocitates fuerint inverſe ut maſſæ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0199-05a" corresp="note-0199-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0199-04" corresp="note-0199-04a" place="margin">500.</note>
              <note xml:space="preserve" xml:id="note-0199-05" corresp="note-0199-05a" n="*" anchored="true" place="margin">498:</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Suſpenſis cylindris F, (Fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">18.) </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">G, (Fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">Tab 18.) <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0199-06a" corresp="note-0199-06" type="noteAnchor" />
cavendum autem, ut hic, argillâ in poſteriori cavitate in-<lb />
<ptr xml:id="note-0199-07a" corresp="note-0199-07" type="noteAnchor" />
truſâ, cum cylindro D (Fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">18.) </s>
          <s xml:space="preserve">æqualiter ponde-<lb />ret; </s>
          <s xml:space="preserve">maſſæ nunc erunt ut quatuor ad duo, aut ut duo ad unum. <lb /></s>
          <s xml:space="preserve">Incurrant hi directionibus contrariis in ſe mutuo, F velo-<lb />citate quinque, &amp; </s>
          <s xml:space="preserve">G velocitate decem, &amp; </s>
          <s xml:space="preserve">poſt ictum qui-<lb />
<ptr xml:id="note-0199-08a" corresp="note-0199-08" type="noteAnchor" />
eſcent. </s>
          <s xml:space="preserve">Cavitas in argilla in V repræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0199-06" corresp="note-0199-06a" place="margin">501.</note>
              <note xml:space="preserve" xml:id="note-0199-07" corresp="note-0199-07a" place="margin"><hi rend="small caps">TAB. XIX</hi> <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0199-08" corresp="note-0199-08a" place="margin"><hi rend="small caps">TAB. XIX</hi> <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires autem in hoc caſu ſunt inverſè ut velocitates <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">er-
<ptr xml:id="note-0199-09a" corresp="note-0199-09" type="noteAnchor" />
go ut corpora inæqualia in contrarias partes lata, poſt ictum <lb />
<ptr xml:id="note-0199-10a" corresp="note-0199-10" type="noteAnchor" />
quieſcant, vires inſitæ inæquales deſiderantur. </s>
          <s xml:space="preserve">Circa quam <lb />inæqualitatem ſequentia experimenta notatu digniſſima <lb />ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0199-09" corresp="note-0199-09a" n="*" anchored="true" place="margin">472.</note>
              <note xml:space="preserve" xml:id="note-0199-10" corresp="note-0199-10a" place="margin">502.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Firmato obice N, (Fig. </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">18.) </s>
          <s xml:space="preserve">in argillam incurrat cy-<lb />
<ptr xml:id="note-0199-11a" corresp="note-0199-11" type="noteAnchor" />
lindrus F ea velocitate, qua in experimento præcedenti mo-<lb />
<ptr xml:id="note-0199-12a" corresp="note-0199-12" type="noteAnchor" />
tus fuit, cavitatem format S (Fig. </s>
          <s xml:space="preserve">3.)</s>
          <s xml:space="preserve">. </s>
          <s xml:space="preserve">Mutato paululum obi-<lb />
<ptr xml:id="note-0199-13a" corresp="note-0199-13" type="noteAnchor" />
ce in hunc incurrat cylindrus D (Fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">18.) </s>
          <s xml:space="preserve">ea ve-<lb />locitate qua cylindrus G, qui in præcedenti experimento <lb />ejuſdem ponderis fuit cum hoc cylindio D, in hoc præce-<lb />denti experimento fuit agitatus, cavitatem formabit duplam <lb />præcedentis, quæ in T (fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">repræſentatur, quod
</s>
          <pb facs="0200" n="134" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
manifeſtè virium inæqualitatem indicat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0199-11" corresp="note-0199-11a" place="margin">503.</note>
              <note xml:space="preserve" xml:id="note-0199-12" corresp="note-0199-12a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0199-13" corresp="note-0199-13a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæ autem duæ cavitates conjunctæ æquales ſunt cavitati <lb />ſoli quæ in præcedenti experimento fuit formata, &amp; </s>
          <s xml:space="preserve">ita an-<lb />te demonſtrata <ptr type="noteAnchor" /> cum Experimentis his exactiſſime congruunt.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0200-01a" corresp="note-0200-01" type="noteAnchor" />
Si enim, adhibito Circino Proportionum conferamus ſoli-<lb />da ſimilia, quorum latera homologa ſunt diametri trium <lb />cavitatum, S, T, V, (Fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">in duobus ultimis experimentis <lb />formatarum, videbimus cavitates has eſſe inter ſe ut unum, <lb />duo, &amp; </s>
          <s xml:space="preserve">tria; </s>
          <s xml:space="preserve">id eſt majorem æqualem eſſe duobus mino-<lb />ribus ſimul ſumtis. </s>
          <s xml:space="preserve">Quod etiam ſequenti experimento <lb />patet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0200-01" corresp="note-0200-01a" n="*" anchored="true" place="margin">464.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Firmato obice N, in hunc impingat velocitate quinque <lb />
<ptr xml:id="note-0200-02a" corresp="note-0200-02" type="noteAnchor" />
cylindrus F; </s>
          <s xml:space="preserve">ſublato hoc &amp; </s>
          <s xml:space="preserve">ſuſpenſo cylindro D, impingat <lb />
<ptr xml:id="note-0200-03a" corresp="note-0200-03" type="noteAnchor" />
hic velocitate decem in obicem, incurrendo in ipſam cavita-<lb />tem jam formatamictu cylindri F; </s>
          <s xml:space="preserve">cavitatem augebit &amp; </s>
          <s xml:space="preserve">hæc <lb />nunc valebit ambas cavitates in Exper. </s>
          <s xml:space="preserve">præcedenti 4<hi rend="superscript">to</hi>. </s>
          <s xml:space="preserve">for-<lb />matas <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">erit æqualis cavitati V (Fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">Exp. </s>
          <s xml:space="preserve">penul-
<ptr xml:id="note-0200-04a" corresp="note-0200-04" type="noteAnchor" />
timi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0200-02" corresp="note-0200-02a" place="margin">504.</note>
              <note xml:space="preserve" xml:id="note-0200-03" corresp="note-0200-03a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0200-04" corresp="note-0200-04a" n="*" anchored="true" place="margin">464.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa hoc Experimentum 5<hi rend="superscript">tum</hi>. </s>
          <s xml:space="preserve">notandum aliquando ictu <lb />
<ptr xml:id="note-0200-05a" corresp="note-0200-05" type="noteAnchor" />
argillæ ſuperficiem compactiorem fieri &amp; </s>
          <s xml:space="preserve">elaſticitatem quan-<lb />dam acquirere in quo caſu Experimentum non procedit. <lb /></s>
          <s xml:space="preserve">Semper autem obſervavi cavitatem, duobus ictibus quibuſ-<lb />cunque formatam, ſi corpus quod ultimum impingit non <lb />reſiliat, æqualem eſſe duobus cavitatibus, quæ iiſdem icti-<lb />bus ſeparatim formari potuiſſent; </s>
          <s xml:space="preserve">ſi vero corpus in cavita-<lb />tem incurrens quantumvis parwm reſiliat indicium habemus <lb />elaſticitatis argillæ, &amp; </s>
          <s xml:space="preserve">in tali caſu cavitatem ex duobus icti-<lb />bus minorem ſemper detexi ſummâ cavitatum ſeparatarum, <lb />eoque minorem quo ictu acquiſita elaſticitas major erat, cla-<lb />re autem patet partes elaſticas argillæ difficilius intropremi <lb />quam aliæ quæ elaſticitate deſtituuntur. </s>
          <s xml:space="preserve">Sequenti etiam <lb />experimento, quod jam præcedentibus patuit, alio modo <lb />demonſtramus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0200-05" corresp="note-0200-05a" place="margin">505.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <note xml:space="preserve" place="margin">506.</note>
        <p>
          <s xml:space="preserve">Incurrant in ſe mutuo uterque velocitate quinque, cylin-<lb />
<ptr xml:id="note-0200-07a" corresp="note-0200-07" type="noteAnchor" />
</s>
          <pb facs="0201" n="135" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
drus ſæpius memoratus F, &amp; </s>
          <s xml:space="preserve">cylindrus cavus argillam <lb />continens H (Fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">18.)</s>
          <s xml:space="preserve">, qui cum præcedenti ſit <lb />ejuſdem ponderis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0200-07" corresp="note-0200-07a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sublatis his incurrant in ſe mutuo uterque velocitate de-<lb />
<ptr xml:id="note-0201-01a" corresp="note-0201-01" type="noteAnchor" />
cem, cylindrus D cum cylindro cavo argillam continenti G, <lb />qui etiam æqualiter ponderent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0201-01" corresp="note-0201-01a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tandem ſublato cylindro D, &amp; </s>
          <s xml:space="preserve">ſubſtituto cylindro F, <lb />
<ptr xml:id="note-0201-02a" corresp="note-0201-02" type="noteAnchor" />
unitâque iterum argillâ cylindri G, incurrant hi in ſe invi-<lb />cem iiſdem velocitatibus, quibus in jam memoratis im-<lb />pactionibus fuere agitati, id eſt, ut in Exp. </s>
          <s xml:space="preserve">3°. </s>
          <s xml:space="preserve">hic velocitate <lb />decem, ille velocitate quinque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0201-02" corresp="note-0201-02a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hiſce tribus occaſionibus poſt ictum corpora quieſcunt; <lb /></s>
          <s xml:space="preserve">cavitates autem ſunt inæquales. </s>
          <s xml:space="preserve">In primo caſu eſt omnium <lb />minima, repræſentatur in T; </s>
          <s xml:space="preserve">in ſecundo eſt omnium maxima, <lb />
<ptr xml:id="note-0201-03a" corresp="note-0201-03" type="noteAnchor" />
vide X; </s>
          <s xml:space="preserve">in tertio media eſt, delineatur in V: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quidem ſunt <lb />cavitates in proportione arithmetica, ut ipſæ vires ictibus <lb />deſtructæ. </s>
          <s xml:space="preserve">In primo caſu maſſæ ſingulæ valent quatuor <lb />velocitate quinque corpus utrumque fertur, id eſt utriuſque <lb />vis eſt centum <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">vis deſtructa valet ducenta.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0201-04a" corresp="note-0201-04" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0201-03" corresp="note-0201-03a" place="margin"><hi rend="small caps">TAB. XIX</hi> <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0201-04" corresp="note-0201-04a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Secundo caſu utriuſque corporis maſſa eſt duo, &amp; </s>
          <s xml:space="preserve"><lb />velocitas decem; </s>
          <s xml:space="preserve">ergo vis ducenta <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vis deſtructa
<ptr xml:id="note-0201-05a" corresp="note-0201-05" type="noteAnchor" />
quadringenta, in hoc etiam caſu cavitas dupla eſt cavitatis <lb />præcedentis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0201-05" corresp="note-0201-05a" n="*" anchored="true" place="margin">470</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In tertio caſu unius corporis vis eſt centum, alterius valet <lb />ducenta &amp; </s>
          <s xml:space="preserve">vis quæ deſtructa eſt valet trecenta; </s>
          <s xml:space="preserve">cavitasideo <lb />media eſt inter cavitates præcedentes.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si in experimento tertio vis minor augeatur, ita tamen <lb />
<ptr xml:id="note-0201-06a" corresp="note-0201-06" type="noteAnchor" />
ut vim alterius corporis nondum æquet, corpus, cujus vis <lb />minor erit, corpus majori vi motum regredi coget; </s>
          <s xml:space="preserve">directo <lb />in hoc caſu experimento demonſtramus vim corporis victi, <lb />alterius vim ſuperare; </s>
          <s xml:space="preserve">eodem modo ac in Exp. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">demon-<lb />ſtravimus vires in Exp. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">fuiſſe inæquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0201-06" corresp="note-0201-06a" place="margin">507.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis corpori inſita alterius vim nunquam immediate de-<lb />
<ptr xml:id="note-0201-07a" corresp="note-0201-07" type="noteAnchor" />
ſtruit <ptr type="noteAnchor" />, perit hæc actione qua partes intropremuntur <ptr type="noteAnchor" />, ita
<ptr xml:id="note-0201-08a" corresp="note-0201-08" type="noteAnchor" />
<ptr xml:id="note-0201-09a" corresp="note-0201-09" type="noteAnchor" />
ut corpus eo majorem amittat vim, quo majorem patitur re-<lb />ſiſtentiam; </s>
          <s xml:space="preserve">ſed hæc a materiæ inertiâ &amp; </s>
          <s xml:space="preserve">a vi contrariâ ori-
</s>
          <pb facs="0202" n="136" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
poteſt, ita ut corporis vis minuenda ſit, ſi hujus inertia, id <lb />eſt, materiæ quantitas <ptr type="noteAnchor" /> augeatur, ut in utroque <ptr type="noteAnchor" /> caſu
<ptr xml:id="note-0202-01a" corresp="note-0202-01" type="noteAnchor" />
æqualiter alii corpori reſiſtat, unde paradoxi explicationem <lb />deducimus. </s>
          <s xml:space="preserve">Nam, ut ex hac obſervatione ſequitur, Quando <lb />
<ptr xml:id="note-0202-02a" corresp="note-0202-02" type="noteAnchor" />
duo corpora in ſe mutuo incurrunt, duæ dantur actiones, &amp; </s>
          <s xml:space="preserve"><lb />duæ reactiones, utraque actio ſuæ reactioni æqualis eſt; </s>
          <s xml:space="preserve">ut <lb />corpora quieſcant poſt ictum, non requiritur ut ante ictum <lb />vires contrariæ ſint æquales, ſed ut utrumque corpus <lb />patiatur reſiſtentiam talem, ut agendo poſſit vim ſuam con-<lb />ſumere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0201-07" corresp="note-0201-07a" place="margin">508.</note>
              <note xml:space="preserve" xml:id="note-0201-08" corresp="note-0201-08a" n="*" anchored="true" place="margin">489.</note>
              <note xml:space="preserve" xml:id="note-0201-09" corresp="note-0201-09a" n="*" anchored="true" place="margin">488.</note>
              <note xml:space="preserve" xml:id="note-0202-01" corresp="note-0202-01a" n="*" anchored="true" place="margin">13.</note>
              <note xml:space="preserve" xml:id="note-0202-02" corresp="note-0202-02a" place="margin">509.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex demonſtratis facile deducimus quomodo datis corpo-<lb />
<ptr xml:id="note-0202-03a" corresp="note-0202-03" type="noteAnchor" />
ribus, &amp; </s>
          <s xml:space="preserve">horum velocitate reſpectiva, vis ictu deſtructa de-<lb />terminetur: </s>
          <s xml:space="preserve">determinatâ, nempe ſummâ virium, poſitis, eâ-<lb />dem velocitate reſpectivâ, motibus contrariis, &amp; </s>
          <s xml:space="preserve">velocita-<lb />
<ptr xml:id="note-0202-04a" corresp="note-0202-04" type="noteAnchor" />
tibus in ratione inverſa maſſarum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hanc autem ſummam
dari in ſcholio 1. </s>
          <s xml:space="preserve">ſequenti demonſtramus, Si produ-<lb />ctum maſſarum per quadratum velocitatis reſpectivæ multi-<lb />plicetur, &amp; </s>
          <s xml:space="preserve">per ſummam maſſarum dividatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0202-03" corresp="note-0202-03a" place="margin">510.</note>
              <note xml:space="preserve" xml:id="note-0202-04" corresp="note-0202-04a" n="*" anchored="true" place="margin">497. 500.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <note xml:space="preserve" place="margin">511.</note>
        <p>
          <s xml:space="preserve">Suſpenſis cylindris E (fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Tab 18.) </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">G, ſæpius memo-<lb />
<ptr xml:id="note-0202-06a" corresp="note-0202-06" type="noteAnchor" />
rato, redacto hoc ad pondus cylindri D, id eſt ſint maſſæ ut <lb />tria ad duo; </s>
          <s xml:space="preserve">incurrant corpora hæc in ſe mutuo dum am-<lb />bo in contrarias partes feruntur, majus velocitate ſeptemde-<lb />cim, minus velocitate tria, in quo caſu velocitas reſpe-<lb />
<ptr xml:id="note-0202-07a" corresp="note-0202-07" type="noteAnchor" />
ctiva eſt viginti <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Poſt ictum moventur ſimul velocitate
novem, id eſt ad nonam uſque diviſionem adſcendunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0202-06" corresp="note-0202-06a" place="margin"><hi rend="small caps">TAB. XXII.</hi> <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0202-07" corresp="note-0202-07a" n="*" anchored="true" place="margin">475.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Multiplicando maſſas habemus 6. </s>
          <s xml:space="preserve">Quadratum velocitatis <lb />reſpectivæ eſt 400. </s>
          <s xml:space="preserve">cujus productum per productum maſſa-<lb />rum eſt 2400; </s>
          <s xml:space="preserve">dividendo numerum hunc per 5. </s>
          <s xml:space="preserve">ſummam <lb />maſſarum habemus, vim amiſſam 480. </s>
          <s xml:space="preserve">Hanc autem bene <lb />determinari demonſtramus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vis corporis majoris ante ictum habetur multiplicando <lb />289. </s>
          <s xml:space="preserve">per 3 <ptr type="noteAnchor" />, eſt ergo 867. </s>
          <s xml:space="preserve">Minoris vis habetur multipli-
<ptr xml:id="note-0202-08a" corresp="note-0202-08" type="noteAnchor" />
cando 9. </s>
          <s xml:space="preserve">per 2 <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">eſt ideo 18; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſumma virium eſt 885.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0202-09a" corresp="note-0202-09" type="noteAnchor" />
Poſt ictum maſſa eſt 5 &amp; </s>
          <s xml:space="preserve">quadratum velocitatis 81, id circo <lb />ſupereſt vis 405, quæ ſi ſubducatur ex 885. </s>
          <s xml:space="preserve">habemus ut an-<lb />te vim amiſſam 480.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0202-08" corresp="note-0202-08a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0202-09" corresp="note-0202-09a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0203" n="137" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
        <p>
          <s xml:space="preserve">Si cylindrus F cujus maſſa eſt quatuor, velocitate undecim, <lb />
<ptr xml:id="note-0203-01a" corresp="note-0203-01" type="noteAnchor" />
demtâ parte vigeſimâ ſecundâ, in obicem firmum incurrat, <lb />cavitatem formabit æqualem illi, quæ in hoc experimento im-<lb />pactione corporum fuit formata, vis in hoc caſu amiſſa eſt <lb />480 {1/121} <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">id eſt vix a vi, in impactione memorata amiſſa,
<ptr xml:id="note-0203-02a" corresp="note-0203-02" type="noteAnchor" />
differt; </s>
          <s xml:space="preserve">quod ergo <ptr type="noteAnchor" /> iterum confirmat, vim ictu deſtructam
<ptr xml:id="note-0203-03a" corresp="note-0203-03" type="noteAnchor" />
regula n. </s>
          <s xml:space="preserve">510. </s>
          <s xml:space="preserve">bene fuiſſe determinatam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0203-01" corresp="note-0203-01a" place="margin"><hi rend="small caps">TAB. XXII.</hi> <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0203-02" corresp="note-0203-02a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0203-03" corresp="note-0203-03a" n="*" anchored="true" place="margin">462</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex demonſtratis de corporibus poſt ictum quieſcentibus <lb />deducimus regulas quibus in omni caſu corporum velocita-<lb />tes poſt ictum determinantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Moveantur corpora, aut verſus eandem partem (fig. </s>
          <s xml:space="preserve">1.) <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0203-04a" corresp="note-0203-04" type="noteAnchor" />
aut in partes contrarias (fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſint maſſæ ut AB &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0203-05a" corresp="note-0203-05" type="noteAnchor" />
BC; </s>
          <s xml:space="preserve">ſit hujus velocitas BE; </s>
          <s xml:space="preserve">illius BN: </s>
          <s xml:space="preserve">velocitas reſpe-<lb />ctiva erit EN <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Dividatur hæc in I ita, ut IN ſit ad
<ptr xml:id="note-0203-06a" corresp="note-0203-06" type="noteAnchor" />
IE, ut BC ad BA, &amp; </s>
          <s xml:space="preserve">erit BI velocitas, qua ambo cor-<lb />pora poſt ictum feruntur; </s>
          <s xml:space="preserve">id eſt mutationes in velocitatibus <lb />ſunt in ratione inver ſa maſſarum, BC acquirit EI dum AB <lb />amittit NI. </s>
          <s xml:space="preserve">Si enim concipiamus navem translatam velo-<lb />citate BI, &amp; </s>
          <s xml:space="preserve">in hac moveatur corpus BC velocitate IE a <lb />prora ad puppim, habet velocitatem abſolutam BE; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />corpus AB feratur a puppi ad proram velocitate IN, ha-<lb />bebit hoc velocitatem abſolutam BN; </s>
          <s xml:space="preserve">hæc corpora, cum <lb />in nave ferantur directionibus contrariis, &amp; </s>
          <s xml:space="preserve">velocitatibus, <lb />quæ ſunt inverſè ut maſiæ, poſt ictum, in nave quie-<lb />ſcunt <ptr type="noteAnchor" />, id eſt eadem cum nave velocitate ferun-
<ptr xml:id="note-0203-07a" corresp="note-0203-07" type="noteAnchor" />
tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0203-04" corresp="note-0203-04a" place="margin">512.</note>
              <note xml:space="preserve" xml:id="note-0203-05" corresp="note-0203-05a" place="margin"><hi rend="small caps">TAB XX.</hi> <lb />fig. 1. 2.</note>
              <note xml:space="preserve" xml:id="note-0203-06" corresp="note-0203-06a" n="*" anchored="true" place="margin">474. 475.</note>
              <note xml:space="preserve" xml:id="note-0203-07" corresp="note-0203-07a" n="*" anchored="true" place="margin">500.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Determinatur BI regulâ facili, quam ut detegamus, ſint <lb />rectangula BM, BF producta maſſarum per ſuas celerita-<lb />tes, &amp; </s>
          <s xml:space="preserve">abſolvantur parallelogramma AO &amp; </s>
          <s xml:space="preserve">CD; </s>
          <s xml:space="preserve">ductâ <lb />DO, ſecat hæc BN in I; </s>
          <s xml:space="preserve">nam triangula DIE &amp; </s>
          <s xml:space="preserve">INQ <lb />ſunt ſimilia, &amp; </s>
          <s xml:space="preserve">IN ad IE, ut NO, aut BC, ad DE, <lb />aut AB. </s>
          <s xml:space="preserve">Per I ducatur HL, parallela AB, &amp; </s>
          <s xml:space="preserve">complementa <lb />IM, IF <ptr type="noteAnchor" />, erunt æqualia; </s>
          <s xml:space="preserve">ergo corporibus tendentibus ad ean-
<ptr xml:id="note-0203-08a" corresp="note-0203-08" type="noteAnchor" />
<ptr xml:id="note-0203-09a" corresp="note-0203-09" type="noteAnchor" />
dem partem, ſi ex ſumma productorum BM, &amp; </s>
          <s xml:space="preserve">BF, maſ-<lb />
<ptr xml:id="note-0203-10a" corresp="note-0203-10" type="noteAnchor" />
ſarum per ſuas velocitates ſubtrahamus MI, &amp; </s>
          <s xml:space="preserve">ejus loco ſub-
</s>
          <pb facs="0204" n="138" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſtituamus IF, prædicta ſumma æqualis erit rectangulo AL, <lb />quod ſi dividatur per <hi rend="small caps">A</hi> C, ſummam maſſarum, quotiens di-<lb />viſionis dabit <hi rend="small caps">A</hi> H, aut BI, velocitatem corporibus com-<lb />munem poſt ictum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0203-08" corresp="note-0203-08a" n="*" anchored="true" place="margin">43. <hi rend="small caps">EL</hi>. 1.</note>
              <note xml:space="preserve" xml:id="note-0203-09" corresp="note-0203-09a" place="margin">513.</note>
              <note xml:space="preserve" xml:id="note-0203-10" corresp="note-0203-10a" place="margin">fig. 1.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Globi duo æquales ex argilla molli ſuſpenduntur, ſi hi <lb />
<ptr xml:id="note-0204-01a" corresp="note-0204-01" type="noteAnchor" />
partem eandem verſus moveantur, P velocitate decem, Q <lb />
<ptr xml:id="note-0204-02a" corresp="note-0204-02" type="noteAnchor" />
velocitate ſex; </s>
          <s xml:space="preserve">poſt ictum motum ſimul continuabunt ve-<lb />locitate octo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0204-01" corresp="note-0204-01a" place="margin">514.</note>
              <note xml:space="preserve" xml:id="note-0204-02" corresp="note-0204-02a" place="margin"><hi rend="small caps">TAB. XXI.</hi> <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum maſſæ ſint æquales unitate deſignari poſſunt, &amp; </s>
          <s xml:space="preserve">ſum-<lb />ma productorum maſſarum per velocitates eſt ſedecim, quæ <lb />ſi per ſummam maſſarum duo dividatur habemus ut in Ex-<lb />perimento velocitatem octo,</s>
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Suſpenſis cylindris, eburneo E cujus maſſa eſt tria, <lb />
<ptr xml:id="note-0204-03a" corresp="note-0204-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">ligneo argillam continenti G, cujus maſſa eſt duo, feran-<lb />
<ptr xml:id="note-0204-04a" corresp="note-0204-04" type="noteAnchor" />
tur hi ad eandem partem, primus velocitate duodecim, ſe-<lb />cundus velocitate ſeptem, poſt ictum ſimul velocitate de-<lb />cem moventur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0204-03" corresp="note-0204-03a" place="margin">515.</note>
              <note xml:space="preserve" xml:id="note-0204-04" corresp="note-0204-04a" place="margin"><hi rend="small caps">TA. XXII.</hi> <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Multiplicando maſſam 3 per velocitatem 12, habemus <lb />36, addito 14, producto maſſæ 2 per velocitatem 7, habe-<lb />mus ſummam productorum 50, quæ ſi dividatur per ſum-<lb />mam maſſarum 5, habemus velocitatem experimento dete-<lb />ctam 10.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si corpora tendant in partes contrarias, &amp; </s>
          <s xml:space="preserve">ex producto <lb />
<ptr xml:id="note-0204-05a" corresp="note-0204-05" type="noteAnchor" />
majori BM ſubtrahamus MI, &amp; </s>
          <s xml:space="preserve">ſubſtituamus IF, habe-<lb />
<ptr xml:id="note-0204-06a" corresp="note-0204-06" type="noteAnchor" />
mus BM æquale gnomoni AHLFEB; </s>
          <s xml:space="preserve">ex quo ſi ſub-<lb />trahamus productum BF, habemus HC diſſerentiam pro-<lb />ductorum maſſarum per ſuas velocitates; </s>
          <s xml:space="preserve">ſi autem hanc di-<lb />vidamus per ſummam maſſarum AC, quotiens erit veloci-<lb />tas quæſita BI, quæ dirigitur ad eandem partem cum BN: <lb /></s>
          <s xml:space="preserve">id eſt ambo corpora, velocitate detectâ, feruntur verſus <lb />eandem partem cum corpore, cujus productum maßæ per <lb />velocitatem alius productum ſimile excedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0204-05" corresp="note-0204-05a" place="margin">516.</note>
              <note xml:space="preserve" xml:id="note-0204-06" corresp="note-0204-06a" place="margin"><hi rend="small caps">TAB. XX.</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0205" n="139" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 10.</head>
        <p>
          <s xml:space="preserve">Suſpenſis globis, ex argilla molli, æqualibus P &amp; </s>
          <s xml:space="preserve">Q, ſint <lb />
<ptr xml:id="note-0205-01a" corresp="note-0205-01" type="noteAnchor" />
hi in contrarias partes moti, P velocitate ſex, Q velocita-<lb />
<ptr xml:id="note-0205-02a" corresp="note-0205-02" type="noteAnchor" />
te quatuordecim, poſt ictum velocitate quatuor motum con-<lb />tinuat, Q ſecum ferens P.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0205-01" corresp="note-0205-01a" place="margin">517.</note>
              <note xml:space="preserve" xml:id="note-0205-02" corresp="note-0205-02a" place="margin"><hi rend="small caps">TAB. XXL.</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quia propter maſſas æquales hæ unitate deſignari poſſunt, <lb />producta maſſarum per velocitates ſunt 6. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">14.</s>
          <s xml:space="preserve">, quorum <lb />differentia eſt 8.</s>
          <s xml:space="preserve">, quæ diviſa per ſummam maſſarum 2, dat <lb />velocitatem poſt ictum quatuor.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 11.</head>
        <p>
          <s xml:space="preserve">Non differt experimentum hoc à colliſione in Experimen-<lb />
<ptr xml:id="note-0205-03a" corresp="note-0205-03" type="noteAnchor" />
to 7. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> memoratâ, poteſt autem velocitas corporum poſt
<ptr xml:id="note-0205-04a" corresp="note-0205-04" type="noteAnchor" />
ictum ex nunc demonſtratis determinari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0205-03" corresp="note-0205-03a" place="margin">518.</note>
              <note xml:space="preserve" xml:id="note-0205-04" corresp="note-0205-04a" place="margin"><hi rend="small caps">TA. XXIL.</hi> <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">511.</note>
        <p>
          <s xml:space="preserve">Multiplicando maſſam E per velocitatem 17.</s>
          <s xml:space="preserve">, habemus 51; <lb /></s>
          <s xml:space="preserve">ſubtractis 6, producto maſſæ 2 per velocitatem 3, reſtat 45; </s>
          <s xml:space="preserve"><lb />quibus diviſis per 5. </s>
          <s xml:space="preserve">ſummam maſſarum, habemus velocita-<lb />tem novem Experimento detectam.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Si corpus unum quieſcat, ex utrâque regulâ ſequitur cor-<lb />
<ptr xml:id="note-0205-06a" corresp="note-0205-06" type="noteAnchor" />
poris moti productum velocitatis per maſſam dividi debere <lb />per maſſarum ſummam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0205-06" corresp="note-0205-06a" place="margin">519.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 12.</head>
        <p>
          <s xml:space="preserve">Globus P ex argillâ molli in globum æqualem quieſcen-<lb />
<ptr xml:id="note-0205-07a" corresp="note-0205-07" type="noteAnchor" />
tem Q, velocitate decem, incurrit, poſt ictum ſimul velo-<lb />citate quinque motum continuant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0205-07" corresp="note-0205-07a" place="margin"><hi rend="small caps">TAB XXI.</hi> <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus in motu alii corpori ſine impactione motum com-<lb />
<ptr xml:id="note-0205-08a" corresp="note-0205-08" type="noteAnchor" />
municare poteſt, in hoc tantum preſſione agendo; </s>
          <s xml:space="preserve">in quo ca-<lb />ſu ſi preſſio qua partes cohærent inter ſe ſuperet preſſionem <lb />corporum mutuam nulla datur partium introceſſio, &amp; </s>
          <s xml:space="preserve">nulla vis <lb />deſtructa <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ideoque ſumma virium ante &amp; </s>
          <s xml:space="preserve">poſt actionem
<ptr xml:id="note-0205-09a" corresp="note-0205-09" type="noteAnchor" />
eadem eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0205-08" corresp="note-0205-08a" place="margin">520.</note>
              <note xml:space="preserve" xml:id="note-0205-09" corresp="note-0205-09a" n="*" anchored="true" place="margin">488;</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut autem demonſtremus quomodo corpora mota, preſſio-<lb />
<ptr xml:id="note-0205-10a" corresp="note-0205-10" type="noteAnchor" />
ne in alia, ſine impactione, motum communicare poſſint, con-<lb />
<ptr xml:id="note-0205-11a" corresp="note-0205-11" type="noteAnchor" />
cipiendum eſt corpus Q, quod formatur revolutione figuræ <lb />a b c d (quæ ſemicirculo &amp; </s>
          <s xml:space="preserve">duobus quadrantibus termina-<lb />tur) circa axem a c.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0205-10" corresp="note-0205-10a" place="margin">521.</note>
              <note xml:space="preserve" xml:id="note-0205-11" corresp="note-0205-11a" place="margin"><hi rend="small caps">TAB. XXI.</hi> <lb />fig 4.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0206" n="140" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Quieſcat hoc, quamvis. </s>
          <s xml:space="preserve">demonſtratio etiam corpori moto <lb />applicari poſſit; </s>
          <s xml:space="preserve">concipiamus ulterius duo corpora P, P; <lb /></s>
          <s xml:space="preserve">duo concipimus ut actio in corpus Q ſit directa; </s>
          <s xml:space="preserve">moveantur <lb />hæc, velocitatibus æqualibus, directionibus parallelis inter ſe, <lb />&amp; </s>
          <s xml:space="preserve">axi corporis Q, moveantur etiam, ut ad Q perveniant ita, ut <lb />corporis Q ſuperſicies tangat corpora P, P, in punctis in <lb />quibus hæc ipſa ſuperſicies parallela eſt ipſi directioni mo-<lb />tus; </s>
          <s xml:space="preserve">Corpora ergo P, P, in corpus Q nullam exerunt acti-<lb />onem, ubiad hoc perveniunt. </s>
          <s xml:space="preserve">Dum motum continuant jux-<lb />ta ſuperſicies excavatas ad, ab, in corpus Q premunt, <lb />quod cum non retineatur cedit <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">dum preſſio continua-
<ptr xml:id="note-0206-01a" corresp="note-0206-01" type="noteAnchor" />
tur acceleratur Q: </s>
          <s xml:space="preserve">donec corpora P, P, hoc deſerant, <lb />quod ſemper fiet antequam corpora P, P, puncta b &amp; </s>
          <s xml:space="preserve">d per-<lb />veniant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0206-01" corresp="note-0206-01a" n="*" anchored="true" place="margin"> 433.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc preſſio nullum exſerit effectum præter mo-<lb />tum quem corpori Q communicat; </s>
          <s xml:space="preserve">ideoque corpora P, P, <lb />ex viribus tantum amittunt, quantum acquirit corpus Q <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0206-02a" corresp="note-0206-02" type="noteAnchor" />
In hiſce attritum ſeponimus qui ſine quadam partium intro-<lb />ceſſione dari non poteſt; </s>
          <s xml:space="preserve">ideoque ſine virium deſtructione. <lb /></s>
          <s xml:space="preserve">In ſcholio autem 3°. </s>
          <s xml:space="preserve">Cap, 28. </s>
          <s xml:space="preserve">ipſos motus poſt concurſum <lb />determinamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0206-02" corresp="note-0206-02a" n="*" anchored="true" place="margin">458.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpus ut P ſimili actione premat in obſtaculum, quod <lb />
<ptr xml:id="note-0206-03a" corresp="note-0206-03" type="noteAnchor" />
hac preſſione non movetur, &amp; </s>
          <s xml:space="preserve">cujus partes ſatis arctè co-<lb />
<ptr xml:id="note-0206-04a" corresp="note-0206-04" type="noteAnchor" />
hæreant, ut huic actioni non cedant, corpus ex vi ſua non <lb />amittet; </s>
          <s xml:space="preserve">in hoc caſu corporis preſſio in obſtaculum reſi-<lb />ſtentiâ obſtaculi, quidem deſtruitur, ſed cum nul-<lb />la detur partium introceſſio, neque vis communicata, nul-<lb />lam etiam corpus P vim amittit; </s>
          <s xml:space="preserve">ſic corpus quod ſuper <lb />plano inclinato deſcendit eodem modo acceleratur ac cor-<lb />pus quod libere cadit ſi ad eandem profunditatem ambo <lb />
<ptr xml:id="note-0206-05a" corresp="note-0206-05" type="noteAnchor" />
deſcendant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">licet illud in planum premat. </s>
          <s xml:space="preserve">In hiſce occa-
ſionibus, illud quod obſtaculum in loco retinet corporis a-<lb />ctionem deſtruit &amp; </s>
          <s xml:space="preserve">corpori vim communicat æqualem illi <lb />quam actione ſua corpus amittit, quare ipſa corporis vis <lb />non mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0206-03" corresp="note-0206-03a" place="margin">522.</note>
              <note xml:space="preserve" xml:id="note-0206-04" corresp="note-0206-04a" place="margin"><hi rend="small caps">TAB. XIX.</hi> <lb />fig. 9.</note>
              <note xml:space="preserve" xml:id="note-0206-05" corresp="note-0206-05a" n="*" anchored="true" place="margin">271.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0207" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0207-01" />
          <label>0207-01</label>
        </figure>
        <pb facs="0207a" />
        <pb facs="0208" />
        <pb facs="0209" n="141" />
        <fw type="head">MATHEMATICA. LIB. I. CAP XXIII.</fw>
        <p>
          <s xml:space="preserve">Ex hiſce patet actione corporis hujus vim, ideoque velo-<lb />
<ptr xml:id="note-0209-01a" corresp="note-0209-01" type="noteAnchor" />
oitatem, non minui ſine ipſius obſtaculi, aut partium hoc <lb />componentium; </s>
          <s xml:space="preserve">translatione ex hac actione oriunda.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0209-01" corresp="note-0209-01a" place="margin">523.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 1.</head>
        <head xml:space="preserve">Demonſtrationes n. 499. 510</head>
        <p>
          <s xml:space="preserve">Dentur duo corpora A &amp; </s>
          <s xml:space="preserve">B; </s>
          <s xml:space="preserve">ſit hujus velocitas b; </s>
          <s xml:space="preserve">illius celeritas a; </s>
          <s xml:space="preserve">velo-<lb />
<ptr xml:id="note-0209-02a" corresp="note-0209-02" type="noteAnchor" />
citas reſpectiva, ſi in contrarias partes ferantur eſt a + b <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hanc dici-
<ptr xml:id="note-0209-03a" corresp="note-0209-03" type="noteAnchor" />
mus d. </s>
          <s xml:space="preserve">Summa virium eſt Aaa + Bbb, quam, manente velocitate reſpecti-<lb />va, diximus omnium minimam poſitis A, B:</s>
          <s xml:space="preserve">: b, a <ptr type="noteAnchor" />, id eſt Aa = Bb.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0209-02" corresp="note-0209-02a" place="margin">524.</note>
              <note xml:space="preserve" xml:id="note-0209-03" corresp="note-0209-03a" n="*" anchored="true" place="margin">475.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">499.</note>
        <p>
          <s xml:space="preserve">Poſitis enim talibus velocitatibus, augeatur a quantitate quacunque e; </s>
          <s xml:space="preserve">vis <lb />corporis A erit nunc Aaa + 2A ae + Aee. </s>
          <s xml:space="preserve">Corporis B velocitas, quia <lb />manet velocitas reſpectiva d = a + b, erit b-e; </s>
          <s xml:space="preserve">nam a + e + b - e = a + b; </s>
          <s xml:space="preserve">er-<lb />go vis corporis B erit Bbb - 2Bbe + Bee, &amp; </s>
          <s xml:space="preserve">ſumma virium eſt Aaa <lb />+ Bbb + Aee + Bee + 2Aae - 2Bbe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sed propter Aa = Bb ſeſe mutuo duo ultimi termini deſtruunt, &amp; </s>
          <s xml:space="preserve">ſum-<lb />ma valet Aaa + Bbb + Aee + Bee, quæ primam excedit. </s>
          <s xml:space="preserve">Similis eſt de-<lb />monſtratio ſi augeatur velocitas b, minutâ, eâdem quantitate, velocitate a; </s>
          <s xml:space="preserve">un-<lb />de patet demonſtratio n. </s>
          <s xml:space="preserve">499.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Poſuimus A, B:</s>
          <s xml:space="preserve">:b, a; </s>
          <s xml:space="preserve">componendo A + B, B:</s>
          <s xml:space="preserve">:b + a = d, a; </s>
          <s xml:space="preserve">ergo <lb />
<ptr xml:id="note-0209-05a" corresp="note-0209-05" type="noteAnchor" />
a = {Bd/A + B}, ſimiliter b = {Ad/A + B}; </s>
          <s xml:space="preserve">idcirco ſumma virium Aaa + Bbb = <lb />{ABBdd + BAAdd/<hi rend="overline">B + A</hi><hi rend="superscript">q</hi>} dividendo numeratorem &amp; </s>
          <s xml:space="preserve">denominatorem per <lb />B + A, quantitas hæc æqualis eſt {ABdd/B + A} ut in n. </s>
          <s xml:space="preserve">510. </s>
          <s xml:space="preserve">monuimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0209-05" corresp="note-0209-05a" place="margin">525.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">Demonſtrationes Algebraicæ n. 513. 516.</head>
        <p>
          <s xml:space="preserve">Geometrice demonſtravimus regulas n. </s>
          <s xml:space="preserve">513. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">516. </s>
          <s xml:space="preserve">algebraice quam ſa-<lb />cillime deducuntur ex propoſitione numeri 512.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit corpus A motum velocitate a; </s>
          <s xml:space="preserve">corpus B agitatum velocitate b: </s>
          <s xml:space="preserve">velo-<lb />citas reſpectiva eſt a - b ſi corpora ad eandem partem tendant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hæc ictu de-
<ptr xml:id="note-0209-06a" corresp="note-0209-06" type="noteAnchor" />
ſtruitur <ptr type="noteAnchor" /> quare eſt ſumma mutationum in velocitatibus corporum poſt ictum.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0209-07a" corresp="note-0209-07" type="noteAnchor" />
B eſt ad A ut mutatio velocitatis in A, ad mutationem velocitatis in B <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0209-08a" corresp="note-0209-08" type="noteAnchor" />
componendo A + B, A:</s>
          <s xml:space="preserve">:a - b, ad mutationem in velocitate corporis B, quæ <lb />
<ptr xml:id="note-0209-09a" corresp="note-0209-09" type="noteAnchor" />
</s>
          <pb facs="0210" n="142" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
mutatio ergo eſt {Aa - Ab/A + B}; </s>
          <s xml:space="preserve">cum velocitas b minor ſit velocitate a, auge-<lb />tur illa in percuſſione: </s>
          <s xml:space="preserve">ideò velocitas corporis B, id eſt velocitas utriuſ-<lb />que corporis <ptr type="noteAnchor" /> poſt impactionem, eſt b + {Aa - Ab/A + B} = {Bb + Aa/A + B} ut ha-
<ptr xml:id="note-0210-01a" corresp="note-0210-01" type="noteAnchor" />
betur in n. </s>
          <s xml:space="preserve">513.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0209-06" corresp="note-0209-06a" place="margin">526.</note>
              <note xml:space="preserve" xml:id="note-0209-07" corresp="note-0209-07a" n="*" anchored="true" place="margin">474.</note>
              <note xml:space="preserve" xml:id="note-0209-08" corresp="note-0209-08a" n="*" anchored="true" place="margin">484.</note>
              <note xml:space="preserve" xml:id="note-0209-09" corresp="note-0209-09a" n="*" anchored="true" place="margin">511.</note>
              <note xml:space="preserve" xml:id="note-0210-01" corresp="note-0210-01a" n="*" anchored="true" place="margin"> 484.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitâ velocitate reſpectiva a + b, tendentibus nempe corporibus in con-<lb />
<ptr xml:id="note-0210-02a" corresp="note-0210-02" type="noteAnchor" />
trarias partes <ptr type="noteAnchor" />, ſimili ratiocinio regula n. </s>
          <s xml:space="preserve">516. </s>
          <s xml:space="preserve">detegitur.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0210-03a" corresp="note-0210-03" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0210-02" corresp="note-0210-02a" place="margin">527.</note>
              <note xml:space="preserve" xml:id="note-0210-03" corresp="note-0210-03a" n="*" anchored="true" place="margin">475.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Haſce ambas regulas de colliſione corporum etiam ex demonſtratis <ptr type="noteAnchor" /> cir-
<ptr xml:id="note-0210-04a" corresp="note-0210-04" type="noteAnchor" />
ca quantitatem vis amiſſæ deduci poſſunt, quam demonſtrationem hìc ſub-<lb />jiciam, ut ſirmitas illorum quæ de viribus inſitis ſuperius demonſtra-<lb />ta ſunt clarius pateat, dum ex ipſis, per vias omnino diverſas, deducimus <lb />regulas experimentis conſirmatas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0210-04" corresp="note-0210-04a" n="*" anchored="true" place="margin">510. 525.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint iterum corpora A &amp; </s>
          <s xml:space="preserve">B; </s>
          <s xml:space="preserve">hujus velocitas b illius a; </s>
          <s xml:space="preserve">tendant ad eandem <lb />
<ptr xml:id="note-0210-05a" corresp="note-0210-05" type="noteAnchor" />
partem, &amp; </s>
          <s xml:space="preserve">velocitas reſpectiva erit a - b.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0210-05" corresp="note-0210-05a" place="margin">528.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Summa virium ante ictum eſt Aaa + Bbb <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">vis ictu deſtructa eſt
<ptr xml:id="note-0210-06a" corresp="note-0210-06" type="noteAnchor" />
{ABaa - 2ABab + ABbb/A + B} <ptr type="noteAnchor" />, ſubtrahendo hancex ſumma virium habemus
<ptr xml:id="note-0210-07a" corresp="note-0210-07" type="noteAnchor" />
vim poſt ictum ſuperſtitem {AAaa + 2ABab + BBbb/A + B}; </s>
          <s xml:space="preserve">corpora poſt i-<lb />ctum non ſeparantur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">maſſa eſt A + B, per quam ſi dividamus vim ſuper-
<ptr xml:id="note-0210-08a" corresp="note-0210-08" type="noteAnchor" />
ſtitem poſt ictum, habemus quadratum velocitatis poſt colliſionem; </s>
          <s xml:space="preserve">quod <lb />quadratum ergo eſt {A Aaa + 2A Bab + BBbb/<hi rend="overline">A + B</hi><hi rend="superscript">q</hi>} = {<hi rend="overline">Aa + Bb</hi><hi rend="superscript">q</hi>/<hi rend="overline">A + B</hi><hi rend="superscript">q</hi>}. </s>
          <s xml:space="preserve">cujus radix <lb />{Aa + Bb/A + B} dat velocitatem quæſitam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0210-06" corresp="note-0210-06a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0210-07" corresp="note-0210-07a" n="*" anchored="true" place="margin">510. 525.</note>
              <note xml:space="preserve" xml:id="note-0210-08" corresp="note-0210-08a" n="*" anchored="true" place="margin">484</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si adhibita velocitate reſpectiva a + b computatio ineatur regula n. </s>
          <s xml:space="preserve">516. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0210-09a" corresp="note-0210-09" type="noteAnchor" />
detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0210-09" corresp="note-0210-09a" place="margin">529.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vulgo quantitas motus, quam ipſius vis inſitæ proportionem ſequi ponunt, <lb />
<ptr xml:id="note-0210-10a" corresp="note-0210-10" type="noteAnchor" />
determinatur multiplicando maſſam non per quadratum velocitatis, ſed per <lb />ipſam velocitatem, ex hocprincipio deduxere Philoſophiipſas illas regulas n. <lb /></s>
          <s xml:space="preserve">513. </s>
          <s xml:space="preserve">516. </s>
          <s xml:space="preserve">quas nos variis methodis ex principiis noſtris deduximus; </s>
          <s xml:space="preserve">mirum <lb />hìc quid contigit, error erroris ſuit deſtructio, &amp; </s>
          <s xml:space="preserve">duplex error ad veritatem <lb />conduxit; </s>
          <s xml:space="preserve">falſum de menſura virium ſecuti ſunt principium, &amp; </s>
          <s xml:space="preserve">quod veri-<lb />tati etiam minime congruum eſt, nullam vim intropremendo partes &amp; </s>
          <s xml:space="preserve">ha-<lb />rum ſuperando cohæſionem corpora amittere poſuere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0210-10" corresp="note-0210-10a" place="margin">530.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0211" n="143" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head xml:space="preserve">De percuſſione corporum lineis rigidis inter ſe cohæ-<lb />rentium, &amp; circa centra agitatorum.</head>
        <p rend="italics">
          <s xml:space="preserve">Sint corpora A &amp; </s>
          <s xml:space="preserve">C, lineâ inflexili conjuncta, &amp; </s>
          <s xml:space="preserve">circa centrum H agitata; </s>
          <s xml:space="preserve">fint <lb />
<ptr xml:id="note-0211-01a" corresp="note-0211-01" type="noteAnchor" />
etiam corpora alia B &amp; </s>
          <s xml:space="preserve">D eodem modo juncta &amp; </s>
          <s xml:space="preserve">circa I agitata.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0211-01" corresp="note-0211-01a" place="margin">531.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin"><hi rend="small caps">TAB. XX.</hi> <lb />fig. 3.</note>
        <p>
          <s xml:space="preserve">Ponamus darihorum corporum percuſſionem directam, quod obtinebit ſi in ſemu-<lb />tuo impingant, unum ex corporibus adhærentibus uni lineæ, cum corpore quo-<lb />cunque ex illis quæ cum alia cohærent lineâ, ut A &amp; </s>
          <s xml:space="preserve">B. </s>
          <s xml:space="preserve">Impactio erit di-<lb />recta ſi hæc corpora directè in ſe mutuo incurrant, quod fieri non poterit <lb />niſi in momento incurſus lineæ quibus corpora cohærent ſint parallelæ in-<lb />ter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si in momento incurſus in quo in eâdem lineâ ambo moventur corpora, <lb />motu quodam communi ferantur non hoc motu in ſe mutuo agent; </s>
          <s xml:space="preserve">impactio <lb />ergo pendebit â velocitate reſpectivâ, qua manente eadem datur partium intro-<lb />
<ptr xml:id="note-0211-03a" corresp="note-0211-03" type="noteAnchor" />
ceſſio <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">eadem vis amiſſa <ptr type="noteAnchor" />, quibuſcunque velocitatibus corpora agi-
<ptr xml:id="note-0211-04a" corresp="note-0211-04" type="noteAnchor" />
tentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0211-03" corresp="note-0211-03a" n="*" anchored="true" place="margin">495.</note>
              <note xml:space="preserve" xml:id="note-0211-04" corresp="note-0211-04a" n="*" anchored="true" place="margin">497</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dari caſum in quo corpora in partes contrarias lata, poſtictum quieſcunt faci-<lb />
<ptr xml:id="note-0211-05a" corresp="note-0211-05" type="noteAnchor" />
le patet; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in hoc caſu, datâ velocitate reſpectivâ, ſummam virium eſſeomnium <lb />minimam etiam liquet, tota enim vis deſtruitur &amp; </s>
          <s xml:space="preserve">minor quantitas nunquam <lb />poteſt deſtrui <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quænam autem ſit ratio velocitatum in hoc caſu di-
<ptr xml:id="note-0211-06a" corresp="note-0211-06" type="noteAnchor" />
cam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0211-05" corresp="note-0211-05a" place="margin">532.</note>
              <note xml:space="preserve" xml:id="note-0211-06" corresp="note-0211-06a" n="*" anchored="true" place="margin">531.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit a diſtantia corporis A â centro H, circa quod rotatur, &amp; </s>
          <s xml:space="preserve">c diſtantia <lb />corporis C ab eodem centro. </s>
          <s xml:space="preserve">Eodem modo ſit b diſtantia corporis B, &amp; </s>
          <s xml:space="preserve">c <lb />diſtantia corporis D, â centro I, circa quod hæc corpora agitantur. </s>
          <s xml:space="preserve">Sit ulte-<lb />rius m velocitas corporis A; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">n velocitas corporis B.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In caſu in quo corpora poſt ictum quieſcunt demonſtramus, poſitis motibus con-<lb />
<ptr xml:id="note-0211-07a" corresp="note-0211-07" type="noteAnchor" />
trariis m, n:</s>
          <s xml:space="preserve">:Bbb + Dddxaa, Aaa + Cccxbb. </s>
          <s xml:space="preserve">id eſt, Aaa + Cccx <lb />bbm = Bbb + Dddxaan.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0211-07" corresp="note-0211-07a" place="margin">533.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In hoc enim caſu ſumma virium, manente velocitate reſpectivâ m + n, eſt o-<lb />
<ptr xml:id="note-0211-08a" corresp="note-0211-08" type="noteAnchor" />
mnium minima.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0211-08" corresp="note-0211-08a" place="margin">534.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Summa virium eſt Amm + {Cccmm/aa} + Bnn + {Dddnn/bb} <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam a, c:</s>
          <s xml:space="preserve">:m,
<ptr xml:id="note-0211-09a" corresp="note-0211-09" type="noteAnchor" />
{mc/a} = velocitati corporis C; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">b, d, :</s>
          <s xml:space="preserve">:n, {dn/b} = velocitati corporis D.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0211-09" corresp="note-0211-09a" place="margin">535.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">470.</note>
        <p>
          <s xml:space="preserve">Ponamus nunc velocitatem m augeri quantitate e, &amp; </s>
          <s xml:space="preserve">eadern quantitate mi-<lb />nui velocitatem n, ut velocitas reſpectiva maneat; </s>
          <s xml:space="preserve">videbimus ſummam eſſe <lb />majorem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Velocitas corporis A nunc eſt m + e; </s>
          <s xml:space="preserve">Corporis C eſt {mc + ec/a}; </s>
          <s xml:space="preserve">corporis B
</s>
          <pb facs="0212" n="144" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
eſt m - e; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tandem celeritas corporis D eſt {nd - ed/b}. </s>
          <s xml:space="preserve">Summa virium nunc <lb />erit Amm + 2Ame + Acc + {Cccmm + 2Cccme + Cccee/aa} + Bnn - 2Bne <lb />+ Bee + {Dddnn - 2Dddne + Dddee/bb}. </s>
          <s xml:space="preserve">Sed <hi rend="overline">Aaa + Ccc</hi> x bbm <lb />= <hi rend="overline">Bbb + Ddd</hi> x aan; </s>
          <s xml:space="preserve">ponimus enim de hoc caſu agi; </s>
          <s xml:space="preserve">dividendo hanc <lb />æquationem per aabb, habemus Am + {Cccm/aa} = Bn + {Dddn/bb}; </s>
          <s xml:space="preserve">idcirco <lb />in ultima ſumma ſeſe mutuo deſtruunt + 2Ame + {2Cccme/aa} &amp; </s>
          <s xml:space="preserve">- 2Bne -<lb />{2Dddne/bb} &amp; </s>
          <s xml:space="preserve">ſumma ad hanc reducitur Amm + Aee + {Cccmm + Cccee/aa} <lb />+ Bnn + Bee + {Dddnn + {Dddee/bb} quæ primâ memoratâ ſummâ major <lb />eſt. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Nec diverſa eſt demonſtratio ſi augeatur n, imminutâ velocitate m.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vis in colliſione quacunque, datâ velocitate reſpectivâ, deſtructa determi-<lb />
<ptr xml:id="note-0212-01a" corresp="note-0212-01" type="noteAnchor" />
nari poteſt, nam valet ſummam virium in caſu in quo hæc minima eſt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sit
<ptr xml:id="note-0212-02a" corresp="note-0212-02" type="noteAnchor" />
nunc m + n = r.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0212-01" corresp="note-0212-01a" place="margin">536.</note>
              <note xml:space="preserve" xml:id="note-0212-02" corresp="note-0212-02a" n="*" anchored="true" place="margin">531.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datur ratio inter m &amp; </s>
          <s xml:space="preserve">n <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">componendo
<ptr xml:id="note-0212-03a" corresp="note-0212-03" type="noteAnchor" />
<hi rend="overline">Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + Ddd</hi> x aa, <hi rend="overline">Aaa x Ccc</hi> x bb:</s>
          <s xml:space="preserve">: <lb />m + n = r, n; <lb /></s>
          <s xml:space="preserve">ergo n = {<hi rend="overline">Aaa + Ccc</hi> x bbr/<hi rend="overline">Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + Ddd</hi> x aa}. </s>
          <s xml:space="preserve">Eodem modo detegi-<lb />mus m = {<hi rend="overline">Bbb + Ddd</hi> x aar/Aaa x Ccc x bb + <hi rend="overline">Bbb + Ddd</hi> x aa}. </s>
          <s xml:space="preserve">Summa virium eſt <lb />{<hi rend="overline">Aaa + Ccc</hi> x mm/aa} + {<hi rend="overline">Bbb + Ddd</hi> x nn/bb} <ptr type="noteAnchor" />, ſubſtituendo pro m &amp; </s>
          <s xml:space="preserve">n
<ptr xml:id="note-0212-04a" corresp="note-0212-04" type="noteAnchor" />
valores ſumma hæc erit <lb />{<hi rend="overline">Aaa + Ccc</hi> x <hi rend="overline">Bbb + Ddd</hi><hi rend="superscript">q</hi> x aarr + <hi rend="overline">Bbb + Ddd</hi> x <hi rend="overline">Aaa + Ccc</hi><hi rend="superscript">q</hi> x bbrr/{<hi rend="overline">/Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + Ddd x aa</hi><hi rend="superscript">q</hi>} <lb />Dividendo numeratorem &amp; </s>
          <s xml:space="preserve">denominatorem per <hi rend="overline">Aaa + Ccc</hi> x bb +
</s>
          <pb facs="0213" n="145" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XXIII.</fw>
<hi rend="overline">Bbb + Ddd</hi> x aa; </s>
          <s xml:space="preserve">habemus {<hi rend="overline">Aaa + Ccc</hi> x <hi rend="overline">Bbb + Ddd</hi> x rr/<hi rend="overline">Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + D dd</hi> x aa} vim <lb />
<ptr xml:id="note-0213-01a" corresp="note-0213-01" type="noteAnchor" />
amiſſam data velocitate reſpectivar.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0212-03" corresp="note-0212-03a" n="*" anchored="true" place="margin">533.</note>
              <note xml:space="preserve" xml:id="note-0212-04" corresp="note-0212-04a" n="*" anchored="true" place="margin">535</note>
              <note xml:space="preserve" xml:id="note-0213-01" corresp="note-0213-01a" place="margin">537.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si Corpora memorata A &amp; </s>
          <s xml:space="preserve">B, cum reliquis circa centra I &amp; </s>
          <s xml:space="preserve">H agitata, ve-<lb />
<ptr xml:id="note-0213-02a" corresp="note-0213-02" type="noteAnchor" />
locitatibus quibuſcunque in ſe mutuo incurrant directè, poſt ictum ambo eâ-<lb />dem velocitate feruntur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſeparantur non ex actione corporum, ſed quia
<ptr xml:id="note-0213-03a" corresp="note-0213-03" type="noteAnchor" />
circa centra diverſa H &amp; </s>
          <s xml:space="preserve">I moventur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0213-02" corresp="note-0213-02a" place="margin">538.</note>
              <note xml:space="preserve" xml:id="note-0213-03" corresp="note-0213-03a" n="*" anchored="true" place="margin">484.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus dari punctum quod eadem velocitate fertur, qua corpora poſt <lb />ictum ante ſeparationem ſeruntur, &amp; </s>
          <s xml:space="preserve">juxta eandem directionem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Reſpectu hujus puncti corpora poſt impactionem quieſcunt; </s>
          <s xml:space="preserve">ideo reſpectu <lb />ipſius anteictum contrariis velocitatibus movebantur in ratione <hi rend="overline">Bbb + Ddd</hi> <lb />x aa ad <hi rend="overline">Aaa + Ccc</hi> x bb <ptr type="noteAnchor" />, haſque velocitates amittunt, cum reſpectu puncti
<ptr xml:id="note-0213-04a" corresp="note-0213-04" type="noteAnchor" />
poſt ictum quieſcant, quare hæ ipſæ velocitates ſunt mutationes, quæ ex ictu <lb />in velocitatibus contingunt, quæ ergo mutationes ſunt in memoratà ratione; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">componendo <hi rend="overline">Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + Ddd</hi> x aa ad <hi rend="overline">Aaa + Ccc</hi> x bb <lb />ut ſumma mutationum, id eſt velocitas reſpectiva, ad mutationem in veloci-<lb />tate corporis B.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0213-04" corresp="note-0213-04a" n="*" anchored="true" place="margin">533.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc velocitas corporis A dicatur p; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">q velocitas corporis B, poſita <lb />hac minori; </s>
          <s xml:space="preserve">velocitas reſpectiva erit p-q ſi motus eandem partem verſus <lb />dirigantur, &amp; </s>
          <s xml:space="preserve">mutatio velocitatis corporis B, detegitur <lb />{<hi rend="overline">Aaa + Ccc</hi> x bbp - <hi rend="overline">Aaa + Ccc</hi> x bbq/<hi rend="overline">Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + Ddd</hi> x aa} quæ mutatio eſt velocitas <lb />acquiſita; </s>
          <s xml:space="preserve">quia minor velocitas in motibus conſpirantibus augetur: </s>
          <s xml:space="preserve">quare ſi <lb />addatur ipſi velocitati q habemus velocitatem amborum corporum <lb />poſt ictum; </s>
          <s xml:space="preserve">quæ ergo eſt {<hi rend="overline">Aaa + Ccc</hi> x bbp + <hi rend="overline">Bbb + Ddd</hi> x aaq/<hi rend="overline">Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + Ddd</hi> x aa}. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0213-05a" corresp="note-0213-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0213-05" corresp="note-0213-05a" place="margin">539.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si motus in contrariam partem dirigantur velocitas reſpectiva eſt p + q &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0213-06a" corresp="note-0213-06" type="noteAnchor" />
velocitas poſt ictum ſimili ratiocinio detegitur <lb />{<hi rend="overline">Aaa + Ccc</hi> x bbp - <hi rend="overline">Bbb + Ddd</hi> x aaq/<hi rend="overline">Aaa + Ccc</hi> x bb + <hi rend="overline">Bbb + Ddd</hi> x aa} ſubtracto nempe in nu-<lb />meratore producto minore ex majore.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0213-06" corresp="note-0213-06a" place="margin">540.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Clarè patet non intereſſe utrum in hac colliſione corpora, quæ eidem lineæ <lb />
<ptr xml:id="note-0213-07a" corresp="note-0213-07" type="noteAnchor" />
juguntur, ad eandem partem dentur centri circa quod linea movetur, an ad <lb />partes diverſas, nam eodem niodo corpus movetur, à quacunque parte centri <lb />detur, ſimodo diſtantia ab hoc ſit eadem, vim etiam centrifugam, qua corpora <lb />a centro recedere conantur, &amp; </s>
          <s xml:space="preserve">actiones quas, dum concurrunt, in retinacu-<lb />la exerunt, non hîc conſiderari debere, ſatis manifeſtum eſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0213-07" corresp="note-0213-07a" place="margin">541.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">523.</note>
        <p>
          <s xml:space="preserve">Demonſtrata hæc ad numerum quemcunque corporum poſſunt applicari, &amp; </s>
          <s xml:space="preserve">u-<lb />
<ptr xml:id="note-0213-09a" corresp="note-0213-09" type="noteAnchor" />
niverſales regulæ ex demonſtratis quam facillime illiciuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0213-09" corresp="note-0213-09a" place="margin">542.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Videmus etiam quid obtineat, Si corpus in lineâ rectâ motum directè in aliudin-<lb />
<ptr xml:id="note-0213-10a" corresp="note-0213-10" type="noteAnchor" />
currat quod cum aliis lineæ rectæ, circa centrum mobili, cohæret; </s>
          <s xml:space="preserve">Corpus enim il-<lb />lud in linea recta motum agit quaſi lineæ rectæ, circa punctum quodcunque <lb />mobili, adhæreret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0213-10" corresp="note-0213-10a" place="margin">543.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0214" n="146" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Quieſcant corpora A &amp; </s>
          <s xml:space="preserve">Cin a &amp; </s>
          <s xml:space="preserve">c, dum ut ante mobilia ſunt circa H. </s>
          <s xml:space="preserve">Po-<lb />namus B aut b in linea recta motum, velociate q directè &amp; </s>
          <s xml:space="preserve">perpendiculariter <lb />ad a H incurrere in a; </s>
          <s xml:space="preserve">velocitatem poſt ictum detegimus ipſâ formulâ præcedenti. <lb /></s>
          <s xml:space="preserve">Pono enim B cum linea cohærere &amp; </s>
          <s xml:space="preserve">agitari circa centrum ad diſtantiam quam-<lb />cunque b; </s>
          <s xml:space="preserve">in hac colliſione p &amp; </s>
          <s xml:space="preserve">D æquales ſunt nihilo, ideo evaneſcunt quan-<lb />titates, quæ per has multiplicantur quare memoratâ formula <ptr type="noteAnchor" /> in hanc mu-
<ptr xml:id="note-0214-01a" corresp="note-0214-01" type="noteAnchor" />
tatur {Bbbaaq/<hi rend="overline">Aaa + Ccc</hi> x bb + Bbbaa} = {Baaq/Aaa + Ccc + Baa}: </s>
          <s xml:space="preserve">ex qua <lb />banc deducimus regulam. </s>
          <s xml:space="preserve">Corpus impingens per quadratum diſtantiæ puncti, in <lb />quod incurrit, âcextro, &amp; </s>
          <s xml:space="preserve">per velocitatem ſuam multiplicatur, productumque boc <lb />dividitur per ſummam omnium corporum, ſingulorum multiplicatorum per quadrata <lb />ſuarum diſtantiarum à centro.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0214-01" corresp="note-0214-01a" n="*" anchored="true" place="margin">539.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propoſitiones n. </s>
          <s xml:space="preserve">500. </s>
          <s xml:space="preserve">510. </s>
          <s xml:space="preserve">512. </s>
          <s xml:space="preserve">513. </s>
          <s xml:space="preserve">516. </s>
          <s xml:space="preserve">ſunt caſus peculiares propoſi-<lb />
<ptr xml:id="note-0214-02a" corresp="note-0214-02" type="noteAnchor" />
tionum in hoc Scholio in n. </s>
          <s xml:space="preserve">533. </s>
          <s xml:space="preserve">537. </s>
          <s xml:space="preserve">538. </s>
          <s xml:space="preserve">539. </s>
          <s xml:space="preserve">540. </s>
          <s xml:space="preserve">demonſtratarum, ut <lb />patet, ſi ponamus duo corpora quæ cum lineis, circa centra quæcunque mo-<lb />bilibus, cohærent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0214-02" corresp="note-0214-02a" place="margin">544.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 3.</head>
        <head rend="italics" xml:space="preserve">Examen Experimenti circa corpora in lancem, aut <lb />brachium, libræ impingentia.</head>
        <p>
          <s xml:space="preserve">Merſennus, de Lanis, &amp; </s>
          <s xml:space="preserve">alii experimentum dedere circa corpora caden-<lb />
<ptr xml:id="note-0214-03a" corresp="note-0214-03" type="noteAnchor" />
tia inſtitutum, &amp; </s>
          <s xml:space="preserve">notarunt corpus in lancem libræ impingens, pondus ma-<lb />jus, in lance oppoſitâ, paululum elevare; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pondera ſic elevari ad exiguam, ſed <lb />æqualem (quam tamen circumſtantiam non notat Merſennus) altitudinem, <lb />ſi corpus quod impingit cadat ab altitudinibus quæ ſunt ut quadrata pon-<lb />derum quæ elevantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0214-03" corresp="note-0214-03a" place="margin">545.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Merſennus tamen notat in quibuſdam circumſtantiis experimentum non pro-<lb />ceſſiſſe, quod &amp; </s>
          <s xml:space="preserve">mihi contigit, experimentum paululum aliter inſtituenti, quod <lb />defectui machinæ tribuebam, &amp; </s>
          <s xml:space="preserve">in illis ſolis altitudinibus, in quibus regulam <lb />ſatis exacte obſervari videbam, defectus, qui in machina me non latebant, <lb />minus noxios credebam. </s>
          <s xml:space="preserve">Cum autem attentius rem examinarem me toto <lb />cælo erraſſe percepi, &amp; </s>
          <s xml:space="preserve">ipſis illis principiis Mechanices, de quibus inter omnes <lb />convenit, adverſari, memoratam dari inter quadrata ponderum elevatorum <lb />proportionem, quæ datur inter altitudines, a quibus cadit corpus, quod in lancem, <lb />aut brachium oppoſitum, impingit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in dubium vocare non potui ipſi defe-<lb />ctui machinæ tribuendum eſſe, ſi aliquando inter certos limites hæc dete-<lb />gatur proportio, ut mihi ſemper contigerat. </s>
          <s xml:space="preserve">Non ſenſibilis fateor dabitur <lb />error, ſi corpus cadens, &amp; </s>
          <s xml:space="preserve">pondustotius libræ, id eſt, jugi &amp; </s>
          <s xml:space="preserve">lancium, admodum <lb />exigua fuerint reſpectu ponderum elevatorum: </s>
          <s xml:space="preserve">ſed in hoc caſu experimen-<lb />tum inſtitui non poterit; </s>
          <s xml:space="preserve">majus enim pondus ſubtiliori libræ imponi non po-<lb />teſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut autem, quæ hoc experimentum ſpectant, clarius paterent, Machinam con-
</s>
          <pb facs="0215" n="147" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
ſtrui curavi, qua, quantum poteſt exacte, &amp; </s>
          <s xml:space="preserve">omnino ſine ſenſibili errore, ex-<lb />perimentum inſtituitur: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">poſt experimentum inſtitutum circa hoc com-<lb />putationem inivi.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">BILANX</head>
        <head rend="italics" xml:space="preserve">Qua altitudines conferuntur, a quibus corpus cadens, pondera <lb />paululum elevat.</head>
        <p>
          <s xml:space="preserve">Libræ jugum eſt AB; </s>
          <s xml:space="preserve">pede ſuſtinetur, dum circa centrum, ut in aliis li-<lb />
<ptr xml:id="note-0215-01a" corresp="note-0215-01" type="noteAnchor" />
bris, volubile eſt: </s>
          <s xml:space="preserve">Lanx L ferrea eſt; </s>
          <s xml:space="preserve">oppoſita M eſt lignea &amp; </s>
          <s xml:space="preserve">orbicularis, <lb />
<ptr xml:id="note-0215-02a" corresp="note-0215-02" type="noteAnchor" />
excavata ad profunditatem pollicis. </s>
          <s xml:space="preserve">Hæc, ubi experimenta inſtituenda ſunt, <lb />argillâ molli repletur, quæ cultro ligneo abraditur, ut inæqualitatibus exem-<lb />ptam, &amp; </s>
          <s xml:space="preserve">horizontalem, habeat ſuperficiem; </s>
          <s xml:space="preserve">qua de cauſa lanx hæc faciletol-<lb />li poteſt, iterumque in loco ſuo ſuſpendi. </s>
          <s xml:space="preserve">Diſtantia B M excedit pedes tres, <lb />quare in menſæ extremitate ponenda Machina eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0215-01" corresp="note-0215-01a" place="margin">546.</note>
              <note xml:space="preserve" xml:id="note-0215-02" corresp="note-0215-02a" place="margin">TAB. XX. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus G filo ſuſpenditur, &amp; </s>
          <s xml:space="preserve">unco laminæ D cohærenti alligatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pondus Q lanci L imponitur, ut detur æquilibrium. </s>
          <s xml:space="preserve">Quibus poſitis, adji-<lb />citur pondus ictu elevandum P, &amp; </s>
          <s xml:space="preserve">ut jugum in ſitu maneat horizontali, bra-<lb />chium A, quod nunc magis gravatur, gnomone ferreo, cum pede cohæren-<lb />ti, ſuſtinetur. </s>
          <s xml:space="preserve">Facile videmus alio pede, gnomone deſtituto, ſuſtineri debe-<lb />re machinam ante impoſitum pondus P, ut de æquilibrio conſtet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Gnomoni in f annectitur lamina elaſtica tenuis fg, quæ extenſa ad i, per-<lb />tingit, ubi extremitas g retinetur, ope laminæ minimæ i, quæ cum brachio <lb />A cohæret; </s>
          <s xml:space="preserve">paululum elevato brachio laxatur g; </s>
          <s xml:space="preserve">unde conſtare poteſt in va-<lb />riis tentaminibus æqualiter elevati, ſi nempe, paululum tantum imminuto i-<lb />ctu, quo agitatur libra, elaſterium non relaxetur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>.</head>
        <p>
          <s xml:space="preserve">Omnibus ut dictum diſpoſitis, poſitoque pondere P æquali unciis quatuor; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0215-03a" corresp="note-0215-03" type="noteAnchor" />
globum G ita ſuſpendi, ut ipſius altitudo, diſtantia nempe inter inferiorem <lb />partem globi &amp; </s>
          <s xml:space="preserve">argillæ ſuperficiem, foret pollicum 6 {7/8}, &amp; </s>
          <s xml:space="preserve">abſciſſo filo, im-<lb />pactione globi, laxata eſt lamina fg: </s>
          <s xml:space="preserve">repetitoque variis vicibus experimen-<lb />to eodem modo proceſſit hoc; </s>
          <s xml:space="preserve">imminuta autem altitudine, quartâ parte polli-<lb />cis, aut etiam minus, nunquam elaſterium fuit relaxatum, qua eadem metho-<lb />do ſequentes altitudines fuere determinatæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0215-03" corresp="note-0215-03a" place="margin">547.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Duplicato pondere P, altitudo globi fuit pollicum 14 {1/8}</s>
        </p>
        <p>
          <s xml:space="preserve">Tandem triplicato pondere P, id eſt, poſito hoc duodecim unciarum altitu-<lb />do fuit 23 {1/2} pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">His omnibus altitudinibus cavitatum ictibus in argillâ formatarum profun-<lb />ditates addendæ ſunt, &amp; </s>
          <s xml:space="preserve">altitudines neglectis exiguis fractionibus erunt <lb />7. </s>
          <s xml:space="preserve">14 {5/16}. </s>
          <s xml:space="preserve">23 {3/4}.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si hac eâdem machinâ eadem inſtituantur Experimenta, aliâ adhibitâ argil-<lb />lâ, altitudines paululum variari poſſunt. </s>
          <s xml:space="preserve">Si argilla minus mollis ſit cavitates <lb />minores erunt, &amp; </s>
          <s xml:space="preserve">altitudines ſupra argillæ ſuperficiem planam majores, in-<lb />tegræ autem altitudines eædem. </s>
          <s xml:space="preserve">Sed ſi magis aut minus ponderet argilla, il-<lb />lud diſcrimen dabit, nam, licet eo non mutetur materia elevanda, materia ta-<lb />men movenda mutatur, unde diſcrimen neceſſario ſequitur, ut hoc compu-<lb />tatione ſequenti clarius patebit.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0216" n="148" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Jugum Bilancis figuram habet quæ in AB repræſentatur, in ipſis locis A &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0216-01a" corresp="note-0216-01" type="noteAnchor" />
B excavatur, ut hoc in fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">videri poteſt, de cætero ubique eſt ejuſdem <lb />
<ptr xml:id="note-0216-02a" corresp="note-0216-02" type="noteAnchor" />
craſſitiei.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0216-01" corresp="note-0216-01a" place="margin">548.</note>
              <note xml:space="preserve" xml:id="note-0216-02" corresp="note-0216-02a" place="margin">TAB. XX. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propter figuram irregularem, admodum difficilis foret computatio; </s>
          <s xml:space="preserve">ideo, <lb />ſervato jugi pondere, mutatam concepi figuram; </s>
          <s xml:space="preserve">remotis partibus quibuſdam <lb />à centro, &amp; </s>
          <s xml:space="preserve">admotis aliis, poſuique figuram illam eſſe, quæ repræſentatur in <lb />fig. </s>
          <s xml:space="preserve">6.</s>
          <s xml:space="preserve">, in qua tota longitudo illa eſt, quæ in Bilance inter puncta ſuſpen-<lb />ſionis datur; </s>
          <s xml:space="preserve">ex qua mutatione exiguus tantum error in computatione dari <lb />poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hujus figuræ ſuperficies, cum jugum ejuſdem ſit craſſitudinis ubique, re-<lb />præſentare poteſt jugi pondus in omnibus partibus. </s>
          <s xml:space="preserve">Figura hæc AB conſt@t <lb />ex parallelogrammo &amp; </s>
          <s xml:space="preserve">duobus triangulis: </s>
          <s xml:space="preserve">junctis triangulis, figura reducitur ad <lb />illam quæ in fig. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">exhibetur, qua adſumtâ computationem inibo.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hunc uſum computatio hæc habere poterit, quod inde patebit, cum <lb />demonſtratis circa percuffionem experimenta noſtra congruere. </s>
          <s xml:space="preserve">Fundamentum <lb />autem ipſius computationis habetur in n. </s>
          <s xml:space="preserve">543.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ante omnia ſingula puncta ſuperficiei ADEB, pondus jugi repræſentan-<lb />
<ptr xml:id="note-0216-03a" corresp="note-0216-03" type="noteAnchor" />
tis, per quadrata diſtantiarum ſuarum a centro motus reſpective multiplicari <lb />debent. </s>
          <s xml:space="preserve">Hoc ſine errore ſenſibili fiet, ſi loco diſtantiarum a centro, di-<lb />ſtantiæ a lineâ CF uſurpentur, quo computatio facilior evadit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0216-03" corresp="note-0216-03a" place="margin">TAB. XX. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc operatio pro parallelogrammo inſtituatur, ſingulæ lineæ parallelæ &amp; </s>
          <s xml:space="preserve"><lb />æquales lineæ DA, per quadratum ſuæ diſtantiæ à CF multiplicandæ ſunt, <lb />id eſt, ſingula hæc quadrata per eandem quantitatem AB aut CG multiplica-<lb />ri debent, id eſt, ſumma quadratorum per CG multiplicanda eſt; </s>
          <s xml:space="preserve">ſumma au-<lb />tem quadratorum eſt pyramis, cujus baſis eſt quadratum AC &amp; </s>
          <s xml:space="preserve">altitudo ea-<lb />dem AC, quæ pyramis valet {1/3} AC<hi rend="superscript">c</hi> <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Multiplicata hac per CG habemus
<ptr xml:id="note-0216-04a" corresp="note-0216-04" type="noteAnchor" />
{1/3} CG x AC x AC<hi rend="superscript">q</hi> ſummam productorum ſingulorum punctorum paralle-<lb />logrammi DC, multiplicatorum per quadrata diſtantiarum ſuarum a <lb />CG.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0216-04" corresp="note-0216-04a" n="*" anchored="true" place="margin">7. El. XII.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Similis ſumma pro ſingulis punctis trianguli DCG æqualis eſt, {1/12} GF <lb />x AC x AC<hi rend="superscript">q</hi>. </s>
          <s xml:space="preserve">Hoc facile detegent ſubtilioris Geometriæ gnari, &amp; </s>
          <s xml:space="preserve">aliis il-<lb />lud explicare inutiliter laborarem. </s>
          <s xml:space="preserve">Duplicando producta hæc habebimus ſi-<lb />milem ſummam pro integra figura ADFEB; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eſt {2/3} CG x AC x AC<hi rend="superscript">q</hi> <lb />+ {1/6} GF x AC x AC<hi rend="superscript">q</hi>, = b x AC<hi rend="superscript">q</hi>; </s>
          <s xml:space="preserve">ponendo b = {2/3} CG x AC + {1/6} GF x <lb />AC.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">His poſitis dicatur a altitudo a qua globus dimittitur, &amp; </s>
          <s xml:space="preserve">velocitas ca-<lb />
<ptr xml:id="note-0216-05a" corresp="note-0216-05" type="noteAnchor" />
dendo acquiſita, qua globus in lancem Mincurrit, &amp; </s>
          <s xml:space="preserve">quæ radici quadratæ <lb />hujus altitudinis proportionalis eſt <ptr type="noteAnchor" />, poterit √ a deſignare.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0216-05" corresp="note-0216-05a" place="margin">549.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">255</note>
        <p>
          <s xml:space="preserve">Multiplicando hanc velocitatem per globum G (fig 4.) </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">per quadratum di-<lb />ſtantiæ AC, &amp; </s>
          <s xml:space="preserve">dividendo hoc productum per ſummam omnium corporum <lb />in experimento motorum, reſpectivè multiplicatorum per quadrata diſtantia-<lb />rum ſuarum a centro motus, habemus velocitatem puncti A poſt ictum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">543.</note>
        <p>
          <s xml:space="preserve">Partem hujus ſummæ jam determinavimus, quoad jugum nempe, quod ſu-<lb />pereſt habemus multiplicando pondera lancium L &amp; </s>
          <s xml:space="preserve">M, ut &amp; </s>
          <s xml:space="preserve">P, Q, &amp; </s>
          <s xml:space="preserve">G (fig. <lb /></s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">per quadratum diſtantiæ AC, nam omnia hæc corpora conſiderari poſſunt <lb />quaſi darentur in ipſis punctis ſupenſionis A &amp; </s>
          <s xml:space="preserve">B<ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Summam ponderum lan-
<ptr xml:id="note-0216-08a" corresp="note-0216-08" type="noteAnchor" />
</s>
          <pb facs="0217" n="149" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
cium ut &amp; </s>
          <s xml:space="preserve">P, Q, &amp; </s>
          <s xml:space="preserve">G, dicimus c, &amp; </s>
          <s xml:space="preserve">velocitas puncti A poſt ictum erit <lb />{AC<hi rend="superscript">q</hi> x Gva/b x AC<hi rend="superscript">q</hi> + c x AC<hi rend="superscript">q</hi>} = {Gva <ptr type="noteAnchor" />/b + c}.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0217-01a" corresp="note-0217-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0216-08" corresp="note-0216-08a" n="*" anchored="true" place="margin">128.</note>
              <note xml:space="preserve" xml:id="note-0217-01" corresp="note-0217-01a" n="*" anchored="true" place="margin">543.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut, data hac velocitate, altitudinem ad quam elevatur punctum A cumal-<lb />titudine a conferamus, determinandum eſt centrum oſcillationis, quod mo-<lb />vetur ut corpus in quod gravitas tantum agit <ptr type="noteAnchor" />, diſtantia autem centri oſcil-
<ptr xml:id="note-0217-02a" corresp="note-0217-02" type="noteAnchor" />
lationis a centro motus eſt {b x AC<hi rend="superscript">q</hi> + c x AC<hi rend="superscript">q</hi>/P x AC <ptr type="noteAnchor" />} = {b x AC + c x AC/P}.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0217-03a" corresp="note-0217-03" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0217-02" corresp="note-0217-02a" n="*" anchored="true" place="margin">296.</note>
              <note xml:space="preserve" xml:id="note-0217-03" corresp="note-0217-03a" n="*" anchored="true" place="margin">3127</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diſtantia autem AC ſe habet ad diſtantiam hanc centri oſcillationis, id eſt <lb />(multiplicando utramque diſtantiam per P, &amp; </s>
          <s xml:space="preserve">dividendo per AC) P ad <lb />b + c, ut velocitas puncti A ad velocitatem centri oſcillationis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in eadem <lb />ratione altitudo ad quam adſcendit A, quam dicimus d, ad altitudinem ad <lb />quam adſcendit centrum oſcillationis; </s>
          <s xml:space="preserve">ergo <lb />P, b + c:</s>
          <s xml:space="preserve">: {Gva/b + c}, {Gva/P} = velocitati centri oſcillationis. </s>
          <s xml:space="preserve">Et <lb />P, b + c:</s>
          <s xml:space="preserve">: d {db + dc/P} = altitudini, ad quam centrum oſcillationis adſcendit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Altitudo hæc etiam quadrato velocitatis hujus centri exprimitur, cum a ex-<lb />primat altitudinem ad quam corpus velociate √ a pertingit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0217-04a" corresp="note-0217-04" type="noteAnchor" />
Habemus ergo hanc æquationem {G<hi rend="superscript">q</hi> x a/P<hi rend="superscript">q</hi>} = {db + dc/P} id eſt G<hi rend="superscript">q</hi> x a = db <lb />x P + dc x P: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">a = {<hi rend="overline">b + c</hi> x d x P/G<hi rend="superscript">q</hi>}</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0217-04" corresp="note-0217-04a" n="*" anchored="true" place="margin">255. 261.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pro litteris ut numeri ſubſtituantur, conſiderandum, b æquale eſſe {2/3} GC <lb />
<ptr xml:id="note-0217-05a" corresp="note-0217-05" type="noteAnchor" />
x AC + {1/6}-GF x AC, dum ipſa figura ADFHB, id eſt <hi rend="superscript">2</hi>GC x AC + <lb />GF x AC <ptr type="noteAnchor" />, Jugi pondus repræſentat; </s>
          <s xml:space="preserve">quare hoc pondus jugi ad b, ut
<ptr xml:id="note-0217-06a" corresp="note-0217-06" type="noteAnchor" />
<hi rend="superscript">2</hi>GC + GF ad {2/3} GC + {1/6} GF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0217-05" corresp="note-0217-05a" place="margin">550.</note>
              <note xml:space="preserve" xml:id="note-0217-06" corresp="note-0217-06a" n="*" anchored="true" place="margin">34. El. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In noſtra machina eſt GC ad GF ut 3 ad 4. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">jugi pondus novemdecim <lb />unciarum cum dragmis duabus &amp; </s>
          <s xml:space="preserve">ſcrupulo uno, id eſt ſcrupulorum 463, <lb />Ergo 15, 4:</s>
          <s xml:space="preserve">: 463, b = 123 {1/2}. </s>
          <s xml:space="preserve">ſcrup.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pondera lancium additis Q &amp; </s>
          <s xml:space="preserve">G id eſt c-P valent 1320. </s>
          <s xml:space="preserve">ſcrupula; </s>
          <s xml:space="preserve">Globus <lb />G, ponderat ſcrupula 67; </s>
          <s xml:space="preserve">altitudo d æqualis eſto, 21. </s>
          <s xml:space="preserve">poll. </s>
          <s xml:space="preserve">id eſt, excedit paulu-<lb />lum quintam pollicis partem.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0218" n="150" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Et præcedens æquatio mutatur in hanc <lb />{a = {<hi rend="overline">b + </hi> c x d x P/G<hi rend="superscript">q</hi>} = {<hi rend="overline">123 {1/2} + 1320 + P</hi> x 21P/67<hi rend="superscript">q</hi> x 100} = {<hi rend="overline">1443 {1/2} + P</hi> x 21P/448900}</s>
        </p>
        <p>
          <s xml:space="preserve">Subſtituendo ſucceſſive pro P quatuor, octo, &amp; </s>
          <s xml:space="preserve">duodecim uncias, id eſt, <lb />ſcrupula 96, 192, 288 detegimus a = 6, 91. </s>
          <s xml:space="preserve">a = 14, 68; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">a = 23, 32.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæ altitudines parum admodum differunt cum altitudinibus experimento de-<lb />tectis; </s>
          <s xml:space="preserve">differentia autem tribuenda eſt mutationi figuræ jugi in computatione <ptr type="noteAnchor" />
<ptr xml:id="note-0218-01a" corresp="note-0218-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0218-01" corresp="note-0218-01a" n="*" anchored="true" place="margin">548.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 4.</head>
        <head rend="italics" xml:space="preserve">De Centro oſcillationis, &amp; percuſſionis.</head>
        <p>
          <s xml:space="preserve">Superius <ptr type="noteAnchor" />, ex demonſtratis circa preſſionem, deduximus methodum determi-
<ptr xml:id="note-0218-02a" corresp="note-0218-02" type="noteAnchor" />
nandi centrum oſcillationis; </s>
          <s xml:space="preserve">eandem ibi traditam regulam quàm facilli-<lb />
<ptr xml:id="note-0218-03a" corresp="note-0218-03" type="noteAnchor" />
me deducimus ex demonſtratis circa vires.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0218-02" corresp="note-0218-02a" place="margin">551.</note>
              <note xml:space="preserve" xml:id="note-0218-03" corresp="note-0218-03a" n="*" anchored="true" place="margin">311. 312.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus eandem acquirit velocitatem, ideoque vim, a certa altitudine caden-<lb />do, quamcunque viam in deſcenſu ſequatur <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">vis acquiſita huic altitudini
<ptr xml:id="note-0218-04a" corresp="note-0218-04" type="noteAnchor" />
proportionalis eſt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Dum corpora pendulo compoſito juncta deſcendunt
<ptr xml:id="note-0218-05a" corresp="note-0218-05" type="noteAnchor" />
nulla actione vis deſcendendo acquiſita deſtruitur; </s>
          <s xml:space="preserve">nihil etiam datur quoau-<lb />geri poſſet, ergo ſumma virium æqualis eſt ſummæ virium quas corpora, <lb />ſeparatim a ſuis altitudinibus cadendo, pot uiſſent acquirere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0218-04" corresp="note-0218-04a" n="*" anchored="true" place="margin">271.</note>
              <note xml:space="preserve" xml:id="note-0218-05" corresp="note-0218-05a" n="*" anchored="true" place="margin">448.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint corpora A, B, C, D, diſtantiæ a puncto ſuſpenſionis a, b, c, &amp; </s>
          <s xml:space="preserve">d. </s>
          <s xml:space="preserve">Alti-<lb />tudines, a quibus corporahæc deſcendunt, ſunt ut a, b, c, &amp; </s>
          <s xml:space="preserve">d &amp; </s>
          <s xml:space="preserve">in eadem ra-<lb />tione velocitates. </s>
          <s xml:space="preserve">Dicatur diſtantia centri oſcillationis à puncto ſuſpenſio-<lb />nis x, &amp; </s>
          <s xml:space="preserve">velocitas acquiſ@ta deſcendendo ab altitudine a qua centrum hoc deſcen-<lb />dit √ x; </s>
          <s xml:space="preserve">ideò velocitas corporis A, ſi libere cecidiſſet, fuiſſet √ a <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">ipſius
<ptr xml:id="note-0218-06a" corresp="note-0218-06" type="noteAnchor" />
vis A a <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſummaque virium ſi ſingula corpora libere cecidiſſent Aa + Bb +
<ptr xml:id="note-0218-07a" corresp="note-0218-07" type="noteAnchor" />
Cc + Dd. </s>
          <s xml:space="preserve">Si quædam corpora dentur ad partem oppoſitam puncti ſuſpenſio-<lb />nis adſcendunt &amp; </s>
          <s xml:space="preserve">horum vires negativæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0218-06" corresp="note-0218-06a" n="*" anchored="true" place="margin">255.</note>
              <note xml:space="preserve" xml:id="note-0218-07" corresp="note-0218-07a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In corporibus pendulo junctis velocitas corporis A detegitur hac regulâ <lb />x, a:</s>
          <s xml:space="preserve">: vx, {a/vx}. </s>
          <s xml:space="preserve">Cæterorumque corporum velocitates ſunt {b/vx}, {c/vx} &amp; </s>
          <s xml:space="preserve"><lb />{d/vx}; </s>
          <s xml:space="preserve">ſummaque virium {Aaa/x} + {Bbb/x} + {Ccc/x} + {Ddd/x} <ptr type="noteAnchor" />, quæ cum memo-
<ptr xml:id="note-0218-08a" corresp="note-0218-08" type="noteAnchor" />
ratæ ſummæ æqualis ſit; </s>
          <s xml:space="preserve">detegimus x = {Aaa + Bbb + Ccc + Ddd/Aa + Bb + Cc + Dd} juxtare-<lb />gulam n. </s>
          <s xml:space="preserve">311.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0218-08" corresp="note-0218-08a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando pendulum compoſitum in obicem fixum, ad quamcunque a cen-<lb />
<ptr xml:id="note-0218-09a" corresp="note-0218-09" type="noteAnchor" />
tro ſuſpenſionis diſtantiam poſitum, impingit, ſæpe in illud quod pendulum <lb />ſuſtinet premit, integram tamen in obicem vim exerit, ſi preſſio quam in cen-
</s>
          <pb facs="0219" n="151" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIII.</fw>
tro ſuſpenſionis exerit nullum ibi generet motum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ita autem obex, in quem
<ptr xml:id="note-0219-01a" corresp="note-0219-01" type="noteAnchor" />
incurrit pendulum, diſponi poteſt ut nullam pendulum in puncto ſuſpenſi-<lb />onis exerat in retinaculum ſuum preſſionem. </s>
          <s xml:space="preserve">Punctum penduli quod in hoc <lb />caſu in obicem incurrit vocatur centrum percuſſionis. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0219-02a" corresp="note-0219-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0218-09" corresp="note-0218-09a" place="margin">552.</note>
              <note xml:space="preserve" xml:id="note-0219-01" corresp="note-0219-01a" n="*" anchored="true" place="margin">523.</note>
              <note xml:space="preserve" xml:id="note-0219-02" corresp="note-0219-02a" place="margin">553.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Centri hujus hæc eſt proprietas, dari æquilibrium inter actiones quibus corpora <lb />ab utraque parte hujus centri in pendulum agunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Poſſumus ergo conſiderare pendulum quaſivectem, cujus ſuſtentaculum eſt <lb />obex, in quem incurrit, poſitus in ipſo centro percuſſionis, &amp; </s>
          <s xml:space="preserve">æquilibrium <lb />dari dum in hunc vectem corpora incurrunt, velocitatibus quibus in pendulo <lb />moventur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Penduli A I formati corporibus A &amp; </s>
          <s xml:space="preserve">D, junctis lineâ inflexi, ſuſpenſâ in <lb />
<ptr xml:id="note-0219-03a" corresp="note-0219-03" type="noteAnchor" />
I, centrum percuſſionis erit H, ſi poſitis, vecte cujus ſuſtentaculum eſt H, <lb />
<ptr xml:id="note-0219-04a" corresp="note-0219-04" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">in hunc incurrentibus corporibus A &amp; </s>
          <s xml:space="preserve">D, in ipſis punctis A &amp; </s>
          <s xml:space="preserve">D, velo-<lb />citatibus quas in pendulo habent, detur inter haſce actiones æquilibrium; </s>
          <s xml:space="preserve">tunc <lb />enim punctum I penduli ullo motu affici non poteſt, aut ſiretineatur, ullam exe-<lb />rere preſſionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0219-03" corresp="note-0219-03a" place="margin">554.</note>
              <note xml:space="preserve" xml:id="note-0219-04" corresp="note-0219-04a" place="margin">TAB. XXIII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut caſum æquilibrii determinemus poſitis variis corporibus, ſingulorum <lb />actiones determinari debent, id eſt, ſunt hæ actiones conferendæ inter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Relictâ nunc penduli conſideratione, ad ſolum vectem attendendo; </s>
          <s xml:space="preserve">ſit Cor-<lb />
<ptr xml:id="note-0219-05a" corresp="note-0219-05" type="noteAnchor" />
poris A velocitas m, &amp; </s>
          <s xml:space="preserve">a diſtantia AH; </s>
          <s xml:space="preserve">Corporis D velocitas n, &amp; </s>
          <s xml:space="preserve">d diſtantia <lb />HD. </s>
          <s xml:space="preserve">Eodem modo in vectem agit corpus A, utrum in A ad partem M, aut in <lb />L ad partem N, eadem velocitate in hunc incurrat poſitis HA &amp; </s>
          <s xml:space="preserve">HL æqualibus. <lb /></s>
          <s xml:space="preserve">Actio etiam erit eadem ſi, ſervatis corporum velocitatibus, concipiamus hæc ro-<lb />tari circa centrum H &amp; </s>
          <s xml:space="preserve">ità agitata in vectem incurrere per e L &amp; </s>
          <s xml:space="preserve">f D. </s>
          <s xml:space="preserve">Conti-<lb />nuetur Hfin G, ut HG &amp; </s>
          <s xml:space="preserve">He, aut HA, ſint æquales, æquilibrium dabitur, <lb />ſi velocitas puncti eſe habeat ad velocitatem puncti G, ut Ddd ad Aaa <ptr type="noteAnchor" />, id eſt
<ptr xml:id="note-0219-06a" corresp="note-0219-06" type="noteAnchor" />
Ddd, Aaa:</s>
          <s xml:space="preserve">: m, {an/d}, hæc enim eſt velocitas-puncti G; </s>
          <s xml:space="preserve">ergo Aam = Ddn; <lb /></s>
          <s xml:space="preserve">unde patet actionem ſequi rationem producti maſſæ corporis per velocitatem, &amp; </s>
          <s xml:space="preserve">di-<lb />ſtantiam a fulcro.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0219-05" corresp="note-0219-05a" place="margin">555.</note>
              <note xml:space="preserve" xml:id="note-0219-06" corresp="note-0219-06a" n="*" anchored="true" place="margin">533.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In pendulo velocitas ſequitur rationem diſtantiæ à puncto ſuſpenſionis; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">diſtantia a fulcro, eſt diſtantia a centro percuſſionis; </s>
          <s xml:space="preserve">ergo actio corporis <lb />ſequitur rationem producti corporis per ſuas diſtantias a centris ſuſpenſionis <lb />&amp; </s>
          <s xml:space="preserve">percuſſionis, daturque æquilibrium inter actiones ab utraque parte centri <lb />percuſſionis, quando producta hæc ab utraque parte hujus centri ſunt æqualia, <lb />quam eandem cùm centrum oſcillationis habeat proprietatem <ptr type="noteAnchor" />, ſequitur hoc
<ptr xml:id="note-0219-07a" corresp="note-0219-07" type="noteAnchor" />
cum centro percuſſionis coincidere. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0219-08a" corresp="note-0219-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0219-07" corresp="note-0219-07a" place="margin">556.</note>
              <note xml:space="preserve" xml:id="note-0219-08" corresp="note-0219-08a" n="*" anchored="true" place="margin">309.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXIV.</head>
        <head rend="italics" xml:space="preserve">De congreſſu corporum Elaſticorum.</head>
        <p>
          <s xml:space="preserve">Corpora elaſtica, poſt ictum, ut jam notavimus, ſeparan-<lb />tur, <ptr type="noteAnchor" /> ſed vi diverſa in circumſtantiis ſimilibus; </s>
          <s xml:space="preserve">nam
<ptr xml:id="note-0219-09a" corresp="note-0219-09" type="noteAnchor" />
in variis corporibus elaſticitas differt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0219-09" corresp="note-0219-09a" n="*" anchored="true" place="margin">483.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0220" n="152" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p rend="italics">
          <s xml:space="preserve">Elaſticitas dicitur perfecta, quando partes ictæ ad pri-<lb />
<ptr xml:id="note-0220-01a" corresp="note-0220-01" type="noteAnchor" />
ſtinum ſitum redeunt, vi æquali illi, cum qua fuere i-<lb />ctæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0220-01" corresp="note-0220-01a" place="margin">557.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De perfecta agimus elaſticitate, licetnulla corpora tali e-<lb />laſticitate prædita nobis nota ſint; </s>
          <s xml:space="preserve">regulæ enim generales ni-<lb />ſi quoad perfectam elaſticitatem tradi non poſſunt; </s>
          <s xml:space="preserve">quo ma-<lb />gis ad hanc corpora accedunt eo magis exacte motus ho-<lb />rum cum regulis congruunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Nulla vis in colliſione corporum perit, niſi quæ intro-<lb />premendo partes conſumitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideo ſi corpora ſint elaſti-
<ptr xml:id="note-0220-02a" corresp="note-0220-02" type="noteAnchor" />
ca tota impenditur in inflexione partium elaſticarum, ſed <lb />æquali vi ad priſtinam figuram hæ redeunt; </s>
          <s xml:space="preserve">ergo vis de-<lb />ſtructa iterum inſtauratur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſumma virium corporibus inſi-<lb />
<ptr xml:id="note-0220-03a" corresp="note-0220-03" type="noteAnchor" />
tarum poſt ictum æqualis eſt ſummæ virium ante ictum; <lb /></s>
          <s xml:space="preserve">quæ demonſtratio univerſalis maximè eſt, &amp; </s>
          <s xml:space="preserve">colliſionibus <lb />quibuſcunque applicari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0220-02" corresp="note-0220-02a" n="*" anchored="true" place="margin">432.</note>
              <note xml:space="preserve" xml:id="note-0220-03" corresp="note-0220-03a" place="margin">558.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hinc ſequitur Corpus elaſticum in obicem firmum elaſticum <lb />
<ptr xml:id="note-0220-04a" corresp="note-0220-04" type="noteAnchor" />
impingens, eâdem celeritate redire qua acceſſit. </s>
          <s xml:space="preserve">Si dire-<lb />ctio perpendicularis ſit ad obicem etiam in eâdem lineâredi-<lb />bit, cum non magis unam quàm aliam partem verſus poſ-<lb />ſit deflecti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0220-04" corresp="note-0220-04a" place="margin">559.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In reliquis de directa impactione tantum in hoc capite <lb />ago.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Elaſterium flexum, poſitum inter duo corpora quieſcentia, <lb />
<ptr xml:id="note-0220-05a" corresp="note-0220-05" type="noteAnchor" />
dum ſeſe expandit ambo movet corpora; </s>
          <s xml:space="preserve">ſi preſſio qua partes <lb />corporis cohærent ſuperet preſſiones quas elaſterium in <lb />corpus hoc exerit, tota elaſterii actio, cum nulla detur <lb />partium introceſſio, in movendis corporibus conſumitur, <lb />&amp; </s>
          <s xml:space="preserve">ſumma virium corporibus communicatarum valet vim qua <lb />elaſterium fuit flexum. </s>
          <s xml:space="preserve">Sed dum elaſterium hæc movet <lb />corpora, duas exerit actiones, quæ ſingulæ æquales <lb />ſunt reactioni quam patiuntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, utraque actio æ-
<ptr xml:id="note-0220-06a" corresp="note-0220-06" type="noteAnchor" />
qualis eſt reſiſtentiæ quam ad partem oppoſitam patitur. <lb /></s>
          <s xml:space="preserve">Reſiſtentiæ hæ ſunt ut quantitates materiæ in corporibus <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0220-07a" corresp="note-0220-07" type="noteAnchor" />
</s>
          <pb facs="0221" n="153" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIV.</fw>
ergo actiones in eadem ratione ad partes oppoſitas; </s>
          <s xml:space="preserve">id <lb />
<ptr xml:id="note-0221-01a" corresp="note-0221-01" type="noteAnchor" />
eſt, ſunt in ratione inverſa corporum motorum, in qua ea-<lb />dem ratione ſunt velocitates corporibus communicatæ. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />
<ptr xml:id="note-0221-02a" corresp="note-0221-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0220-05" corresp="note-0220-05a" place="margin">560.</note>
              <note xml:space="preserve" xml:id="note-0220-06" corresp="note-0220-06a" n="*" anchored="true" place="margin">247.</note>
              <note xml:space="preserve" xml:id="note-0220-07" corresp="note-0220-07a" n="*" anchored="true" place="margin">13.</note>
              <note xml:space="preserve" xml:id="note-0221-01" corresp="note-0221-01a" place="margin">561.</note>
              <note xml:space="preserve" xml:id="note-0221-02" corresp="note-0221-02a" n="*" anchored="true" place="margin">472.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Caſus hic exſtat, ſi duo corpora elaſtica in ſe mutuo incur-<lb />
<ptr xml:id="note-0221-03a" corresp="note-0221-03" type="noteAnchor" />
rant velocitatibus quæ ſunt inversè ut maſſæ; </s>
          <s xml:space="preserve">nam poſitis <lb />his non elaſticis, poſt ictum quieſcunt; </s>
          <s xml:space="preserve">ergo in ipſo mo-<lb />mento concurſus, ante figuram inſtauratam, datur elaſte-<lb />rium flexum inter duo corpora quieſcentia. </s>
          <s xml:space="preserve">Separantur <lb />ideo hæc velocitatibus quæ ſunt inversè ut maſſæ <ptr type="noteAnchor" />,
<ptr xml:id="note-0221-04a" corresp="note-0221-04" type="noteAnchor" />
id eſt, velocitates poſt ictum in eadem ſunt ratione in qua <lb />ante ictum erant; </s>
          <s xml:space="preserve">unde ſequitur corpus utrumque redire <lb />eâdem velocitate quam ante ictum habuit, nam ſi minuatur <lb />in uno, non ſervabitur ratio niſi &amp; </s>
          <s xml:space="preserve">in altero minuatur, qua-<lb />re ſumma virium minor erit, quod impoſſibile <ptr type="noteAnchor" />, demon-
<ptr xml:id="note-0221-05a" corresp="note-0221-05" type="noteAnchor" />
ſtratio eadem eſt ſi quis unius corporis auctam velocitatem <lb />dicat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0221-03" corresp="note-0221-03a" place="margin">562.</note>
              <note xml:space="preserve" xml:id="note-0221-04" corresp="note-0221-04a" n="*" anchored="true" place="margin">561.</note>
              <note xml:space="preserve" xml:id="note-0221-05" corresp="note-0221-05a" n="*" anchored="true" place="margin">558.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Experimenta de corporibus elaſticis inſtituuntur alteru-<lb />trâ Machinarum ſuperius <ptr type="noteAnchor" /> explicatarum, &amp; </s>
          <s xml:space="preserve">adhibitis glo-
<ptr xml:id="note-0221-06a" corresp="note-0221-06" type="noteAnchor" />
bis eburneis aut cylindris in fig. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">18. </s>
          <s xml:space="preserve">delinea-<lb />tis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0221-06" corresp="note-0221-06a" n="*" anchored="true" place="margin">490. 491.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Corpora duo P &amp; </s>
          <s xml:space="preserve">Q, quorum maſſæ ſunt ut unum ad <lb />
<ptr xml:id="note-0221-07a" corresp="note-0221-07" type="noteAnchor" />
tria, in ſe mutuo incurrunt, hoc velocitate quinque, illud <lb />
<ptr xml:id="note-0221-08a" corresp="note-0221-08" type="noteAnchor" />
velocitate quindecim, poſt ictum utrumque ad eandem fe-<lb />rè à qua cecidit altitudinem redit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0221-07" corresp="note-0221-07a" place="margin">563.</note>
              <note xml:space="preserve" xml:id="note-0221-08" corresp="note-0221-08a" place="margin">TAB. XXI. <lb />fig. 9.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Defectus elaſticitatis in cauſa eſt quare non exactè ad eaſ-<lb />dem, à quibus cecidêre, redeant altitudines.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæ de elaſterio, inter corpora quieſcentia ſeſe expan-<lb />dente, demonſtrata ſunt, ad elaſterium inter corpora, eâdem <lb />cum his velocitate tranſlatum, &amp; </s>
          <s xml:space="preserve">reſpectu corporum <lb />quieſcens, referri debent; </s>
          <s xml:space="preserve">ſi ergo in nave duo corpora ela-<lb />
<ptr xml:id="note-0221-09a" corresp="note-0221-09" type="noteAnchor" />
ſtica velocitatibus, quæ ſunt inverſe ut maſſæ, in ſe mu-<lb />tuo impingant, velocitatibus iiſdem in nave redibunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0221-09" corresp="note-0221-09a" place="margin">564.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitis quæ in n. </s>
          <s xml:space="preserve">512. </s>
          <s xml:space="preserve">dicta ſunt, in nave, quæ velocitate <lb />
<ptr xml:id="note-0221-10a" corresp="note-0221-10" type="noteAnchor" />
BI fertur, corpora non elaſtica poſt ictum quieſcunt, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0221-11a" corresp="note-0221-11" type="noteAnchor" />
mutationes in velocitatibus ſunt in versè ut maſſæ, deſtru-
</s>
          <pb facs="0222" n="146" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ctis velocitatibus quibus in nave ad ſe invicem acceſſere; <lb /></s>
          <s xml:space="preserve">ſi fuerint elaſtica, in nave a ſe mutuo recedunt iiſdem hiſce <lb />velocitatibus quibus in nave ad ſe mutuo acceſſere <ptr type="noteAnchor" />, id eſt
<ptr xml:id="note-0222-01a" corresp="note-0222-01" type="noteAnchor" />
ſecunda in velocitatibus datur mutatio æqualis primæ, quare <lb />utrumque corpus duplam patitur in velocitate mutationem, <lb />&amp; </s>
          <s xml:space="preserve">velocitas reſpectiva poſt ictum æqualis eſt velocitati re-<lb />
<ptr xml:id="note-0222-02a" corresp="note-0222-02" type="noteAnchor" />
ſpectivæ ante ictum. </s>
          <s xml:space="preserve">In fig, 1. </s>
          <s xml:space="preserve">corpus motum velocitate <lb />BN, in nave ante ictum habebat velocitatem IN, hanc <lb />amiſit, &amp; </s>
          <s xml:space="preserve">huic æqualem in contrariam partem acquiſivit <lb />IG, habet ideo velocitatem BG. </s>
          <s xml:space="preserve">Corpus aliud cujus <lb />velocitas erat BE in nave ante ictum redibat id eſt lentius <lb />ipſa nave movebatur quantitate IE poſt ictum æquali velo-<lb />citate in contrariam partem id eſt celerius ipſâ nave fer-<lb />tur velocitaſque eſt BP, poſitis IE &amp; </s>
          <s xml:space="preserve">IP æquali-<lb />bus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0221-10" corresp="note-0221-10a" place="margin">565.</note>
              <note xml:space="preserve" xml:id="note-0221-11" corresp="note-0221-11a" place="margin">TAB. XX. <lb />fig. 1. 2.</note>
              <note xml:space="preserve" xml:id="note-0222-01" corresp="note-0222-01a" n="*" anchored="true" place="margin">564.</note>
              <note xml:space="preserve" xml:id="note-0222-02" corresp="note-0222-02a" place="margin">566.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem modo in fig. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Corpus quod habebat velocitatem <lb />BN, amiſit velocitatem IN, quam in nave habebat, &amp; </s>
          <s xml:space="preserve">velocitate, <lb />huic æquali, IG nunc in nave redit, id eſt velocitate BG poſt <lb />ictum fertur; </s>
          <s xml:space="preserve">corpus aliud cujus velocitas erat BE, in na-<lb />ve redibat velocitate IE nunc mutato motu velocitate huic <lb />æquali IP in nave a pupiad proram fertur, &amp; </s>
          <s xml:space="preserve">ipſius velocitas <lb />abſoluta eſt BP.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hiſce deducimus regulas duas quibus corporum ela-<lb />ſticorum velocitates poſt ictum determinamus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Regula</hi> I.</head>
        <p rend="italics">
          <s xml:space="preserve">Si corporis velocitas, poſitis corporibus non elaſticis in ſe <lb />
<ptr xml:id="note-0222-03a" corresp="note-0222-03" type="noteAnchor" />
mutuo impingentibus, ictu augeatur, augmentum duplica-<lb />tum priori velocitati eſt addendum, ut celeritas poſt impa-<lb />ctum determinetur, ſi corpora fuerint elaſtica.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0222-03" corresp="note-0222-03a" place="margin">567.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Regula</hi> II.</head>
        <p rend="italics">
          <s xml:space="preserve">Duobus corporibus non elaſticis in ſe mutuo impingenti-<lb />
<ptr xml:id="note-0222-04a" corresp="note-0222-04" type="noteAnchor" />
bus, ſi corpus ex velocitate amittat, pars amiſſa duplican-<lb />da eſt, quando elaſtica ſunt corpora; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">a priori velocitate <lb />ſubtrahenda, ad determinandam celeritatem poſt percuſſio-<lb />nem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0222-04" corresp="note-0222-04a" place="margin">568.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa ſecundam regulam obſervandum, corpus quod <lb />
<ptr xml:id="note-0222-05a" corresp="note-0222-05" type="noteAnchor" />
</s>
          <pb facs="0223" n="155" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIV.</fw>
redit non modo amittere priſtinam velocitatem, ſed præte-<lb />rea pro velocitate amiſſa etiam haberi velocitatem, in con-<lb />trariam partem acquiſitam; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in hoc caſu ſumma ambarum <lb />harum velocitatum duplicanda eſt &amp; </s>
          <s xml:space="preserve">expriori celeritate ſub-<lb />trahenda. </s>
          <s xml:space="preserve">Quando autem major velocitas ex minori ſubdu-<lb />citur, exceſſus in contrariam partem ſumendus eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0222-05" corresp="note-0222-05a" place="margin">569.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Corpus P, cujus maſſa eſt duo, &amp; </s>
          <s xml:space="preserve">celeritas novem, im-<lb />
<ptr xml:id="note-0223-01a" corresp="note-0223-01" type="noteAnchor" />
pingitur in corpus quieſcens Q, cujus maſſa eſt unum; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0223-02a" corresp="note-0223-02" type="noteAnchor" />
poſt impactum Q fertur celeritate duodecim, &amp; </s>
          <s xml:space="preserve">P mo-<lb />tum continuat velocitate tria; </s>
          <s xml:space="preserve">quod cum prædictis Regu-<lb />lis congruit: </s>
          <s xml:space="preserve">nam ſi corpora non eſſent elaſtica, celeritas <lb />amborum poſt occurſum eſſet ſex <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">corpus ergo Q ac-
<ptr xml:id="note-0223-03a" corresp="note-0223-03" type="noteAnchor" />
quireret ſex gradus velocitatis; </s>
          <s xml:space="preserve">ideo per Reg. </s>
          <s xml:space="preserve">I. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> acquirit
<ptr xml:id="note-0223-04a" corresp="note-0223-04" type="noteAnchor" />
nunc duodecim gradus. </s>
          <s xml:space="preserve">Corpus P quod ſepoſita elaſtici-<lb />tate amittit tres gradus velocitatis, per Reg. </s>
          <s xml:space="preserve">II. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> amittit
<ptr xml:id="note-0223-05a" corresp="note-0223-05" type="noteAnchor" />
ſex, quiſi ſubtrahantur a novem, velocitate priori, reſtant <lb />tres gradus velocitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0223-01" corresp="note-0223-01a" place="margin">570.</note>
              <note xml:space="preserve" xml:id="note-0223-02" corresp="note-0223-02a" place="margin">TAB XXI. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0223-03" corresp="note-0223-03a" n="*" anchored="true" place="margin">519.</note>
              <note xml:space="preserve" xml:id="note-0223-04" corresp="note-0223-04a" n="*" anchored="true" place="margin">567.</note>
              <note xml:space="preserve" xml:id="note-0223-05" corresp="note-0223-05a" n="*" anchored="true" place="margin">568.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Corpus P, cujus maſſa eſt duo, &amp; </s>
          <s xml:space="preserve">velocitas octo, in-<lb />
<ptr xml:id="note-0223-06a" corresp="note-0223-06" type="noteAnchor" />
currit in corpus Q, cuius maſſa eſt unum, &amp; </s>
          <s xml:space="preserve">quod veloci-<lb />
<ptr xml:id="note-0223-07a" corresp="note-0223-07" type="noteAnchor" />
tate quinque eandem partem verſus fertur; </s>
          <s xml:space="preserve">poſt occurſum <lb />corpus Q movetur velocitate novem, &amp; </s>
          <s xml:space="preserve">P velocitate ſex <lb />fertur. </s>
          <s xml:space="preserve">Quod iterum per Regulas præcedentes potuiſſet <lb />determinari. </s>
          <s xml:space="preserve">Si corpora non eſſent elaſtica, ambo celeri-<lb />tate ſeptem poſt impactum moverentur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">corpus Q acqui-
<ptr xml:id="note-0223-08a" corresp="note-0223-08" type="noteAnchor" />
reret duos gradus celeritatis, qui per Reg. </s>
          <s xml:space="preserve">I. </s>
          <s xml:space="preserve">duplicari de-<lb />bent, &amp; </s>
          <s xml:space="preserve">priori celeritati quinque addi, unde habemus no-<lb />vem: </s>
          <s xml:space="preserve">corpus P amiſit unum gradum velocitatis, per Reg. <lb /></s>
          <s xml:space="preserve">II. </s>
          <s xml:space="preserve">amittit duos, ei ergo reſtant ſex.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0223-06" corresp="note-0223-06a" place="margin">571.</note>
              <note xml:space="preserve" xml:id="note-0223-07" corresp="note-0223-07a" place="margin">TAB. XXI. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0223-08" corresp="note-0223-08a" n="*" anchored="true" place="margin">513.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Corpus P in aliud Q, quieſcens &amp; </s>
          <s xml:space="preserve">triplum, velocitate <lb />
<ptr xml:id="note-0223-09a" corresp="note-0223-09" type="noteAnchor" />
duodecim impingitur, &amp; </s>
          <s xml:space="preserve">velocitate ſex regreditur. </s>
          <s xml:space="preserve">In hoc <lb />
<ptr xml:id="note-0223-10a" corresp="note-0223-10" type="noteAnchor" />
caſu corpora non elaſtica moverentur celeritate tria; </s>
          <s xml:space="preserve">cor-<lb />pus ergo Pamiſiſſet novem gradus velocitatis, amittit ergo per <lb />Reg. </s>
          <s xml:space="preserve">II. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> octodecim gradus; </s>
          <s xml:space="preserve">qui ſi ſubtrahantur a priori ve-
<ptr xml:id="note-0223-11a" corresp="note-0223-11" type="noteAnchor" />
</s>
          <pb facs="0224" n="156" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
locitate duodecim, dantur ſex grad. </s>
          <s xml:space="preserve">in contrariam partem <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0224-01a" corresp="note-0224-01" type="noteAnchor" />
eodem modo ſequentibus Experimentis confirmatur quod <lb />per Regulas detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0223-09" corresp="note-0223-09a" place="margin">572.</note>
              <note xml:space="preserve" xml:id="note-0223-10" corresp="note-0223-10a" place="margin">TAB. XXI. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0223-11" corresp="note-0223-11a" n="*" anchored="true" place="margin">568.</note>
              <note xml:space="preserve" xml:id="note-0224-01" corresp="note-0224-01a" n="*" anchored="true" place="margin">569.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Corpus P velocitate novendecim fertur eandem partem <lb />
<ptr xml:id="note-0224-02a" corresp="note-0224-02" type="noteAnchor" />
verſus cum corpore triplo Q, moto celeritate tria; </s>
          <s xml:space="preserve">poſt im-<lb />
<ptr xml:id="note-0224-03a" corresp="note-0224-03" type="noteAnchor" />
pactum corpus P regreditur velocitate quinque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0224-02" corresp="note-0224-02a" place="margin">573.</note>
              <note xml:space="preserve" xml:id="note-0224-03" corresp="note-0224-03a" place="margin"><hi rend="small caps">TAB. XXI</hi>. <lb />fig 8.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Corpus P celeritate quinque, &amp; </s>
          <s xml:space="preserve">corpus Q triplum ce-<lb />
<ptr xml:id="note-0224-04a" corresp="note-0224-04" type="noteAnchor" />
leritate undecim, in partes contrarias feruntur; </s>
          <s xml:space="preserve">poſt occur-<lb />
<ptr xml:id="note-0224-05a" corresp="note-0224-05" type="noteAnchor" />
ſum, Q motum continuat celeritate tria, &amp; </s>
          <s xml:space="preserve">P regreditur <lb />velocitate novemdecim.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0224-04" corresp="note-0224-04a" place="margin">574.</note>
              <note xml:space="preserve" xml:id="note-0224-05" corresp="note-0224-05a" place="margin"><hi rend="small caps">TAB. XXI</hi>. <lb />fig. 10.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Eadem corpora P &amp; </s>
          <s xml:space="preserve">Q in contrarias partes feruntur, P <lb />
<ptr xml:id="note-0224-06a" corresp="note-0224-06" type="noteAnchor" />
celeritate ſedecim, &amp; </s>
          <s xml:space="preserve">Q velocitate octo; </s>
          <s xml:space="preserve">ambo poſt impa-<lb />
<ptr xml:id="note-0224-07a" corresp="note-0224-07" type="noteAnchor" />
ctum regrediuntur, P cum viginti &amp; </s>
          <s xml:space="preserve">Q cum quatuor gradi-<lb />bus velocitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0224-06" corresp="note-0224-06a" place="margin">575.</note>
              <note xml:space="preserve" xml:id="note-0224-07" corresp="note-0224-07a" place="margin"><hi rend="small caps">TAB. XXI</hi>. <lb />fig. 11.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omnes caſus percuſſionum corporum elaſticorum Regu-<lb />lis memoratis determinantur; </s>
          <s xml:space="preserve">ſequentem etiam ex illis de-<lb />ducimus propoſitionem.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quando corpora ſunt æqualia, &amp; </s>
          <s xml:space="preserve">eandem partem ver ſivs <lb />
<ptr xml:id="note-0224-08a" corresp="note-0224-08" type="noteAnchor" />
feruntur, permutatis velocitatibus motum continuant; </s>
          <s xml:space="preserve">ſi in <lb />contrarias partes ferantur, permutatis velocitatibus regre-<lb />diuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0224-08" corresp="note-0224-08a" place="margin">576.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cas. </s>
          <s xml:space="preserve">I. </s>
          <s xml:space="preserve">Tendant corpora ad eandem plagam, &amp; </s>
          <s xml:space="preserve">ſit A B <lb />
<ptr xml:id="note-0224-09a" corresp="note-0224-09" type="noteAnchor" />
velocitas unius corporis, B C velocitas alterius corporis; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0224-10a" corresp="note-0224-10" type="noteAnchor" />
propter maſſas æquales, ſunt velocitates ut producta maſſa-<lb />rum per velocitates. </s>
          <s xml:space="preserve">Dividatur linea A C in duas partes <lb />æquales in D, &amp; </s>
          <s xml:space="preserve">ſit D b æqualis DB; </s>
          <s xml:space="preserve">AD aut DC de-<lb />notat celeritatem utriuſque corporis poſt occurſum, ſi non <lb />ſint elaſtica <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">celeritas BC augetur quantitate DB, du-
<ptr xml:id="note-0224-11a" corresp="note-0224-11" type="noteAnchor" />
plici quantitate tali augeri debet propter elaſticitatem <ptr type="noteAnchor" />, id
<ptr xml:id="note-0224-12a" corresp="note-0224-12" type="noteAnchor" />
eſt, fiet b C: </s>
          <s xml:space="preserve">celeritas AB; </s>
          <s xml:space="preserve">in corporibus non elaſticis, <lb />minuitur quantitate DB; </s>
          <s xml:space="preserve">duplici illa quantitate minui de-<lb />bet, ex prædicta ratione <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">fiet a b. </s>
          <s xml:space="preserve">Velocitates igi-
<ptr xml:id="note-0224-13a" corresp="note-0224-13" type="noteAnchor" />
tur AB &amp; </s>
          <s xml:space="preserve">BC mutantur in velocitates A b &amp; </s>
          <s xml:space="preserve">b C; </s>
          <s xml:space="preserve">A
</s>
          <pb facs="0225" n="157" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIV.</fw>
B vero &amp; </s>
          <s xml:space="preserve">b C, ut &amp; </s>
          <s xml:space="preserve">BC &amp; </s>
          <s xml:space="preserve">A b, ſunt æquales inter <lb />ſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0224-09" corresp="note-0224-09a" place="margin">577.</note>
              <note xml:space="preserve" xml:id="note-0224-10" corresp="note-0224-10a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0224-11" corresp="note-0224-11a" n="*" anchored="true" place="margin">513.</note>
              <note xml:space="preserve" xml:id="note-0224-12" corresp="note-0224-12a" n="*" anchored="true" place="margin">567.</note>
              <note xml:space="preserve" xml:id="note-0224-13" corresp="note-0224-13a" n="*" anchored="true" place="margin">568</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Corpora duo æqualia &amp;</s>
          <s xml:space="preserve">, primum velocitate decem, alte-<lb />
<ptr xml:id="note-0225-01a" corresp="note-0225-01" type="noteAnchor" />
rum velocitate quinque, eandem partem verſus feruntur; <lb /></s>
          <s xml:space="preserve">mutatis velocitatibus poſt impactum motum continuant: </s>
          <s xml:space="preserve"><lb />quod etiam detegitur computatione ex præcedentibus Re-<lb />gulis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0225-01" corresp="note-0225-01a" place="margin">578.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cas. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Sit AB celeritas unius corporis, CB celeritas <lb />
<ptr xml:id="note-0225-02a" corresp="note-0225-02" type="noteAnchor" />
alterius; </s>
          <s xml:space="preserve">differentia AC dividatur in duas partes æqua-<lb />
<ptr xml:id="note-0225-03a" corresp="note-0225-03" type="noteAnchor" />
les, &amp; </s>
          <s xml:space="preserve">fiat A b æqualis CB. </s>
          <s xml:space="preserve">Quando corpora non ſunt <lb />elaſtica, velocitas utriuſque poſt occurſum, verſus ean-<lb />dem partem, eſt AD <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">corpus ergo primum amiſit ve-
<ptr xml:id="note-0225-04a" corresp="note-0225-04" type="noteAnchor" />
locitatem DB, corpus alterum amiſit totam velocitatem CB <lb />&amp; </s>
          <s xml:space="preserve">in contrariam partem acquiſivit DC; </s>
          <s xml:space="preserve">tota ergo quan-<lb />
<ptr xml:id="note-0225-05a" corresp="note-0225-05" type="noteAnchor" />
titas amiſſa etiam eſt DB <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hæc quantitas ſi duplicetur,
erit b B quantitas celeritatis ab utroque corpore amiſſa <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0225-06a" corresp="note-0225-06" type="noteAnchor" />
quæ ſubtracta ex velocitate utriuſque corporis, dat in u-<lb />troque caſu velocitatem in contrariam partem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">differen-
<ptr xml:id="note-0225-07a" corresp="note-0225-07" type="noteAnchor" />
tia hæc reſpectu motus AB eſt b A, pro motu CB eſt <lb />C b; </s>
          <s xml:space="preserve">C b vero &amp; </s>
          <s xml:space="preserve">AB, ut &amp; </s>
          <s xml:space="preserve">b A &amp; </s>
          <s xml:space="preserve">CB, ſunt æquales <lb />inter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0225-02" corresp="note-0225-02a" place="margin">579.</note>
              <note xml:space="preserve" xml:id="note-0225-03" corresp="note-0225-03a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0225-04" corresp="note-0225-04a" n="*" anchored="true" place="margin">516.</note>
              <note xml:space="preserve" xml:id="note-0225-05" corresp="note-0225-05a" n="*" anchored="true" place="margin">569.</note>
              <note xml:space="preserve" xml:id="note-0225-06" corresp="note-0225-06a" n="*" anchored="true" place="margin">568.</note>
              <note xml:space="preserve" xml:id="note-0225-07" corresp="note-0225-07a" n="*" anchored="true" place="margin">569.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Si corpora æqualia, unum celeritate decem, alte-<lb />
<ptr xml:id="note-0225-08a" corresp="note-0225-08" type="noteAnchor" />
rum velocitate quinque, in contrarias partes ferantur, per-<lb />mutatis velocitatibus ambo regrediuntur poſt percuſſio-<lb />nem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0225-08" corresp="note-0225-08a" place="margin">580.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Corpus impingitur in alind æquale quieſcens, ſi velocitates <lb />
<ptr xml:id="note-0225-09a" corresp="note-0225-09" type="noteAnchor" />
permutentur, corpus primum poſt impactum quieſcet, alte-<lb />rum vero cum velocitate prioris movebitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0225-09" corresp="note-0225-09a" place="margin">581.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 10.</head>
        <p>
          <s xml:space="preserve">Corpus velocitate decem impingat in corpus æquale quie-<lb />
<ptr xml:id="note-0225-10a" corresp="note-0225-10" type="noteAnchor" />
tum, primum poſt occurſum quieſcet, &amp; </s>
          <s xml:space="preserve">aliud celeritate de-<lb />cem movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0225-10" corresp="note-0225-10a" place="margin">582.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In omnibus hiſce experimentis notandum, hæc hìc tra-<lb />di ut obtinerent ſi perfecta foret elaſticitas, ad cujus defe-<lb />ctum ſemper attendere debemus.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0226" n="158" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">In corporibus elaſticis ſubita admodum eſt elaterii actio. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0226-01a" corresp="note-0226-01" type="noteAnchor" />
Ideo ſi varia corpora elaſtica ſint contigua, &amp; </s>
          <s xml:space="preserve">extremum <lb />percutiatur, omnia ſequentia agitantur quaſi eſſent ſe-<lb />parata; </s>
          <s xml:space="preserve">etiam ſi ex variis contiguis, eâdem velocitate <lb />motis, antecedens in corpus quodcumque incurrat, agit <lb />ut à reliquis ſeparatum ageret; </s>
          <s xml:space="preserve">Unde ſequitur corpus move-<lb />
<ptr xml:id="note-0226-02a" corresp="note-0226-02" type="noteAnchor" />
ri ſola actione corporis vicini, &amp; </s>
          <s xml:space="preserve">in vicinum corpus tantum <lb />agere, partibus elaſticis ad figuram redeuntibus, antequam <lb />actio corpori ſequenti communicari poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0226-01" corresp="note-0226-01a" place="margin">583.</note>
              <note xml:space="preserve" xml:id="note-0226-02" corresp="note-0226-02a" place="margin">584.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 11.</head>
        <p>
          <s xml:space="preserve">I. </s>
          <s xml:space="preserve">Sint corpora plurima æqualia P, Q, R, S, T, V, <lb />
<ptr xml:id="note-0226-03a" corresp="note-0226-03" type="noteAnchor" />
in eadem linea diſpoſita, &amp; </s>
          <s xml:space="preserve">ſeſe mutuo tangentia; </s>
          <s xml:space="preserve">corpus <lb />
<ptr xml:id="note-0226-04a" corresp="note-0226-04" type="noteAnchor" />
P impingatur in Q. </s>
          <s xml:space="preserve">quacunque velocitate, poſt occur-<lb />ſum P,Q,R,S, &amp; </s>
          <s xml:space="preserve">T quieta manent, &amp; </s>
          <s xml:space="preserve">V ſolum movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0226-03" corresp="note-0226-03a" place="margin">585.</note>
              <note xml:space="preserve" xml:id="note-0226-04" corresp="note-0226-04a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Moveantur æqualibus velocitatibus P &amp; </s>
          <s xml:space="preserve">Q, ita ut Q im-<lb />
<ptr xml:id="note-0226-05a" corresp="note-0226-05" type="noteAnchor" />
pingatur in R, poſt impactum P,Q,R, &amp; </s>
          <s xml:space="preserve">S quieſcunt, T <lb />&amp; </s>
          <s xml:space="preserve">V vero ſimul moventur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0226-05" corresp="note-0226-05a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Eodem modo ſi tria moventur, poſt occurſum tria etiam <lb />
<ptr xml:id="note-0226-06a" corresp="note-0226-06" type="noteAnchor" />
moventur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0226-06" corresp="note-0226-06a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Tandem ſi, P,Q,R, S &amp; </s>
          <s xml:space="preserve">ſimul moveantur, &amp; </s>
          <s xml:space="preserve">S per-<lb />
<ptr xml:id="note-0226-07a" corresp="note-0226-07" type="noteAnchor" />
cutiat T, poſt percuſſionem P &amp; </s>
          <s xml:space="preserve">Q quieſcunt, R, S, T, <lb />&amp; </s>
          <s xml:space="preserve">V ſimul moventur. </s>
          <s xml:space="preserve">Generaliter quicunque ſit globorum <lb />numerus, quot moventur ante occurſum, tot etiam poſt il-<lb />lum moventur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0226-07" corresp="note-0226-07a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 9.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Agunt hæc corpora quaſi eſſent ſeparata <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In primo cafu P
<ptr xml:id="note-0226-08a" corresp="note-0226-08" type="noteAnchor" />
impingitur in Q &amp; </s>
          <s xml:space="preserve">quieſcit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Q ictu agitatum impingitur in
<ptr xml:id="note-0226-09a" corresp="note-0226-09" type="noteAnchor" />
R &amp; </s>
          <s xml:space="preserve">etiam quieſcit, &amp; </s>
          <s xml:space="preserve">ſic de cæteris, donec tandem T per-<lb />
<ptr xml:id="note-0226-10a" corresp="note-0226-10" type="noteAnchor" />
cutiat V, quod, cùm nullo obſtaculo retineatur, ſolum in <lb />motu continuat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0226-08" corresp="note-0226-08a" place="margin"><hi rend="small caps">TA. XXII</hi> <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0226-09" corresp="note-0226-09a" n="*" anchored="true" place="margin">583.</note>
              <note xml:space="preserve" xml:id="note-0226-10" corresp="note-0226-10a" n="*" anchored="true" place="margin">501.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſecundo caſu, corpus Q eodem modo corpus V <lb />
<ptr xml:id="note-0226-11a" corresp="note-0226-11" type="noteAnchor" />
propellit; </s>
          <s xml:space="preserve">inſequitur immediate P impingens in Q, <lb />quod jam ex priori impactu quieſcit, motus ille etiam <lb />eodem modo communicatur corpori T, quod non pot-<lb />eſt percutere V jam in motu; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cum motus corporum <lb />P &amp; </s>
          <s xml:space="preserve">Q æque veloces ſint, &amp; </s>
          <s xml:space="preserve">illa corpora quam proxi-<lb />me ſeſe inſequantur, ſenſibile tempus inter illas duas mo-
</s>
          <pb facs="0227" n="159" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIV.</fw>
tus communicationes non datur, unde etiam corpora V &amp; </s>
          <s xml:space="preserve"><lb />T æque velociter moventur &amp; </s>
          <s xml:space="preserve">non ſeparantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0226-11" corresp="note-0226-11a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">A lio experimento conſtat, ita ſubitam eſſe elaſterii actio-<lb />nem ut vix concipiatur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 12.</head>
        <p>
          <s xml:space="preserve">Globus eburneus cavus, diametri circiter@ duorum pol-<lb />
<ptr xml:id="note-0227-01a" corresp="note-0227-01" type="noteAnchor" />
licum, ex duobus conſtat hemiſphæriis A &amp; </s>
          <s xml:space="preserve">B, quæ cochleâ <lb />
<ptr xml:id="note-0227-02a" corresp="note-0227-02" type="noteAnchor" />
quàm arctiſſimè inter ſe conjungi poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0227-01" corresp="note-0227-01a" place="margin">586.</note>
              <note xml:space="preserve" xml:id="note-0227-02" corresp="note-0227-02a" place="margin"><hi rend="small caps">TA. XXII</hi>. <lb />fig. 10.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hemiſphærium B dimittitur ita, ab altitudine quacunque, <lb />ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">octodecim pollicum, ut plano marmoreo cœru-<lb />leo, paululum madefacto, impingat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quidem ut pun-<lb />ctum medium ſuperficiei in planum incurrat. </s>
          <s xml:space="preserve">Hoc haud <lb />difficulter obtineri poteſt, ſi in eo loco majorem ha-<lb />beat craſſitiem hemiſphærium quâm extrema verſus. </s>
          <s xml:space="preserve">Men-<lb />furetur macula quam in marmore corpus impactu impri-<lb />mit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Conjungatur hemiſphærium A, &amp; </s>
          <s xml:space="preserve">dimittatur ab eadem <lb />altitudine globus ita, ut idem punctum ſuperficiei hemi-<lb />ſphærii B in planum marmoreum incurrat, quod facile fiet ſi <lb />hemiſphærium A alio levius fuerit: </s>
          <s xml:space="preserve">Macula priori quam ex-<lb />actiſſime æqualis erit, &amp; </s>
          <s xml:space="preserve">globus multo minus reſiliet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tandem in globi cavitatem inſeratur plumbi fruſtum P, <lb />ejuſdem ponderis cum ipſo globo, ibique firmetur; </s>
          <s xml:space="preserve">dimiſſo <lb />eodem modo globo, &amp; </s>
          <s xml:space="preserve">in hoc tertio caſu macula eadem <lb />erit, &amp; </s>
          <s xml:space="preserve">globus vix reſiliet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dimiſſo autem ab eadem altitudine globo ſolido ex ebo-<lb />re, globo memorato æquali, macula major eſt, &amp; </s>
          <s xml:space="preserve">fere ad il-<lb />lam à qua cecidit altitudinem globus redit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hoc experimento videmus, partes ictas hemiſphærii <lb />B ad figuram rediiſſe, antequam huic hemiſphærio actio <lb />hemiſphærii A, aut plumbi inſerti, communicari potuerit, <lb />licet ſatis arcte hæc corpora cohæreant.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0228" n="160" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM I.</head>
        <head xml:space="preserve">Uberior demonſtratio n. 558.</head>
        <p>
          <s xml:space="preserve">Demonſtravimus in congreſſu corporum elaſticorum ſummam virium ante <lb />
<ptr xml:id="note-0228-01a" corresp="note-0228-01" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">poſt ictum eſſe eandem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">unde ſequitur, poſitis explicatis in n. </s>
          <s xml:space="preserve">565. </s>
          <s xml:space="preserve">566.</s>
          <s xml:space="preserve">
AB x BN<hi rend="superscript">q</hi> + BC x BE<hi rend="superscript">q</hi> = AB x BG<hi rend="superscript">q</hi> + BC x BP<hi rend="superscript">q</hi>; </s>
          <s xml:space="preserve">cujus &amp; </s>
          <s xml:space="preserve">hìc geometri-<lb />
<ptr xml:id="note-0228-02a" corresp="note-0228-02" type="noteAnchor" />
cam dabimus demonſtrationem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0228-01" corresp="note-0228-01a" place="margin"><hi rend="small caps">TAB. XX</hi>. <lb />fig. 12.</note>
              <note xml:space="preserve" xml:id="note-0228-02" corresp="note-0228-02a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Primo tendant corpora eandem partem verſus. </s>
          <s xml:space="preserve">Formentur quadrata li-<lb />
<ptr xml:id="note-0228-03a" corresp="note-0228-03" type="noteAnchor" />
nearum BE, BG, BN, &amp; </s>
          <s xml:space="preserve">BP; </s>
          <s xml:space="preserve">ducatur omnium diagonalis BV. </s>
          <s xml:space="preserve">Du-<lb />
<ptr xml:id="note-0228-04a" corresp="note-0228-04" type="noteAnchor" />
catur IS parallela ad PV; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">per S, punctum, in quo diagonalem ſecat, <lb />ducatur XSK, parallela PB; </s>
          <s xml:space="preserve">continuentur GR &amp; </s>
          <s xml:space="preserve">EQ in Z &amp; </s>
          <s xml:space="preserve">K; </s>
          <s xml:space="preserve">quia <lb />IN &amp; </s>
          <s xml:space="preserve">IG ſunt æquales, ut &amp; </s>
          <s xml:space="preserve">IP &amp; </s>
          <s xml:space="preserve">IE, triangula YST, RSZ ſunt æ-<lb />qualia, etiam triangula SXV, SKQ. </s>
          <s xml:space="preserve">Idcirca Trapezium GRTN æ-<lb />quale eſt rectangulo GZYN, &amp; </s>
          <s xml:space="preserve">trapezium EQVP æquale rectangulo <lb />EKXP.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0228-03" corresp="note-0228-03a" place="margin">587.</note>
              <note xml:space="preserve" xml:id="note-0228-04" corresp="note-0228-04a" place="margin"><hi rend="small caps">TAB. XX</hi>. <lb />fig. 18.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Semidifferentia quadratorum linearum BN, BG eſt trapezium GRTN, <lb />id eſt rectangulum GZYN. </s>
          <s xml:space="preserve">Eodem modo ſemidifterentia quadratorum linea-<lb />rum BP, BE eſt rectangulum EKXP; </s>
          <s xml:space="preserve">Sed rectangula hæc, propter communem <lb />altitudinem IS, ſunt ut baſes <ptr type="noteAnchor" />, aut ut baſium ſemiſſes IN, IE; </s>
          <s xml:space="preserve">etiam ut
<ptr xml:id="note-0228-05a" corresp="note-0228-05" type="noteAnchor" />
ſunt ſemidifferentiæ quadratorum ita integræ differentiæ: </s>
          <s xml:space="preserve">ergo</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0228-05" corresp="note-0228-05a" n="*" anchored="true" place="margin">1. El. VI.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">BN<hi rend="superscript">q</hi> - BG<hi rend="superscript">q</hi>, BP<hi rend="superscript">q</hi> - BE<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">:IN, IE, id eſt ut BC ad AB ex conſtructione. <lb /></s>
          <s xml:space="preserve">Idcirco AB x BN<hi rend="superscript">q</hi> - AB x BG<hi rend="superscript">q</hi> = BC x BP<hi rend="superscript">q</hi> - BC x BE<hi rend="superscript">q</hi>; </s>
          <s xml:space="preserve">ideo AB x BN<hi rend="superscript">q</hi> <lb />+ BC x BE<hi rend="superscript">q</hi> = AB x BG<hi rend="superscript">q</hi> + BC x BP<hi rend="superscript">q</hi>. </s>
          <s xml:space="preserve">quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tendant nunc corpora in partes contrarias. </s>
          <s xml:space="preserve">Formentur iterum quadrata <lb />
<ptr xml:id="note-0228-06a" corresp="note-0228-06" type="noteAnchor" />
linearum BP, BN, BE aut B e, &amp; </s>
          <s xml:space="preserve">BG aut B g. </s>
          <s xml:space="preserve">Propter æquales IN, <lb />
<ptr xml:id="note-0228-07a" corresp="note-0228-07" type="noteAnchor" />
IG, &amp; </s>
          <s xml:space="preserve">IP, IE, æquales ſunt NP, EG, aut e g; </s>
          <s xml:space="preserve">addamus utrim-<lb />que e N, erunt æquales e P, g N. </s>
          <s xml:space="preserve">Differentia quadratorum BV &amp; </s>
          <s xml:space="preserve">BQ, <lb />id eſt quadratorum linearum BP, BE, eſt rectangulum, cujus baſis eſt PV, <lb />&amp; </s>
          <s xml:space="preserve">e Q, id eſt PE, &amp; </s>
          <s xml:space="preserve">altitudo e P; </s>
          <s xml:space="preserve">differentia quadratorum BT, BR, <lb />id eſt quadratorum linearum BN, B g aut BG, eſt rectangulum, cujus ba-<lb />ſis eſt NT, &amp; </s>
          <s xml:space="preserve">g R, id eſt NG, &amp; </s>
          <s xml:space="preserve">altitudo g N; </s>
          <s xml:space="preserve">propter æquales alti-<lb />tudines rectangula hæc ſunt ut baſes PE, NG, aut ut harum ſemiſſes IE, <lb />IN, quæ ſuntut AB, BC; </s>
          <s xml:space="preserve">ergo <lb />BP<hi rend="superscript">q</hi> - BE<hi rend="superscript">q</hi>, BN<hi rend="superscript">q</hi> - BG<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: AB, BC</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0228-06" corresp="note-0228-06a" place="margin">588.</note>
              <note xml:space="preserve" xml:id="note-0228-07" corresp="note-0228-07a" place="margin"><hi rend="small caps">TAB. XX</hi>. <lb />fig. 29.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Idcirco AB x BN<hi rend="superscript">q</hi> - AB x BG<hi rend="superscript">q</hi> = BC x BP<hi rend="superscript">q</hi> - BC x B<hi rend="superscript">Eq</hi>; </s>
          <s xml:space="preserve">unde <lb />deducimus AB x BN<hi rend="superscript">q</hi> + BC x BE<hi rend="superscript">q</hi> = AB x BG<hi rend="superscript">q</hi> + BC x BP<hi rend="superscript">q</hi>. </s>
          <s xml:space="preserve">Quod <lb />demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0229" />
        <pb facs="0229a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0229a-01" />
          <label>0229a-01</label>
        </figure>
        <pb facs="0230" />
        <pb facs="0231" n="161" />
        <fw type="head">MATHEMATICA. LIB. I. CAP XXIV.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">Illuſtratio circa mutuam corporum elaſticorum <lb />actionem.</head>
        <p>
          <s xml:space="preserve">Licet circa ſummæ virium æqualitatem ante &amp; </s>
          <s xml:space="preserve">poſt ictum dubium ſapereſſe <lb />
<ptr xml:id="note-0231-01a" corresp="note-0231-01" type="noteAnchor" />
nullum poſſit, cum hæc ex ipſa perſecta claſticitate ſequatur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">etiam,
<ptr xml:id="note-0231-02a" corresp="note-0231-02" type="noteAnchor" />
utin præcedenti ſcholio fecimus, ex regulis computationis deducatur, obſcurum <lb />quid nihilominus in hiſce dari non diffiteor; </s>
          <s xml:space="preserve">cum ex demonſtratis non pa-<lb />teat, quomodo elaſterium, quod dum ſe inter corpora expandit, &amp; </s>
          <s xml:space="preserve">ad partes <lb />oppoſitas vires, quæ ſuntinverſè ut maſſæ, communicat <ptr type="noteAnchor" />, poſſit ſæpe unico
<ptr xml:id="note-0231-03a" corresp="note-0231-03" type="noteAnchor" />
corpori integram non modo, qua ſe expandit, imprimere vim; </s>
          <s xml:space="preserve">ſed præter-<lb />ea quantum ex vi aliûs corporis tollit. </s>
          <s xml:space="preserve">Si Ex. </s>
          <s xml:space="preserve">C. </s>
          <s xml:space="preserve">corpus A duobus gradi-<lb />
<ptr xml:id="note-0231-04a" corresp="note-0231-04" type="noteAnchor" />
bus velocitatis, id eſt, cum quatuor grad. </s>
          <s xml:space="preserve">vis <ptr type="noteAnchor" />, incurrat in corpus B æquale
quieſcens, poſt ictum, ſepoſita elaſticitate, ambo unico gradu velocitatis gau-<lb />
<ptr xml:id="note-0231-05a" corresp="note-0231-05" type="noteAnchor" />
dent <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">ſingula unicum gradum vis habent <ptr type="noteAnchor" />, id eſt, amborum vis valet duo,
<ptr xml:id="note-0231-06a" corresp="note-0231-06" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">duobus reliquis gradibus vis partes fuere compreſſæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, ſi corpora
<ptr xml:id="note-0231-07a" corresp="note-0231-07" type="noteAnchor" />
ſint elaſtica, hac ipſa vielaſterium fuit flexum, &amp; </s>
          <s xml:space="preserve">eadem vi ſeſe expandit <ptr type="noteAnchor" />:</s>
          <s xml:space="preserve">
<ptr xml:id="note-0231-08a" corresp="note-0231-08" type="noteAnchor" />
Poſt ictum verò corpus B duos habet gradus velocitatis <ptr type="noteAnchor" />, id eſt vim qua-
<ptr xml:id="note-0231-09a" corresp="note-0231-09" type="noteAnchor" />
tuor <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">quieſcit A; </s>
          <s xml:space="preserve">Elaſterium ergo ipſi B tres gradus vis communicavit,
<ptr xml:id="note-0231-10a" corresp="note-0231-10" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">gradum unum ex A ſuſtulit; </s>
          <s xml:space="preserve">quamvis duobus tantum gradibus vis fuerit <lb />flexum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">licet propter corpora æqualia, æquales impreſſiones ab utraque <lb />parte exeruerit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0231-01" corresp="note-0231-01a" place="margin">589.</note>
              <note xml:space="preserve" xml:id="note-0231-02" corresp="note-0231-02a" n="*" anchored="true" place="margin">557.</note>
              <note xml:space="preserve" xml:id="note-0231-03" corresp="note-0231-03a" n="*" anchored="true" place="margin">561.</note>
              <note xml:space="preserve" xml:id="note-0231-04" corresp="note-0231-04a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0231-05" corresp="note-0231-05a" n="*" anchored="true" place="margin">519.</note>
              <note xml:space="preserve" xml:id="note-0231-06" corresp="note-0231-06a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0231-07" corresp="note-0231-07a" n="*" anchored="true" place="margin">488.</note>
              <note xml:space="preserve" xml:id="note-0231-08" corresp="note-0231-08a" n="*" anchored="true" place="margin">557.</note>
              <note xml:space="preserve" xml:id="note-0231-09" corresp="note-0231-09a" n="*" anchored="true" place="margin">576.</note>
              <note xml:space="preserve" xml:id="note-0231-10" corresp="note-0231-10a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut hæc tollatur difficultas, inter vim abſolutam &amp; </s>
          <s xml:space="preserve">relativam diſtinguen-<lb />
<ptr xml:id="note-0231-11a" corresp="note-0231-11" type="noteAnchor" />
dum. </s>
          <s xml:space="preserve">Elaſterium inter corpora poſitum vires ipſis communicat, quæ ſuut inverſè <lb />ut maſſæ, ſi inter corpora quieſcat <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, ſi, translatis corporibus, eodem
<ptr xml:id="note-0231-12a" corresp="note-0231-12" type="noteAnchor" />
motu cum hiſce feratur; </s>
          <s xml:space="preserve">quales ideò motus corporibus communicantur in <lb />nave quæ eadem velocitate cum corporibus fertur, &amp; </s>
          <s xml:space="preserve">in qua idcirco hæc cum e-<lb />laſterio quieſcunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſed propoſitio hæc ad motus abſolutos referrinon debet, quo-
<ptr xml:id="note-0231-13a" corresp="note-0231-13" type="noteAnchor" />
rum unus acceleratur, alter retardatur, translato jam ipſo elaſterio ante hu-<lb />jus actionem, ad caſum ita conſideratum demonſtratio propoſitionis appli-<lb />cari nequit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0231-11" corresp="note-0231-11a" place="margin">590.</note>
              <note xml:space="preserve" xml:id="note-0231-12" corresp="note-0231-12a" n="*" anchored="true" place="margin">561.</note>
              <note xml:space="preserve" xml:id="note-0231-13" corresp="note-0231-13a" n="*" anchored="true" place="margin">564.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa vires abſolutas notandum, has corpori ſæpe communicari, cauſâ mo-<lb />venti quæ ipſa transfertur, in quo caſu non ſola cauſa movens in corpus agit, <lb />
<ptr xml:id="note-0231-14a" corresp="note-0231-14" type="noteAnchor" />
ſed &amp; </s>
          <s xml:space="preserve">in corpus datur actio illa quæ ipſam transfert canſam moventem, corporique <lb />communicatur vis, quæ valet ſummam barum actionem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam vis hæc eſt ef-
<ptr xml:id="note-0231-15a" corresp="note-0231-15" type="noteAnchor" />
fectus ambarum actionum conjunctarum; </s>
          <s xml:space="preserve">agitur enim de caſu in quo hæ a-<lb />lium nullum effectum edunt. </s>
          <s xml:space="preserve">Hæc jam alia occaſione notavimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0231-14" corresp="note-0231-14a" place="margin">591.</note>
              <note xml:space="preserve" xml:id="note-0231-15" corresp="note-0231-15a" n="*" anchored="true" place="margin">249.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">446.</note>
        <p>
          <s xml:space="preserve">Quando elaſterium obſtaculo inſiſtit quod ad partem oppoſitam non cedit, <lb />totam vim qua fuit infiexum corpori quod ab obſtaculo repellit communicat, <lb />ut hoc antea notavimus <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſequitur ex demonſtrationen. </s>
          <s xml:space="preserve">561. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">confirmatur
<ptr xml:id="note-0231-17a" corresp="note-0231-17" type="noteAnchor" />
experimentis memoratis <ptr type="noteAnchor" /> addita propoſitione n. </s>
          <s xml:space="preserve">559; </s>
          <s xml:space="preserve">quæ, poſitâ perfectâ ela-
<ptr xml:id="note-0231-18a" corresp="note-0231-18" type="noteAnchor" />
ſticitate, in dubium a nemine vocatur, neque vocari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0231-17" corresp="note-0231-17a" n="*" anchored="true" place="margin">441.</note>
              <note xml:space="preserve" xml:id="note-0231-18" corresp="note-0231-18a" n="*" anchored="true" place="margin">492.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si autem elaſterium quod ab una parte inſiſtit obſtaculo quod non cedit <lb />totam ſuam ad oppoſitam partem vim exerat, multo magis Elaſterium quod <lb />
<ptr xml:id="note-0231-19a" corresp="note-0231-19" type="noteAnchor" />
ad illam transſertur partem ad quam agit, integram vim, quarelaxatur, corpori com-<lb />municabit, cui etiam imprimet vim quæ valet actionem, quæ ipſum transfert ela-<lb />ſterium dum relaxatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0231-19" corresp="note-0231-19a" place="margin">592.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">591.</note>
        <pb facs="0232" n="162" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p rend="italics">
          <s xml:space="preserve">Ex quibus quoque ſequitur, quando obſtaculo non omnino immobili inſi ſtit E-<lb />
<ptr xml:id="note-0232-01a" corresp="note-0232-01" type="noteAnchor" />
laſterium hoc ad partem oppoſitam exerere vim ſuam totam, demtâ illâ, quâ obſtacu-<lb />lum poteſt movere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0232-01" corresp="note-0232-01a" place="margin">593.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si hæc applicemus ad caſum memoratum, facile videmus corpori B com-<lb />
<ptr xml:id="note-0232-02a" corresp="note-0232-02" type="noteAnchor" />
municari duos gradus vis, quibus partes elaſticæ fuere flexæ, &amp; </s>
          <s xml:space="preserve">prætereaim-<lb />preſſionem qua elaſterium fuit translatum, durante expanſione <ptr type="noteAnchor" />, quæ impreſ-
<ptr xml:id="note-0232-03a" corresp="note-0232-03" type="noteAnchor" />
ſio eſt actio corporis A in Elaſterium, &amp; </s>
          <s xml:space="preserve">valet vim a corpore A in hac a-<lb />ctione amiſſam <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Amiſit autem A unum gradum vis, qui ergo ipſi B, præ-
<ptr xml:id="note-0232-04a" corresp="note-0232-04" type="noteAnchor" />
ter duos memoratos, fuit communicatus; </s>
          <s xml:space="preserve">accepit ergo B tres gradus vis, qui <lb />additi uni gradui, quem ante elaſterii actionem habebat, dant quatuor gra-<lb />dus vis. </s>
          <s xml:space="preserve">Quod explicandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0232-02" corresp="note-0232-02a" place="margin">594.</note>
              <note xml:space="preserve" xml:id="note-0232-03" corresp="note-0232-03a" n="*" anchored="true" place="margin">591.</note>
              <note xml:space="preserve" xml:id="note-0232-04" corresp="note-0232-04a" n="*" anchored="true" place="margin">478.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ratiocinium omnino ſimile eſt in aliis caſibus, in quibus poſt ſeparatio-<lb />
<ptr xml:id="note-0232-05a" corresp="note-0232-05" type="noteAnchor" />
nem ad eandem partem corpora tendunt, aut unum quieſcit; </s>
          <s xml:space="preserve">ſi autem ad <lb />partes propoſitas poſt ictum moveantur ex iiſdem principiis difficultas tolli-<lb />tur, uthoc patebit exemplo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0232-05" corresp="note-0232-05a" place="margin">595.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit corpus A cujus maſſa eſt I. </s>
          <s xml:space="preserve">quod velocitate 6.</s>
          <s xml:space="preserve">, id eſt, cum vi 36. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, in-
<ptr xml:id="note-0232-06a" corresp="note-0232-06" type="noteAnchor" />
currit in corpus duplum quieſcens B; </s>
          <s xml:space="preserve">ponimus corpora perfecte elaſtica. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0232-07a" corresp="note-0232-07" type="noteAnchor" />
Poſt ictum B habebit velocitatem 4, id eſt, vim 32. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">A redibit velocitate 2, <lb />
<ptr xml:id="note-0232-08a" corresp="note-0232-08" type="noteAnchor" />
habebitque vim. </s>
          <s xml:space="preserve">4 <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hoc, jam ante demonſtratum, nunc eſt illuſtrandum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0232-06" corresp="note-0232-06a" place="margin">596.</note>
              <note xml:space="preserve" xml:id="note-0232-07" corresp="note-0232-07a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0232-08" corresp="note-0232-08a" n="*" anchored="true" place="margin">519. 567. <lb />568.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ante inſtauratam figuram, corpora ambo cum duobus gradibus velocita-<lb />tis moventur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">Elaſtrum fuit flexum vi 24. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si navem concipiamus in
<ptr xml:id="note-0232-09a" corresp="note-0232-09" type="noteAnchor" />
qua corpora poſt ictum, ante ſeparationem quieſcunt, id eſt cujus velocitas <lb />
<ptr xml:id="note-0232-10a" corresp="note-0232-10" type="noteAnchor" />
etiam eſt duo; </s>
          <s xml:space="preserve">corpora in hac ſeparantur viribus &amp; </s>
          <s xml:space="preserve">velocitatibus, quæ ſunt in-<lb />verſe ut maſſæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">B velocitate 2.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">A celeritate 4.</s>
          <s xml:space="preserve">, ſi Elaſtrum minus fuiſ-
<ptr xml:id="note-0232-11a" corresp="note-0232-11" type="noteAnchor" />
ſet flexum, etiam vires fuiſſent inverſè ut maſſæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo, pro parte relaxato
<ptr xml:id="note-0232-12a" corresp="note-0232-12" type="noteAnchor" />
Elaſterio, in hac ratione ſunt vires, ideoque velocitates <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">idcirco ubi B ha-
<ptr xml:id="note-0232-13a" corresp="note-0232-13" type="noteAnchor" />
bet unum gradum velocitatis in nave, A duos habet, &amp; </s>
          <s xml:space="preserve">actio elaſtri valet 6. <lb /></s>
          <s xml:space="preserve">gradus vis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0232-09" corresp="note-0232-09a" n="*" anchored="true" place="margin">519.</note>
              <note xml:space="preserve" xml:id="note-0232-10" corresp="note-0232-10a" n="*" anchored="true" place="margin">510.</note>
              <note xml:space="preserve" xml:id="note-0232-11" corresp="note-0232-11a" n="*" anchored="true" place="margin">472 561.</note>
              <note xml:space="preserve" xml:id="note-0232-12" corresp="note-0232-12a" n="*" anchored="true" place="margin">564.</note>
              <note xml:space="preserve" xml:id="note-0232-13" corresp="note-0232-13a" n="*" anchored="true" place="margin">472.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tum, motus abſolutos conſiderando, B habet velocitatem 3, &amp; </s>
          <s xml:space="preserve">A quieſcit; <lb /></s>
          <s xml:space="preserve">Elaſtrum verò vim 18. </s>
          <s xml:space="preserve">ſuperſtitem exerit, dum corpori B ſecundum gradum <lb />velocitatis in nave &amp; </s>
          <s xml:space="preserve">corpori A tertium &amp; </s>
          <s xml:space="preserve">quartum in ipſa communicat. </s>
          <s xml:space="preserve">Ha-<lb />bet nunc B, ſepoſita nave, velocitatem 4. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">redit A velocìtate 2.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus B ante elaſtrum relaxatum vim habet 8 <ptr type="noteAnchor" />, dum Elaſtrum primos
<ptr xml:id="note-0232-14a" corresp="note-0232-14" type="noteAnchor" />
6. </s>
          <s xml:space="preserve">gradus vis exerit nondum redit A, verſamurque in caſu n. </s>
          <s xml:space="preserve">595. </s>
          <s xml:space="preserve">ideo ſex <lb />hi gradus corpori B communicantur, &amp; </s>
          <s xml:space="preserve">præterea quantum amittit A ut hoc <lb />in n. </s>
          <s xml:space="preserve">594. </s>
          <s xml:space="preserve">explicavimus, id eſt 4; </s>
          <s xml:space="preserve">habetque B vim 18. </s>
          <s xml:space="preserve">quæ reſpondet velo-<lb />citati 3 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">maſſa enim eſt duo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0232-14" corresp="note-0232-14a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">470.</note>
        <p>
          <s xml:space="preserve">Elaſtrum nunc ab una parte inſiſtit corpori quieſcenti, ad alteram corpo-<lb />ri agitato, ipſumque huc uſque totum fuit translatum, nunc autem pro par-<lb />te tantum transfertur &amp; </s>
          <s xml:space="preserve">poteſt repellere corpus A vi 4, ideoque reliquam tan-<lb />tum vim 14 poterit ipſi B imprimere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hi additi ad 18, dant gradus 32. </s>
          <s xml:space="preserve">quos
<ptr xml:id="note-0232-16a" corresp="note-0232-16" type="noteAnchor" />
ut ex aute demonſtratis liquet revera habet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0232-16" corresp="note-0232-16a" n="*" anchored="true" place="margin">593.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0233" />
        <pb facs="0233a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0233a-01" />
          <label>0233a-01</label>
        </figure>
        <pb facs="0234" />
        <pb facs="0235" n="163" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXIV.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 3.</head>
        <head rend="italics" xml:space="preserve">Paradoxi explicatio.</head>
        <p>
          <s xml:space="preserve">Ex corporum elafticorum proprietate in n. </s>
          <s xml:space="preserve">584. </s>
          <s xml:space="preserve">memorata deducitur para-<lb />
<ptr xml:id="note-0235-01a" corresp="note-0235-01" type="noteAnchor" />
doxi, quod non minus notabile eſt quàm vulgare, explicatio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0235-01" corresp="note-0235-01a" place="margin">597.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fabri argentarii, qui domus cujuſcunque partem ſuperiorem occupant, <lb />incudem pulvino ſuperimponunt, quo magis ictibus mallei incus reſiſtit, &amp; </s>
          <s xml:space="preserve"><lb />minus tremit domus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponamus, ſublato pulvino, trabi incudem imponi, incus corpus eſt elaſti-<lb />cum, &amp; </s>
          <s xml:space="preserve">trabs, quæ in extremitatibus fixa eſt, etiam corpus eſt elaſticum. <lb /></s>
          <s xml:space="preserve">Ponamus malleo incudem percuti.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dicatur mallei maſſa M; </s>
          <s xml:space="preserve">incudis maſſa I; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">maſſa trabis cum corporibus <lb />cohærentibus &amp; </s>
          <s xml:space="preserve">quæ cum ipſa agitantur T; </s>
          <s xml:space="preserve">ſit etiam velocitas mallei v. <lb /></s>
          <s xml:space="preserve">Multiplicando M per v, &amp; </s>
          <s xml:space="preserve">dividendo productum per ſummam Maſſarum <lb />mallei &amp; </s>
          <s xml:space="preserve">incudis &amp; </s>
          <s xml:space="preserve">habemus dimidium velocitatis incudi communicatæ <ptr type="noteAnchor" />,
<ptr xml:id="note-0235-02a" corresp="note-0235-02" type="noteAnchor" />
nam licet trabi impoſita ſit incus agitatur quaſi ſola eſſet <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ipſius velocitas
<ptr xml:id="note-0235-03a" corresp="note-0235-03" type="noteAnchor" />
eſt {2Mxv/M + I}, qua velocitate incus percutit trabem &amp; </s>
          <s xml:space="preserve">corpora cum hac conjun-<lb />cta; </s>
          <s xml:space="preserve">multiplicando velocitatem incudis per maſſam habemus {2MxIxv/M + I} divi-<lb />dendo duplum hujus producti per ſummam maſſarum habemus {4MxIxv/M + Ix1 + T} <lb />trabis velocitatem <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Denominator hujus fractionis MxI + IxI + TxM
<ptr xml:id="note-0235-04a" corresp="note-0235-04" type="noteAnchor" />
+ TxI, propter M exiguum reſpectu 1 &amp; </s>
          <s xml:space="preserve">T, vix ab hoc alio differt M x I <lb />+ IxI + TxI, quo poſito, velocitas detecta mutatur in hanc {4Mxv/M + I + T}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0235-02" corresp="note-0235-02a" n="*" anchored="true" place="margin">519 567.</note>
              <note xml:space="preserve" xml:id="note-0235-03" corresp="note-0235-03a" n="*" anchored="true" place="margin">585.</note>
              <note xml:space="preserve" xml:id="note-0235-04" corresp="note-0235-04a" n="*" anchored="true" place="margin">519. 585.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Interpoſito corpore molli, pulvino nempe, inter trabem &amp; </s>
          <s xml:space="preserve">incudem, cor-<lb />pora hæc unicam quaſi formant maſſam, ideoque cum nunc malleus majus <lb />percutiat corpus majorem patitur refiſtentiam, &amp; </s>
          <s xml:space="preserve">velocitas trabi communicata <lb />habetur dividendo 2 Mxv per ſummam maſſarum M + I + T <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">velocitas eſt
<ptr xml:id="note-0235-05a" corresp="note-0235-05" type="noteAnchor" />
{2Mxv/M + I + T} dimidium velocitatis ſublato pulvino; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">agitatio, ſublato hoc i-<lb />pſo, quadruplum poteſt edere effectum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0235-05" corresp="note-0235-05a" n="*" anchored="true" place="margin">519. 567.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">447. 459.</note>
        <pb facs="0236" n="164" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXV.</head>
        <head rend="italics" xml:space="preserve">De motu compoſito.</head>
        <p rend="italics">
          <s xml:space="preserve">SI corpus moveatur, &amp; </s>
          <s xml:space="preserve">hujus celeritas augenda aut minu-<lb />
<ptr xml:id="note-0236-01a" corresp="note-0236-01" type="noteAnchor" />
enda ſit, manente directione, evidens eſt, impre ſſionem <lb />requiri, quæ proportionalis ſit differentiæ quadratorum ve-<lb />locitatis quam corpus ante actionem habuit, &amp; </s>
          <s xml:space="preserve">illius quam <lb />poſt actionem habet, huic enim differentiæ vis communicata <lb />aut ſublata proportionalis eſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0236-02a" corresp="note-0236-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0236-01" corresp="note-0236-01a" place="margin">598.</note>
              <note xml:space="preserve" xml:id="note-0236-02" corresp="note-0236-02a" place="margin">447.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus duas actiones eodem tempore in corpus juxta e an-<lb />
<ptr xml:id="note-0236-03a" corresp="note-0236-03" type="noteAnchor" />
dem directionem agere. </s>
          <s xml:space="preserve">Dum augetur velocitas; </s>
          <s xml:space="preserve">creſcit in <lb />ratione duplicata vis corpori inſita <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt hujus augmen-
<ptr xml:id="note-0236-04a" corresp="note-0236-04" type="noteAnchor" />
tum ſequitur proportionem augmenti trianguli quod dum <lb />augetur eidem ſimile manet, &amp; </s>
          <s xml:space="preserve">cujus latus unum velocitatem <lb />
<ptr xml:id="note-0236-05a" corresp="note-0236-05" type="noteAnchor" />
repræſentat <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">vis dum velocitas eſt A g, eſt ad vim ubi
<ptr xml:id="note-0236-06a" corresp="note-0236-06" type="noteAnchor" />
velocitas eſt A l, ut area A g r ad A l s.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0236-03" corresp="note-0236-03a" place="margin">599.</note>
              <note xml:space="preserve" xml:id="note-0236-04" corresp="note-0236-04a" place="margin">447.</note>
              <note xml:space="preserve" xml:id="note-0236-05" corresp="note-0236-05a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0236-06" corresp="note-0236-06a" n="*" anchored="true" place="margin">19. El. vi.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus, actiones alternatim in corpus agere per in-<lb />tervalla temporis æqualia; </s>
          <s xml:space="preserve">actione primâ communicari vim <lb />A d o, ſecundâ vim d o p e; </s>
          <s xml:space="preserve">iterum actione prima commu-<lb />nicari vim p e f q, &amp; </s>
          <s xml:space="preserve">ſecundâ f q r g &amp; </s>
          <s xml:space="preserve">ſic ulterius; </s>
          <s xml:space="preserve">ſumma <lb />arearum albarum repræſentat vim integram prima actione <lb />communicatam, &amp; </s>
          <s xml:space="preserve">ſumma nigrarum deſignat vim integram <lb />ſecundâ actione corpori impreſſam. </s>
          <s xml:space="preserve">Cum per tempora æ-<lb />qualia actiones egerint, vires hæ, id eſt, ſummæ arearum, <lb />ſunt ut ipſæ actiones, in qua etiam ratione eſt area. </s>
          <s xml:space="preserve">quæcun-<lb />que alba ad ſuam vicinam nigram: </s>
          <s xml:space="preserve">ſi momenta temporum <lb />fuerint inſinitè exigua, ut ſunt quando actiones ſimul agunt, <lb />areæ hæ pro parallelogrammis haberi poſſunt, &amp; </s>
          <s xml:space="preserve">parallelogram-<lb />ma vicina eandem habebunt altitudinem; </s>
          <s xml:space="preserve">ideoque erunt in-<lb />ter ſe ut baſes <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo baſis albi ad baſim vicini nigri, ut
<ptr xml:id="note-0236-07a" corresp="note-0236-07" type="noteAnchor" />
actio prima ad ſecundam, &amp; </s>
          <s xml:space="preserve">in eadem ratione ſumma ba-<lb />ſium parallelogrammorum alborum ad ſummam baſium ni-<lb />grorum; </s>
          <s xml:space="preserve">id eſt, ita ſe habet velocit as quam communicavit <lb />actio prima ad velocitatem ex ſecundâ oriundam. </s>
          <s xml:space="preserve">Quæ ea-
</s>
          <pb facs="0237" n="165" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XXV.</fw>
dem demonſtratio in acceleratione quacunque corporis ex <lb />duabus actionibus locum habet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0236-07" corresp="note-0236-07a" place="margin">I. El. VI.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si in corpus motum, actio detur juxta directionem di-<lb />verſam a directione motus primi, mutationem in directione <lb />dari ſuperius vidimus <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">quæ velocitates in hiſce caſibus
<ptr xml:id="note-0237-01a" corresp="note-0237-01" type="noteAnchor" />
fpectant examinavimus <ptr type="noteAnchor" />, de viribus nunc agendum. </s>
          <s xml:space="preserve">Movea-
<ptr xml:id="note-0237-02a" corresp="note-0237-02" type="noteAnchor" />
tur corpus per AD, celeritate, quam hac lineâ deſigna-<lb />mus, &amp; </s>
          <s xml:space="preserve">vis nova hoc pellat per AE, celeritate, quam hac <lb />
<ptr xml:id="note-0237-03a" corresp="note-0237-03" type="noteAnchor" />
linea deſignamus; </s>
          <s xml:space="preserve">corpus duabus celeritatibus latum, mo-<lb />vetur per AB <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Non tamen in ſingulis hiſce caſibus im-
<ptr xml:id="note-0237-04a" corresp="note-0237-04" type="noteAnchor" />
preſſione æ quali æ qualis communicatur velocitas lateralis; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0237-05a" corresp="note-0237-05" type="noteAnchor" />
ponimus AB &amp; </s>
          <s xml:space="preserve">AE in tribus figuris reſpectivè æquales. <lb /></s>
          <s xml:space="preserve">In fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">motus ſecundus, pro parte cum motu primo con-<lb />ſpirat, ita ut in hoc motu contineatur acceleratio motus <lb />per AD. </s>
          <s xml:space="preserve">Eodem modo retardatio velocitatis per AD con-<lb />tinetur in motu per AE in fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">Idcirco impreſſiones, qui-<lb />bus corpora per AE pelluntur, ut velocitatem hac lineâ <lb />deſignatam corporibus ſingulis communicent, non ſunt æ-<lb />quales inter ſe <ptr type="noteAnchor" />, neque impreſſioni, qua corpori quieſcenti
<ptr xml:id="note-0237-06a" corresp="note-0237-06" type="noteAnchor" />
hæc poſſet communicari velocitas <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0237-01" corresp="note-0237-01a" n="*" anchored="true" place="margin">245.</note>
              <note xml:space="preserve" xml:id="note-0237-02" corresp="note-0237-02a" place="margin">246.</note>
              <note xml:space="preserve" xml:id="note-0237-03" corresp="note-0237-03a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 314. 5.</note>
              <note xml:space="preserve" xml:id="note-0237-04" corresp="note-0237-04a" place="margin">600.</note>
              <note xml:space="preserve" xml:id="note-0237-05" corresp="note-0237-05a" place="margin">246.</note>
              <note xml:space="preserve" xml:id="note-0237-06" corresp="note-0237-06a" n="*" anchored="true" place="margin">443.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">440.</note>
        <p>
          <s xml:space="preserve">In ſolo caſu fig. </s>
          <s xml:space="preserve">3, in quo angulus EAD eſt rectus, motus <lb />
<ptr xml:id="note-0237-08a" corresp="note-0237-08" type="noteAnchor" />
lateralis neque conſpirat neque contrarie agit cum motu per <lb />AD, &amp; </s>
          <s xml:space="preserve">impreſſio, qua corpus movetur, in corpus agit quaſi <lb />quieſceret; </s>
          <s xml:space="preserve">idcirco in hoc caſu vis corpori communicata pro-<lb />portionalis eſt quadrato ſuæ velocitatis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">cùm impreſſio
non poſſit vim per AE minuere, corporis vis integra pro-<lb />
<ptr xml:id="note-0237-09a" corresp="note-0237-09" type="noteAnchor" />
portionalis eſt ambobus quadratis linearum AD &amp; </s>
          <s xml:space="preserve">AE, quod <lb />congruit cum demonſtratis: </s>
          <s xml:space="preserve">nam fertur corpus celeritate AB,<ptr type="noteAnchor" />
<ptr xml:id="note-0237-10a" corresp="note-0237-10" type="noteAnchor" />
cujus quadratum valet memorata duo quadrata <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0237-08" corresp="note-0237-08a" place="margin">601.</note>
              <note xml:space="preserve" xml:id="note-0237-09" corresp="note-0237-09a" n="*" anchored="true" place="margin">447.</note>
              <note xml:space="preserve" xml:id="note-0237-10" corresp="note-0237-10a" n="*" anchored="true" place="margin">246.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">[47. El I.</note>
        <p>
          <s xml:space="preserve">Ex his virium menſura ſi hæc ignota eſſet, detegi poſſet. </s>
          <s xml:space="preserve">Cor-<lb />
<ptr xml:id="note-0237-12a" corresp="note-0237-12" type="noteAnchor" />
pori, quod habet vim quæ reſpondet celeritati AD, communi-<lb />catur vis quæ velocitati AE reſpondet, quæ cum corpori com-<lb />municetur quaſi quieſceret, vim primam mutare non poteſt; </s>
          <s xml:space="preserve">va-<lb />let ideò corporis vis integra ſummam harum virium, dum <lb />ipſius velocitas eſt AB; </s>
          <s xml:space="preserve">ergo vis quæ huic reſpondet velocitati, <lb />memoratæ ſummæ æqualis eſt. </s>
          <s xml:space="preserve">Quod ſieri non poterit in omni
</s>
          <pb facs="0238" n="166" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
caſu niſi quadratis velocitatis vires proportionales ſint <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0237-12" corresp="note-0237-12a" place="margin">601.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">47. El. v.</note>
        <p>
          <s xml:space="preserve">Deducimus ex his non intereſſe neque reſpectu impreſ-<lb />
<ptr xml:id="note-0238-02a" corresp="note-0238-02" type="noteAnchor" />
ſionum, quibus corpus agitatur, neque reſpectu virium, ne-<lb />que velocitatum, utrum corpus per AB feratur celeritate <lb />AB, an per AD &amp; </s>
          <s xml:space="preserve">AE celeritatibus hiſce lineis proportio-<lb />nalibus, quæ inter ſe angulum rectum continent. </s>
          <s xml:space="preserve">Quare <lb />motus per AB, juxta directionem ut AD, nil continet præ-<lb />
<ptr xml:id="note-0238-03a" corresp="note-0238-03" type="noteAnchor" />
ter motum velocitate AD.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0238-02" corresp="note-0238-02a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0238-03" corresp="note-0238-03a" place="margin">603.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Deducimus etiam motum corporis reſolvi poſſe in duos <lb />
<ptr xml:id="note-0238-04a" corresp="note-0238-04" type="noteAnchor" />
alios innumeris modis, quod fiet, ſi linea, in directione motus da-<lb />ti poſita, &amp; </s>
          <s xml:space="preserve">longitudine celeritatem deſignans, ſit hypotenu-<lb />ſa trianguli rectanguli; </s>
          <s xml:space="preserve">nam hujus reliqua duo latera ſitu <lb />motuum quæ ſitorum directiones dabunt, &amp; </s>
          <s xml:space="preserve">longitudinibus ſuis <lb />reſpective velocitates horum expriment: </s>
          <s xml:space="preserve">eruntque vires juxta <lb />has directiones quadratis velocitatum proportionales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0238-04" corresp="note-0238-04a" place="margin">604.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut nunc determinemus, qua vi corpus per AE ſit agitandum, <lb />
<ptr xml:id="note-0238-05a" corresp="note-0238-05" type="noteAnchor" />
ut ei communicetur celeritas AE, in caſu in quo motus hic cum <lb />
<ptr xml:id="note-0238-06a" corresp="note-0238-06" type="noteAnchor" />
primo motu pro parte conſpirat; </s>
          <s xml:space="preserve">motum per A Ein duos reſol-<lb />
<ptr xml:id="note-0238-07a" corresp="note-0238-07" type="noteAnchor" />
vo <ptr type="noteAnchor" /> per A f &amp; </s>
          <s xml:space="preserve">A g, ângulum rectum continentes, &amp; </s>
          <s xml:space="preserve">ducitur E g
parallelâ A f. </s>
          <s xml:space="preserve">Per A f tantum corpori vis communicanda eſt, <lb />qua corpus ſi quieſceret hac celeritate poſſet ferri, &amp; </s>
          <s xml:space="preserve">quæ <lb />proportionalis eſt quadrato A f <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">per A g autem vis com-
<ptr xml:id="note-0238-08a" corresp="note-0238-08" type="noteAnchor" />
municanda eſt, qua celeritas AD quantitate A g augeatur, <lb />id eſt fiat A h, quæ vis proportionalis eſt differentiæ qua-<lb />
<ptr xml:id="note-0238-09a" corresp="note-0238-09" type="noteAnchor" />
dratorum A h, AD <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hæ vires ſimul communicandæ e-
runt juxta AE ut corpus hac celeritate poſſit ferri; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vis <lb />integra corporis proportionalis eſt quadrato lineæ AD, dif-<lb />ferentiæ quadratorum linearum A h &amp; </s>
          <s xml:space="preserve">AD, &amp; </s>
          <s xml:space="preserve">quadrato <lb />A f; </s>
          <s xml:space="preserve">primis duobus ex hiſce tribus quantitatibus in unam <lb />ſummam collectis, habemus quadratum lineæ A h, cui ſi <lb />addatur quadratum lineæ A f, aut h B, habemus quadra-<lb />tum lineæ AB; </s>
          <s xml:space="preserve">cui proportionalem eſſe vim corpori inſi-<lb />
<ptr xml:id="note-0238-10a" corresp="note-0238-10" type="noteAnchor" />
tam ex ante demonſtratis ſequitur <ptr type="noteAnchor" />, cum conſtet corpus
<ptr xml:id="note-0238-11a" corresp="note-0238-11" type="noteAnchor" />
celeritate AB ferri <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0238-12a" corresp="note-0238-12" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0238-05" corresp="note-0238-05a" place="margin">605.</note>
              <note xml:space="preserve" xml:id="note-0238-06" corresp="note-0238-06a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0238-07" corresp="note-0238-07a" n="*" anchored="true" place="margin">246.</note>
              <note xml:space="preserve" xml:id="note-0238-08" corresp="note-0238-08a" n="*" anchored="true" place="margin">601. 447.</note>
              <note xml:space="preserve" xml:id="note-0238-09" corresp="note-0238-09a" n="*" anchored="true" place="margin">591.</note>
              <note xml:space="preserve" xml:id="note-0238-10" corresp="note-0238-10a" n="*" anchored="true" place="margin">447. <lb />*246.</note>
              <note xml:space="preserve" xml:id="note-0238-11" corresp="note-0238-11a" place="margin">606.</note>
              <note xml:space="preserve" xml:id="note-0238-12" corresp="note-0238-12a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simotum per AE eodem modo in duos reſolvamus per A f &amp; </s>
          <s xml:space="preserve"><lb />A g <ptr type="noteAnchor" />, motu hoc ſecundo retardatur motus per AD; </s>
          <s xml:space="preserve">unde ſequi-
<ptr xml:id="note-0238-13a" corresp="note-0238-13" type="noteAnchor" />
tur, ut corpus per AE, celeritate hac lineâ deſignatâ feratur, illi
</s>
          <pb facs="0239" n="167" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXV.</fw>
communicandam eſſe vim, quæ proportionalis ſit quadrato <lb />A f, &amp; </s>
          <s xml:space="preserve">impreſſionem, qua agitatur, ulterius tantum valere <lb />debere, ut quantitate A g poſſit minuere velocitatem AD, <lb />in hoc caſu corpus juxta directionem AD tantum ſuperſti-<lb />tem habebit vim proportionalem quadrato A b <ptr type="noteAnchor" />, cui ſi ad-
<ptr xml:id="note-0239-01a" corresp="note-0239-01" type="noteAnchor" />
datur vis proportionalis quadrato A f<ptr type="noteAnchor" />, habemus vim propor-
<ptr xml:id="note-0239-02a" corresp="note-0239-02" type="noteAnchor" />
tionalem quadrato AB; </s>
          <s xml:space="preserve">quod iterum cum ante demonſtra-<lb />tis congruit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0238-13" corresp="note-0238-13a" n="*" anchored="true" place="margin">604.</note>
              <note xml:space="preserve" xml:id="note-0239-01" corresp="note-0239-01a" n="*" anchored="true" place="margin">598.</note>
              <note xml:space="preserve" xml:id="note-0239-02" corresp="note-0239-02a" n="*" anchored="true" place="margin">601.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">246 447.</note>
        <p>
          <s xml:space="preserve">Propoſitionem hanc, vim ſequi proportionem quadrati <lb />
<ptr xml:id="note-0239-04a" corresp="note-0239-04" type="noteAnchor" />
velocitatis, non poſſe referri ad illam cum qua alia in ea-<lb />dem linea agit, facile ex ante demonſtratis ſequitur <ptr type="noteAnchor" />, hac
<ptr xml:id="note-0239-05a" corresp="note-0239-05" type="noteAnchor" />
de causâ ubi vim in duas reſolvimus, hæ quadratis veloci-<lb />tatum proportionales non erunt, niſi ambarum directiones <lb />angulum rectum contineant ne aliter pro parte conſpirent <lb />aut contrarie agant <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ex quibus deducimus vim reſolu-
<ptr xml:id="note-0239-06a" corresp="note-0239-06" type="noteAnchor" />
tam non iterum poſſe reſolvi. </s>
          <s xml:space="preserve">Motus per AB reſolvitur <lb />in duos motus ejuſdem corporis per AD &amp; </s>
          <s xml:space="preserve">AE, &amp; </s>
          <s xml:space="preserve">vires <lb />
<ptr xml:id="note-0239-07a" corresp="note-0239-07" type="noteAnchor" />
quadratis velociratum ſunt proportionales; </s>
          <s xml:space="preserve">ſed ſi motus per <lb />AE iterum in duos per AF &amp; </s>
          <s xml:space="preserve">AG angulum rectum con-<lb />tinentes ſeparetur, non erunt hæ ultimæ quadratis veloci-<lb />tatum proportionales, &amp; </s>
          <s xml:space="preserve">non poterit hîc applicari n. </s>
          <s xml:space="preserve">604, <lb />in quo agitur de viribus, quæ non modo inter ſe non con-<lb />fpirant, neque contrarie agunt, ſed quæ cum tertiâ nil <lb />commune habent. </s>
          <s xml:space="preserve">Hîc autem ipſe motus corporis per <lb />AB in tres motus reſolvitur per AD, AF &amp; </s>
          <s xml:space="preserve">AG, in qui-<lb />bus AF &amp; </s>
          <s xml:space="preserve">AD pro parte conſpirant, AD &amp; </s>
          <s xml:space="preserve">AG partim <lb />contrariè agunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">reſolutio quæ ad velocitates poteſtappli-<lb />cari, cùm demonſtratio n. </s>
          <s xml:space="preserve">246. </s>
          <s xml:space="preserve">eadem ſit, ſive motus in re-<lb />folutione conſpirent, ſive contrarie agunt, ad vires non poſſe <lb />referri ex ante demonſtratis clarum eſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0239-08a" corresp="note-0239-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0239-04" corresp="note-0239-04a" place="margin">607.</note>
              <note xml:space="preserve" xml:id="note-0239-05" corresp="note-0239-05a" n="*" anchored="true" place="margin">598. 599</note>
              <note xml:space="preserve" xml:id="note-0239-06" corresp="note-0239-06a" n="*" anchored="true" place="margin">601.</note>
              <note xml:space="preserve" xml:id="note-0239-07" corresp="note-0239-07a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig 54.</note>
              <note xml:space="preserve" xml:id="note-0239-08" corresp="note-0239-08a" place="margin">440. 443.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In n. </s>
          <s xml:space="preserve">605. </s>
          <s xml:space="preserve">606. </s>
          <s xml:space="preserve">motum per AB compoſitum habemus ex <lb />
<ptr xml:id="note-0239-09a" corresp="note-0239-09" type="noteAnchor" />
duobus, quorum unum in alios reſolvimus, ſed ita, ut poſt <lb />
<ptr xml:id="note-0239-10a" corresp="note-0239-10" type="noteAnchor" />
reſolutionem omnes motus darentur in duabus lineis, angu-<lb />lum rectum continentibus: </s>
          <s xml:space="preserve">quare motus in ſingulis lineis, <lb />ſeparatim conſiderari potuere, quod nunquam fieri poteſt <lb />ubi motus varii in pluribus quàm duabus lineis dantur, tunce-
</s>
          <pb facs="0240" n="168" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
nim quidam neceſſario motuspro parte conſpirant, aut con-<lb />trarie agunt; </s>
          <s xml:space="preserve">de his nihil demonſtravimus, ex eadem tamen <lb />theoria virium deduci poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0239-09" corresp="note-0239-09a" place="margin">608.</note>
              <note xml:space="preserve" xml:id="note-0239-10" corresp="note-0239-10a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 4. 5.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXVI.</head>
        <head rend="italics" xml:space="preserve">De Percuſſione obliqua.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">ANgulus incidentiæ vocatur angulus quem directio motus <lb />
<ptr xml:id="note-0240-01a" corresp="note-0240-01" type="noteAnchor" />
corporis, ad aliud accedentis, efficit cum perpendicula-<lb />ri ad ſuperficiem hujus in puncto, in quo percutitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0240-01" corresp="note-0240-01a" place="margin">609.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>. 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Angulus reflexionis eſt angulus, quem cum eadem per-<lb />
<ptr xml:id="note-0240-02a" corresp="note-0240-02" type="noteAnchor" />
pendiculari efficit directio motus corporis poſt percuſſio-<lb />nem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0240-02" corresp="note-0240-02a" place="margin">610.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si Corpus elaſticum P in obicem firmum elaſticum FG in-<lb />
<ptr xml:id="note-0240-03a" corresp="note-0240-03" type="noteAnchor" />
currat, obliquè juxta directionem P a, redibit per a p, i-<lb />
<ptr xml:id="note-0240-04a" corresp="note-0240-04" type="noteAnchor" />
ta, ut angulus incidentiæ P a B æqualis ſit angulo reflexio-<lb />nis B a p. </s>
          <s xml:space="preserve">Motus per P a, quam longitudine celeritatem <lb />corporis deſignare ponimus, poteſt reſolvi in duos, quorum <lb />unius directio parallela ſit lineæ B a, alterius huic perpen-<lb />dicularis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">corpus in obicem incurret in a, quaſi celeritati-<lb />bus C a, B a, &amp; </s>
          <s xml:space="preserve">juxta haſce directiones, ad hunc accederet *. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0240-05a" corresp="note-0240-05" type="noteAnchor" />
Motus per C a ictu non mutatur &amp; </s>
          <s xml:space="preserve">celeritate a E corpus <lb />motum continuat, poſitis C a, a E æqualibus; </s>
          <s xml:space="preserve">motu per <lb />B a directè in obſtaculum incurrit, &amp; </s>
          <s xml:space="preserve">per eandem lineam, <lb />ea qua acceſſit celeritate redit <ptr type="noteAnchor" />, id eſt per a B; </s>
          <s xml:space="preserve">hiſce au-
<ptr xml:id="note-0240-06a" corresp="note-0240-06" type="noteAnchor" />
tem duobus motibus agitatum corpus redit per a p, diago-<lb />nalem rectanguli lineis a E, a B, formati <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Triangula ve-
<ptr xml:id="note-0240-07a" corresp="note-0240-07" type="noteAnchor" />
rò BP a, B a p eſſe æqualia liquet, unde conſtat propoſi-<lb />tum. </s>
          <s xml:space="preserve">Simili methodo detegimus motus corporum oblique <lb />in ſe mutuo impingentium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0240-03" corresp="note-0240-03a" place="margin">611.</note>
              <note xml:space="preserve" xml:id="note-0240-04" corresp="note-0240-04a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0240-05" corresp="note-0240-05a" n="*" anchored="true" place="margin">604.</note>
              <note xml:space="preserve" xml:id="note-0240-06" corresp="note-0240-06a" n="*" anchored="true" place="margin">559.</note>
              <note xml:space="preserve" xml:id="note-0240-07" corresp="note-0240-07a" n="*" anchored="true" place="margin">246.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus Q quieſcit, corpus P, directione &amp; </s>
          <s xml:space="preserve">celeritate <lb />
<ptr xml:id="note-0240-08a" corresp="note-0240-08" type="noteAnchor" />
PA, in illud impingitur. </s>
          <s xml:space="preserve">Per centra amborum corporum, <lb />cum P in A pervenerit, ducatur linea DB, &amp; </s>
          <s xml:space="preserve">ad illam
</s>
          <pb facs="0241" n="169" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXVI.</fw>
perpendicularis PB, &amp; </s>
          <s xml:space="preserve">abſolvatur parallelogrammum ABPC; <lb /></s>
          <s xml:space="preserve">motus per PA reſolvitur in duos alios per PB &amp; </s>
          <s xml:space="preserve">PC, aut <lb />BA, CA <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">motu per CA corpus P non agit in corpus Q;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0241-01a" corresp="note-0241-01" type="noteAnchor" />
actio ergo oritur ex ſolo motu per BA, id eſt, corpus P, <lb />
<ptr xml:id="note-0241-02a" corresp="note-0241-02" type="noteAnchor" />
impactu obliquo per PA, celeritate PA, in corpus 2 agit, <lb />eodem modo ac ſi directe in illud incurreret per BA, cele-<lb />ritate BA. </s>
          <s xml:space="preserve">Quare motus corporis Q ex illa actione, ſive <lb />corpora ſint elaſtica, ſive non, determinatur ex iis quæ de <lb />impactu directo dicta ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0240-08" corresp="note-0240-08a" place="margin"><hi rend="small caps">TAB XXII</hi>. <lb />fig. 11. &amp; 12.</note>
              <note xml:space="preserve" xml:id="note-0241-01" corresp="note-0241-01a" n="*" anchored="true" place="margin">604.</note>
              <note xml:space="preserve" xml:id="note-0241-02" corresp="note-0241-02a" place="margin">612</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus corporis P poft impactum ex iiſdem principiis de-<lb />
<ptr xml:id="note-0241-03a" corresp="note-0241-03" type="noteAnchor" />
ducitur Motus per C A non mutatur; </s>
          <s xml:space="preserve">ergo motu illo <lb />æquali celeritate corpus P fertur, directione AE; </s>
          <s xml:space="preserve">ſit ideo <lb />AE æqualis CA. </s>
          <s xml:space="preserve">Mutatio in motu BA determinatur re-<lb />ſpectu corporis P, eodem modo ac motus corporis Q, ex <lb />iis quæ de colliſione directâ explicata ſunt. </s>
          <s xml:space="preserve">Sit celeritas poſt <lb />impactum AD, in ſig. </s>
          <s xml:space="preserve">11.</s>
          <s xml:space="preserve">, quando corpus progreditur, &amp; </s>
          <s xml:space="preserve"><lb />in fig. </s>
          <s xml:space="preserve">12.</s>
          <s xml:space="preserve">, quando regreditur; </s>
          <s xml:space="preserve">ex iſto motu &amp; </s>
          <s xml:space="preserve">motu per <lb />AE oritur motus compoſitus per diagonalem A p, quæ ſitu <lb />&amp; </s>
          <s xml:space="preserve">longitudine directionem &amp; </s>
          <s xml:space="preserve">celeritatem corporis P poſt im-<lb />pactum denotat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0241-03" corresp="note-0241-03a" place="margin">613</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">246.</note>
        <p>
          <s xml:space="preserve">Quando corpora ſunt æqualia &amp; </s>
          <s xml:space="preserve">elaſtica, totus motus per <lb />
<ptr xml:id="note-0241-05a" corresp="note-0241-05" type="noteAnchor" />
BA ex percuſſione deſtruitur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſolus motus per C A ſu-
<ptr xml:id="note-0241-06a" corresp="note-0241-06" type="noteAnchor" />
pereſt, qua directione tunc etiam fertur corpus P. </s>
          <s xml:space="preserve">In hoc <lb />caſu ſemper poſt impulſum corpora ambo, quocunque modo <lb />corpus P ad aliud accedat, ſeparantur directionibus angulum <lb />rectum continentibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0241-05" corresp="note-0241-05a" place="margin">614.</note>
              <note xml:space="preserve" xml:id="note-0241-06" corresp="note-0241-06a" n="*" anchored="true" place="margin">581.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi>.</head>
        <p rend="italics">
          <s xml:space="preserve">Qua Experimenta quæ dam de Colliſione obliqua, &amp; </s>
          <s xml:space="preserve"><lb />compoſita, inſtituuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Duo plana lignea CDE, CDE, ad formam trianguli rectan-<lb />
<ptr xml:id="note-0241-07a" corresp="note-0241-07" type="noteAnchor" />
guli, cujus latus CD eſt longitudinis circiter trium pedum <lb />
<ptr xml:id="note-0241-08a" corresp="note-0241-08" type="noteAnchor" />
cum ſemiſſe, latus DE unius pedis cum ſemiſſe, laborata, <lb />verticaliter poſita, circa cardines A &amp; </s>
          <s xml:space="preserve">B convertuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0241-07" corresp="note-0241-07a" place="margin">615</note>
              <note xml:space="preserve" xml:id="note-0241-08" corresp="note-0241-08a" place="margin"><hi rend="small caps">TAB XXIV</hi>. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Experimenta in hac Machina adhibitis globis eburneis in-<lb />ſtituuntur diametri unius pollicis cum ſemiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Plana ita conjunguntur, ut ſi hiſce alia parallela, ad diſtan-
</s>
          <pb facs="0242" n="170" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tiam quæ paululum ſemidiametrum globorum excedit, <lb />concipiantur, horum interſectio ſit ipſe axis circumvolutio-<lb />nis: </s>
          <s xml:space="preserve">quod præſtatur ſi cardines adhibeantur ut G (fig. </s>
          <s xml:space="preserve">2.) <lb /></s>
          <s xml:space="preserve">quorum partes b, b, ad majorem firmitatem, ligno inſerun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In centro cardinis ſuperioris A, datur cylindrus parvus a, <lb />(fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">in cujus baſi foramen datur, quod cum alio a latere <lb />conjungitur, ita ut per illa immittatur filum i h, quo glo-<lb />bus P ſuſpenditur, &amp; </s>
          <s xml:space="preserve">quod paxillo annectitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ope cochlearum F, F, F, F, F, Machina in ſitu ver-<lb />ticali diſponitur, ita ut filum h i cum axe Machinæ coinci-<lb />dat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In m, m, clavi duo planis memoratis inſeruntur, his glo-<lb />bi Q, Q, ſuſpenduntur, ad talem diſtantiam a planis ut unum-<lb />quodque illud, cui applicatur, fere tangat; </s>
          <s xml:space="preserve">id eſt, ut linea, <lb />quæ concipitur per centra globorum P &amp; </s>
          <s xml:space="preserve">Q, huic plano ſit <lb />parallela; </s>
          <s xml:space="preserve">requiritur ulterius, ut hi globi, ad eandem altitudi-<lb />nem poſiti, ſeſe mutuo tangant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Fila, quibus globi Q &amp; </s>
          <s xml:space="preserve">Q ſuſpenduntur, trajiciunt fora-<lb />mina in prædictis clavis, &amp; </s>
          <s xml:space="preserve">paxillis l, l annectuntur, ut <lb />commode elevari, deprimique, &amp; </s>
          <s xml:space="preserve">omnium globorum cen-<lb />tra in eodem plano, ad horizontem parallelo, diſponi poſ-<lb />ſint. </s>
          <s xml:space="preserve">Regula ænea R, ita inflexa ut juxta illam globus Pin <lb />ſuo motu adſcendat, convertitur circa extremitatum alte-<lb />ram, &amp; </s>
          <s xml:space="preserve">centrum motus cum axe Machinæ coïncidit. </s>
          <s xml:space="preserve">In-<lb />ſervit ad notandam viam globi P, &amp; </s>
          <s xml:space="preserve">altitudinem ad quam <lb />adſcendit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Globus uterque Q juxta planum cui applicatur dimittitur, <lb />&amp; </s>
          <s xml:space="preserve">altitudo a qua dimittitur notatur indice plano infixo, ad <lb />quod in utroque plano foramina quatuor dantur, angulos <lb />æquales, reſpectu motus filorum, continentia.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando globus Q a certa altitudine dimittitur, in glo-<lb />bum P impingit, illumque ſecundum eandem directionem <lb />propellit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. I.</head>
        <note xml:space="preserve" place="margin">616</note>
        <p>
          <s xml:space="preserve">Exhibetur hic horizontalis ſectio hujus Machinæ, cui <lb />
<ptr xml:id="note-0242-02a" corresp="note-0242-02" type="noteAnchor" />
</s>
          <pb facs="0243" />
          <s xml:space="preserve">
<pb facs="0243a" />
<ptr xml:id="fig-0243a-01a" corresp="fig-0243a-01" type="figureAnchor" />
<pb facs="0244" />
<pb facs="0245" n="171" /><fw type="head">MATHEMATICA. LIB. I. CAP. XXVI.</fw>
ſuſpenduntur globus P, &amp; </s>
          <s xml:space="preserve">unus ex globis Q. </s>
          <s xml:space="preserve">Planis ad angulum <lb />rectum diſpoſitis, quacunque directione, &amp; </s>
          <s xml:space="preserve">à quacunque <lb />altitudine cadendo, corpus P impingatur in corpus Q, poſt <lb />impactum corpora directiones planorum ſequuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0242-02" corresp="note-0242-02a" place="margin"><hi rend="small caps">TAB. XXIV</hi>. <lb />fig. 3.</note>
              <figure xml:id="fig-0243a-01" corresp="fig-0243a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0243a-01" />
                <label>0243a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex iiſdem principiis etiam deducitur motus duorum cor-<lb />
<ptr xml:id="note-0245-01a" corresp="note-0245-01" type="noteAnchor" />
porum poſt percuſſionem, quando ambo moventur, quo-<lb />modocunque in ſe mutuo ferantur. </s>
          <s xml:space="preserve">Caſus præcipui repræ-<lb />ſentantur in Tab. </s>
          <s xml:space="preserve">XXIII, &amp; </s>
          <s xml:space="preserve">omnes eodem modo reſolvun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0245-01" corresp="note-0245-01a" place="margin">617</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus P moveatur directione &amp; </s>
          <s xml:space="preserve">celeritate P A; </s>
          <s xml:space="preserve">corpus <lb />
<ptr xml:id="note-0245-02a" corresp="note-0245-02" type="noteAnchor" />
Q directione &amp; </s>
          <s xml:space="preserve">celeritate Q a; </s>
          <s xml:space="preserve">ducatur linea B b, tranſiens <lb />per amborum corporum centra ubiſeſe mutuo tangunt; </s>
          <s xml:space="preserve">ad <lb />illam ſint CA &amp; </s>
          <s xml:space="preserve">c a perpendiculares, &amp; </s>
          <s xml:space="preserve">abſolvantur pa-<lb />rallelogramma PBAC &amp; </s>
          <s xml:space="preserve">Q b a c. </s>
          <s xml:space="preserve">Motus corporis P re-<lb />ſolvitur in duos alios, quorum celeritates &amp; </s>
          <s xml:space="preserve">directiones <lb />deſignant CA, BA. </s>
          <s xml:space="preserve">Motus, in quos reſolvitur motus cor-<lb />poris Q, deſignantur per c a, b a <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Motibus per CA &amp; </s>
          <s xml:space="preserve">c a
<ptr xml:id="note-0245-03a" corresp="note-0245-03" type="noteAnchor" />
corpora non agunt in ſe mutuo, non mutantur ergo hi mo-<lb />tus, &amp; </s>
          <s xml:space="preserve">poſt occurſum deſignantur per A E &amp; </s>
          <s xml:space="preserve">a e, ipſis AC <lb />&amp; </s>
          <s xml:space="preserve">a c æquales; </s>
          <s xml:space="preserve">percuſſio ex motibus per lineas B A, b a eſt <lb />directa, &amp; </s>
          <s xml:space="preserve">determinatur in capitibus <hi rend="small caps">XXIII. XXIV.</hi>: </s>
          <s xml:space="preserve">ſit mo-<lb />tus corporis P verſus D, &amp; </s>
          <s xml:space="preserve">ejus celeritas AD; </s>
          <s xml:space="preserve">corporis Q <lb />motus verſus d, &amp; </s>
          <s xml:space="preserve">ejus celeritas a d. </s>
          <s xml:space="preserve">Poſt occurſum ergo <lb />motus corporis P componitur ex motibus per AE &amp; </s>
          <s xml:space="preserve">AD, <lb />&amp; </s>
          <s xml:space="preserve">movetur per diagonalem A p Corporis Q motus poſt <lb />impactum componitur ex motibus per a e &amp; </s>
          <s xml:space="preserve">a d, unde cor-<lb />pus illud fertur per diagonalem a q; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">longitudines illarum <lb />diagonalium celeritates corporum poſt occurſum denotant <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0245-04a" corresp="note-0245-04" type="noteAnchor" />
In Fig. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">8. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">9. </s>
          <s xml:space="preserve">corpora non elaſtica ponuntur. </s>
          <s xml:space="preserve">Fig. </s>
          <s xml:space="preserve">10. <lb /></s>
          <s xml:space="preserve">11. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">12. </s>
          <s xml:space="preserve">eoſdem caſus datis corporibus elaſticis repræſen-<lb />tant. </s>
          <s xml:space="preserve">In fig. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">litteræ quædam deſunt, quia puncta ipſis <lb />deſignata cum aliis coincidunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0245-02" corresp="note-0245-02a" place="margin"><hi rend="small caps">TAB. XXIII.</hi> <lb />fig 7. 8. 9. <lb />10. 11. &amp; <lb />12.</note>
              <note xml:space="preserve" xml:id="note-0245-03" corresp="note-0245-03a" n="*" anchored="true" place="margin">604</note>
              <note xml:space="preserve" xml:id="note-0245-04" corresp="note-0245-04a" n="*" anchored="true" place="margin">246.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0246" n="172" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXVII.</head>
        <head xml:space="preserve">De Colliſione compoſita.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi></head>
        <p>
          <s xml:space="preserve">COmpoſitam dicimus colliſionem ubi plura dantur quam <lb />
<ptr xml:id="note-0246-01a" corresp="note-0246-01" type="noteAnchor" />
duo corpor a concurrentia, aut ubi corpus unum in plu-<lb />ra plana eodem tempore incurrit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0246-01" corresp="note-0246-01a" place="margin">618</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc capite quædam examinabo circa colliſionem tri-<lb />um corporum, &amp; </s>
          <s xml:space="preserve">impactionem corporis in duo pla-<lb />na.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus P, velocitate AP, incurrit in angulum GCF, juxta <lb />
<ptr xml:id="note-0246-02a" corresp="note-0246-02" type="noteAnchor" />
directionem AP; </s>
          <s xml:space="preserve">determinandum qua actione in utrumque <lb />
<ptr xml:id="note-0246-03a" corresp="note-0246-03" type="noteAnchor" />
planum GC &amp; </s>
          <s xml:space="preserve">FC incurrit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0246-02" corresp="note-0246-02a" place="margin">619</note>
              <note xml:space="preserve" xml:id="note-0246-03" corresp="note-0246-03a" place="margin"><hi rend="small caps">TAB. XXV.</hi> <lb />fig 1. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Notandum corpus, integram ſuam amittere vim; </s>
          <s xml:space="preserve">ponimus <lb />enim obſtaculum fixum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ductis AB &amp; </s>
          <s xml:space="preserve">AD, quæ cum CG &amp; </s>
          <s xml:space="preserve">CF angulos effi-<lb />ciunt rectos, ſint PE &amp; </s>
          <s xml:space="preserve">PH ad has reſpectivè parallelæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si nunc concipiamus Corpus P, eodem tempore ferri per <lb />AE &amp; </s>
          <s xml:space="preserve">AH, velocitatibus hiſce lineis proportionalibus, revera <lb />
<ptr xml:id="note-0246-04a" corresp="note-0246-04" type="noteAnchor" />
movebitur per AP velocitate AP <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò poſſumus conſi-
derare corpus, dum pertingit ad P, agitari velocitatibus <lb />HP &amp; </s>
          <s xml:space="preserve">EP, &amp; </s>
          <s xml:space="preserve">juxta haſce directiones in plana CG, CF <lb />incurrere directè ita ut quæſtio eo reducatur, quibus viribus <lb />corpus eodem tempore per AE &amp; </s>
          <s xml:space="preserve">AH ferri poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0246-04" corresp="note-0246-04a" n="*" anchored="true" place="margin">246.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si angulus FCG eſſet rectus, &amp; </s>
          <s xml:space="preserve">rectus eſſet angulus <lb />EAH; </s>
          <s xml:space="preserve">idcirco motus hi neque contrarie agerent, neque <lb />ad eandem partem tenderent, &amp; </s>
          <s xml:space="preserve">quadratis velocitatum AE <lb />&amp; </s>
          <s xml:space="preserve">AH actiones proportionales eſſent <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0246-05a" corresp="note-0246-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0246-05" corresp="note-0246-05a" n="*" anchored="true" place="margin">604.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ubi autem angulus, quem plana continent, eſt acutus, aut <lb />obtuſus; </s>
          <s xml:space="preserve">ut in hiſce figuris, ducendæ ſunt ad AP perpen-<lb />diculares EL, HI. </s>
          <s xml:space="preserve">In motu per AE continetur motus <lb />per AP velocitate AL; </s>
          <s xml:space="preserve">in motu per AH continetur motus <lb />per AP velocitate AI, &amp; </s>
          <s xml:space="preserve">nil præterea ex motu per A P <lb />in his motibus continetur, propter angulum rectum AIH <ptr type="noteAnchor" />,
<ptr xml:id="note-0246-06a" corresp="note-0246-06" type="noteAnchor" />
Ita ut non interſit, quantum ad motum corporis, utrum eo-
</s>
          <pb facs="0247" />
          <s xml:space="preserve">
<pb facs="0247a" />
<ptr xml:id="fig-0247a-01a" corresp="fig-0247a-01" type="figureAnchor" />
<pb facs="0248" />
<pb facs="0249" n="173" /><fw type="head">MATHEMATICA. LIB. I. CAP. XXVII.</fw>
dem tempore moveatur corpus per AH &amp; </s>
          <s xml:space="preserve">AE, velocitatibus <lb />hiſce lineis proportionalibus; </s>
          <s xml:space="preserve">an in linea AP moveatur eo-<lb />dem tempore velocitatibus AI &amp; </s>
          <s xml:space="preserve">AL. </s>
          <s xml:space="preserve">In utroque caſu <lb />revera movetur corpus per AP, velocitate AP; </s>
          <s xml:space="preserve">quæ ergo <lb />valet ambas velocitates AL, AI, quod &amp; </s>
          <s xml:space="preserve">aliunde conſtat: <lb /></s>
          <s xml:space="preserve">Nam AL &amp; </s>
          <s xml:space="preserve">IP ſunt æquales propter triangula ſimilia &amp; </s>
          <s xml:space="preserve"><lb />æqualia AEL, HIP habentia latera reſpectivè parallela, <lb />quorum AE &amp; </s>
          <s xml:space="preserve">HP ſunt æqualia <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0249-01a" corresp="note-0249-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0246-06" corresp="note-0246-06a" n="*" anchored="true" place="margin">603.</note>
              <figure xml:id="fig-0247a-01" corresp="fig-0247a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0247a-01" />
                <label>0247a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0249-01" corresp="note-0249-01a" n="*" anchored="true" place="margin">34. El 17</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Jam cum motus per A L contineatur in motu per AE <lb />quo agit in planum GC, &amp; </s>
          <s xml:space="preserve">motus per AI contineatur in <lb />motu per AH, quo in aliud planum corpus agit; </s>
          <s xml:space="preserve">ſequitur <lb />actiones in plana eſſe vires quibus corpus eodem tempore <lb />fertur velocitatibus AL &amp; </s>
          <s xml:space="preserve">AI: </s>
          <s xml:space="preserve">vires verò hæ ſunt ut ipſæ <lb />velocitates <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">integra vis corporis, quæ quadrato veloci-
<ptr xml:id="note-0249-02a" corresp="note-0249-02" type="noteAnchor" />
tatis AP proportionalis eſt <ptr type="noteAnchor" />, ſecari debet in duas partes
<ptr xml:id="note-0249-03a" corresp="note-0249-03" type="noteAnchor" />
quæ ſint inter ſe ut AL &amp; </s>
          <s xml:space="preserve">AI; </s>
          <s xml:space="preserve">partes hæ ſunt rectangula <lb />AP per AL, &amp; </s>
          <s xml:space="preserve">AP per AI.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0249-02" corresp="note-0249-02a" n="*" anchored="true" place="margin">599.</note>
              <note xml:space="preserve" xml:id="note-0249-03" corresp="note-0249-03a" n="*" anchored="true" place="margin">447.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si, poſito angulo GCF obtuſo, directio motus AP cum <lb />
<ptr xml:id="note-0249-04a" corresp="note-0249-04" type="noteAnchor" />
crure uno, ut CF, angulum etiam efficiat obtuſum, in <lb />
<ptr xml:id="note-0249-05a" corresp="note-0249-05" type="noteAnchor" />
hoc ultimum planum tantum actionem exerit corpus, pro-<lb />portionalem quadrato lineæ AD, perpendiculari ad FC, <lb />&amp; </s>
          <s xml:space="preserve">ictu non integram amittit vim, ſed per CF motum <lb />poſt impactionem continuat, velocitate linea DC proportio-<lb />nali.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0249-04" corresp="note-0249-04a" place="margin">620</note>
              <note xml:space="preserve" xml:id="note-0249-05" corresp="note-0249-05a" place="margin"><hi rend="small caps">TAB. XXV.</hi> <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc ex reſolutione motus <ptr type="noteAnchor" /> ſequuntur. </s>
          <s xml:space="preserve">Nam aliundè
<ptr xml:id="note-0249-06a" corresp="note-0249-06" type="noteAnchor" />
demonſtrabimus nullam in planum GC dari actionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0249-06" corresp="note-0249-06a" n="*" anchored="true" place="margin">604</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In caſu fig. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">ubi angulus; </s>
          <s xml:space="preserve">quem AP cum CF efficit, eſt <lb />acutus, actio in planum GC minuitur, aucto angulo hoc, <lb />ſi hic rectus ſit, ut in fig 3. </s>
          <s xml:space="preserve">datâ corporis directione a P, <lb />parallelogrammi AEPH diagonalis AP coincidit cum latere <lb />AH, &amp; </s>
          <s xml:space="preserve">latus aliud AE, ideoque AL, evaneſcunt, &amp; </s>
          <s xml:space="preserve">cum <lb />hiſce actio in planum GC etiam tollitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ ergo auctâ
<ptr xml:id="note-0249-07a" corresp="note-0249-07" type="noteAnchor" />
inclinatione viæ corporis ad planum hoc etiam nulla e-<lb />rit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0249-07" corresp="note-0249-07a" n="*" anchored="true" place="margin">619.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In determinandis quæſpectant directam colliſionem trium <lb />corporum, illi ſimili utimur methodo quam circa duorum cor-
</s>
          <pb facs="0250" n="174" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
porum colliſionem in cap. </s>
          <s xml:space="preserve"><hi rend="small caps">XXIII.</hi> adhibuimus. </s>
          <s xml:space="preserve">Vbitria dantur <lb />
<ptr xml:id="note-0250-01a" corresp="note-0250-01" type="noteAnchor" />
corpora duæ dantur velocitates reſpectivæ à quibus pendent <lb />actiones corporum in ſe mutuo <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">partium introceſſio-
<ptr xml:id="note-0250-02a" corresp="note-0250-02" type="noteAnchor" />
nes, quæ manentibus corporibus, &amp; </s>
          <s xml:space="preserve">hiſce duabus velocita-<lb />tibus, eadem ſemper eſt, ideoque &amp; </s>
          <s xml:space="preserve">vis ictu deſtructa <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quan-
<ptr xml:id="note-0250-03a" corresp="note-0250-03" type="noteAnchor" />
do corpora poſt ictum quieſcunt ſumma virium eſt, datis ve-<lb />
<ptr xml:id="note-0250-04a" corresp="note-0250-04" type="noteAnchor" />
locitatibus reſpectivis, omnium minima; </s>
          <s xml:space="preserve">ſi enim ſumma mi-<lb />nor daretur minor vis ictu deſtruetur, quod fieri non pot-<lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0250-01" corresp="note-0250-01a" place="margin">621.</note>
              <note xml:space="preserve" xml:id="note-0250-02" corresp="note-0250-02a" n="*" anchored="true" place="margin">494.</note>
              <note xml:space="preserve" xml:id="note-0250-03" corresp="note-0250-03a" place="margin">622</note>
              <note xml:space="preserve" xml:id="note-0250-04" corresp="note-0250-04a" n="*" anchored="true" place="margin">488.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Demonſtramus autem in Scholio 1. </s>
          <s xml:space="preserve">hujus cap. </s>
          <s xml:space="preserve">vim, datis ve-<lb />
<ptr xml:id="note-0250-05a" corresp="note-0250-05" type="noteAnchor" />
locitatibus reſpectivis, eſſe omnium minimam, ſi motis duobus <lb />corporibus unam partem verſus, aliud in contrariam partem <lb />ita feratur, ut bujus maſſæ productum per ſuam velocitatem <lb />valeat ſummam productorum maſſarum reliquorum duo-<lb />rum, ſingularum multiplicatarum per ſuas velocita-<lb />tes.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0250-05" corresp="note-0250-05a" place="margin">623</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc autem caſu corpora poſt ictum quieſcere, &amp; </s>
          <s xml:space="preserve">ideo <lb />ſummam virium eſſe omnium minimam etiam deducimus ex <lb />demonſtratis circa colliſionem corporum duorum, ad quam <lb />trium corporum colliſionem referimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sint corpora tria A, B, C; </s>
          <s xml:space="preserve">velocitas primi f b; </s>
          <s xml:space="preserve">ſecundi <lb />
<ptr xml:id="note-0250-06a" corresp="note-0250-06" type="noteAnchor" />
g i; </s>
          <s xml:space="preserve">tertii l i. </s>
          <s xml:space="preserve">Ponimus producta A per f b &amp; </s>
          <s xml:space="preserve">B per g i, <lb />
<ptr xml:id="note-0250-07a" corresp="note-0250-07" type="noteAnchor" />
ſimul ſumta, valere productum C per l i.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0250-06" corresp="note-0250-06a" place="margin">624</note>
              <note xml:space="preserve" xml:id="note-0250-07" corresp="note-0250-07a" place="margin"><hi rend="small caps">TAB XXV.</hi> <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus corpus C in duas partes reſolvi D &amp; </s>
          <s xml:space="preserve">E ita, <lb />
<ptr xml:id="note-0250-08a" corresp="note-0250-08" type="noteAnchor" />
ut D per l i valeat A per f b, &amp; </s>
          <s xml:space="preserve">E per l i æquale ſit B per <lb />g i; </s>
          <s xml:space="preserve">id eſt ſit D ad E, ut A per f b ad B per g i. </s>
          <s xml:space="preserve">In hoc <lb />caſu A ad D, ut l i ad f b, &amp; </s>
          <s xml:space="preserve">corpora hæc concurrentia poſt <lb />
<ptr xml:id="note-0250-09a" corresp="note-0250-09" type="noteAnchor" />
ictum quieſcunt <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">quieſcunt etiam B &amp; </s>
          <s xml:space="preserve">E <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quia B ad E,
<ptr xml:id="note-0250-10a" corresp="note-0250-10" type="noteAnchor" />
ut l i ad g i. </s>
          <s xml:space="preserve">Hæc autem quatuor corpora à tribus da-<lb />tis, memoratis velocitatibus agitatis, non differunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0250-08" corresp="note-0250-08a" place="margin"><hi rend="small caps">TAB. XXV.</hi> <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0250-09" corresp="note-0250-09a" n="*" anchored="true" place="margin">500.</note>
              <note xml:space="preserve" xml:id="note-0250-10" corresp="note-0250-10a" n="*" anchored="true" place="margin">500.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis in ictu quocunque amiſſa datis velocitatibus reſpectivis <lb />valet ſummam virium in caſu in quo corpora quieſcunt <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0250-11a" corresp="note-0250-11" type="noteAnchor" />
hæc autem ſumma ſolis datis velocitatibus reſpectivis exprimi <lb />poteſt &amp;</s>
          <s xml:space="preserve">, ut in Scholio 1. </s>
          <s xml:space="preserve">demonſtramus. </s>
          <s xml:space="preserve">In omni concurſu <lb />
<ptr xml:id="note-0250-12a" corresp="note-0250-12" type="noteAnchor" />
directo trium corporum, vis amiſſa proportionem ſequitur <lb />ſummætrium productorum, quæ formantur multiplicatis dua-
</s>
          <pb facs="0251" n="175" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XXVII.</fw>
bus maſſis in ſe mutuo, &amp; </s>
          <s xml:space="preserve">per quadratum velocitatis reſpe-<lb />ctivæ barum ipſarum, diviſâ ſummâ bacper ſummam trium <lb />maſſarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0250-11" corresp="note-0250-11a" n="*" anchored="true" place="margin">622.</note>
              <note xml:space="preserve" xml:id="note-0250-12" corresp="note-0250-12a" place="margin">625.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datis corporibus A, B, &amp; </s>
          <s xml:space="preserve">C; </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">multiplicari debet maſſa <lb />A per maſſam B &amp; </s>
          <s xml:space="preserve">productum hoc per quadratum velocita-<lb />tis reſpectivæ A &amp; </s>
          <s xml:space="preserve">B; </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">productum maſſæ A per maſſam C <lb />multiplicandum eſt per quadratum velocitatis reſpectivæ ho-<lb />rum corporum; </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">tandem ductis maſſis B &amp; </s>
          <s xml:space="preserve">C in ſe invi-<lb />cem, productum multiplicari debet per quadratum velocita-<lb />tis reſpectivæ horum corporum; </s>
          <s xml:space="preserve">ſumma verò trium horum <lb />productorum dividenda eſt per ſummam maſſarum, &amp; </s>
          <s xml:space="preserve">habe-<lb />bimus vim ictu amiſſam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si non fuerint elaſtica tria corpora, de talibus enim agi-<lb />
<ptr xml:id="note-0251-01a" corresp="note-0251-01" type="noteAnchor" />
mus, poſt ictum eadem velocitate feruntur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">hæc eſt ve-
<ptr xml:id="note-0251-02a" corresp="note-0251-02" type="noteAnchor" />
locitas quam navis haberet, in qua corpora juxta legem in <lb />n. </s>
          <s xml:space="preserve">610. </s>
          <s xml:space="preserve">indicatam agitata forent; </s>
          <s xml:space="preserve">quia poſt ictum in nave <lb />corpora quieſcerent, translatis ipſis eadem cum nave ve-<lb />locitate. </s>
          <s xml:space="preserve">Navis velocitatem in Scholio 1. </s>
          <s xml:space="preserve">detegimus, &amp; </s>
          <s xml:space="preserve">ha-<lb />betur, multiplicando ſingulorum corporum maſſas per ſuas <lb />velocitates &amp; </s>
          <s xml:space="preserve">dividendo per ſummam maſſarum ſummam <lb />productorum, ſi tria corpora ad eandem partem tendant; </s>
          <s xml:space="preserve">ſin <lb />minus, motuum contrariorum producta à ſe invicem ſub-<lb />trabi debent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0251-01" corresp="note-0251-01a" place="margin">626</note>
              <note xml:space="preserve" xml:id="note-0251-02" corresp="note-0251-02a" n="*" anchored="true" place="margin">484.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Videmus quæ ſpectant trium corporum colliſionem, in <lb />multis cum iis quæ de duobus corporibus demonſtrata ſunt <lb />convenire, quod etiam referri poteſt ad demonſtrata de mu-<lb />tationibus velocitatum in ratione inverſa maſſarum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Nam
<ptr xml:id="note-0251-03a" corresp="note-0251-03" type="noteAnchor" />
ut in Scholio 1. </s>
          <s xml:space="preserve">demonſtramus; </s>
          <s xml:space="preserve">Mutationes in velocitatibus <lb />
<ptr xml:id="note-0251-04a" corresp="note-0251-04" type="noteAnchor" />
duorum corporum, oriundæ ex actione mutua borum corporum <lb />in colliſione, ſunt inverſe ut corporum maſſæ, licet &amp; </s>
          <s xml:space="preserve">aliâ a-<lb />ctione eodem tempore unius motus mutetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0251-03" corresp="note-0251-03a" n="*" anchored="true" place="margin">512.</note>
              <note xml:space="preserve" xml:id="note-0251-04" corresp="note-0251-04a" place="margin">627</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc concipiamus corpora perfectè elaſtica, hæc in <lb />
<ptr xml:id="note-0251-05a" corresp="note-0251-05" type="noteAnchor" />
nave memoratâ, ſolâ elaſterii actione moventur, &amp; </s>
          <s xml:space="preserve">à ſe in-<lb />vicem recedunt iiſdem celeritatibus, &amp; </s>
          <s xml:space="preserve">viribus, quibus ad <lb />ſe invicem acceſſere; </s>
          <s xml:space="preserve">in hoc enim caſu ſingula elaſteria, <lb />quæ, dum relaxantur, vires generant æquales illis, quibus,
</s>
          <pb facs="0252" n="176" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
fuere flexa <ptr type="noteAnchor" />, deſideratam, ut hunc præſtent effectum, pati-
<ptr xml:id="note-0252-01a" corresp="note-0252-01" type="noteAnchor" />
untur reſiſtentiam, æqualem nempe illi, quam in inflexione <lb />paſſa ſunt, nam eodem modo corpus reſiſtit, dum certam a-<lb />mittit vim &amp; </s>
          <s xml:space="preserve">dum eandem acquirit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0251-05" corresp="note-0251-05a" place="margin">628</note>
              <note xml:space="preserve" xml:id="note-0252-01" corresp="note-0252-01a" n="*" anchored="true" place="margin">557.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde generalem hanc deducimus concluſionem, mutationem <lb />
<ptr xml:id="note-0252-02a" corresp="note-0252-02" type="noteAnchor" />
in velocitate, in impactione corporum elaſticorum quorumcun-<lb />que, reſpectu ſingulorum duplam eſſe illius quæ in eodem in-<lb />curſu, datis corporibus non elaſticis, locum baberet: </s>
          <s xml:space="preserve">ideo <lb />regulæ n 567. </s>
          <s xml:space="preserve">568. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hìc applicari poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0252-02" corresp="note-0252-02a" place="margin">629</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In demonſtratione hac ponimus actione mutua duorum <lb />
<ptr xml:id="note-0252-03a" corresp="note-0252-03" type="noteAnchor" />
corporum ut A &amp; </s>
          <s xml:space="preserve">Belaſticas horum corporum partes tantum <lb />
<ptr xml:id="note-0252-04a" corresp="note-0252-04" type="noteAnchor" />
intropremi, id eſt, illud tantum flecti elaſterium quod da-<lb />tur inter hæc corpora ubi in a, b, concurrunt nullamque <lb />hujus actionis partem transferri ad inflectendas partes elaſti-<lb />cas inter b &amp; </s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0252-03" corresp="note-0252-03a" place="margin">630</note>
              <note xml:space="preserve" xml:id="note-0252-04" corresp="note-0252-04a" place="margin"><hi rend="small caps">TAB. XXV.</hi> <lb />fig 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc ſic ſeſe revera haberi ſequi videtur ex ſubitâ admo-<lb />dum partium elaſticarum inflexione &amp; </s>
          <s xml:space="preserve">inſtauratione, quam <lb />ſuperius demonſtravimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0252-05a" corresp="note-0252-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0252-05" corresp="note-0252-05a" n="*" anchored="true" place="margin">583. 584.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si autem concipiamus partes lentius intropremi, ut in-<lb />tropremuntur partes corporum mollium non ſeparantur cor-<lb />pora elaſtica, ut ad ſe mutuo acceſſere, &amp; </s>
          <s xml:space="preserve">difficilior eſt mo-<lb />tus determinatio.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In concurſu trium Corporum mollium A, B, &amp; </s>
          <s xml:space="preserve">C, eodemmo-<lb />
<ptr xml:id="note-0252-06a" corresp="note-0252-06" type="noteAnchor" />
mento ad ſe mutuo accedentium, introceſſiones ſunt æquales <lb />inter a &amp; </s>
          <s xml:space="preserve">b &amp; </s>
          <s xml:space="preserve">inter b &amp; </s>
          <s xml:space="preserve">c, licet actiones ſint inæquales; </s>
          <s xml:space="preserve">nam <lb />dum, Cagit in B, ſi hæc actio, actionem ſuperet quam A in B <lb />ad partem oppoſitam exerit non modo c intropremit partes <lb />inter b &amp; </s>
          <s xml:space="preserve">c; </s>
          <s xml:space="preserve">ſed &amp; </s>
          <s xml:space="preserve">premit, in b ita ut augeatur actio in-<lb />ter b &amp; </s>
          <s xml:space="preserve">a; </s>
          <s xml:space="preserve">quareactione mutua corporum c &amp; </s>
          <s xml:space="preserve">b, non modo <lb />partes inter hæc corpora intropremuntur, ſed &amp; </s>
          <s xml:space="preserve">augetur <lb />introceſſio partium inter a &amp; </s>
          <s xml:space="preserve">c, &amp; </s>
          <s xml:space="preserve">hæc actio diſpergitur ita, <lb />ut b, quod inter a &amp; </s>
          <s xml:space="preserve">c quieſcit, æqualiter ab utraque par-<lb />te prematur; </s>
          <s xml:space="preserve">quare ab utraque parte, introceſſiones ſi æque <lb />facile partes introcedant, æquales ſunt; </s>
          <s xml:space="preserve">ſumma vero cavi-<lb />tatum ambarum ſequitur proportionem vis deſtructæ in his <lb />formandis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0252-07a" corresp="note-0252-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0252-06" corresp="note-0252-06a" place="margin">631</note>
              <note xml:space="preserve" xml:id="note-0252-07" corresp="note-0252-07a" n="*" anchored="true" place="margin">464. 488.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0253" n="177" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXVII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 1</head>
        <p>
          <s xml:space="preserve">Suſpendatur Globus ex argillâ molli ita, ut reſpondeat me-<lb />dio Machinæ n. </s>
          <s xml:space="preserve">491. </s>
          <s xml:space="preserve">tranſmiſſo filo per foramen medium f <lb />(Tab. </s>
          <s xml:space="preserve">18. </s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">ad latera hujus duo ſuſpendantur cylin-<lb />dri D &amp; </s>
          <s xml:space="preserve">F, (Tab. </s>
          <s xml:space="preserve">18. </s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">adhibitis uncis YY, loco <lb />uncorum V, V, (fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">Quieſcente globo, in hunc di-<lb />mittantur, eodem momento, cylindri, major ve-<lb />locitate quinque, &amp; </s>
          <s xml:space="preserve">alter velocitate decem, quæ <lb />velocitates ſunt inversè ut maſſæ, in qua ratione et-<lb />iam ſunt vires <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">poſt ictum tria corpora quieſcunt &amp; </s>
          <s xml:space="preserve">ca-
vitates ab utraque parte ſunt æquales. </s>
          <s xml:space="preserve">Inæquales eſſe ca-<lb />vitates ſi corpora hæc ipſa eodem modo mota impingant in <lb />
<ptr xml:id="note-0253-01a" corresp="note-0253-01" type="noteAnchor" />
obicem fixum ſuperius vidimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0253-01" corresp="note-0253-01a" place="margin"><ptr type="noteAnchor" />503.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc experimento vis majoris cylindri habetur multi-<lb />plicando maſſam quatuor per quadratum velocitatis viginti <lb />quinque <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">eſt 100; </s>
          <s xml:space="preserve">eodem modo vis alîus cylindri de-
<ptr xml:id="note-0253-02a" corresp="note-0253-02" type="noteAnchor" />
tegitur 200.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">ſumma virium 300; </s>
          <s xml:space="preserve">vis hæc ictu perit, &amp; </s>
          <s xml:space="preserve"><lb />cum cavitates ſint æquales in utraque formanda conſu-<lb />mitur vis 150. </s>
          <s xml:space="preserve">quod experimento ſequenti confirma-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0253-02" corresp="note-0253-02a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Iiſdem poſitis quæ in experimento primo, tollatur cy-<lb />
<ptr xml:id="note-0253-03a" corresp="note-0253-03" type="noteAnchor" />
lindrus major &amp; </s>
          <s xml:space="preserve">in ipſius locum ſuſpendatur cylindrus minori <lb />ſimilis &amp; </s>
          <s xml:space="preserve">æqualis. </s>
          <s xml:space="preserve">Si globus paululum convertatur &amp; </s>
          <s xml:space="preserve">in <lb />hunc cylindri ambo dimittantur velocitate 8 {2/3}, poſt ictum <lb />corpora quieſcunt, &amp; </s>
          <s xml:space="preserve">cavitates erunt æquales inter ſe, &amp; </s>
          <s xml:space="preserve"><lb />illis quæ in primo experimento formatæ ſunt. </s>
          <s xml:space="preserve">Cum vires <lb />ſint æquales &amp; </s>
          <s xml:space="preserve">cavitates æquales, corpus utrumque ſuam <lb />format cavitatem, vis autem quæ conſumitur habetur multi-<lb />plicando maſſam duo per quadratum velocitatis 75 {1/9}, &amp; </s>
          <s xml:space="preserve">eſt <lb />150 {2/9}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0253-03" corresp="note-0253-03a" place="margin">632.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc concipiamus partes elaſticas flecti, ut memo-<lb />
<ptr xml:id="note-0253-04a" corresp="note-0253-04" type="noteAnchor" />
ratorum corporum mollium partes introcedunt, inflexio in-<lb />
<ptr xml:id="note-0253-05a" corresp="note-0253-05" type="noteAnchor" />
ter a &amp; </s>
          <s xml:space="preserve">b æqualis erit illi quæ datur inter b &amp; </s>
          <s xml:space="preserve">c; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">con-<lb />ſideranda ſunt corpora quaſi ſeparata actione elaſterio-<lb />rum duorum æquè potentium inter hæc poſitorum. </s>
          <s xml:space="preserve">Quo-
</s>
          <pb facs="0254" n="178" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
modo in hoc caſu ſeparatio determinetur in Scholio 2. <lb /></s>
          <s xml:space="preserve">videbimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0253-04" corresp="note-0253-04a" place="margin">633.</note>
              <note xml:space="preserve" xml:id="note-0253-05" corresp="note-0253-05a" place="margin"><hi rend="small caps">TA. XXV.</hi> <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quomodo duo corpora, directionibus diverſis mota, in <lb />tertium eodem momento directè incurrentia hoc agitent, <lb />etiam explicabimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dentur corporaA,B, directè eodem momento, velocitatibus <lb />
<ptr xml:id="note-0254-01a" corresp="note-0254-01" type="noteAnchor" />
quibuſcunque, incurrentia in corpus quieſcens C, directio-<lb />
<ptr xml:id="note-0254-02a" corresp="note-0254-02" type="noteAnchor" />
nibus AK, BK. </s>
          <s xml:space="preserve">Productis hiſce directionibus, ſint KD velo-<lb />citas corporis A, &amp; </s>
          <s xml:space="preserve">KE corporis B celeritas; </s>
          <s xml:space="preserve">erigantur <lb />D Fad K D normalis, &amp; </s>
          <s xml:space="preserve">EG cum K E angulum rectum <lb />efficiens; </s>
          <s xml:space="preserve">dividatur KD in H ita, ut KH ſe habeat ad <lb />HD, ut maſſa corporis A ad maſſam C; </s>
          <s xml:space="preserve">eodem modo di-<lb />videnda eſt KE in L, ut KL ſit LE; </s>
          <s xml:space="preserve">ut maſſa B ad maſ-<lb />ſam C. </s>
          <s xml:space="preserve">Ductis nunc F H, GL, ſeſe mutuo interſecanti-<lb />bus in N, linea K N ſitu directionem, &amp; </s>
          <s xml:space="preserve">longitudine velo-<lb />citatem, demonſtrabit corporis C poſt ictum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0254-01" corresp="note-0254-01a" place="margin">634.</note>
              <note xml:space="preserve" xml:id="note-0254-02" corresp="note-0254-02a" place="margin"><hi rend="small caps">TA. XXV.</hi> <lb />fig 6.7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpora autem A &amp; </s>
          <s xml:space="preserve">B in lineis K D, K E, motum con-<lb />tinuant, cum nullâ actione horum directio mutari poſſit. <lb /></s>
          <s xml:space="preserve">Velocitates verò determinantur dimiſſis ex N ad KD &amp; </s>
          <s xml:space="preserve">KE <lb />perpendicularibus NI, NM; </s>
          <s xml:space="preserve">eſtque KI corporis A, &amp; </s>
          <s xml:space="preserve"><lb />K M corporis B velocitas poſt ictum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Nulla datur actio qua corpora A &amp; </s>
          <s xml:space="preserve">Cin ictu directo, cum <lb />
<ptr xml:id="note-0254-03a" corresp="note-0254-03" type="noteAnchor" />
non ſint elaſtica, ſeparari poſſint <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">licet actione corpo-
<ptr xml:id="note-0254-04a" corresp="note-0254-04" type="noteAnchor" />
ris B moveatur corpus C, eo quidem minuitur actio corpo-<lb />ris A, ſed non C ab A juxta directionem KD ſeparat; </s>
          <s xml:space="preserve">tunc <lb />enim C ab actione ipſius A ſubduceret; </s>
          <s xml:space="preserve">ergo poſt ictum A <lb />&amp; </s>
          <s xml:space="preserve">C eadem velocitate moventur juxta directionem K D; <lb /></s>
          <s xml:space="preserve">idcirco ſi C percurrit AN, velocitate quam hac lineâ ex-<lb />primimus, movebitur A velocitate KI; </s>
          <s xml:space="preserve">motus enim per KN, <lb />juxta directionem K D, nil continet præter velocitatem <lb />KI <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">corpus A amittet velocitatem DI.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0254-03" corresp="note-0254-03a" place="margin">635.</note>
              <note xml:space="preserve" xml:id="note-0254-04" corresp="note-0254-04a" n="*" anchored="true" place="margin">484.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">603.</note>
        <p>
          <s xml:space="preserve">Ulterius ad hoc debemus attendere, ductis lineis <lb />NO, NP, parallelis KE &amp; </s>
          <s xml:space="preserve">KD, corpus C impactucor-<lb />porum A &amp; </s>
          <s xml:space="preserve">B eodem tempore juxta directiones K O &amp; </s>
          <s xml:space="preserve"><lb />KP propelli, &amp; </s>
          <s xml:space="preserve">quidem velocitatibus hiſce lineis propor-
</s>
          <pb facs="0255" n="179" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP XXVII.</fw>
tionalibus, ſi per KN, velocitate KN moveatur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">mu-
<ptr xml:id="note-0255-01a" corresp="note-0255-01" type="noteAnchor" />
tatio in velocitate corporis quieſcentis C, ex actione cor-<lb />poris <hi rend="small caps">A</hi> erit KO; </s>
          <s xml:space="preserve">ergo KO ad ID, ſi N ritè ſit determi-<lb />natum, ut maſſa <hi rend="small caps">A</hi> ad maſſam C <ptr type="noteAnchor" />, id eſt ut KH ad HD,
<ptr xml:id="note-0255-02a" corresp="note-0255-02" type="noteAnchor" />
quod tantum obtinet ſi punctum N detur in FH; </s>
          <s xml:space="preserve">produ-<lb />cta enim PN donec ſecet FD in Q, habemus PN ad NQ, <lb />ut KH ad HD, ſed PN æqualis eſt KO, &amp; </s>
          <s xml:space="preserve">NQ ipſi ID <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0255-03a" corresp="note-0255-03" type="noteAnchor" />
Eodem modo demonſtramus quæſitum punctum N dari in <lb />linea GL; </s>
          <s xml:space="preserve">ideoque in interſectione hujus lineæ cum linea <lb />FH. </s>
          <s xml:space="preserve">Quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0255-01" corresp="note-0255-01a" n="*" anchored="true" place="margin">246.</note>
              <note xml:space="preserve" xml:id="note-0255-02" corresp="note-0255-02a" n="*" anchored="true" place="margin">6271.</note>
              <note xml:space="preserve" xml:id="note-0255-03" corresp="note-0255-03a" n="*" anchored="true" place="margin">34. El. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpora ſint elaſtica, mutationes velocitatum duplæ <lb />
<ptr xml:id="note-0255-04a" corresp="note-0255-04" type="noteAnchor" />
ſunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo ſi producatur &amp; </s>
          <s xml:space="preserve">duplicetur KN, habebimus
<ptr xml:id="note-0255-05a" corresp="note-0255-05" type="noteAnchor" />
motum corporis C per K n, velocitate K n; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſumtis, I i <lb />ipſi l D, &amp; </s>
          <s xml:space="preserve">M m lineæ ME, æqualibus, habebimus K i &amp; </s>
          <s xml:space="preserve"><lb />K m corporum A &amp; </s>
          <s xml:space="preserve">B velocitates. </s>
          <s xml:space="preserve">In hoc caſu ſummæ viri-<lb />
<ptr xml:id="note-0255-06a" corresp="note-0255-06" type="noteAnchor" />
um ante &amp; </s>
          <s xml:space="preserve">poſt ictum ſunt æquales <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod etiam ex hac ve-
<ptr xml:id="note-0255-07a" corresp="note-0255-07" type="noteAnchor" />
locitatum determinatione ſequi in Scholio 3. </s>
          <s xml:space="preserve">demonſtrabi-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0255-04" corresp="note-0255-04a" place="margin">636.</note>
              <note xml:space="preserve" xml:id="note-0255-05" corresp="note-0255-05a" n="*" anchored="true" place="margin">629.</note>
              <note xml:space="preserve" xml:id="note-0255-06" corresp="note-0255-06a" place="margin">637.</note>
              <note xml:space="preserve" xml:id="note-0255-07" corresp="note-0255-07a" n="*" anchored="true" place="margin">558.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando angulus EKG eſt obtuſus cum corporum A &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0255-08a" corresp="note-0255-08" type="noteAnchor" />
B motus pro parte contrarii ſint &amp; </s>
          <s xml:space="preserve">hîc referri debent quæ <lb />in n. </s>
          <s xml:space="preserve">630. </s>
          <s xml:space="preserve">notata fuere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0255-08" corresp="note-0255-08a" place="margin">638.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Difficile admodum eſt demonſtrata hæc experimentis con-<lb />
<ptr xml:id="note-0255-09a" corresp="note-0255-09" type="noteAnchor" />
firmare. </s>
          <s xml:space="preserve">Experimenta circa corpora non elaſtica inſtitui non <lb />poſſunt, quia globi ex argillâ ſi omni elaſterio deſtituantur, quod <lb />in experimentis deſideratur, poſtictum cohærent inter ſe; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />præterea quod etiam in corporibus elaſticis locum habet <lb />nunquam certi ſumus an exactiſſimè eodem momento ambo <lb />corpora incurrant, de quo, ubi agitur de deferentiâ mini-<lb />mâ, niſi ex viâ quam ſequitur corpus C judicium ferre non <lb />poſſumus, quæ ergo experimento determinari nequit. </s>
          <s xml:space="preserve">In eo <lb />ſolo caſu in quo corpora A &amp; </s>
          <s xml:space="preserve">B ſunt æqualia, &amp; </s>
          <s xml:space="preserve">æqualibus <lb />velocitatibus mota, primo intuitu patet corpora hæc eodem <lb />momento in C impegiſſe, ſi hujus via angulum DKE in duas <lb />partes æquales dividat: </s>
          <s xml:space="preserve">de hoc caſu ſequens inſtitui poteſt <lb />experimentum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0255-09" corresp="note-0255-09a" place="margin">639.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0256" n="180" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Sectio horizontalis Machinæ, in n. </s>
          <s xml:space="preserve">615 deſcriptæ, hîc re-<lb />
<ptr xml:id="note-0256-01a" corresp="note-0256-01" type="noteAnchor" />
præſentatur, applicatis huic Machinæ tribus globis ebur-<lb />
<ptr xml:id="note-0256-02a" corresp="note-0256-02" type="noteAnchor" />
neis in deſcriptione memoratis. </s>
          <s xml:space="preserve">Si corpora Q, Q, eodem <lb />momento dimittantur ab æqualibus altitudinibus, &amp; </s>
          <s xml:space="preserve">forme-<lb />tur parallelogrammum abcf cujus latera ab, ac, ſunt dire-<lb />ctiones corporum Q, Q, continuatæ, &amp; </s>
          <s xml:space="preserve">æqualia ſubtenſis <lb />arcuum per quos corpora Q, Q, deſcendunt; </s>
          <s xml:space="preserve">corpus P, <lb />ſi angulus QPQ ſit acutus minori adſcendit velocitate, quàm <lb />qua adſcendendo poſſet percurrere arcum cujus ſubtenſa me-<lb />morati parallelogrammi foret diagonalis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0256-01" corresp="note-0256-01a" place="margin">640.</note>
              <note xml:space="preserve" xml:id="note-0256-02" corresp="note-0256-02a" place="margin"><hi rend="small caps">TA XXIV.</hi> <lb />fig. 4.5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſito autem angulo obtuſo ad majorem adſcendit alti-<lb />tudinem quam quæ diagonali parallelogrammi determina-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæ cum explicatis in n. </s>
          <s xml:space="preserve">634. </s>
          <s xml:space="preserve">636. </s>
          <s xml:space="preserve">conveniunt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 1.</head>
        <head xml:space="preserve">Demonſtrationes n. 623. 625. 626. 627.</head>
        <p>
          <s xml:space="preserve">Dentur tria corpora A, B, C, directè in ſe mutuo impingentia, poſitâ pri-<lb />
<ptr xml:id="note-0256-03a" corresp="note-0256-03" type="noteAnchor" />
mi velocitate a, ſecundi b, tertii c, ſumma virium eſt A a a - B b b -<lb />C c c <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi A &amp; </s>
          <s xml:space="preserve">B ad eandem partem &amp; </s>
          <s xml:space="preserve">C in contrariam tendant, ciximus in
<ptr xml:id="note-0256-04a" corresp="note-0256-04" type="noteAnchor" />
n. </s>
          <s xml:space="preserve">623. </s>
          <s xml:space="preserve">ſummam hanc fore, datis velocitatibus reſpectivis omnium mini-<lb />mam, ſi A a - B b = C c; </s>
          <s xml:space="preserve">Quod ex quiete corporum poſt ictum, in n. </s>
          <s xml:space="preserve">624. <lb /></s>
          <s xml:space="preserve">demonſtrato, quidem ſequitur, ſed directè etiam probatur, ſi velocitatem <lb />quamcunque concipiamus auctam aut diminutam quantitate quacunque ut x, <lb />&amp; </s>
          <s xml:space="preserve">computatio ineatur de ſumma virium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0256-03" corresp="note-0256-03a" place="margin">641.</note>
              <note xml:space="preserve" xml:id="note-0256-04" corresp="note-0256-04a" n="*" anchored="true" place="margin">470.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Ex. </s>
          <s xml:space="preserve">Gr. </s>
          <s xml:space="preserve">Corporis A velocitas a - x; </s>
          <s xml:space="preserve">ut ſerventur velocitates reſpecti-<lb />væ movetur B velocitate b - x; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">corporis C velocitas erit c - x. </s>
          <s xml:space="preserve">ſumma <lb />virium eſt A aa + 2A a x + A xx + B bb + 2B bx + B xx + C cc - 2C cx <lb />+ C x x, quæ excedit primam quantitate A x x + B x x + C x x ſublatis 2A a x + <lb />2 B b x - C c x quæ ſeſe mutuo deſtruunt; </s>
          <s xml:space="preserve">cum autem exceſſus detur quo-<lb />modocunque velocitates mutatas ſervatis velocitatibus reſpectivis, conci-<lb />piamus, ſequitur ſummam in caſu memorato fuiſſe minimam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">liſdem poſitis, velocitas reſpectiva corporum A &amp; </s>
          <s xml:space="preserve">B eſt a-b <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">corporum
<ptr xml:id="note-0256-05a" corresp="note-0256-05" type="noteAnchor" />
<ptr xml:id="note-0256-06a" corresp="note-0256-06" type="noteAnchor" />
A &amp; </s>
          <s xml:space="preserve">C eſt a + c <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tandem velocitas reſpectiva corporum B &amp; </s>
          <s xml:space="preserve">C valet
<ptr xml:id="note-0256-07a" corresp="note-0256-07" type="noteAnchor" />
b + c <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Vis amiſſa datis hiſce velocitatibus reſpectivis valet ſummam vi-
<ptr xml:id="note-0256-08a" corresp="note-0256-08" type="noteAnchor" />
rium in hoc caſu, in quo ſumma hæc eſt minima <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in quo A a + B b = C c.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0256-09a" corresp="note-0256-09" type="noteAnchor" />
Vim hanc amiſſam diximus æqualem eſſe
</s>
          <pb facs="0257" />
          <s xml:space="preserve">
<ptr xml:id="fig-0257-01a" corresp="fig-0257-01" type="figureAnchor" />
<pb facs="0257a" />
<pb facs="0258" />
<pb facs="0259" n="181" /><fw type="head">MATHEMATICA. LIB. I. CAP. XXVII.</fw>
{ABx <hi rend="overline">a-b</hi><hi rend="superscript">2</hi> + ACx<hi rend="overline">a + c</hi><hi rend="superscript">2</hi> + BCx<hi rend="overline">b + c</hi><hi rend="superscript">2</hi>/A + B + C} <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quod ut demonſtremus pto-
<ptr xml:id="note-0259-01a" corresp="note-0259-01" type="noteAnchor" />
bandum quantitatem hanc æqualem eſſe A a a + B bb + C cc. </s>
          <s xml:space="preserve">aut <lb />{ABx<hi rend="overline">a-b</hi><hi rend="superscript">2</hi>/x A + B + C. </s>
          <s xml:space="preserve">+ ACx<hi rend="overline">a + c</hi><hi rend="superscript">2</hi> + BCx<hi rend="overline">b + c</hi><hi rend="superscript">2</hi> = Aaa + Bbb + Ccc}</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0256-05" corresp="note-0256-05a" place="margin">642.</note>
              <note xml:space="preserve" xml:id="note-0256-06" corresp="note-0256-06a" n="*" anchored="true" place="margin">474.</note>
              <note xml:space="preserve" xml:id="note-0256-07" corresp="note-0256-07a" n="*" anchored="true" place="margin">475.</note>
              <note xml:space="preserve" xml:id="note-0256-08" corresp="note-0256-08a" n="*" anchored="true" place="margin">475.</note>
              <note xml:space="preserve" xml:id="note-0256-09" corresp="note-0256-09a" n="*" anchored="true" place="margin">621.</note>
              <figure xml:id="fig-0257-01" corresp="fig-0257-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0257-01" />
                <label>0257-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0259-01" corresp="note-0259-01a" n="*" anchored="true" place="margin">625.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quia A a + B b = C c etiam AA aa + 2AB ab + BB bb = CC cc = AC ac <lb />+ BC bc unde deducimus AA aa + BB bb + CC cc = 2AC ac + 2BC bc <lb />-2AB ab. </s>
          <s xml:space="preserve">Sed multiplicatis A aa + B bb + C cc per A + B + C habemus <lb />AA aa + BA aa + CA aa + AB bb + BB bb + CB bb + AC cc <lb />BC cc + CC cc, &amp; </s>
          <s xml:space="preserve">ſubſtituendo pro AA aa + BB bb + CC cc <lb />valorem detectum, habemus A aa + B bb + C cc x A + B + C = AB aa <lb />-2AB ab + AB bb + AC aa + 2AC ac + AC cc + BC bb +  <lb />2BC bc + BC cc + ABx<hi rend="overline">a-b</hi><hi rend="superscript">2</hi> + ACx<hi rend="overline">a + c</hi><hi rend="superscript">2</hi> + BC<hi rend="overline">b + c</hi><hi rend="superscript">2</hi>. </s>
          <s xml:space="preserve">Quod <lb />demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sint iterum tria corpora A, B, C; </s>
          <s xml:space="preserve">velocitas primi m; </s>
          <s xml:space="preserve">ſecundi n; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tertii p. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0259-02a" corresp="note-0259-02" type="noteAnchor" />
Ut regulam n. </s>
          <s xml:space="preserve">626. </s>
          <s xml:space="preserve">demonſtremus, dicimus x velocitatem navis ibi <lb />memoratæ &amp; </s>
          <s xml:space="preserve">velocitates corporum A &amp; </s>
          <s xml:space="preserve">B in nave, ſi concipiamus hæc i-<lb />pſâ nave celerius ferri, erunt m-x &amp; </s>
          <s xml:space="preserve">n-x; </s>
          <s xml:space="preserve">C vero, ſi hoc nave lentius mo-<lb />veatur, in hac in contrariam partem fertur velocitate x-p. </s>
          <s xml:space="preserve">Cum agatur de <lb />caſu in quo poſt ictum corpora quieſcunt habemus A m-A x + B n-B x <lb />= C x-C p <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0259-02" corresp="note-0259-02a" place="margin">643.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">622. 615. <lb />641.</note>
        <p>
          <s xml:space="preserve">Unde deducimus x = {Am + Bn + Cp/A + B + C}. </s>
          <s xml:space="preserve">Quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si non omnia corpora ad eandem partem tendant illorum quæ in con-<lb />trariam partem feruntur velocitates ſunt negativæ &amp; </s>
          <s xml:space="preserve">producta in numeratore <lb />negativa.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponamus ut in præcedentibus demonſtrationibus corpora A, B, &amp; </s>
          <s xml:space="preserve">C, &amp; </s>
          <s xml:space="preserve">con-<lb />
<ptr xml:id="note-0259-04a" corresp="note-0259-04" type="noteAnchor" />
cipiamus hæc ad eandem partem ferri ita, ut in nave, quæ movetur ea velo-<lb />
<ptr xml:id="note-0259-05a" corresp="note-0259-05" type="noteAnchor" />
citate qua corpora poſt ictum agitantur, velocitates corporum A &amp; </s>
          <s xml:space="preserve">B à pup-<lb />pi ad proram ſint f h, g i, corporis C velocitas à prorâ ad puppim l i. </s>
          <s xml:space="preserve">In <lb />hoc caſu corpus ſolum C lentius nave movetur, &amp; </s>
          <s xml:space="preserve">actione amborum alio-<lb />rum acceleratur. </s>
          <s xml:space="preserve">Cum in nave corpora poſt ictum quieſcant ſumma pro <lb />ductorum A per f b, &amp; </s>
          <s xml:space="preserve">B per g i, valet C per l i <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0259-04" corresp="note-0259-04a" place="margin">644.</note>
              <note xml:space="preserve" xml:id="note-0259-05" corresp="note-0259-05a" place="margin"><hi rend="small caps">TAB. XXV</hi> <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">622. 623.</note>
        <note xml:space="preserve" place="margin">641.</note>
        <p>
          <s xml:space="preserve">Diviſo C in duas partes D &amp; </s>
          <s xml:space="preserve">E, ut ſupra <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">quæ ſint inter ſe ut A per fh
<ptr xml:id="note-0259-08a" corresp="note-0259-08" type="noteAnchor" />
<ptr xml:id="note-0259-09a" corresp="note-0259-09" type="noteAnchor" />
ad B per g i, ſi A agat in D, &amp; </s>
          <s xml:space="preserve">B in E, etiam corpora in nave quieſcunt <ptr type="noteAnchor" />,
id eſt; </s>
          <s xml:space="preserve">conſiderando motus abſolutos, non attendendo ad navem, agitatis <lb />
<ptr xml:id="note-0259-10a" corresp="note-0259-10" type="noteAnchor" />
D &amp; </s>
          <s xml:space="preserve">E ante ictum æqualibus velocitatibus, &amp; </s>
          <s xml:space="preserve">æqualiter accelerantur hæc <lb />actionibus corporum A &amp; </s>
          <s xml:space="preserve">B, quantitate nempe i l &amp; </s>
          <s xml:space="preserve">vires iis communican-<lb />tur quæ ſunt inter ſe ut maſſæ D &amp; </s>
          <s xml:space="preserve">E <ptr type="noteAnchor" />, id eſt, ut producta A per f b &amp; </s>
          <s xml:space="preserve">B
<ptr xml:id="note-0259-11a" corresp="note-0259-11" type="noteAnchor" />
per g i. </s>
          <s xml:space="preserve">Unde ſequitur, in colliſione trium horum corporum, actiones cor-<lb />
<ptr xml:id="note-0259-12a" corresp="note-0259-12" type="noteAnchor" />
porum A &amp; </s>
          <s xml:space="preserve">B in C, dum ſimul accelerant motum hujus corporis, eſſe in-<lb />ter ſe ut A per f b &amp; </s>
          <s xml:space="preserve">B per g i, in qua ratione ſunt etiam velocitates, quæ <lb />hiſce actionibus corpori C communicantur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0259-08" corresp="note-0259-08a" place="margin"><hi rend="small caps">TAB. XXV.</hi> <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0259-09" corresp="note-0259-09a" n="*" anchored="true" place="margin">624.</note>
              <note xml:space="preserve" xml:id="note-0259-10" corresp="note-0259-10a" n="*" anchored="true" place="margin">624.</note>
              <note xml:space="preserve" xml:id="note-0259-11" corresp="note-0259-11a" n="*" anchored="true" place="margin">450.</note>
              <note xml:space="preserve" xml:id="note-0259-12" corresp="note-0259-12a" place="margin"><hi rend="small caps">TAB. XXV.</hi> <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">199.</note>
        <p>
          <s xml:space="preserve">Diviſâ integrâ velocitate communicatâ i l in duas partes i m, m l, quæ ſint
</s>
          <pb facs="0260" n="182" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
inter ſeut A per f b ad B per g i, erit i m velocitas communicata actione cor-<lb />poris A.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Multiplicando i m &amp; </s>
          <s xml:space="preserve">m l per C, quo ratio non mutatur, habemus i m per <lb />C ad m l per C, ut A per f b ad B per g i; </s>
          <s xml:space="preserve">unde deducimus i m per C plus <lb />m l per C, id eſt C per i l, ad i m per C, ut A per f b plus B per g i ad Aper <lb />f b: </s>
          <s xml:space="preserve">antecedentia autem ſunt æqualia ergo &amp; </s>
          <s xml:space="preserve">conſequentia.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Idcirco A ad C. </s>
          <s xml:space="preserve">ut i m mutatio velocitatis in corpore C ex actione cor-<lb />poris A, ad f b mutationem in velocitate corporis A. </s>
          <s xml:space="preserve">Id eſt, mutationes <lb />in velocitatibus horum corporum oriundæ ex actione mutua in colliſione. <lb /></s>
          <s xml:space="preserve">ſunt inverſè ut maſſæ, ut hoc notavimus in num. </s>
          <s xml:space="preserve">627.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head xml:space="preserve">Inveſtigatio motus memorati in n. 633.</head>
        <p>
          <s xml:space="preserve">Concipiamus tria corpora A, B, C, perfecte elaſtica; </s>
          <s xml:space="preserve">ſit primi velocitas m, <lb />
<ptr xml:id="note-0260-01a" corresp="note-0260-01" type="noteAnchor" />
ſecundi n; </s>
          <s xml:space="preserve">tertii p; </s>
          <s xml:space="preserve">tendant hæc ad eandem partem: </s>
          <s xml:space="preserve">Poſt ictum ante in-<lb />ſtauratam figuram velocitas eſt {Am + Bn + Cp/A + B + C} <ptr type="noteAnchor" />, dicatur hæc v.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0260-01" corresp="note-0260-01a" place="margin">645.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">626. 643.</note>
        <p>
          <s xml:space="preserve">Vis ictu deſtructa eſt {ABx<hi rend="overline">m-n</hi><hi rend="superscript">2</hi> + ACx<hi rend="overline">m-p</hi><hi rend="superscript">2</hi> + BCx<hi rend="overline">n-p</hi><hi rend="superscript">2</hi>/A + B + C} <ptr type="noteAnchor" />
<ptr xml:id="note-0260-03a" corresp="note-0260-03" type="noteAnchor" />
Sit hæc æqualis 2Aff + 2Bff + 2Cff.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0260-03" corresp="note-0260-03a" n="*" anchored="true" place="margin">625. 641.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si non omnia corpora ad eandem partem tenderent velocitas poſt ictum, <lb />&amp; </s>
          <s xml:space="preserve">vis deſtructa, iiſdem regulis determinari poſſent,</s>
        </p>
        <p>
          <s xml:space="preserve">Sepoſito elaſterio poſt ictum corpora in nave, velocitate v motâ, quie-<lb />ſcerent, ſolo ergo elaſterio in hac poſt ictum moventur &amp; </s>
          <s xml:space="preserve">iiſdem velocitati-<lb />bus in nave moventur, quibus iiſdem elaſteriis corpora ſi revera quieſce-<lb />rent, agitarentur; </s>
          <s xml:space="preserve">determinatis ergo motibus in hoc ultimo caſu habebimus <lb />motus in nave, unde motus abſoluti facile deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponimus igitur corpora quieſcentia A, B, C, &amp; </s>
          <s xml:space="preserve">inter hæc elaſteria flexa <lb />
<ptr xml:id="note-0260-04a" corresp="note-0260-04" type="noteAnchor" />
viribus quibus in ictu partes fuere compreſſæ, quæ valent 2 A ff + 2 B ff +  <lb />2C ff. </s>
          <s xml:space="preserve">Cum agatur de caſu in quo inter A &amp; </s>
          <s xml:space="preserve">B, &amp; </s>
          <s xml:space="preserve">inter B &amp; </s>
          <s xml:space="preserve">C, partes <lb />æqualiter inflectuntur, vis qua elaſterium utrumque comprimitur eſt A ff <lb />+ B ff + C ff talemque vim dum elaſterium ſeſe expandit corporibus com-<lb />municat <ptr type="noteAnchor" />,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0260-04" corresp="note-0260-04a" place="margin">646.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">560.</note>
        <p>
          <s xml:space="preserve">Elaſterium inter A &amp; </s>
          <s xml:space="preserve">B ſeſe expandens Corpori A communicat vim B ff <lb />+ C ff, &amp; </s>
          <s xml:space="preserve">in corpus B actionem exerit, quæ valet vim A ff <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Eodem mo-
<ptr xml:id="note-0260-06a" corresp="note-0260-06" type="noteAnchor" />
do elaſterium aliud corpori C communicat vim A ff + B ff &amp; </s>
          <s xml:space="preserve">in Bexerit a-<lb />ctionem quæ valet vim C ff <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0260-06" corresp="note-0260-06a" n="*" anchored="true" place="margin">561.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">561.</note>
        <p>
          <s xml:space="preserve">Corpus B premitur ergo duabus actionibus in partes oppoſitas, ſi A ſuperet <lb />C, magis hoc corpus verſus premitur corpus B, actione quæ valet differen-<lb />tiam actionum A ff &amp; </s>
          <s xml:space="preserve">C ff, de cætero actiones in utramque partem ſunt æ-<lb />quales inter ſe &amp; </s>
          <s xml:space="preserve">valent C ff.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0261" n="183" />
        <fw type="head">MATHEMATICA. Lib. I. Cap. XXVII.</fw>
        <p>
          <s xml:space="preserve">Dum elaſteria actionibus æqualibus in ſe mutuo premunt, utrumque agit <lb />quaſi obſtaculo immobili inſiſteret; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">integram ſuam vim in partem oppoſitam <lb />exerit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt elaſteria agunt in corpora A &amp; </s>
          <s xml:space="preserve">C ita, ut ſingulis, præter me-
<ptr xml:id="note-0261-01a" corresp="note-0261-01" type="noteAnchor" />
moratas vires, communicent vim C ff; </s>
          <s xml:space="preserve">quare vis corpori A communicata va-<lb />let B ff + 2C ff, &amp; </s>
          <s xml:space="preserve">C movetur vi A ff + B ff + Cff, dum B ad par-<lb />tem Cpellitur actione quæ valet A ff-C ff.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0261-01" corresp="note-0261-01a" n="*" anchored="true" place="margin">561.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sed B non poteſt moveri, quin eâdem velocitate propellatur elaſterium <lb />inter B &amp; </s>
          <s xml:space="preserve">C, &amp; </s>
          <s xml:space="preserve">ab elaſterio ita agitato accipit corpus C vim ftatim memo-<lb />ratam eodem modo ac in nave, in qua elaſterium obſtaculo cede-<lb />re neſcio inſiſteret, actione elaſterii moveretur; </s>
          <s xml:space="preserve">id eſt velocitas qua <lb />corpus C a B recedit, aut B celerius movetur, illa eſt quæ competit impreſſio-<lb />ni ſtatim memoratæ, quæ velocitas eſt f {√A + B + C\x{0020}/C} <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si corporis B ve-
<ptr xml:id="note-0261-02a" corresp="note-0261-02" type="noteAnchor" />
locitas dicatur x, erit x + f {√A + B + C\x{0020}/C} velocitas corporis C. </s>
          <s xml:space="preserve">Summa viri-<lb />um horum corporum eſt A ff + B ff + C ff &amp; </s>
          <s xml:space="preserve">præterea A ff-C ff, ideſt <lb />valet ſumma hæc 2 A ff + B ff; </s>
          <s xml:space="preserve">Unde deducimus {B xx + C xx +  <lb />2fx √AC + BC + CC\x{0020} + A ff + B ff + C ff = 2Aff + Bff <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0261-03a" corresp="note-0261-03" type="noteAnchor" />
aut {x x + 2f x √AC + BC + CC\x{0020}/B + C = Aff-Cff/B + C}; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />{x = f√AB + 2AC\x{0020}-f√AC + BC + CC\x{0020}/B + C}: </s>
          <s xml:space="preserve">additâ velocitate <lb />f√A + B + C\x{0020}/C} qua C recedit à B habemus ipſius C velocitatem <lb />{fC √AB + 2AC\x{0020} + fB √AC + BC + CC\x{0020}/BC + CC}</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0261-02" corresp="note-0261-02a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0261-03" corresp="note-0261-03a" n="*" anchored="true" place="margin">479.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corporis autem A velocitas ex ipſius vi ante determinata detegitur eſtque <lb />velocitas hæc {f√AB + 2AC\x{0020}/A}.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Velocitates hæ ex velocitate v ſunt ſubtrahendæ, aut ipſi ſunt addendæ, <lb />
<ptr xml:id="note-0261-04a" corresp="note-0261-04" type="noteAnchor" />
pro ut cum motu navis conſpirant aut contrariæ agunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0261-04" corresp="note-0261-04a" place="margin">647.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si in primo motu A celerius B feratur, id eſt m ſuperet n, velocitas cor-<lb />poris A poſt ictum erit {v-f√AB + 2AC\x{0020}/A}; </s>
          <s xml:space="preserve">reliquæ velocitates detectæ <lb />corporum B &amp; </s>
          <s xml:space="preserve">C ipſi v addendæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In ſcholio 2. </s>
          <s xml:space="preserve">Capitis ſequentis demonſtrabimus ſummam virium poſt ictum <lb />
<ptr xml:id="note-0261-05a" corresp="note-0261-05" type="noteAnchor" />
æqualem eſſe A mm + B nn + C pp; </s>
          <s xml:space="preserve">quod cum ante demonſtratis congruit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0261-05" corresp="note-0261-05a" place="margin">648.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">558.</note>
        <pb facs="0262" n="184" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 3.</head>
        <head xml:space="preserve">Demonſtratio n. 637.</head>
        <p>
          <s xml:space="preserve">Diximus ſummam virium poſt ictum æqualem eſſe ſummæ virium ante i-<lb />ctum in colliſione in n. </s>
          <s xml:space="preserve">636. </s>
          <s xml:space="preserve">explicata; </s>
          <s xml:space="preserve">Poſitâ igitur velocitatum determi-<lb />
<ptr xml:id="note-0262-01a" corresp="note-0262-01" type="noteAnchor" />
natione ibi traditâ demonſtrandum Corpus C tantum virium acquirere quan-<lb />tum amittunt A &amp; </s>
          <s xml:space="preserve">B.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0262-01" corresp="note-0262-01a" place="margin"><hi rend="small caps">TAB. XXV.</hi> <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quadratum lineæ KN æquale eſt quadratis linearum KO &amp; </s>
          <s xml:space="preserve">ON, aut <lb />
<ptr xml:id="note-0262-02a" corresp="note-0262-02" type="noteAnchor" />
KP, &amp; </s>
          <s xml:space="preserve">bis rectangulo IOK <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">etiam æquale eſt idem quadratum quadratis
<ptr xml:id="note-0262-03a" corresp="note-0262-03" type="noteAnchor" />
KO &amp; </s>
          <s xml:space="preserve">KP &amp; </s>
          <s xml:space="preserve">bis rectangulo MPK <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">unde ſequitur æqualia eſſe rectangula hæc,
<ptr xml:id="note-0262-04a" corresp="note-0262-04" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">quadratum KN valere quadratum KO, &amp; </s>
          <s xml:space="preserve">rectangulum IOK, ut &amp; </s>
          <s xml:space="preserve"><lb />quadratum KP cum rectangulo MPK; </s>
          <s xml:space="preserve">ergo quadratum KN æquale eſt <lb />rectangulis IKO &amp; </s>
          <s xml:space="preserve">MKP; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quadratum K n, duplæ ipſius KN, quod <lb />quadruplum eſt quadrati KN, valebit quater ſummam rectangulorum IKO <lb />&amp; </s>
          <s xml:space="preserve">MKP. </s>
          <s xml:space="preserve">Multiplicatis his per C, habemus vim corporis C, ictu acquiſi-<lb />tam, æqualem 4CxKOxKl + 4CxKPxKM <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0262-02" corresp="note-0262-02a" place="margin">649.</note>
              <note xml:space="preserve" xml:id="note-0262-03" corresp="note-0262-03a" n="*" anchored="true" place="margin">12. El. 11.</note>
              <note xml:space="preserve" xml:id="note-0262-04" corresp="note-0262-04a" n="*" anchored="true" place="margin">12. El. 11.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis, quam ictu amiſit corpus A, habetur multiplicando A per difterenti-<lb />
<ptr xml:id="note-0262-05a" corresp="note-0262-05" type="noteAnchor" />
am quadratorum KD, K i, velocitatum ante &amp; </s>
          <s xml:space="preserve">poſt ictum <ptr type="noteAnchor" />, Differentia
<ptr xml:id="note-0262-06a" corresp="note-0262-06" type="noteAnchor" />
autem hæc propter æquales DI, I i, valet quater rectangulum KID <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vis a-
<ptr xml:id="note-0262-07a" corresp="note-0262-07" type="noteAnchor" />
miſſa eſt 4AxIDxKI: </s>
          <s xml:space="preserve">Sed in n, 635 vidimus A, C:</s>
          <s xml:space="preserve">:KO, ID; </s>
          <s xml:space="preserve">ergo <lb />AxID = CxKO, &amp; </s>
          <s xml:space="preserve">vis quam amittit A eſt 4CxKOxKI.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0262-05" corresp="note-0262-05a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0262-06" corresp="note-0262-06a" n="*" anchored="true" place="margin">598.</note>
              <note xml:space="preserve" xml:id="note-0262-07" corresp="note-0262-07a" n="*" anchored="true" place="margin">8. El. 11.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem modo demonſtramus vim quam amittit B æqualem eſſe 4CxKP <lb />xKM, ideoque ſummam virium amiſſarum valere vim quam C acquiſivit <lb />Q. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vix differt demonſtratio quando agitur de caſu fig. </s>
          <s xml:space="preserve">7.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXVIII.</head>
        <head xml:space="preserve">De Motu Centri gravitatis.</head>
        <p>
          <s xml:space="preserve">IN colliſione corporum, motus reſpectivos, a motibus ab-<lb />ſolutis diſtingui, in variis occaſionibus jam notavimus; <lb /></s>
          <s xml:space="preserve">his nunc ulterius addendum, corporum ipſorum motus ab-<lb />ſolutos, cum motu abſoluto omnium corporum ſimul conſi-<lb />deratorum non debere confundi.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi></head>
        <p rend="italics">
          <s xml:space="preserve">Motum abſolutum corporum quorumcumque ſimul conſider a-<lb />
<ptr xml:id="note-0262-08a" corresp="note-0262-08" type="noteAnchor" />
torum vocamus motum centri gravitatis communis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0262-08" corresp="note-0262-08a" place="margin">650.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut in ſingulis corporibus de motu dijudicamus ex motu <lb />centri gravitatis, &amp; </s>
          <s xml:space="preserve">hoc ad plura ſimul conſiderata applica-<lb />ri poſſe clarum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0263" n="185" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXVIII.</fw>
        <p>
          <s xml:space="preserve">Circa motum hunc abſolutum plurimorum corporum nota-<lb />
<ptr xml:id="note-0263-01a" corresp="note-0263-01" type="noteAnchor" />
mus, ipſum, actione reſpectivâ, qualis eſt omnis colliſio, non <lb />mutari; </s>
          <s xml:space="preserve">ideoque Centrum gravitatis commune variorum <lb />
<ptr xml:id="note-0263-02a" corresp="note-0263-02" type="noteAnchor" />
corporum in eâdem lineâ, eâdem velocitate, ante &amp; </s>
          <s xml:space="preserve">poſt i-<lb />ctum moveri. </s>
          <s xml:space="preserve">Quod in omnibus colliſionibus ante explica-<lb />tis obtineri demonſtrabimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0263-01" corresp="note-0263-01a" place="margin">650.</note>
              <note xml:space="preserve" xml:id="note-0263-02" corresp="note-0263-02a" place="margin">651.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint A &amp; </s>
          <s xml:space="preserve">B centra gravitatis duorum corporum, ſi ad C, <lb />
<ptr xml:id="note-0263-03a" corresp="note-0263-03" type="noteAnchor" />
centrum gravit atis commune, accedant ambo corpora, veloci-<lb />
<ptr xml:id="note-0263-04a" corresp="note-0263-04" type="noteAnchor" />
tatibus quæ ſunt inter ſe ut diſtantiæ ſuæ à centro, nempeut <lb />AC ad BC, id eſt, inverſe ut maſſæ ipſorum corporum <ptr type="noteAnchor" />,
<ptr xml:id="note-0263-05a" corresp="note-0263-05" type="noteAnchor" />
quieſcit in hoc motu centrum gravitatis; </s>
          <s xml:space="preserve">nam dum eodem <lb />tempore percurrunt A a, B b, quæ ſunt ut AC, BC, <lb />reſtant a C, b C in eâdem ratione inverſa maſſarum, qua-<lb />re &amp; </s>
          <s xml:space="preserve">in hoc ſitu C eſt commune gravitatis centrum <ptr type="noteAnchor" />, quod
<ptr xml:id="note-0263-06a" corresp="note-0263-06" type="noteAnchor" />
in motu hoc non fuit tranſlatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0263-03" corresp="note-0263-03a" place="margin"><hi rend="small caps">TA. XXV.</hi> <lb />fig. 8.</note>
              <note xml:space="preserve" xml:id="note-0263-04" corresp="note-0263-04a" place="margin">652.</note>
              <note xml:space="preserve" xml:id="note-0263-05" corresp="note-0263-05a" n="*" anchored="true" place="margin">134. 143.</note>
              <note xml:space="preserve" xml:id="note-0263-06" corresp="note-0263-06a" n="*" anchored="true" place="margin">134.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Eadem demonſtratio poteſt applicari ad motum corpo-<lb />
<ptr xml:id="note-0263-07a" corresp="note-0263-07" type="noteAnchor" />
rum à commune gravitatis centro recedentium, velocitati-<lb />bus quæ ſunt inverſe ut maſſæ, in quo caſu ergo etiam cen-<lb />trum hoc quieſcit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0263-07" corresp="note-0263-07a" place="margin">653.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si varia dentur corpora, ut A, B, D, &amp; </s>
          <s xml:space="preserve">hæc in eâdem <lb />
<ptr xml:id="note-0263-08a" corresp="note-0263-08" type="noteAnchor" />
lineâ mota, accedant omnia ad C commune gravitatis centrum, <lb />
<ptr xml:id="note-0263-09a" corresp="note-0263-09" type="noteAnchor" />
aut recedant ab hoc, velocitatibus quæ in ſingulis corpori-<lb />bus ſunt ut diſtantiæ ab hoc centro quieſcit etiam hoc ipſum. <lb /></s>
          <s xml:space="preserve">Nam cum in ſitu A, B, D ſumma productorum maſſarum <lb />per diſtantias a C ab una parte hujus puncti æqualis ſit ſimi-<lb />li ſummæ ad aliam partem <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">hoc locum habebit muta-
<ptr xml:id="note-0263-10a" corresp="note-0263-10" type="noteAnchor" />
tis omnibus diſtantiis, ut hîc fit, in eadem ratione, quare <lb />C manet centrum commune gravitatis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod ergo quie-
<ptr xml:id="note-0263-11a" corresp="note-0263-11" type="noteAnchor" />
ſcit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0263-08" corresp="note-0263-08a" place="margin">654.</note>
              <note xml:space="preserve" xml:id="note-0263-09" corresp="note-0263-09a" place="margin"><hi rend="small caps">TA. XXV.</hi> <lb />fig. 9.</note>
              <note xml:space="preserve" xml:id="note-0263-10" corresp="note-0263-10a" n="*" anchored="true" place="margin">141. 143.</note>
              <note xml:space="preserve" xml:id="note-0263-11" corresp="note-0263-11a" n="*" anchored="true" place="margin">141.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In hoc caſu, multiplicatis ſingulis maſſis per ſuas veloci-<lb />tates, ſumma productorum ab una parte centri gravitatis, <lb />æqualis eſt ſimili ſummæ ad aliam partem; </s>
          <s xml:space="preserve">ponimus enim <lb />velocitates ut diſtantias à centro hoc.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hiſce ſequentes deducimus concluſiones.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Corporum duorum, aut trium, in ſe mutuo directè incur-<lb />
<ptr xml:id="note-0263-12a" corresp="note-0263-12" type="noteAnchor" />
rentium ita, ut poſt ictum, ſi non ſint elaſtica, quieſcant, an-
</s>
          <pb facs="0264" n="186" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
te ictum quieſcit centrum gravitatis <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In hoc eodem con-
<ptr xml:id="note-0264-01a" corresp="note-0264-01" type="noteAnchor" />
<ptr xml:id="note-0264-02a" corresp="note-0264-02" type="noteAnchor" />
curſu, etiam quieſcit centrum hoc ſi @orpora ſint elaſtica <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0264-03a" corresp="note-0264-03" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0263-12" corresp="note-0263-12a" place="margin">655.</note>
              <note xml:space="preserve" xml:id="note-0264-01" corresp="note-0264-01a" place="margin">656</note>
              <note xml:space="preserve" xml:id="note-0264-02" corresp="note-0264-02a" n="*" anchored="true" place="margin">500. 652. <lb />622. 623. <lb />654.</note>
              <note xml:space="preserve" xml:id="note-0264-03" corresp="note-0264-03a" n="*" anchored="true" place="margin">562 629. <lb />653. 654.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpora duo aut tria directe in ſ<unclear reason="illegible" />e mutuo incurrant &amp; </s>
          <s xml:space="preserve"><lb />navis concipiatur ita agitata, ut corpora, poſitis his non e-<lb />laſticis, in hac poſt ictum quieſcant, in hac ipſa anteictum <lb />
<ptr xml:id="note-0264-04a" corresp="note-0264-04" type="noteAnchor" />
quieſcit centrum gravitatis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in tali conflictu poſt ictum
<ptr xml:id="note-0264-05a" corresp="note-0264-05" type="noteAnchor" />
etiam quieſcit idem hoc centrum, ſi corpora ſint elaſtica <ptr type="noteAnchor" />,
<ptr xml:id="note-0264-06a" corresp="note-0264-06" type="noteAnchor" />
unde ſequitur navem hanc moveri ea velocitate, qua an-<lb />te &amp; </s>
          <s xml:space="preserve">poſt ictum, commune corporum gravitatis centrum <lb />fertur, cujus ergo centri motus non mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0264-04" corresp="note-0264-04a" place="margin">657.</note>
              <note xml:space="preserve" xml:id="note-0264-05" corresp="note-0264-05a" n="*" anchored="true" place="margin">655.</note>
              <note xml:space="preserve" xml:id="note-0264-06" corresp="note-0264-06a" n="*" anchored="true" place="margin">656.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hoc quoque locum habere in motibus memoratis in n. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0264-07a" corresp="note-0264-07" type="noteAnchor" />
633. </s>
          <s xml:space="preserve">634. </s>
          <s xml:space="preserve">636. </s>
          <s xml:space="preserve">demonſtrabimus in ſcholio ſequenti 2.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0264-07" corresp="note-0264-07a" place="margin">658.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In concurſu obliquo duorum corporum duos conſideravi-<lb />
<ptr xml:id="note-0264-08a" corresp="note-0264-08" type="noteAnchor" />
mus motus, unum quo directe in ſe mutuo incurrunt, al-<lb />terum lateralem <ptr type="noteAnchor" />, qui in impactu non mutatur; </s>
          <s xml:space="preserve">quare ne-
<ptr xml:id="note-0264-09a" corresp="note-0264-09" type="noteAnchor" />
que mutatur centri gravitatis motus lateralis; </s>
          <s xml:space="preserve">ſed neque <lb />juxta aliam directionem centri gravitatis motus mutari po-<lb />teſt, quia impactu directo non mutatur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Idcirco nullo
<ptr xml:id="note-0264-10a" corresp="note-0264-10" type="noteAnchor" />
reſpectu motus hic variat &amp; </s>
          <s xml:space="preserve">velocitatem directionemque ſuam <lb />ſervat commune corporum gravitatis centrum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0264-08" corresp="note-0264-08a" place="margin">659.</note>
              <note xml:space="preserve" xml:id="note-0264-09" corresp="note-0264-09a" n="*" anchored="true" place="margin">617.</note>
              <note xml:space="preserve" xml:id="note-0264-10" corresp="note-0264-10a" n="*" anchored="true" place="margin">657.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unicum circa motum centri gravitatis notandum ſuper <lb />eſt quod in Scholio ſequenti 1. </s>
          <s xml:space="preserve">demonſtramus; </s>
          <s xml:space="preserve">ſummam <lb />
<ptr xml:id="note-0264-11a" corresp="note-0264-11" type="noteAnchor" />
virium corporum quorumcumque concurrentium, æqualem <lb />eſſe ſummæ vis quam haberent omnia corpora, ſimul agita-<lb />ta ea velocitate, qua fertur cummune gravitatis centrum, <lb />&amp; </s>
          <s xml:space="preserve">omnium virium quibus corpora reſpectu centri bujus mo-<lb />ventur. </s>
          <s xml:space="preserve">Id eſt ſi ſumma maſſarum per quadratum veloci-<lb />tatis centri gravitatis multiplicetur, &amp; </s>
          <s xml:space="preserve">ſingulæ maſſæ mul-<lb />tiplicentur per quadrata velocitatum, quibus ad gravitatis <lb />
<ptr xml:id="note-0264-12a" corresp="note-0264-12" type="noteAnchor" />
centrum tendunt, id eſt, quibus in nave, in qua centrum <lb />gravitatis quieſceret agitata forent, ſumma omnium produ-<lb />ctorum æqualis erit ſummæ productorum ſingularum maſ-<lb />ſarum ductarum in quadrata velocitatum ſuarum. </s>
          <s xml:space="preserve">Id circo <lb />ſi mutatis motibus, ſuma virium in hac nave non mutetur, <lb />neque mutabitur ſumma virium abſolutarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0264-11" corresp="note-0264-11a" place="margin">660.</note>
              <note xml:space="preserve" xml:id="note-0264-12" corresp="note-0264-12a" place="margin">661.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propoſitio hæc univerſalis eſt; </s>
          <s xml:space="preserve">ſed cum in hiſce omnibus
</s>
          <pb facs="0265" n="187" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXVIII.</fw>
de colliſione agatur, corpora tantum concurrentia conſide-<lb />ramus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 1.</head>
        <head rend="italics" xml:space="preserve">Demonſtratio n. 660.</head>
        <p>
          <s xml:space="preserve">QUamdiu corpora moventur in eâdem lineâ propoſitio ultimum memo-<lb />
<ptr xml:id="note-0265-01a" corresp="note-0265-01" type="noteAnchor" />
rata ſimplici algebraica computatione patet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0265-01" corresp="note-0265-01a" place="margin">662.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint corpora A, B, C, primi velocitas m; </s>
          <s xml:space="preserve">ſecundi n, tertii p; </s>
          <s xml:space="preserve">centri gravi-<lb />tatis velocitas d. </s>
          <s xml:space="preserve">Tendant corpora ad eandem partem; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſint m &amp; </s>
          <s xml:space="preserve">n majores <lb />ipſa d; </s>
          <s xml:space="preserve">p verò minor: </s>
          <s xml:space="preserve">Ergo velocitates, quibus corpora ad centrum gravitatis <lb />tendunt ſunt m - d, n - d, d - p; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">A x <hi rend="overline">m - d</hi> + B x <hi rend="overline">n - d</hi> = C x <hi rend="overline">d - p<ptr type="noteAnchor" /></hi>; </s>
          <s xml:space="preserve">quare
<ptr xml:id="note-0265-02a" corresp="note-0265-02" type="noteAnchor" />
2 A md - 2A dd + 2B nd - 2 B dd = 2 C dd - 2C dp, multiplicando inte-<lb />gram æquationem per 2d. </s>
          <s xml:space="preserve">Demonſtrandum A mm + B nn + C pp = <hi rend="overline">A + B + C</hi> <lb />x dd + A x <hi rend="overline">m - d</hi><hi rend="superscript">2</hi> + B x <hi rend="overline">n - d</hi><hi rend="superscript">2</hi> + C x <hi rend="overline">d - p</hi><hi rend="superscript">2</hi>. </s>
          <s xml:space="preserve">Ultima hæc quantitas ſic pot-<lb />eſt exprimi A mm-2 A md + 2 A dd + B nn - 2B nd + 2 B dd + C pp <lb />- 2 C pd + 2C dd. </s>
          <s xml:space="preserve">Sed - 2A md + 2A dd - 2B nd + 2B dd &amp; </s>
          <s xml:space="preserve">- 2C pd <lb />+ 2 C dd ſeſe mutuo deſtruunt &amp; </s>
          <s xml:space="preserve">quantitas hæc tantum valet A mm + B nn <lb />+ C pp. </s>
          <s xml:space="preserve">Quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0265-02" corresp="note-0265-02a" n="*" anchored="true" place="margin">654.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint iterum tria corpora A, B, C, quorum tantum gravitatis centra conſi-<lb />
<ptr xml:id="note-0265-03a" corresp="note-0265-03" type="noteAnchor" />
deramus; </s>
          <s xml:space="preserve">ſit commune gravitatis centrum D; </s>
          <s xml:space="preserve">ponamus corpora moveri per <lb />
<ptr xml:id="note-0265-04a" corresp="note-0265-04" type="noteAnchor" />
AE, BE, CF, velocitatibus hiſce lineis proportionalibus. </s>
          <s xml:space="preserve">Directio &amp; </s>
          <s xml:space="preserve">ce-<lb />leritas centri gravitatis D eſt DE. </s>
          <s xml:space="preserve">Velocitates, quibus corpora ad centrum <lb />commune gravitatis tendunt, ſunt AD, BD, CD, hæ enim eſſent corpo-<lb />rum velocitates in nave, in qua centrum gravitatis quieſceret. </s>
          <s xml:space="preserve">Idcirco de-<lb />monſtrandum A x AE<hi rend="superscript">q</hi> + B x BE<hi rend="superscript">q</hi> + C x CE<hi rend="superscript">q</hi> = A + B + C x DE<hi rend="superscript">q</hi> + A x AD<hi rend="superscript">q</hi> <lb />+ B x BD<hi rend="superscript">q</hi> + C x CD<hi rend="superscript">q</hi>.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0265-03" corresp="note-0265-03a" place="margin">663.</note>
              <note xml:space="preserve" xml:id="note-0265-04" corresp="note-0265-04a" place="margin"><hi rend="small caps">TA. XXV.</hi> <lb />fig. 10.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ad DE ducantur perpendieulares AF, BG, CH, LDL. </s>
          <s xml:space="preserve">Diſtantiæ <lb />corporum A, B, C à linea LDL ſunt FD, GD, HD; </s>
          <s xml:space="preserve">ergo, quia D eſt <lb />centrum commune gravitatis A x FD + B x GD = C x D <ptr type="noteAnchor" /> unde patet D
<ptr xml:id="note-0265-05a" corresp="note-0265-05" type="noteAnchor" />
eorum corporum eſſe commune gravitatis centrum poſitis his in F, G <lb />&amp; </s>
          <s xml:space="preserve">H <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si in hoc ſitu concipiamus corpora moveri A velocitate FE, B
<ptr xml:id="note-0265-06a" corresp="note-0265-06" type="noteAnchor" />
velocitate GE, &amp; </s>
          <s xml:space="preserve">tandem C velocitate HE; </s>
          <s xml:space="preserve">centri gravitatis velocitas <lb />erit DE; </s>
          <s xml:space="preserve">Ergo A x FE<hi rend="superscript">q</hi> + B x GE<hi rend="superscript">q</hi> + C x HE<hi rend="superscript">q</hi> = <hi rend="overline">A + B + C</hi> x DE<hi rend="superscript">q</hi> <lb />+ A x FD<hi rend="superscript">q</hi> + B x GD<hi rend="superscript">q</hi> + C x HD<hi rend="superscript">q</hi> <ptr type="noteAnchor" /> addendo utrimque A x AF<hi rend="superscript">q</hi> +
<ptr xml:id="note-0265-07a" corresp="note-0265-07" type="noteAnchor" />
B x BG<hi rend="superscript">q</hi> + C x CH<hi rend="superscript">q</hi> &amp; </s>
          <s xml:space="preserve">ſubſtituendo triangulorum rectangulorum AFD, <lb />BGD, CHD, AFE, BGE, CHE, quadrata Hypotenuſarum pro <lb />quadratis laterum <ptr type="noteAnchor" />, habebimus propoſitum.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0265-08a" corresp="note-0265-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0265-05" corresp="note-0265-05a" n="*" anchored="true" place="margin">141. 159</note>
              <note xml:space="preserve" xml:id="note-0265-06" corresp="note-0265-06a" n="*" anchored="true" place="margin">141.</note>
              <note xml:space="preserve" xml:id="note-0265-07" corresp="note-0265-07a" n="*" anchored="true" place="margin">661.</note>
              <note xml:space="preserve" xml:id="note-0265-08" corresp="note-0265-08a" n="*" anchored="true" place="margin">47. <hi rend="small caps">EL</hi> @</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0266" n="188" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">Demonſtrationes n. 658. ut &amp; 648.</head>
        <p>
          <s xml:space="preserve">DIximus <ptr type="noteAnchor" /> in caſu n. </s>
          <s xml:space="preserve">633. </s>
          <s xml:space="preserve">quem in n. </s>
          <s xml:space="preserve">645. </s>
          <s xml:space="preserve">peculiarius explicavimus etiam
<ptr xml:id="note-0266-01a" corresp="note-0266-01" type="noteAnchor" />
motum centri gravitatis non mutari, quod ut demonſtrctur, probandum <lb />corpora ita à ſe invicem ſeparari, ut conſideratis ſolis motibus quibus ſepa-<lb />rantur, quieſcat centrum gravitatis; </s>
          <s xml:space="preserve">tunc enim ſi concipiamus corpora ſe-<lb />parari in nave, ea velocitate mota qua corpora conjunctim ante ſeparationem <lb />moventur, velocitate qua navis fertur commune gravitatis centrum motum <lb />continuabit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0266-01" corresp="note-0266-01a" n="*" anchored="true" place="margin">658.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitis quæ in n. </s>
          <s xml:space="preserve">645. </s>
          <s xml:space="preserve">fuere expllcata demonſtrandum A multiplicatum <lb />
<ptr xml:id="note-0266-02a" corresp="note-0266-02" type="noteAnchor" />
per velocitatem ibi determinatam quod productum eſt@ f √AB + 2AC\x{0020}, <lb />valere ſummam productorum corporum B &amp; </s>
          <s xml:space="preserve">C, ſingulorum multiplicato-<lb />rum per velocitates ibi detectas <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Producta hæc ſunt
<ptr xml:id="note-0266-03a" corresp="note-0266-03" type="noteAnchor" />
{fB√AB + 2AC\x{0020} - fB√AC + BC + CC\x{0020}/B + C} &amp; </s>
          <s xml:space="preserve"><lb />{fC√AB + 2AC\x{0020} + fB√AC + BC + CC\x{0020}/B + C} quorum ſumma eſt <lb />{fB√AB + 2AC\x{0020} + fC√AB + 2AC\x{0020}/B + C}, id eſt f√AB + 2AC\x{0020}. <lb /></s>
          <s xml:space="preserve">Quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0266-02" corresp="note-0266-02a" place="margin">664.</note>
              <note xml:space="preserve" xml:id="note-0266-03" corresp="note-0266-03a" n="*" anchored="true" place="margin">654.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hiſce demonſtratis facile patent, quæ in n. </s>
          <s xml:space="preserve">648. </s>
          <s xml:space="preserve">fuere memorata, ſummam <lb />virium ante &amp; </s>
          <s xml:space="preserve">poſt ictum, in motu in n. </s>
          <s xml:space="preserve">645. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſeq. </s>
          <s xml:space="preserve">memorato eſſe æqualem. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0266-04a" corresp="note-0266-04" type="noteAnchor" />
Vires quibus partes elaſticas inflexas poſuimus, ſunt vires quibus ad centrum <lb />commune gravitatis acceſſere corpora <ptr type="noteAnchor" />, ſervatâ eâdem virium ſummâ à ſe-
invicem, uti ex computatione ipſa ſequitur, fuere ſeparata, id eſt, illa ipſa <lb />
<ptr xml:id="note-0266-05a" corresp="note-0266-05" type="noteAnchor" />
fuit ſumma virium quibus à centro gravitatis receſſere, cum hujus centri ve-<lb />locitas ictu non fuerit mutatâ <ptr type="noteAnchor" />, unde ſequitur ſummam virium abſoluta-
rum etiam eandem eſſe ante &amp; </s>
          <s xml:space="preserve">poſt ictum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0266-04" corresp="note-0266-04a" place="margin">665.</note>
              <note xml:space="preserve" xml:id="note-0266-05" corresp="note-0266-05a" n="*" anchored="true" place="margin">642. 654.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">664.</note>
        <p>
          <s xml:space="preserve">In n. </s>
          <s xml:space="preserve">658. </s>
          <s xml:space="preserve">diximus etiam centrum commune gravitatis corporum in col-<lb />
<ptr xml:id="note-0266-07a" corresp="note-0266-07" type="noteAnchor" />
liſionibus compoſitis in n. </s>
          <s xml:space="preserve">634. </s>
          <s xml:space="preserve">636 memoratis, eadem directione &amp; </s>
          <s xml:space="preserve">veloci-<lb />
<ptr xml:id="note-0266-08a" corresp="note-0266-08" type="noteAnchor" />
tate motum poſt corporum concurſum continuare.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0266-07" corresp="note-0266-07a" n="*" anchored="true" place="margin">661</note>
              <note xml:space="preserve" xml:id="note-0266-08" corresp="note-0266-08a" place="margin">666.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si concipiamus corpora A &amp; </s>
          <s xml:space="preserve">B ultra K eadem velocitate, qua anteictum <lb />movebantur, motum continuare quieſcente eodem modo corpore C, neque <lb />
<ptr xml:id="note-0266-09a" corresp="note-0266-09" type="noteAnchor" />
directio neque velocitas centri gravitatis communis mutata erit; </s>
          <s xml:space="preserve">conſtabit <lb />ergo propoſitum ſi demonſtremus in eodem puncto verſari centrum gravita-<lb />tis, poſitis corporibus, C in K, A in D, &amp; </s>
          <s xml:space="preserve">B in E; </s>
          <s xml:space="preserve">aut poſitis his, C in N, <lb />A in I, &amp; </s>
          <s xml:space="preserve">B in M; </s>
          <s xml:space="preserve">aut tandem poſitis, C in n, A in i, &amp; </s>
          <s xml:space="preserve">B in m. </s>
          <s xml:space="preserve">Patebit <lb />autem in hiſce tribus occaſionibus idem eſſe gravitatis centrum ſi demonſtre-<lb />mus hujus diſtantias à lineis KF &amp; </s>
          <s xml:space="preserve">KG non mutari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0266-09" corresp="note-0266-09a" place="margin"><hi rend="small caps">TA. XXV</hi> <lb />fig. 6. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reſpectu lineæ utriusque demonſtratio eadem eſt, quare de KF tantum a-<lb />gam.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0267" n="189" />
        <fw type="head">MATHEMATICA. LIB. I. CAP. XXVIII.</fw>
        <p>
          <s xml:space="preserve">Diſtantia puncti N ab hac linea eſt NM; </s>
          <s xml:space="preserve">puncti n eſt 2NM; </s>
          <s xml:space="preserve">puncto-<lb />rum D, I, &amp; </s>
          <s xml:space="preserve">i diſtantiæ ab cadem KF deteguntur hiſce proportionibus <lb />PN, NM:</s>
          <s xml:space="preserve">: { KD, {NM x KD/PN} \\ KI, {NM x KI/PN} \\ Ki, {NM x Ki/PN} <lb />Quibus detectis, diſtantiæ centri gravitatis communis corporum, à memo-<lb />ratâ lineâ KF, in tribus memoratis corporum diſpoſitionibus, deteguntur <lb />{NM x KD x A/PN x A + B + C}, {NM x C/A + B + C} + {NM x KI x A/PN x A + B + C}, &amp; </s>
          <s xml:space="preserve">{2 NM x C/A + B + C} <lb />+ {NM x Ki + A/PN x A + B + C} <ptr type="noteAnchor" /> quas æquales demonſtramus.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0267-01a" corresp="note-0267-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0267-01" corresp="note-0267-01a" n="*" anchored="true" place="margin">159.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex conſtructione ſequitur PN ſe habere ad NQ, &amp; </s>
          <s xml:space="preserve">etiam 2 PN ad <lb />2 NQ, ut A ad C; </s>
          <s xml:space="preserve">NQ æqualis eſt ID, &amp; </s>
          <s xml:space="preserve">valet KD-KI ergo PN x C <lb />= KD x A - KI x A, &amp; </s>
          <s xml:space="preserve">PN x C + KI x A = KD x A.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Eodem modo 2NQ valet 2ID, id eſt iD, &amp; </s>
          <s xml:space="preserve">æqualis eſt KD - Ki; <lb /></s>
          <s xml:space="preserve">unde deducimus 2PN x C + Ki x A = KD x A.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Multiplicatis hiſce tribus quantitatibus æqualibus KD x A, PN x C + <lb />KI x A, &amp; </s>
          <s xml:space="preserve">2PN x C + Ki x A, per NM &amp; </s>
          <s xml:space="preserve">diviſis productis per <lb />PN x <hi rend="overline">A + B + C</hi>, habebimus quotientes æquales, à diſtantiis detectis non di-<lb />verſos. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 3.</head>
        <p>
          <s xml:space="preserve">SI demonſtratam in hoc capite propoſitionem, ante &amp; </s>
          <s xml:space="preserve">poſt colliſionem <lb />
<ptr xml:id="note-0267-02a" corresp="note-0267-02" type="noteAnchor" />
centrum gravitatis eâdem velocitate ferri, applicemus ad colliſionem in n. <lb /></s>
          <s xml:space="preserve">521. </s>
          <s xml:space="preserve">memoratam, corporum poſt colliſionem velocitates determinare poſſu-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0267-02" corresp="note-0267-02a" place="margin">667.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tria corpora poſt ictum, juxta directionem primi motus feruntur veloci-<lb />tate, qua ante ictum centrum gravitatis fertur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam nulla datur actio qua
<ptr xml:id="note-0267-03a" corresp="note-0267-03" type="noteAnchor" />
directe ſeparari poſſint; </s>
          <s xml:space="preserve">velocitas hæc detegitur regulâ in n. </s>
          <s xml:space="preserve">519. </s>
          <s xml:space="preserve">traditâ. <lb /></s>
          <s xml:space="preserve">itaque moventur ut corpora mollia poſt impactionem directam, ſed quæ in <lb />hac corporum mollium impactione deſtruitur, corpora impingentia vim ſer-<lb />vant in caſu quem examinamus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hac idcirco lateraliter feruntur <ptr type="noteAnchor" /> quæ vis
<ptr xml:id="note-0267-04a" corresp="note-0267-04" type="noteAnchor" />
datur <ptr type="noteAnchor" /> quare lateralis velocitas, quæ nempe cum prima directione angulumeffi-
<ptr xml:id="note-0267-05a" corresp="note-0267-05" type="noteAnchor" />
cit rectum, detegi poteſt: </s>
          <s xml:space="preserve">ideoque directiones &amp; </s>
          <s xml:space="preserve">velocitates abſolutas qui-<lb />bus corpora impingentia poſt ictum moventur facile determinantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0267-03" corresp="note-0267-03a" n="*" anchored="true" place="margin">652.</note>
              <note xml:space="preserve" xml:id="note-0267-04" corresp="note-0267-04a" n="*" anchored="true" place="margin">601.</note>
              <note xml:space="preserve" xml:id="note-0267-05" corresp="note-0267-05a" n="*" anchored="true" place="margin">510. 525.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dicatur Q maſſa corporis quieſcentis; </s>
          <s xml:space="preserve">ſint aliorum maſſæ P, P; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">horum <lb />
<ptr xml:id="note-0267-06a" corresp="note-0267-06" type="noteAnchor" />
volocitas v.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0267-06" corresp="note-0267-06a" place="margin"><hi rend="small caps">TAB XXI.</hi> <lb />fig. 4</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0268" n="190" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Poſt ictum corpus Q movetur velocitate {2Pv/2P + Q} <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eâdem velocitate, jux-
<ptr xml:id="note-0268-01a" corresp="note-0268-01" type="noteAnchor" />
ta eandem directionem, feruntur corpora P, P, ſed hæc præterea laterali-<lb />ter feruntur viribus quæ valent {2PQvv/2P + Q} <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare utriuſque lateralis ve-
<ptr xml:id="note-0268-02a" corresp="note-0268-02" type="noteAnchor" />
locitas eſt {v√Q\x{0020}/√2P + Q\x{0020}} <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">velocitas abſoluta {v √4PP + 2PQ + QQ\x{0020}/2P + Q} <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0268-03a" corresp="note-0268-03" type="noteAnchor" />
<ptr xml:id="note-0268-04a" corresp="note-0268-04" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0268-01" corresp="note-0268-01a" n="*" anchored="true" place="margin">519.</note>
              <note xml:space="preserve" xml:id="note-0268-02" corresp="note-0268-02a" n="*" anchored="true" place="margin">510. 525.</note>
              <note xml:space="preserve" xml:id="note-0268-03" corresp="note-0268-03a" n="*" anchored="true" place="margin">470.</note>
              <note xml:space="preserve" xml:id="note-0268-04" corresp="note-0268-04a" n="*" anchored="true" place="margin">610.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXIX.</head>
        <head rend="italics" xml:space="preserve">De Legibus Elaſticitatis.</head>
        <p>
          <s xml:space="preserve">QUid ſit Elaſticitas, &amp; </s>
          <s xml:space="preserve">unde oriatur, jam vidimus <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0268-05a" corresp="note-0268-05" type="noteAnchor" />
etiam quid ex eo in congreſſu corporum, ſive dire-<lb />cte, ſive oblique, in ſe mutuo impingentium eve-<lb />niat; </s>
          <s xml:space="preserve">ſupereſt ut ipſius Elaſticitatis leges examinemus, il-<lb />ludque ex Phænomenis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0268-05" corresp="note-0268-05a" n="*" anchored="true" place="margin">701.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omnia corpora, in quibus Elaſticitatem obſervamus, <lb />conſtant ex filamentis tenuibus, aut ſaltem quaſi ex talibus <lb />conſtantia conſiderari poſſunt, corpus enim in fila diviſum <lb />concipi poteſt; </s>
          <s xml:space="preserve">illaque fila, ad ſe mutuo appoſita, corpus <lb />formare; </s>
          <s xml:space="preserve">ut ergo in caſu omnium minime compoſito E-<lb />laſticitas examinetur, chordæ conſiderandæ ſunt, &amp; </s>
          <s xml:space="preserve">qui-<lb />dem metallicæ; </s>
          <s xml:space="preserve">chordæ enim exinteſtinis ovium ſpiram for-<lb />mant, &amp; </s>
          <s xml:space="preserve">non ut fibræ, ex quibus corpora formantur, con-<lb />ſiderari queunt.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Fibrarum Elaſticitas in eo ſita eſt, quod extendi poſſint, <lb />
<ptr xml:id="note-0268-06a" corresp="note-0268-06" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">ſublata vi qua producuntur, iterum ad priſtinam longi-<lb />tudinem redeant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0268-06" corresp="note-0268-06a" place="margin">668.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fibræ nullam habent Elaſticitatem, niſi certâ vi ten-<lb />
<ptr xml:id="note-0268-07a" corresp="note-0268-07" type="noteAnchor" />
ſæ ſint; </s>
          <s xml:space="preserve">ut patet ex chordis parum tenſis, &amp; </s>
          <s xml:space="preserve">quarum ex-<lb />tremitates fixæ ſunt; </s>
          <s xml:space="preserve">quæ ſi a ſitu paululum removeantur, <lb />ad illum ſponte non redeunt: </s>
          <s xml:space="preserve">quiſnam vero ſit gradus ten-<lb />ſionis, in quo Elaſticitas inchoetur, Experimentis nondum <lb />fuit determinatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0268-07" corresp="note-0268-07a" place="margin">669.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando nimia vi fibra tenditur, Elaſticitatem amittit; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0268-08a" corresp="note-0268-08" type="noteAnchor" />
</s>
          <pb facs="0269" />
          <s xml:space="preserve">
<pb facs="0269a" />
<ptr xml:id="fig-0269a-01a" corresp="fig-0269a-01" type="figureAnchor" />
<pb facs="0270" />
<pb facs="0271" n="191" /><fw type="head">MATHEMATICA. LIB. I. CAP XXIX.</fw>
&amp; </s>
          <s xml:space="preserve">neque gradus hicce tenſionis notus eſt; </s>
          <s xml:space="preserve">illud conſtat, <lb />tenſionem fibrarum, quæ Elaſticitatem conſtituit, certis <lb />limitibus terminari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0268-08" corresp="note-0268-08a" place="margin">670.</note>
              <figure xml:id="fig-0269a-01" corresp="fig-0269a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0269a-01" />
                <label>0269a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce patet differentia corporum elaſticorum &amp; </s>
          <s xml:space="preserve">non <lb />
<ptr xml:id="note-0271-01a" corresp="note-0271-01" type="noteAnchor" />
elaſticorum; </s>
          <s xml:space="preserve">quare corpus elaſticum Elaſticitatem amit tit, <lb />&amp; </s>
          <s xml:space="preserve">quomodo Elaſticitate deſtitutum proprietatem hanc acqui-<lb />rit. </s>
          <s xml:space="preserve">Lamina metallica, repetitis mallei ictibus, quibus fibræ <lb />tenduntur, fit elaſtica, calefacta vim hanc amittit, dum vi <lb />ignis ſitus partium turbatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0271-01" corresp="note-0271-01a" place="margin">671.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inter limites tenſionis, quibus elaſticitas terminatur, pro <lb />vario tenſionis gradu, vis diverſa requiritur, ad chordam <lb />certa quantítate producendam; </s>
          <s xml:space="preserve">quænam hic proportio lo-<lb />cum habeat Experimentis determinari debet, quæ, ut jam <lb />dictum, cum chordis metallicis inſtituenda ſunt. </s>
          <s xml:space="preserve">Cum ve-<lb />ro hæ chordæ vix ſenſibiliter producantur, directe produ-<lb />ctionum proportiones menſurari nequeunt; </s>
          <s xml:space="preserve">alia methodo <lb />hæ determinantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit chorda horizontalis AB, certa vi tenſa; </s>
          <s xml:space="preserve">cujus extre <lb />
<ptr xml:id="note-0271-02a" corresp="note-0271-02" type="noteAnchor" />
mitates in A &amp; </s>
          <s xml:space="preserve">B fixæ ſunt; </s>
          <s xml:space="preserve">pondere in medio chordæ ap-<lb />penſo inflectatur chorda, ut ſitum ACB acquirat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0271-02" corresp="note-0271-02a" place="margin"><hi rend="small caps">TA XXVI</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi></head>
        <p rend="italics">
          <s xml:space="preserve">Linea ut C c a puncto medio chordæ poſt inflexionem, ad <lb />
<ptr xml:id="note-0271-03a" corresp="note-0271-03" type="noteAnchor" />
punctum medium in ſitu naturali, vocatur chordæ ſagit-<lb />ta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0271-03" corresp="note-0271-03a" place="margin">672.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit c e circuli portio, centro B, &amp; </s>
          <s xml:space="preserve">radio B c, deſcripti. <lb /></s>
          <s xml:space="preserve">Inflexione dimidia pars chordæ producta fuit quantita-<lb />te C e, quæ quantitas cum ſagitta C c certam relationem <lb />habet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pondus etiam, quo chorda inflectitur, certam cum vi, <lb />qua fibra producitur, id eſt, per BC trahitur, relationem <lb />habet; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita in variis Experimentis ex comparationibus ſa-<lb />gittarum, &amp; </s>
          <s xml:space="preserve">ponderum quibus chordæ inflectuntur, pro-<lb />ductionum proportiones determinari poſſunt, ut ſequentibus <lb />Experimentis patebit.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0272" n="192" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head rend="italics" xml:space="preserve">Qua Experimenta de Elaſticitate inſtituuntur.</head>
        <p>
          <s xml:space="preserve">Machinæ hujus pars præcipua eſt tabula lignea verti-<lb />
<ptr xml:id="note-0272-01a" corresp="note-0272-01" type="noteAnchor" />
calis, longitudinis circiter trium pedum, altitudinis unius <lb />
<ptr xml:id="note-0272-02a" corresp="note-0272-02" type="noteAnchor" />
pedis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0272-01" corresp="note-0272-01a" place="margin">673.</note>
              <note xml:space="preserve" xml:id="note-0272-02" corresp="note-0272-02a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Regulæ ligneæ mn, mn, tabulæ cohærent, &amp; </s>
          <s xml:space="preserve">iis ſuſti-<lb />nentur duo Priſmata H, H, ad formam cunei, quæ juxta illas <lb />regulas moventur, &amp; </s>
          <s xml:space="preserve">ubique ope cochlearum tranſeuntium <lb />per ſcisſuras in tabula firmantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dantur inter A &amp; </s>
          <s xml:space="preserve">B diviſiones æquales, a medio tabulæ <lb />partem utramque verſus, ad ſitum Priſmatum determinan-<lb />dum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In O datur ſulcus, quo Machinæ a latere connectitur tro-<lb />chlea T, cujus figura datur in F, fig. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">X.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Chorda, cum qua Experimenta fiunt, ab una parte an-<lb />nectitur extremitati regulæ m n, &amp; </s>
          <s xml:space="preserve">ad aliam partem circumit <lb />trochleam T, pondere P illam tendente, &amp; </s>
          <s xml:space="preserve">Priſmatibus H. <lb /></s>
          <s xml:space="preserve">H, in punctis, quæ a medio Machinæ æque diſtant, illam <lb />ſuſtinentibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Medio Tabulæ inſeritur lamina ænea d e, in partes mini-<lb />mas diviſa, juxta quas diviſiones movetur lamina ænea fg, <lb />quæ chordæ appenditur, &amp; </s>
          <s xml:space="preserve">in qua foramen datur per quod <lb />hæc immittitur; </s>
          <s xml:space="preserve">huic laminæ conjuncta eſt lanx L, quæ unâ <lb />cum lamina f g exacte eſt ponderis unius unciæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Longitudo chordæ in Experimentis æqualis eſt di-<lb />ſtantiæ inter apices Priſmatum H, H; </s>
          <s xml:space="preserve">nam in inflexionibus <lb />minimis, circa quas ſolas Experimenta fiunt; </s>
          <s xml:space="preserve">ponderibus in <lb />C appenſis, chorda ſuper Priſmatibus non movetur, pondus <lb />P non elevatur, &amp; </s>
          <s xml:space="preserve">pars, ut AB, ſola inflexionibus iſtis <lb />producitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In chordæ inflexionibus ſagittæ menſurantur diviſioni-<lb />bus laminæ e d, nam extremitas g laminæ g c æqualiter ſemper <lb />cum puncto C, in chordæ inflexione, deſcendit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum. i.</hi></head>
        <p>
          <s xml:space="preserve">Sit pondus P duarum librarum, &amp; </s>
          <s xml:space="preserve">inflectatur chorda in <lb />
<ptr xml:id="note-0272-03a" corresp="note-0272-03" type="noteAnchor" />
C pondere unius unciæ, id eſt, pondere lancis &amp; </s>
          <s xml:space="preserve">laminæ
</s>
          <pb facs="0273" n="193" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIX.</fw>
f g, noteturque diviſio in lamina de ad quam extremitas <lb />g laminæ f g deſcendit. </s>
          <s xml:space="preserve">Mutetur pondus P, &amp; </s>
          <s xml:space="preserve">ſit quatuor <lb />librarum, duplicandum etiam eſt pondus, quo chorda infle-<lb />ctitur, ut deſcendat g ad eandem diviſionem, &amp; </s>
          <s xml:space="preserve">pondus hoc <lb />eſt duarum unciarum; </s>
          <s xml:space="preserve">tres unciæ ad eandem inflexionem <lb />requiruntur, quando pondus P eſt ſex librarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0272-03" corresp="note-0272-03a" place="margin">674.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hoc Experimento ſequitur, pondus, quo certa quan-<lb />
<ptr xml:id="note-0273-01a" corresp="note-0273-01" type="noteAnchor" />
titate producitur fibra, in variis gradibus tenſionis fibræ, <lb />eandem cum tenſione rationem ſequi: </s>
          <s xml:space="preserve">ſi dentur ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">tres <lb />fibræ ejuſdem generis, longitudinis, &amp; </s>
          <s xml:space="preserve">craſſitiei, quarum <lb />tenſiones ſunt ut 1. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">3.</s>
          <s xml:space="preserve">; pondera quæcunque in eadem <lb />proportione æqualiter producunt illas fibras.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0273-01" corresp="note-0273-01a" place="margin">675.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ejuſdem fibræ productiones minimæ ſunt inter ſe quam <lb />
<ptr xml:id="note-0273-02a" corresp="note-0273-02" type="noteAnchor" />
proxime ut vires quibus fibræ producuntur. </s>
          <s xml:space="preserve">Detur ex. <lb /></s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">fibra tenſa pondere centum unciarum, ſi ſeparatim <lb />producatur viribus unius unciæ, duarum unciarum, &amp; </s>
          <s xml:space="preserve">tri-<lb />um unciarum, productiones erunt quam proxime ut unum, <lb />duo, &amp; </s>
          <s xml:space="preserve">tria <ptr type="noteAnchor" />, id eſt, unaquæque uncia ſuperaddita fere
<ptr xml:id="note-0273-03a" corresp="note-0273-03" type="noteAnchor" />
æqualiter producit fibram: </s>
          <s xml:space="preserve">nam tenſiones ponderibus 100. <lb /></s>
          <s xml:space="preserve">101. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">102. </s>
          <s xml:space="preserve">unciarum, quibus in ſingulis caſibus, quando <lb />uncia ſuperadditur, tenditur fibra, parum inter ſe diffe-<lb />runt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0273-02" corresp="note-0273-02a" place="margin">676.</note>
              <note xml:space="preserve" xml:id="note-0273-03" corresp="note-0273-03a" n="*" anchored="true" place="margin">673.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc fibrarum proprietas ad inflexionem ipſarum appli-<lb />
<ptr xml:id="note-0273-04a" corresp="note-0273-04" type="noteAnchor" />
cari poteſt, &amp; </s>
          <s xml:space="preserve">magni uſus eſt. </s>
          <s xml:space="preserve">Inflectatur chorda AB, ita ut <lb />
<ptr xml:id="note-0273-05a" corresp="note-0273-05" type="noteAnchor" />
ſitus A c B, A c B, &amp; </s>
          <s xml:space="preserve">ACB acquirat, ita tamen ut in maxima <lb />inflexione ſagitta non ſit quartæ partis unius pollicis, po-<lb />ſitâ chordæ longitudine duorum pedum cum ſemiſſe; </s>
          <s xml:space="preserve">in <lb />iſtis caſibus productiones chordæ ſunt admodum parvæ, er-<lb />go in ratione virium, a quibus oriuntur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">iſtas vires de-
<ptr xml:id="note-0273-06a" corresp="note-0273-06" type="noteAnchor" />
ſignant; </s>
          <s xml:space="preserve">denotet c D vim qua chorda non inflexa tenditur, <lb />&amp; </s>
          <s xml:space="preserve">centro B deſcribatur circulus Dd; </s>
          <s xml:space="preserve">lineæ dc, dc, dC, quæ <lb />ſingulæ ſuperant lineam cD, quantitate, qua in ſingulis inflexio-<lb />nibus fibra fuit producta, exprimunt vires integras, quibus in <lb />ſingulis caſibus fibra tenditur. </s>
          <s xml:space="preserve">Sed hic arcus D d vix eſt unius <lb />gradus, &amp; </s>
          <s xml:space="preserve">D ſemper a puncto c ſatis diſtat, quare D d pro linea <lb />recta ipſic C parallela haberi poteſt, &amp; </s>
          <s xml:space="preserve">lineæ cd, cd, C d
</s>
          <pb facs="0274" n="194" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
in eadem ſunt ratione cum lineis cB, cB, CB. </s>
          <s xml:space="preserve">Punctum <lb />ideo C verſus B &amp; </s>
          <s xml:space="preserve">A ſemper trahitur, viribus lineæ CB <lb />aut CA proportionalibus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vis qua chorda inflectitur, cu-<lb />jus directio eſt per c C, duplicatæ ſagittæ rationem ſequi-<lb />
<ptr xml:id="note-0274-01a" corresp="note-0274-01" type="noteAnchor" />
tur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">eſt ut ipſa ſagitta. </s>
          <s xml:space="preserve">In omnibus ergo chordæ cu-
<ptr xml:id="note-0274-02a" corresp="note-0274-02" type="noteAnchor" />
juſcunque inflexionibus minimis, ſagitta creſcit &amp; </s>
          <s xml:space="preserve">minuitur <lb />in eadem ratione cum vi qua chorda inflectitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0273-04" corresp="note-0273-04a" place="margin">677.</note>
              <note xml:space="preserve" xml:id="note-0273-05" corresp="note-0273-05a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0273-06" corresp="note-0273-06a" n="*" anchored="true" place="margin">676.</note>
              <note xml:space="preserve" xml:id="note-0274-01" corresp="note-0274-01a" n="*" anchored="true" place="margin">220, 231.</note>
              <note xml:space="preserve" xml:id="note-0274-02" corresp="note-0274-02a" place="margin">678.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Chorda AB, pondere quocunque tenſa, inflectitur pon-<lb />
<ptr xml:id="note-0274-03a" corresp="note-0274-03" type="noteAnchor" />
deribus unius unciæ, duarum, &amp; </s>
          <s xml:space="preserve">trium unciarum, deſcen-<lb />
<ptr xml:id="note-0274-04a" corresp="note-0274-04" type="noteAnchor" />
ſus puncti g, id eſt, ipſæ ſagittæ, ſunt inter ſe ut unum, <lb />duo, &amp; </s>
          <s xml:space="preserve">tria.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0274-03" corresp="note-0274-03a" place="margin">679.</note>
              <note xml:space="preserve" xml:id="note-0274-04" corresp="note-0274-04a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In chordis ejuſdem generis, craſſitiei, &amp; </s>
          <s xml:space="preserve">æqualiter tenſis, <lb />
<ptr xml:id="note-0274-05a" corresp="note-0274-05" type="noteAnchor" />
ſed diverſæ longitudinis, productiones, quæ ex ſuperadditis <lb />æqualibus ponderibus oriuntur, ſunt inter ſe ut chor darum <lb />longitudines. </s>
          <s xml:space="preserve">Ex eo hoc patet, quod chorda in omnibus <lb />punctis ſit æque tenſa; </s>
          <s xml:space="preserve">productio ergo integræ chordæ eſt <lb />dupla productionis dimidiæ partis, aut chordæ dimidiæ lon-<lb />gitudinis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0274-05" corresp="note-0274-05a" place="margin">680.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quod ad inflexionem harum chordarum attinet, ſint <lb />
<ptr xml:id="note-0274-06a" corresp="note-0274-06" type="noteAnchor" />
AB, ab, chordæ ejuſdem generis &amp; </s>
          <s xml:space="preserve">craſſitiei, ſed diverſæ <lb />
<ptr xml:id="note-0274-07a" corresp="note-0274-07" type="noteAnchor" />
longitudinis, æque tenſæ &amp; </s>
          <s xml:space="preserve">ita inflexæ, ut ACB ſit ſitus <lb />illius; </s>
          <s xml:space="preserve">adb hujus inflexio; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſint triangula BCc &amp; </s>
          <s xml:space="preserve">bDd ſi-<lb />milia: </s>
          <s xml:space="preserve">cB eſt ad Db, id eſt, ſunt chordarum longitudines, <lb />ut CB ad db; </s>
          <s xml:space="preserve">chordæ ergo proportionaliter ad longitudi-<lb />nes producuntur, &amp; </s>
          <s xml:space="preserve">ideo viribus æqualibus, juxta directio-<lb />nes bd, ad, BC, AC trahuntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">propter ſimilitudinem
<ptr xml:id="note-0274-08a" corresp="note-0274-08" type="noteAnchor" />
autem triangulorum ſtatim memoratorum vires etiam juxta <lb />cC &amp; </s>
          <s xml:space="preserve">Dd agentes ſunt æquales inter ſe <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſagittæ cC,
<ptr xml:id="note-0274-09a" corresp="note-0274-09" type="noteAnchor" />
Dd ſunt ut chordarum longitudines; </s>
          <s xml:space="preserve">quod igitur, cæteris <lb />
<ptr xml:id="note-0274-10a" corresp="note-0274-10" type="noteAnchor" />
paribus, in chordis inæqualibus &amp; </s>
          <s xml:space="preserve">inflexis ſemper obti-<lb />net.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0274-06" corresp="note-0274-06a" place="margin">681.</note>
              <note xml:space="preserve" xml:id="note-0274-07" corresp="note-0274-07a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0274-08" corresp="note-0274-08a" n="*" anchored="true" place="margin">680.</note>
              <note xml:space="preserve" xml:id="note-0274-09" corresp="note-0274-09a" place="margin">682.</note>
              <note xml:space="preserve" xml:id="note-0274-10" corresp="note-0274-10a" n="*" anchored="true" place="margin">200. 232.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Chorda A B pondere quocunque tenditur, applicatis <lb />
<ptr xml:id="note-0274-11a" corresp="note-0274-11" type="noteAnchor" />
Priſmatibus H, H, ab utraque parte ad ſextam diviſionem; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0274-12a" corresp="note-0274-12" type="noteAnchor" />
inflectatur pondere quocunque, ita ut ſagitta ſit ſex divi-
</s>
          <pb facs="0275" n="195" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIX.</fw>
ſionum laminæ ed. </s>
          <s xml:space="preserve">Mutentur Priſmata &amp; </s>
          <s xml:space="preserve">ad quartam ta-<lb />bulæ diviſionem ab utraque parte ponantur, ſagitta erit qua-<lb />tuor diviſionum laminæ, &amp; </s>
          <s xml:space="preserve">ſic pro quocunque ſitu Priſma-<lb />tum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0274-11" corresp="note-0274-11a" place="margin">683.</note>
              <note xml:space="preserve" xml:id="note-0274-12" corresp="note-0274-12a" place="margin"><hi rend="small caps">TA. XXVI</hi> <lb />fig. a.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fibræ ejuſdem generis, ſed diverſæ craſſitiei, ſi inter ſe <lb />comparantur, poſſunt conſiderari quaſi formatæ ex multis <lb />fibris tenuiſſimis ejuſdem craſſitiei, quarum numerus in fi-<lb />bris memoratis erit in ratione ſoliditatis harum fibrarum, <lb />id eſt, ut quadrata diametrorum, aut ut pondera quando <lb />
<ptr xml:id="note-0275-01a" corresp="note-0275-01" type="noteAnchor" />
fibræ ſunt æquales. </s>
          <s xml:space="preserve">Viribus ergo in eadem ratione quadra-<lb />torum diametrorum, hæ fibræ æqualiter tenduntur; </s>
          <s xml:space="preserve">quæ <lb />etiam ratio inter vires, quibus chordæ inflectuntur, requi-<lb />ritur, ut ſagittæ datis fibris æqualibus ſint æquales. </s>
          <s xml:space="preserve">Sed <lb />minuendo in eadem ratione vim, qua fibra tenditur, cum <lb />vi, qua inflectitur, ſagitta non mutatur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">poſitis igitur vi-
<ptr xml:id="note-0275-02a" corresp="note-0275-02" type="noteAnchor" />
ribus, quibus fibræ tenduntur, æqualibus, ſi æqualibus vi-<lb />ribus inflectantur, etiam in eo caſu ſagittæ erunt æquales, <lb />quæcunque fuerit craſſitiei diverſitas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0275-01" corresp="note-0275-01a" place="margin">684.</note>
              <note xml:space="preserve" xml:id="note-0275-02" corresp="note-0275-02a" n="*" anchored="true" place="margin">673.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Dentur chordæ quæcunque ejuſdem generis, &amp; </s>
          <s xml:space="preserve">inæqua-<lb />
<ptr xml:id="note-0275-03a" corresp="note-0275-03" type="noteAnchor" />
lis craſſitiei; </s>
          <s xml:space="preserve">ſeparatim applicentur Machinæ, relictis Priſma-<lb />
<ptr xml:id="note-0275-04a" corresp="note-0275-04" type="noteAnchor" />
tìbus H, H, ſi eodem pondere Ptendantur, &amp; </s>
          <s xml:space="preserve">etiam eodem <lb />pondere Linflectantur, ſagittæ erunt æquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0275-03" corresp="note-0275-03a" place="margin">685.</note>
              <note xml:space="preserve" xml:id="note-0275-04" corresp="note-0275-04a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sichordautcunque tenſa AB inflectatur, ut figuram ACB <lb />
<ptr xml:id="note-0275-05a" corresp="note-0275-05" type="noteAnchor" />
acquirat, &amp; </s>
          <s xml:space="preserve">ſibirelinquatur, ex elaſticitate ad primam figuram <lb />
<ptr xml:id="note-0275-06a" corresp="note-0275-06" type="noteAnchor" />
redit, &amp; </s>
          <s xml:space="preserve">in eo caſu motus puncti C eſt acceleratus; </s>
          <s xml:space="preserve">nam in ſitu <lb />ACB chordæ, punctum Cmovetur, nam trahitur vi qua in illo <lb />ſitu retineri poteſt; </s>
          <s xml:space="preserve">motus hicce non deſtruitur, &amp; </s>
          <s xml:space="preserve">ei ſuperad-<lb />ditur, in ſingulis punctis ſagittæ, motus oriundus ex vi qua pun-<lb />ctum C in ipſis retineri poſſet; </s>
          <s xml:space="preserve">celeritas omnium maxima eſt <lb />in c, &amp; </s>
          <s xml:space="preserve">eâ punctum C ulterius fertur, deinde redit, variaſ-<lb />que vibrationes peragit, in quibus punctum C niſi parva ſpa-<lb />tia non excurrit; </s>
          <s xml:space="preserve">qua de cauſa vis, qua, in omnibus diſtan-<lb />tiis a c, agitatur punctum C, eſt ut hæc diſtantia <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Congruit
<ptr xml:id="note-0275-07a" corresp="note-0275-07" type="noteAnchor" />
ergo motus hicce cum motu corporis in cycloïde vibrati, <lb />&amp; </s>
          <s xml:space="preserve">vibrationes licet inæquales ſunt æque diuturnæ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0275-08a" corresp="note-0275-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0275-05" corresp="note-0275-05a" place="margin">686.</note>
              <note xml:space="preserve" xml:id="note-0275-06" corresp="note-0275-06a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0275-07" corresp="note-0275-07a" n="*" anchored="true" place="margin">678.</note>
              <note xml:space="preserve" xml:id="note-0275-08" corresp="note-0275-08a" n="*" anchored="true" place="margin">380. 387</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0276" n="196" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Nam cum cauſa movens ſit chordæ Elaſticitas transfertur <lb />
<ptr xml:id="note-0276-01a" corresp="note-0276-01" type="noteAnchor" />
cauſa hæc cum ipſa fibra, quæ reſpectu ipſius quieſcit, quare in <lb />hanc, licet agitatam, premit quaſi quieſceret hæc, ita ut <lb />hìc vis movens ſit ejuſdem generis cum gravitate <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0276-01" corresp="note-0276-01a" place="margin">687.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">252.</note>
        <p>
          <s xml:space="preserve">Poſitis duabus chordis ſimilibus &amp; </s>
          <s xml:space="preserve">æqualibus, ſed inæ-<lb />
<ptr xml:id="note-0276-03a" corresp="note-0276-03" type="noteAnchor" />
qualiter tenſis, vires inæquales requiruntur ut æqualiter <lb />inflectantur; </s>
          <s xml:space="preserve">ergo vibrationes temporibus inæqualibus pera-<lb />gunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0276-03" corresp="note-0276-03a" place="margin">688.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus illarum conferri poſſunt cum motibus pendulo-<lb />rum in cycloïdibus vibratorum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">æquales cycloïdes, viri-
<ptr xml:id="note-0276-04a" corresp="note-0276-04" type="noteAnchor" />
bus diverſis, deſcribentium; </s>
          <s xml:space="preserve">quæ vires ſunt inverſe ut qua-<lb />drata temporum vibrationum <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">in chordis ergo etiam qua-
<ptr xml:id="note-0276-05a" corresp="note-0276-05" type="noteAnchor" />
drata temporum vibrationum ſunt inter ſe inverſe, ut vires <lb />quibus æqualiter inflectuntur; </s>
          <s xml:space="preserve">quæ ſunt ut pondera quibus <lb />chordæ tenduntur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0276-06a" corresp="note-0276-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0276-04" corresp="note-0276-04a" n="*" anchored="true" place="margin">685.</note>
              <note xml:space="preserve" xml:id="note-0276-05" corresp="note-0276-05a" n="*" anchored="true" place="margin">301.</note>
              <note xml:space="preserve" xml:id="note-0276-06" corresp="note-0276-06a" n="*" anchored="true" place="margin">674.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando chordæ ſunt ſimiles, æque tenſæ, ſed diverſæ <lb />
<ptr xml:id="note-0276-07a" corresp="note-0276-07" type="noteAnchor" />
longitudinis, motus harum cum motu pendulorum etiam <lb />
<ptr xml:id="note-0276-08a" corresp="note-0276-08" type="noteAnchor" />
confertur. </s>
          <s xml:space="preserve">Non intereſt quantum ad actionem gravitatis <lb />in corpus, &amp; </s>
          <s xml:space="preserve">ideo quantum ad motum corporis ex gravi-<lb />tate, utrum manente materiâ, ipſa vis gravitatis minuatur <lb />in certa ratione, an vero manente hac vi materia in ea-<lb />dem ratione augeatur <ptr type="noteAnchor" />, quod ergo ad motum chordæ et-
<ptr xml:id="note-0276-09a" corresp="note-0276-09" type="noteAnchor" />
iam applicari poteſt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ergo chordæ, ACB, adb, quæ
<ptr xml:id="note-0276-10a" corresp="note-0276-10" type="noteAnchor" />
ponderibus æqualibus inflectuntur, agitantur ut corpora in <lb />quibus gravitates agerent, quæ forent inter ſe ut ab, ad <lb />AB; </s>
          <s xml:space="preserve">in hac enim ratione inverſa ſunt quantitates materiæ <lb />in chordis. </s>
          <s xml:space="preserve">Chordæ etiam hæ moventur ut pendula, quo-<lb />rum longitudines ſunt ut cB ad Db, aut AB ad ab; </s>
          <s xml:space="preserve">ergo <lb />quadrata durationum vibrationum, quæ ſunt inversè ut vi-<lb />res, &amp; </s>
          <s xml:space="preserve">directè ut longitudines pendulorum <ptr type="noteAnchor" />, ſunt in ra-
<ptr xml:id="note-0276-11a" corresp="note-0276-11" type="noteAnchor" />
tione compoſita ex inverſa ratione ab ad AB, id eſt, AB <lb />ad ab, &amp; </s>
          <s xml:space="preserve">directa ipſius AB ad ab; </s>
          <s xml:space="preserve">quæ ratio compoſita <lb />eſt ratio quadratorum longitudinum; </s>
          <s xml:space="preserve">chordarum igitur lon-<lb />gitudines ſunt ut vibrationum tempora.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0276-07" corresp="note-0276-07a" place="margin">689.</note>
              <note xml:space="preserve" xml:id="note-0276-08" corresp="note-0276-08a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0276-09" corresp="note-0276-09a" n="*" anchored="true" place="margin">111.</note>
              <note xml:space="preserve" xml:id="note-0276-10" corresp="note-0276-10a" n="*" anchored="true" place="margin">687.</note>
              <note xml:space="preserve" xml:id="note-0276-11" corresp="note-0276-11a" n="*" anchored="true" place="margin">3@2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem modo comparantur tempora vibrationum chorda-<lb />
<ptr xml:id="note-0276-12a" corresp="note-0276-12" type="noteAnchor" />
rum diverſæ craſſitiei, poſitis chordis æqualibus, &amp; </s>
          <s xml:space="preserve">aqua-
</s>
          <pb facs="0277" n="197" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIX.</fw>
libus ponderibus tenſis; </s>
          <s xml:space="preserve">hæ æqualibus ponderibus æqualiter <lb />inflectuntur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ideò agitantur ut pendula æqualia, in quæ
<ptr xml:id="note-0277-01a" corresp="note-0277-01" type="noteAnchor" />
agunt gravitates, quæ ſunt inversè ut quantitates materiæ <lb />in chordis <ptr type="noteAnchor" />, id eſt, ut quadrata diametrorum; </s>
          <s xml:space="preserve">quæ ratio
<ptr xml:id="note-0277-02a" corresp="note-0277-02" type="noteAnchor" />
iterum invertenda eſt ad habendam proportionem quadra-<lb />torum durationum vibrationum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Ideo diametri ipſæ ſunt
<ptr xml:id="note-0277-03a" corresp="note-0277-03" type="noteAnchor" />
ut durationes.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0276-12" corresp="note-0276-12a" place="margin">690.</note>
              <note xml:space="preserve" xml:id="note-0277-01" corresp="note-0277-01a" n="*" anchored="true" place="margin">684</note>
              <note xml:space="preserve" xml:id="note-0277-02" corresp="note-0277-02a" n="*" anchored="true" place="margin">112.</note>
              <note xml:space="preserve" xml:id="note-0277-03" corresp="note-0277-03a" n="*" anchored="true" place="margin">301.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datis chordis ejuſdem generis quibuſcunque, vibratio <lb />
<ptr xml:id="note-0277-04a" corresp="note-0277-04" type="noteAnchor" />
num durationes ſunt in ratione compoſita, ex ratione inver-<lb />ſa radicum quadratarum ponderum, quibus chordæ tendun-<lb />tur <ptr type="noteAnchor" />, ratione longitudinum chordarum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ratione dia-
<ptr xml:id="note-0277-05a" corresp="note-0277-05" type="noteAnchor" />
metrorum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Multiplicando diametrum per longitudinem,
<ptr xml:id="note-0277-06a" corresp="note-0277-06" type="noteAnchor" />
dividendo productum per radicem quadratam ponderis, <lb />
<ptr xml:id="note-0277-07a" corresp="note-0277-07" type="noteAnchor" />
quo chorda tenditur, ſi pro variis chordis eadem operatio <lb />inſtituatur, quotientes diviſionum erunt inter ſe ut vibra-<lb />tionum tempora.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0277-04" corresp="note-0277-04a" place="margin">691.</note>
              <note xml:space="preserve" xml:id="note-0277-05" corresp="note-0277-05a" n="*" anchored="true" place="margin">868.</note>
              <note xml:space="preserve" xml:id="note-0277-06" corresp="note-0277-06a" n="*" anchored="true" place="margin">689.</note>
              <note xml:space="preserve" xml:id="note-0277-07" corresp="note-0277-07a" n="*" anchored="true" place="margin">690.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lamina elaſtica pro congerie chordarum haberi poteſt: <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0277-08a" corresp="note-0277-08" type="noteAnchor" />
quando lamina inflectitur, fibræ quædam producuntur, &amp; </s>
          <s xml:space="preserve"><lb />productiones inæquales ſunt in diverſis laminæ punctis, &amp; </s>
          <s xml:space="preserve"><lb />ex iis, quæ de chordis dicta ſunt, curva, quæ a lamina in-<lb />flexa formatur, detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0277-08" corresp="note-0277-08a" place="margin">692.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Comparando inter ſe varias ejuſdem laminæ inflexiones, <lb />
<ptr xml:id="note-0277-09a" corresp="note-0277-09" type="noteAnchor" />
hæ proportionales ſunt viribus quibus lamina flectitur. </s>
          <s xml:space="preserve">Sit <lb />
<ptr xml:id="note-0277-10a" corresp="note-0277-10" type="noteAnchor" />
lamina AB, cujus extremitas A fixa eſt, duabus inflecta-<lb />tur viribus, quibus perveniat ad ab &amp; </s>
          <s xml:space="preserve">ab; </s>
          <s xml:space="preserve">ſi una fuerit <lb />alterius dupla, bb &amp; </s>
          <s xml:space="preserve">bB erunt æquales; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideo in vi-<lb />brationibus motus laminæ eodem modo acceleratur ac <lb />
<ptr xml:id="note-0277-11a" corresp="note-0277-11" type="noteAnchor" />
motus chordæ <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">hæ vibrationes ſunt æque diutur-
<ptr xml:id="note-0277-12a" corresp="note-0277-12" type="noteAnchor" />
næ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0277-13a" corresp="note-0277-13" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0277-09" corresp="note-0277-09a" place="margin">693.</note>
              <note xml:space="preserve" xml:id="note-0277-10" corresp="note-0277-10a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0277-11" corresp="note-0277-11a" place="margin">694.</note>
              <note xml:space="preserve" xml:id="note-0277-12" corresp="note-0277-12a" n="*" anchored="true" place="margin">678.</note>
              <note xml:space="preserve" xml:id="note-0277-13" corresp="note-0277-13a" n="*" anchored="true" place="margin">686.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Lamina A ex variis laminis elaſticis junctis conſtat, The-<lb />
<ptr xml:id="note-0277-14a" corresp="note-0277-14" type="noteAnchor" />
cæ B inſeritur, ibique ad latus utrumque movetur inter re-<lb />
<ptr xml:id="note-0277-15a" corresp="note-0277-15" type="noteAnchor" />
gulas cd, cd; </s>
          <s xml:space="preserve">fila duo ſupremæ parti laminæ annectuntur, <lb />&amp; </s>
          <s xml:space="preserve">per foramina e, e, in fundo Thecæ, immittuntur. </s>
          <s xml:space="preserve">Pon-<lb />dus ſemi-libræ filis appenditur, &amp; </s>
          <s xml:space="preserve">deſcendit hoc per ſpatium <lb />ſemi-pollicis; </s>
          <s xml:space="preserve">ſuperaddito æquali pondere, deſcenſus iterum
</s>
          <pb facs="0278" n="198" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
eſt ſemi-pollicis, &amp; </s>
          <s xml:space="preserve">ſic ulterius donec non amplius compri-<lb />mi poſſit lamina.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0277-14" corresp="note-0277-14a" place="margin">695.</note>
              <note xml:space="preserve" xml:id="note-0277-15" corresp="note-0277-15a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unaquæque lamina minor proportionaliter ad pondus in-<lb />flectitur, &amp; </s>
          <s xml:space="preserve">motus ponderis, ex omnibus inflexionibus jun-<lb />ctis, eandem proportionem ſequitur. </s>
          <s xml:space="preserve">Cum pluribus laminis <lb />junctis Experimentum inſtituitur, quia in variis inflexioni-<lb />bus directio actionis ponderis in laminas ſenſibiliter non <lb />mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæ de inflexione laminarum dicta ſunt, ad laminam <lb />
<ptr xml:id="note-0278-01a" corresp="note-0278-01" type="noteAnchor" />
curvam ACB transferri poſſunt; </s>
          <s xml:space="preserve">ſi illa duobus ponderibus <lb />
<ptr xml:id="note-0278-02a" corresp="note-0278-02" type="noteAnchor" />
gravetur ut ſitus acb, acb acquirat, &amp; </s>
          <s xml:space="preserve">pondera ſint inter ſe <lb />ut unum ad duo, diſtantiæ cc &amp; </s>
          <s xml:space="preserve">cC erunt æquales <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in-
<ptr xml:id="note-0278-03a" corresp="note-0278-03" type="noteAnchor" />
troceſſiones igitur puncti C ſunt ut pondera quibus lamina <lb />gravatur: </s>
          <s xml:space="preserve">quod etiam referri poteſt ad introceſſiones pluri-<lb />marum laminarum junctarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0278-01" corresp="note-0278-01a" place="margin">696.</note>
              <note xml:space="preserve" xml:id="note-0278-02" corresp="note-0278-02a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0278-03" corresp="note-0278-03a" n="*" anchored="true" place="margin">693.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non tamen in Globo ACB, ex materia elaſtica, qui quaſi <lb />
<ptr xml:id="note-0278-04a" corresp="note-0278-04" type="noteAnchor" />
ex variis laminis conſtans conſiderari poteſt; </s>
          <s xml:space="preserve">introceſſiones <lb />
<ptr xml:id="note-0278-05a" corresp="note-0278-05" type="noteAnchor" />
puncti ut C erunt proportionales viribus, quibus corpus <lb />comprimitur. </s>
          <s xml:space="preserve">Nam ſi introceſſio duplicetur, dupla vis qui-<lb />dem requiritur propter duplam laminarum inflexionem, ſed <lb />augenda ulterius eſt vis propter majorem numerum lamina-<lb />rum inflexarum, &amp; </s>
          <s xml:space="preserve">experimentis conſtat, hac de cauſa <lb />vim duplicandam eſſe, ita ut vis quadiupla requiratur: </s>
          <s xml:space="preserve">et-<lb />iam in genere experimentis conſtat, quadratum introceſſio-<lb />nis ſequi eandem proportionem cum vi, qua globus com-<lb />primitur, id eſt, ſi ipſe globus in obicem firmum incurrat, <lb />ſunt introceſſiones ut velocitates, quibus in hunc impingi-<lb />tur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0278-06a" corresp="note-0278-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0278-04" corresp="note-0278-04a" place="margin">697.</note>
              <note xml:space="preserve" xml:id="note-0278-05" corresp="note-0278-05a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 8.</note>
              <note xml:space="preserve" xml:id="note-0278-06" corresp="note-0278-06a" n="*" anchored="true" place="margin">447.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Impingat, variis vicibus, punctum C globi ACBE in <lb />
<ptr xml:id="note-0278-07a" corresp="note-0278-07" type="noteAnchor" />
planum quodcunque, &amp; </s>
          <s xml:space="preserve">punctum C introcedat ad d, d, &amp; </s>
          <s xml:space="preserve">D, <lb />
<ptr xml:id="note-0278-08a" corresp="note-0278-08" type="noteAnchor" />
velocitates in ictibus erunt inter ſe ut lineæ Cd, Cd, CD; </s>
          <s xml:space="preserve">in <lb />primo ictu pars aCb plana fit, in ſecundo pars aCb, in tertio <lb />pars ACB: </s>
          <s xml:space="preserve">cum hìc ſemper agatur de arcubus minimis, arcus, <lb />id eſt, diametri ſuperficierum planarum ex ictibus, ſunt in-<lb />ter ſe ad ſenſum ut chordæ Ca, Ca &amp; </s>
          <s xml:space="preserve">CA; </s>
          <s xml:space="preserve">ergo ipſæ <lb />ſuperficies ut quadrata illarum chordarum, in qua etiam
</s>
          <pb facs="0279" n="199" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. I. CAP. XXIX.</fw>
ratione, ſunt lineæ Cd, Cd, &amp; </s>
          <s xml:space="preserve">CD <ptr type="noteAnchor" />, quæ ſunt inter
<ptr xml:id="note-0279-01a" corresp="note-0279-01" type="noteAnchor" />
ſe ut velocitates <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In Sphæra igitur elaſtica ſuperficies pla-
<ptr xml:id="note-0279-02a" corresp="note-0279-02" type="noteAnchor" />
næ ex ictibus eandem cum velocitatibus, quibus in obicem <lb />
<ptr xml:id="note-0279-03a" corresp="note-0279-03" type="noteAnchor" />
incurrit, proportionem ſequuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0278-07" corresp="note-0278-07a" place="margin">698.</note>
              <note xml:space="preserve" xml:id="note-0278-08" corresp="note-0278-08a" place="margin"><hi rend="small caps">TA. XXVI.</hi> <lb />fig. 9.</note>
              <note xml:space="preserve" xml:id="note-0279-01" corresp="note-0279-01a" n="*" anchored="true" place="margin">293.</note>
              <note xml:space="preserve" xml:id="note-0279-02" corresp="note-0279-02a" n="*" anchored="true" place="margin">698.</note>
              <note xml:space="preserve" xml:id="note-0279-03" corresp="note-0279-03a" place="margin">699.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Detur planum marmoreum, cæruleum, horizontaliter <lb />
<ptr xml:id="note-0279-04a" corresp="note-0279-04" type="noteAnchor" />
aliquo in loco firmatum, &amp; </s>
          <s xml:space="preserve">paululum madefactum, quan-<lb />
<ptr xml:id="note-0279-05a" corresp="note-0279-05" type="noteAnchor" />
tum neceſſe eſt, ut color magis ſit intenſus; </s>
          <s xml:space="preserve">ſi in illud glo-<lb />bus eburneus cadendo impingat, pars globi, quæ plana <lb />facta ſeſe lapidi applicat, maculam circinnatam in hujus ſu-<lb />perficie relinquit. </s>
          <s xml:space="preserve">Cadat globus ab altitudine novem pol-<lb />licum, &amp; </s>
          <s xml:space="preserve">ſit macula illa E; </s>
          <s xml:space="preserve">cadat ab altitudine trium pe-<lb />dum prioris quadrupla, &amp; </s>
          <s xml:space="preserve">ſit macula F; </s>
          <s xml:space="preserve">tandem cadat ab <lb />altitudine ſex pedum &amp; </s>
          <s xml:space="preserve">novem pollicum noncupla prioris, <lb />&amp; </s>
          <s xml:space="preserve">ſit macula G. </s>
          <s xml:space="preserve">In hoc Experimento velocitates corporis <lb />ſunt inter ſe, ut unum, duo, &amp; </s>
          <s xml:space="preserve">tria <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in qua etiam ratio-
<ptr xml:id="note-0279-06a" corresp="note-0279-06" type="noteAnchor" />
ne ſunt maculæ E, F, &amp; </s>
          <s xml:space="preserve">G; </s>
          <s xml:space="preserve">nam formando triangula re-<lb />ctangula DAB, DBC, in quibus latera DA, AB, BC <lb />ſunt æqualia inter ſe &amp; </s>
          <s xml:space="preserve">diametro maculæ E, linea BC ex-<lb />actiſſime æqualis erit diametro maculæ F, &amp; </s>
          <s xml:space="preserve">linea CD dia-<lb />metro maculæ G, unde conſtat propoſitum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0279-07a" corresp="note-0279-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0279-04" corresp="note-0279-04a" place="margin">700.</note>
              <note xml:space="preserve" xml:id="note-0279-05" corresp="note-0279-05a" place="margin"><hi rend="small caps">TA XXVI.</hi> <lb />fig. 10.</note>
              <note xml:space="preserve" xml:id="note-0279-06" corresp="note-0279-06a" n="*" anchored="true" place="margin">255.</note>
              <note xml:space="preserve" xml:id="note-0279-07" corresp="note-0279-07a" n="*" anchored="true" place="margin">47. El. 7. <lb />2, El, XI@.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM.</head>
        <p>
          <s xml:space="preserve">IN comparandis motibus chordarum, ipſarum inflexionem tantum conſide-<lb />
<ptr xml:id="note-0279-08a" corresp="note-0279-08" type="noteAnchor" />
ravimus in puncto medio, non attendendo ad curvaturam ipſius fibræ dum <lb />agitatur, quo demonſtrationes de comparandis variarum fibrarum vibratio-<lb />nibus non mutatur, fi autem tempus ipſum vibrationis cujuſcunque detegen-<lb />dum eſſet, quod fit determinando longitudinem penduli eodem tempore vi-<lb />brationes peragentis cum fibra, curvatura hæc conſideranda foret; </s>
          <s xml:space="preserve">ſed de hoc <lb />tempore hìc non agam, neque de curvâ elaſticâ in n. </s>
          <s xml:space="preserve">691. </s>
          <s xml:space="preserve">memoratâ; </s>
          <s xml:space="preserve">quia <lb />in hiſce uſus Methodorum fluxionum directæ &amp; </s>
          <s xml:space="preserve">inverſæ deſideratur, quod ad <lb />ipſa Elementa Phyſices ſpectare mihi non videtur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0279-08" corresp="note-0279-08a" place="margin">701.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">FINIS LIBRI PRIMI.</head>
        <pb facs="0280" n="200" />
      </div>
      <div type="section">
        <head xml:space="preserve">PHYSICES</head>
        <head xml:space="preserve">ELEMENTA MATHEMATICA</head>
        <head xml:space="preserve">EXPERIMENTIS CONFIRMATA.</head>
        <head rend="italics" xml:space="preserve">LIBER II. <lb />Pars I. de Gravitate, &amp; Preſſione Fluidorum.</head>
        <head xml:space="preserve">CAPUT I. <lb />De Gravitate partium Fluidorum, &amp; illius Effectu in <lb />ipſis Fluidis.</head>
        <p>
          <s xml:space="preserve">FLuidum vocatur corpus, cujus partes impreſſioni <lb />cuicunque cedunt, &amp; </s>
          <s xml:space="preserve">cedendo facillime mo-<lb />ventur inter ſe <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Unde ſequitur fluiditatem ex
<ptr xml:id="note-0280-01a" corresp="note-0280-01" type="noteAnchor" />
eo oriri, quod partes non arcte inter ſe cohære-<lb />
<ptr xml:id="note-0280-02a" corresp="note-0280-02" type="noteAnchor" />
ant, &amp; </s>
          <s xml:space="preserve">quod motus non impediatur inæqualita-<lb />tibus in Partium ſuperficiebus, ut fit in pulveribus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0280-01" corresp="note-0280-01a" n="*" anchored="true" place="margin">50.</note>
              <note xml:space="preserve" xml:id="note-0280-02" corresp="note-0280-02a" place="margin">702.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Particulæ autem, ex quibus fluida conſtant, non diffe-<lb />
<ptr xml:id="note-0280-03a" corresp="note-0280-03" type="noteAnchor" />
runt ab aliorum corporum particulis, &amp; </s>
          <s xml:space="preserve">cum his eaſdem pro-<lb />prietates habent; </s>
          <s xml:space="preserve">fluida enim ſæpe in ſolida convertuntur, <lb />quando magis arcta inter partes cohæſio datur, ut glacies: <lb /></s>
          <s xml:space="preserve">metalla contra liquefacta exemplum ſolidi in fluidum mu-<lb />tati præbent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0280-03" corresp="note-0280-03a" place="margin">703.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fluida &amp; </s>
          <s xml:space="preserve">eo cum corporibus ſolidis congruunt, quod con-<lb />
<ptr xml:id="note-0280-04a" corresp="note-0280-04" type="noteAnchor" />
ſtent ex particulis gravibus, gravitatem materiæ quanti-<lb />tati proportionalem, ubicunque poſitæ, habentibus. </s>
          <s xml:space="preserve">Si in <lb />ipſo fluido gravitas ſenſibilis non ſit, ex eo hoc oritur, <lb />quod partes inferiores ſuperiores ſuſtineant, haſque deſcen-
</s>
          <pb facs="0281" />
          <s xml:space="preserve">
</s>
          <pb facs="0281a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0281a-01a" corresp="fig-0281a-01" type="figureAnchor" />
</s>
          <pb facs="0282" />
          <s xml:space="preserve">
</s>
          <pb facs="0283" n="201" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. I.</fw>
ſu arceant; </s>
          <s xml:space="preserve">ipſam vero gravitatem eo non deſtrui liquet, <lb />cum vaſe contentum fluidum pro ſua quantitate gravet li-<lb />bram, cui vas appenditur; </s>
          <s xml:space="preserve">etiam ſequenti Experimento <lb />ubique in fluido particulas gravitatem ſervare probatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0280-04" corresp="note-0280-04a" place="margin">704.</note>
              <figure xml:id="fig-0281a-01" corresp="fig-0281a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0281a-01" />
                <label>0281a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Bilanx</hi> <hi rend="small caps">Hydrostatica</hi>.</head>
        <p>
          <s xml:space="preserve">In hoc, ut &amp; </s>
          <s xml:space="preserve">in aliis multis Experimentis Hydroſtaticis, <lb />
<ptr xml:id="note-0283-01a" corresp="note-0283-01" type="noteAnchor" />
id eſt, circa gravitatem fluidorum, utimur bilance, quan-<lb />
<ptr xml:id="note-0283-02a" corresp="note-0283-02" type="noteAnchor" />
tum fieri poteſt, exacta, jugi longitudo eſt circiter octo pol-<lb />licum; </s>
          <s xml:space="preserve">in medio inferiorum ſuperficierum lancium unci <lb />junguntur, quibus corpora fluidis immergenda ſuſpendun-<lb />tur; </s>
          <s xml:space="preserve">cum lancibus etiam ſingulis cohærent pedes tres mino-<lb />res, longitudinis circiter ſemi pollicis, quibus ſuſtinentur <lb />quando lances, ſuſpensâ bilance, tabellæ T imponuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0283-01" corresp="note-0283-01a" place="margin">705.</note>
              <note xml:space="preserve" xml:id="note-0283-02" corresp="note-0283-02a" place="margin"><hi rend="small caps">TAB. XXVII,</hi> <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Suſpenditur autem bilanx duobus funibus, qui ſinguli <lb />duobus trochleis cum columna C cohærentibus, ut A &amp; </s>
          <s xml:space="preserve">B, <lb />circumponuntur ita, ut moto pondere P, bilanx elevetur, <lb />&amp; </s>
          <s xml:space="preserve">deprimatur, donec lances ipſi tabellæ T imponantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In tabella hac foramina duo, diametri trium partium <lb />quartarum pollicis, dantur, quæ uncis lancium reſpondent, <lb />&amp; </s>
          <s xml:space="preserve">per quæ tranſeunt fila ænea, aut capilli equini, quibus <lb />corpora libræ applicanda uncis junguntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Duplicem adhibemus funem, ut bilancis circumvolutio-<lb />nem cohibeamus, ipſius autem nimiam agitationem vita-<lb />mus, imponendo lances tabellæ T, &amp; </s>
          <s xml:space="preserve">haſce dein lente <lb />paululum tantum elevando.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Phiala D clauſa, libræ memoratæ capillo equino juncta, <lb />
<ptr xml:id="note-0283-03a" corresp="note-0283-03" type="noteAnchor" />
aquâ immergitur, &amp; </s>
          <s xml:space="preserve">pondere lanci E impoſito datur æqui-<lb />librium; </s>
          <s xml:space="preserve">ſi phiala, manente immerſâ, aperiatur &amp; </s>
          <s xml:space="preserve">aquâ im-<lb />pleatur, aqua in phiala gravabit libram, licet cum aqua ex-<lb />teriori communicationem habeat; </s>
          <s xml:space="preserve">ſi novo pondere æquili-<lb />brium inſtauretur, ſervabitur ad quamcumque altitudinem <lb />phiala aquâ immergatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0283-03" corresp="note-0283-03a" place="margin">706.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hac gravitate ſequitur, ſuperficiem fluidi, vaſe in-<lb />
<ptr xml:id="note-0283-04a" corresp="note-0283-04" type="noteAnchor" />
cluſi ne effluat, ſi ſuperne illud non prematur, aut æqualiter <lb />prematur, quo gravitatis actio non mutatur, planam fieri,
</s>
          <pb facs="0284" n="202" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
&amp; </s>
          <s xml:space="preserve">borizonti parallelam. </s>
          <s xml:space="preserve">Cum enim impreſſioni cuicunque <lb />particulæ cedant, tam diu gravitate moventur, donec de-<lb />ſcenſui locus non amplius detur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0283-04" corresp="note-0283-04a" place="margin">707.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Particulæ inſeriores ſuperiores ſuſtinent, &amp; </s>
          <s xml:space="preserve">hiſce premun-<lb />
<ptr xml:id="note-0284-01a" corresp="note-0284-01" type="noteAnchor" />
tur, preſſioque bæc ſequitur proportionem materiæ incum-<lb />bentis, id eſt, altitudinis fluidi ſupra particulam preſſam; <lb /></s>
          <s xml:space="preserve">cum vero ſuperficies ſuprema fluidi ſit ad horizontem paral-<lb />lela <ptr type="noteAnchor" />, omnia puncta ſuperficiei cujuſcunque, quæ con-
<ptr xml:id="note-0284-02a" corresp="note-0284-02" type="noteAnchor" />
cipitur in fluido ad horizontem parallela, æqualiter pre-<lb />muntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0284-01" corresp="note-0284-01a" place="margin">708.</note>
              <note xml:space="preserve" xml:id="note-0284-02" corresp="note-0284-02a" n="*" anchored="true" place="margin">707.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ergo in aliquo loco talis ſuperficiei preſſio detur minor <lb />
<ptr xml:id="note-0284-03a" corresp="note-0284-03" type="noteAnchor" />
quàm in cæteris punctis, fluidum, quod impreſſioni cui-<lb />cunque cedit, ibi movebitur, id eſt, adſcendet, donec preſ-<lb />ſio fuerit æqualis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0284-03" corresp="note-0284-03a" place="margin">709.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Tubi vitrei C ab utraque parte aperti, cujus extremitas <lb />
<ptr xml:id="note-0284-04a" corresp="note-0284-04" type="noteAnchor" />
una digito clauditur, extremitas altera aquâ immergitur; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0284-05a" corresp="note-0284-05" type="noteAnchor" />
cum tubus aëre repleatur, aqua in hunc ad parvam admo-<lb />dum altitudinem adſcendit; </s>
          <s xml:space="preserve">ſi digitus tollatur ut aër preſ-<lb />ſus exeat, ſuperficies, quæ in aqua concipitur horizonti <lb />parallela juxta partem inferiorem tubi, minus in parte re-<lb />ſpondenti aperturæ tubi premitur, aqua etiam in tubum <lb />tunc adſcendit, donec in eo habeat altitudinem æqualem <lb />cum aqua exteriori.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0284-04" corresp="note-0284-04a" place="margin">710.</note>
              <note xml:space="preserve" xml:id="note-0284-05" corresp="note-0284-05a" place="margin"><hi rend="small caps">TAB. XXVII</hi>. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Preſſio in particulas inferiores, quæ oritur ex gravitate <lb />
<ptr xml:id="note-0284-06a" corresp="note-0284-06" type="noteAnchor" />
fluidi ſuperioris, actionem ſuam exerit verſus omnes par-<lb />tes, &amp; </s>
          <s xml:space="preserve">quidem æqualiter. </s>
          <s xml:space="preserve">Quod ex natura fluidi ſequitur; <lb /></s>
          <s xml:space="preserve">nam hujus partes impreſſioni cuicunque cedunt, &amp; </s>
          <s xml:space="preserve">facil-<lb />lime moventur; </s>
          <s xml:space="preserve">gutta ergo quæcunque locum quem occu-<lb />pat non ſervabit, ſi, dum à fluido ſuperiori premitur, ab <lb />omni parte non æqualiter prematur; </s>
          <s xml:space="preserve">moveri autem non poteſt <lb />propter guttas vicinas, quæ eodem modo &amp; </s>
          <s xml:space="preserve">eadem cum vi <lb />à fluido ſupereminenti premuntur; </s>
          <s xml:space="preserve">quieſcit idcirco gutta pri-<lb />ma, &amp; </s>
          <s xml:space="preserve">æqualiter ab omni parte, id eſt, juxta directionem <lb />quamcunque, premitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0284-06" corresp="note-0284-06a" place="margin">711.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0285" n="203" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. I.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Tubi vitrei A, B, D, eodem modo, ac de tubo A in <lb />
<ptr xml:id="note-0285-01a" corresp="note-0285-01" type="noteAnchor" />
præcedenti Experimento dictum, aquâ immerguntur, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0285-02a" corresp="note-0285-02" type="noteAnchor" />
aqua in omnes, ſublato digito, ad eandem altitudinem ad-<lb />ſcendit, quàm in tubo C; </s>
          <s xml:space="preserve">in hoc preſſio ſurſum dirigitur; <lb /></s>
          <s xml:space="preserve">in tubo B deorſum; </s>
          <s xml:space="preserve">in tubo A eſt lateralis; </s>
          <s xml:space="preserve">in tubo D ob-<lb />liqua; </s>
          <s xml:space="preserve">in unoquoque tamen preſſio æqualis eſt; </s>
          <s xml:space="preserve">ſi major <lb />fluidi quantitas vaſe infundatur, æqualiter etiam aqua in ſin-<lb />gulis tubis elevatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0285-01" corresp="note-0285-01a" place="margin">712.</note>
              <note xml:space="preserve" xml:id="note-0285-02" corresp="note-0285-02a" place="margin"><hi rend="small caps">TAB. XXVII</hi>. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur fluidorum particulas ſingulas ab omni <lb />
<ptr xml:id="note-0285-03a" corresp="note-0285-03" type="noteAnchor" />
parte æqualiter premi, &amp; </s>
          <s xml:space="preserve">ideo quieſcere; </s>
          <s xml:space="preserve">illaſque non con-<lb />tinuo inter ſe moveri, ut a multis ſtatuitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0285-03" corresp="note-0285-03a" place="margin">713.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In tubis communicantibus, ſive æqualibus, ſive inæqua-<lb />
<ptr xml:id="note-0285-04a" corresp="note-0285-04" type="noteAnchor" />
libus, ſive rectis, ſive obliquis, fluidum eandem adipiſcitur <lb />altitudinem; </s>
          <s xml:space="preserve">id eſt, omnes ſuperficies ſupremæ ſunt in eo-<lb />dem plano horizonti parallelo; </s>
          <s xml:space="preserve">quod facile ex dictis dedu-<lb />citur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0285-04" corresp="note-0285-04a" place="margin">714.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit vas A, tubus verticalis B, &amp; </s>
          <s xml:space="preserve">tubus inclinatus D; </s>
          <s xml:space="preserve">com-<lb />
<ptr xml:id="note-0285-05a" corresp="note-0285-05" type="noteAnchor" />
municationem habeant ope tubi CE; </s>
          <s xml:space="preserve">detur in his fluidum, <lb />
<ptr xml:id="note-0285-06a" corresp="note-0285-06" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">concipiatur ſuperficies horizonti parallela fgb; </s>
          <s xml:space="preserve">ſi alti-<lb />tudines fi &amp; </s>
          <s xml:space="preserve">gl ſuerint inæquales, aqua adſcendet ubi mi-<lb />nor eſt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ex eadem ratione niſi preſſiones in g &amp; </s>
          <s xml:space="preserve">b fue-
<ptr xml:id="note-0285-07a" corresp="note-0285-07" type="noteAnchor" />
rint æquales, aqua non quieſcet; </s>
          <s xml:space="preserve">ſunt vero æquales, quan-<lb />do l &amp; </s>
          <s xml:space="preserve">n ſunt in eodem plano horizontali; </s>
          <s xml:space="preserve">nam cum preſ-<lb />ſio oriatur ex gravitate partium, quæ tendit ad terræ cen-<lb />trum, altitudo fluidi prementis juxta hanc directionem <lb />menſurari debet, id eſt, erit bm; </s>
          <s xml:space="preserve">obliquitas vero colu-<lb />mnæ bn nullam mutationem adfert; </s>
          <s xml:space="preserve">quia ad eandem pro-<lb />funditatem ubique preſſio verſus omnes partes æqualis da-<lb />tur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0285-08a" corresp="note-0285-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0285-05" corresp="note-0285-05a" place="margin">715.</note>
              <note xml:space="preserve" xml:id="note-0285-06" corresp="note-0285-06a" place="margin"><hi rend="small caps">TAB XXVII</hi>. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0285-07" corresp="note-0285-07a" n="*" anchored="true" place="margin">709.</note>
              <note xml:space="preserve" xml:id="note-0285-08" corresp="note-0285-08a" n="*" anchored="true" place="margin">711.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Machinæ hic delineatæ aqua infunditur; </s>
          <s xml:space="preserve">poſt agitatio-<lb />
<ptr xml:id="note-0285-09a" corresp="note-0285-09" type="noteAnchor" />
nem quamcunque non quieſcit, niſi omnes ſuperficies <lb />
<ptr xml:id="note-0285-10a" corresp="note-0285-10" type="noteAnchor" />
ſint in eodem plano horizonti parallelo. </s>
          <s xml:space="preserve">Vas vitreum A <lb />cum tubis vitreis B &amp; </s>
          <s xml:space="preserve">D, ope tubi ænei CE, conjungi-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0285-09" corresp="note-0285-09a" place="margin">716.</note>
              <note xml:space="preserve" xml:id="note-0285-10" corresp="note-0285-10a" place="margin"><hi rend="small caps">TAB. XXVII</hi>. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0286" n="204" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Non omnia fluida ſunt æque gravia, id eſt, non eandem <lb />materiæ quantitatem in eodem ſpatio continent, in ſingu-<lb />lis tamen prædicta locum habent.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quando fluida diver ſæ gravitatis eodem vaſe continentur, <lb />
<ptr xml:id="note-0286-01a" corresp="note-0286-01" type="noteAnchor" />
gravius locum infimum occupat, &amp; </s>
          <s xml:space="preserve">premitur a leviori, illud-<lb />que pro altitudine bujus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0286-01" corresp="note-0286-01a" place="margin">717.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 5.</head>
        <p>
          <s xml:space="preserve">Detur aqua, aliquo colore tincta, in vaſe vitreo A, ad al-<lb />
<ptr xml:id="note-0286-02a" corresp="note-0286-02" type="noteAnchor" />
titudinem bc; </s>
          <s xml:space="preserve">ei immergatur tubus vitreus de; </s>
          <s xml:space="preserve">aquain hunc <lb />
<ptr xml:id="note-0286-03a" corresp="note-0286-03" type="noteAnchor" />
adſcendit ad altitudinem bc <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nunc infundatur oleum te-
rebinthinæ, quod fluidum eſt aquâ levius, ſtatim aqua in <lb />tubo adſcendet; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eo magis quo ad majorem altitudinem <lb />oleum infunditur; </s>
          <s xml:space="preserve">non tamen aqua in tubo ad eandem per-<lb />tingit altitudinem cum oleo in vaſe; </s>
          <s xml:space="preserve">quia cum aqua gravi-<lb />or ſit, non eadem quam olei altitudo requiritur, ut preſſio-<lb />nes ſint æquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0286-02" corresp="note-0286-02a" place="margin">718.</note>
              <note xml:space="preserve" xml:id="note-0286-03" corresp="note-0286-03a" place="margin"><hi rend="small caps">TAB. XXVII</hi>. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Qui hocce Experimentum cum Mercurio &amp; </s>
          <s xml:space="preserve">aqua inſti-<lb />tuere voluerit, majorem inter altitudines reperiet differen-<lb />tiam, propter majus inter gravitates diſcrimen.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Immergatur tubi extremitas aquâ; </s>
          <s xml:space="preserve">oleumque tubo infun-<lb />
<ptr xml:id="note-0286-04a" corresp="note-0286-04" type="noteAnchor" />
datur; </s>
          <s xml:space="preserve">aqua in tubo deprimitur ad d; </s>
          <s xml:space="preserve">altitudo tamen olei <lb />
<ptr xml:id="note-0286-05a" corresp="note-0286-05" type="noteAnchor" />
de major eſt altitudine aquæ in vaſe; </s>
          <s xml:space="preserve">ſi profundius im-<lb />mergatur tubus, aqua majori quantitate hunc ingreditur; <lb /></s>
          <s xml:space="preserve">ſi elevetur, aqua iterum exit, ipſumque oleum inſequitur, <lb />ſi ad illam tollatur altitudinem ut olei preſſio aquæ preſſio-<lb />nem, in parte inferiori tubi, ſuperet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0286-04" corresp="note-0286-04a" place="margin">719.</note>
              <note xml:space="preserve" xml:id="note-0286-05" corresp="note-0286-05a" place="margin"><hi rend="small caps">TAB. XXVII</hi>. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT II.</head>
        <head rend="italics" xml:space="preserve">De Actione Fluidorum in Fundos, Latera, &amp; Opercula, <lb />vaſorum quibus continentur.</head>
        <p>
          <s xml:space="preserve">FVndus &amp; </s>
          <s xml:space="preserve">latera vaſis, quo fluidum continetur, ut &amp; </s>
          <s xml:space="preserve">o-<lb />
<ptr xml:id="note-0286-06a" corresp="note-0286-06" type="noteAnchor" />
perculum, quando ſupra hoc in tubo fluidum elevatur, <lb />a partibus fluidi illa immediate tangentibus premuntur, &amp;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0287" n="205" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. II.</fw>
propter actioni æqualem reactionem <ptr type="noteAnchor" />, æqualem etiam
<ptr xml:id="note-0287-01a" corresp="note-0287-01" type="noteAnchor" />
particulæ iſtæ preſſionem ſuſtinent. </s>
          <s xml:space="preserve">Cum vero preſſio in <lb />fluidis omnes partes verſus ſit æqualis, fundus &amp; </s>
          <s xml:space="preserve">latera æ-<lb />que premuntur ac partes fluidi vicinæ actio ergo hæc ad <lb />inſtar altitudinis fluidi’ creſcit <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ubique ad eandem
<ptr xml:id="note-0287-02a" corresp="note-0287-02" type="noteAnchor" />
profunditatem eſt æqualis, pendetque ab illa altitudine, &amp; </s>
          <s xml:space="preserve"><lb />nullo modo a fluidi quantitate. </s>
          <s xml:space="preserve">Manente igitur fluidi altitu-<lb />dine, &amp; </s>
          <s xml:space="preserve">fundi magnitudine, æqualis ſemper erit actio in <lb />fundum, utcunque mutetur vaſis figura. </s>
          <s xml:space="preserve">In omni caſu preſ-<lb />
<ptr xml:id="note-0287-03a" corresp="note-0287-03" type="noteAnchor" />
ſio, quam patitur ſuperficies quæcunque, valet pondus co-<lb />lumnæ ex fluido, cujus baſis eſt ipſa ſuperficies, &amp; </s>
          <s xml:space="preserve">altitudo, <lb />in ſingulis punctis, diſtantia verticalis ſupremæ ſuperficiei <lb />fluidi ab his punctis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0286-06" corresp="note-0286-06a" place="margin">720.</note>
              <note xml:space="preserve" xml:id="note-0287-01" corresp="note-0287-01a" n="*" anchored="true" place="margin"> 2471</note>
              <note xml:space="preserve" xml:id="note-0287-02" corresp="note-0287-02a" n="*" anchored="true" place="margin">711. 708.</note>
              <note xml:space="preserve" xml:id="note-0287-03" corresp="note-0287-03a" place="margin">721.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Talem eſſe in vaſe priſmatico verticali preſſionem in fun-<lb />dum non facile in dubium quis vocabit; </s>
          <s xml:space="preserve">nam totum fluidi <lb />pondus, &amp; </s>
          <s xml:space="preserve">nil præterea, ſuſtinet fundus: </s>
          <s xml:space="preserve">ſervatâ autem alti-<lb />tudine fluidi, &amp; </s>
          <s xml:space="preserve">baſi vaſeos, non mutatur preſſio in fun-<lb />dum, licet, mutatâ figurâ, vas majorem aut minorem flui-<lb />di copiam contineat; </s>
          <s xml:space="preserve">quod cum experimentis congruit, &amp; </s>
          <s xml:space="preserve"><lb />ex natura fluiditatis deducitur, ut, poſt expoſita experi-<lb />menta, dicam.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <p rend="italics">
          <s xml:space="preserve">Qua Experimenta de Fluidorum Preſſione inſtituun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cylindrus cavus A, ab utraque parte apertus, ab inte-<lb />
<ptr xml:id="note-0287-04a" corresp="note-0287-04" type="noteAnchor" />
riori parte exactiſſime politur; </s>
          <s xml:space="preserve">hujus diameter ut &amp; </s>
          <s xml:space="preserve">altitu-<lb />
<ptr xml:id="note-0287-05a" corresp="note-0287-05" type="noteAnchor" />
do parum excedunt tres pollices cum ſemiſſe, &amp; </s>
          <s xml:space="preserve">aqua in hoc <lb />cylindro ad altitudinem trium pollicum ponderat libram u-<lb />nam, ope cochleæ ei additur annulus E, ut a tripode ſu-<lb />ſtineatur. </s>
          <s xml:space="preserve">Pedes autem cochleis annulo junguntur, ut, ubi <lb />neceſſe hoc eſt, tollantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0287-04" corresp="note-0287-04a" place="margin">722.</note>
              <note xml:space="preserve" xml:id="note-0287-05" corresp="note-0287-05a" place="margin"><hi rend="small caps">TAB. XXVII</hi>. <lb />fig 7. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In cylindro datur ſundus æneus mobilis F, cum quo an-<lb />nulus G, etiam æneus, ab interiori parte cochleam conti-<lb />nens, conjungitur; </s>
          <s xml:space="preserve">hoc annulo retinetur &amp; </s>
          <s xml:space="preserve">firmatur an-<lb />nulus coriaceus ab omni parte fundum quantitate ſemi-pol-<lb />licis excedens; </s>
          <s xml:space="preserve">obtegit hic annuli ænei ſuperficiem exterio-
</s>
          <pb facs="0288" n="206" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
rem, quando fundus cylindro intruditur, impeditque ne <lb />aqua dum fundus movetur effluat. </s>
          <s xml:space="preserve">Corium hocce oleo im-<lb />mergitur, poſt aliquot dies extrahitur, ut per æquale tem-<lb />pus in aqua maceretur; </s>
          <s xml:space="preserve">qua adhibita præparatione, co-<lb />rium probe oleo &amp; </s>
          <s xml:space="preserve">aqua illinitur, moveturque fundus va-<lb />riis vicibus per cylindrum, &amp; </s>
          <s xml:space="preserve">per biduum aut triduum <lb />in hoc relinquitur. </s>
          <s xml:space="preserve">Ita præparatum corium per multos an-<lb />nos experimentis inſervire poteſt, ſi, ubi hæc inſtituenda <lb />ſunt, corium cum fundo jungatur, oleo &amp; </s>
          <s xml:space="preserve">aquâ illiniatur, tunc-<lb />que per aliquot horas, aut integrum diem in cylindro relin-<lb />quatur, antequam Experimenta inſtituantur. </s>
          <s xml:space="preserve">Immediate <lb />etiam ante Experimenta iterum oleo &amp; </s>
          <s xml:space="preserve">aquâ illiniri debet, &amp; </s>
          <s xml:space="preserve"><lb />facile tunc fundus movetur, &amp; </s>
          <s xml:space="preserve">exacte aquam retinet. </s>
          <s xml:space="preserve">Co-<lb />rium neque nimis tenue neque nimis craſſum adhibendum; <lb /></s>
          <s xml:space="preserve">quod judicio artificis relinquitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In centro fundi cum hoc cohæret cylindrus æneus tenuis <lb />hi, quo motus fundi dirigitur, tranſit enim hicce cylin-<lb />drus per forameo m in lamina B, quæ cylindro majori A <lb />ſuperimponitur, &amp; </s>
          <s xml:space="preserve">in ejus ora in inciſione hæret. </s>
          <s xml:space="preserve">In ſuperio-<lb />ri parte cylindri hi foramen datur, ut cum fundo, ope unci <lb />n, jungatur catena ænea pn, quæ per tubum ſtatim memo-<lb />randum D immittitur, ut ope hujus catenæ fundus cum bra-<lb />chio libræ conjungatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cylindrus A operculo C tegitur, &amp; </s>
          <s xml:space="preserve">ne aqua effluere poſ-<lb />ſit obtegenda eſt ora cylindri annulo coriaceo, qui ope co-<lb />chleæ, qua operculum jungitur cum cylindro, inter oram <lb />&amp; </s>
          <s xml:space="preserve">ipſum operculum arcte comprimitur; </s>
          <s xml:space="preserve">operculo ut &amp; </s>
          <s xml:space="preserve">ipſi <lb />cylindro adduntur anſæ, ut magis commode aperiatur &amp; </s>
          <s xml:space="preserve">clau-<lb />datur cylindrus. </s>
          <s xml:space="preserve">In medio perforatur operculum, &amp; </s>
          <s xml:space="preserve">cylin-<lb />drus cavus l, ab exteriori parte cochleâ circumdatus, cum <lb />illo cohæret, ut tubus D cum machina conjungatur; </s>
          <s xml:space="preserve">etiam <lb />hîc adhibito corio aquæ effluxus cohibetur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Partibus machinæ, ut dictum, junctis, catena, quæ cum <lb />
<ptr xml:id="note-0288-01a" corresp="note-0288-01" type="noteAnchor" />
fundo mobili cohæret, brachio libræ annectatur, ita ut ju-<lb />gum libræ ſit in fitu horizontali, quando fundus ab opercu-
</s>
          <pb facs="0289" />
          <s xml:space="preserve">
<pb facs="0289a" />
<ptr xml:id="fig-0289a-01a" corresp="fig-0289a-01" type="figureAnchor" />
<pb facs="0290" />
<pb facs="0291" n="207" /><fw type="head">MATHEMATICA. LIB. II. CAP. II.</fw>
lo diſtat duobus pollicibus; </s>
          <s xml:space="preserve">lanci, brachio oppoſito ſuſpen-<lb />ſæ, pondus imponitur, ut detur æquilibrium cum ponde-<lb />re ſolius fundi &amp; </s>
          <s xml:space="preserve">catenæ; </s>
          <s xml:space="preserve">quantum ponderis ad hoc requi-<lb />ritur antea explorandum. </s>
          <s xml:space="preserve">Cum tubo D, cujus longitudo eſt <lb />pollicum triginta duorum in ſuperiori parte, ope cochleæ in-<lb />fundibulum conjungitur cylindricum cujus diameter eſt cir-<lb />citer novem pollicum, &amp; </s>
          <s xml:space="preserve">in hac figura non exhibetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0288-01" corresp="note-0288-01a" place="margin">723.</note>
              <figure xml:id="fig-0289a-01" corresp="fig-0289a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0289a-01" />
                <label>0289a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Jugo libræ horizontaliter diſpoſito infundatur aqua tubo <lb />D, ut ad altitudinem duorum pollicum in infundibulo per-<lb />tingat: </s>
          <s xml:space="preserve">pondere duodecim librarum lanci impoſito æquili-<lb />brium datur; </s>
          <s xml:space="preserve">diminuto, aut aucto, pondere, adſcendit, aut <lb />deſcendit, fundus. </s>
          <s xml:space="preserve">Quantitate tamen non admodum exi-<lb />gua, exempli gratia unius libræ, augendum aut minuendum <lb />eſt pondus, propter attritum fundi, ſæpe major differentia <lb />deſideratur, quod ab attritu pendet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Altitudo ſupremæ ſuperficiei aquæ ſupra fundum, in hoc <lb />Experimento, eſt trium pedum, columnæ aqueæ, cujus <lb />hæc eſt altitudo, &amp; </s>
          <s xml:space="preserve">quæ baſin æqualem fundo cylindri ha-<lb />bet, pondus eſt duodecim librarum, &amp; </s>
          <s xml:space="preserve">tantum etiam valet <lb />preſſio aquæ in fundum, licet exigua tantum aquæ copia <lb />in fundum premat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum de ſolo motu fundi agatur, machina firmanda eſt <lb />ne tota elevetur, quod fit impoſitis ponderibus, qualia re-<lb />præſentantur in P, P, fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">XXIX.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Sublato operculo cum tubo, cylindrus A conjungatur <lb />
<ptr xml:id="note-0291-01a" corresp="note-0291-01" type="noteAnchor" />
cum cono truncato inverſo DE, cui in inferiori parte co-<lb />
<ptr xml:id="note-0291-02a" corresp="note-0291-02" type="noteAnchor" />
hæret annulus cochleam continens; </s>
          <s xml:space="preserve">aqua huic machinæ in-<lb />funditur ad eandem altitudinem ſupra fundum ac in præ-<lb />cedenti Experimento; </s>
          <s xml:space="preserve">Experimentum de cætero eodem <lb />modo peragitur, &amp; </s>
          <s xml:space="preserve">eodem modo procedit; </s>
          <s xml:space="preserve">preſſioque, <lb />ſervata aquæ altitudine, ex mutato vaſe &amp; </s>
          <s xml:space="preserve">aquæ quantitate; <lb /></s>
          <s xml:space="preserve">non mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0291-01" corresp="note-0291-01a" place="margin">724.</note>
              <note xml:space="preserve" xml:id="note-0291-02" corresp="note-0291-02a" place="margin"><hi rend="small caps">TAB. XXVIII</hi>. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Vas cylindricum A libræ ſuſpenditur, pro parte hocce <lb />
<ptr xml:id="note-0291-03a" corresp="note-0291-03" type="noteAnchor" />
repletur cylindro ligneo D e, quod cum ligno B c, quomo-<lb />
<ptr xml:id="note-0291-04a" corresp="note-0291-04" type="noteAnchor" />
</s>
          <pb facs="0292" n="208" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
docunque firmato, cohæret, &amp; </s>
          <s xml:space="preserve">neque latera neque fun-<lb />dum vaſis memorati tangit; </s>
          <s xml:space="preserve">ſi vaſi aqua ad quamcunque al-<lb />titudinem infundatur, &amp; </s>
          <s xml:space="preserve">pondere lanci oppoſitæ impoſito <lb />æquilibrium detur; </s>
          <s xml:space="preserve">hocce pondus erit pondus totius aquæ <lb />quæ in vaſe, ſublato cylindro, continetur, poſita hac ad ean-<lb />dem altitudinem quam in Experimento; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">parva aquæ <lb />quantitas, cujus ſuprema ſuperficies elevatur, qua preſſio in <lb />fundum augetur, magnum pondus ſuſtinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0291-03" corresp="note-0291-03a" place="margin">725.</note>
              <note xml:space="preserve" xml:id="note-0291-04" corresp="note-0291-04a" place="margin"><hi rend="small caps">TAB. XXVIII</hi>. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Preſſionem lateralem verticali æquari, adhibita ſequenti <lb />machina, ad oculum patebit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head rend="italics" xml:space="preserve">Qua demonſtratur Preſſio Fluidorum <lb />lateralis.</head>
        <p>
          <s xml:space="preserve">Vas DB eſt parallelopipedum ligneum altitudinis circi-<lb />
<ptr xml:id="note-0292-01a" corresp="note-0292-01" type="noteAnchor" />
ter viginti pollicum; </s>
          <s xml:space="preserve">a latere fundum verſus datur foramen, <lb />
<ptr xml:id="note-0292-02a" corresp="note-0292-02" type="noteAnchor" />
in quo hæret annulus æneus cochleam continens, ut cylin-<lb />drus A, quem ſupra memoravimus <ptr type="noteAnchor" />, ibi firmetur, ſubla-
<ptr xml:id="note-0292-03a" corresp="note-0292-03" type="noteAnchor" />
tis pedibus, qui cochleis annulo inferiori annectuntur. </s>
          <s xml:space="preserve">Mo-<lb />tus fundi in cylindro in hoc caſu eſt horizontalis. </s>
          <s xml:space="preserve">Ad la-<lb />tera machinæ huic junguntur duæ regulæ ligneæ, quarum <lb />una videtur in GH, ſuper his horizontaliter movetur <lb />regula CC, quæ in medio F latior eſt, ut hujus motu in-<lb />trudatur cylindri fundus, quem regula premit paululum <lb />infra centrum. </s>
          <s xml:space="preserve">In C &amp; </s>
          <s xml:space="preserve">C funes ut CE huic regulæ alli-<lb />gantur, qui juxta regulas ut GH protenduntur, tranſeun-<lb />tes ſuper trochleis in harum regularum extremitatibus ut T, <lb />&amp; </s>
          <s xml:space="preserve">iis appenduntur pondera ut P.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0292-01" corresp="note-0292-01a" place="margin">726.</note>
              <note xml:space="preserve" xml:id="note-0292-02" corresp="note-0292-02a" place="margin"><hi rend="small caps">TAB XXVIII</hi>. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0292-03" corresp="note-0292-03a" n="*" anchored="true" place="margin">722.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Infundatur aqua vaſi BD, ita ut aquæ ſuperficies altior ſit <lb />
<ptr xml:id="note-0292-04a" corresp="note-0292-04" type="noteAnchor" />
regula CC quindecim pollicibus, ſint pondera ut P duarum <lb />librarum cum ſemiſſe, ita ut ſimul ſumta valeant quinque <lb />libras, preſſio aquæ hocce pondus ſuſtinebit, &amp; </s>
          <s xml:space="preserve">fundus in <lb />hoc caſu æque facile intruditur ac extrahitur</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0292-04" corresp="note-0292-04a" place="margin">727.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vim, qua aqua ſurſum premit, æqualem eſſe illi qua deor-<lb />ſum &amp; </s>
          <s xml:space="preserve">ad latera premit, ſequenti Experimento probatur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0293" n="209" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. II.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Inmedio ſuperficiei ſuperioris ſuſtentaculi B, datur cy-<lb />
<ptr xml:id="note-0293-01a" corresp="note-0293-01" type="noteAnchor" />
lindrus diametri circiter duorum pollicum, cui imponitur <lb />
<ptr xml:id="note-0293-02a" corresp="note-0293-02" type="noteAnchor" />
fundus mobilis cylindri ſæpius memorati A <ptr type="noteAnchor" />, ita ut ma-
<ptr xml:id="note-0293-03a" corresp="note-0293-03" type="noteAnchor" />
nente fundo ipſe cylindrus moveri poſſit; </s>
          <s xml:space="preserve">hic operculo ſuo <lb />obtegitur, &amp; </s>
          <s xml:space="preserve">cum eo conjungitur tubus D longitudinis tri-<lb />um pedum cum ſemiſſe, cui in ſuperiori extremitate additur <lb />infundibulum cujus diameter eſt trium aut quatuor poll. <lb /></s>
          <s xml:space="preserve">Infunditur aqua, qua, manente fundo, machina elevatur; </s>
          <s xml:space="preserve"><lb />imponuntur operculo pondera P, P, P, quæ ſimul valent <lb />libras novem, hæc, cum pondere totius machinæ, ab aqua in <lb />tubo ſuſtinentur; </s>
          <s xml:space="preserve">pondus vero machinæ cum tubis &amp; </s>
          <s xml:space="preserve">infun-<lb />dibulo excedit quatuor libras cum ſemiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0293-01" corresp="note-0293-01a" place="margin">728.</note>
              <note xml:space="preserve" xml:id="note-0293-02" corresp="note-0293-02a" place="margin"><hi rend="small caps">TAB. XXIX</hi>. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0293-03" corresp="note-0293-03a" n="*" anchored="true" place="margin">722.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis, quæ in operculum agit, valet pondus columnæ aqueæ, <lb />cujus baſis eſt operculum, demto foramine cui reſpondet tu-<lb />bus, &amp; </s>
          <s xml:space="preserve">cujus altitudo eſt, aquæ elevatio in tubo ſupra ſu-<lb />perficiem interiorem operculi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod cum hoc Experimen-
<ptr xml:id="note-0293-04a" corresp="note-0293-04" type="noteAnchor" />
to congruit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0293-04" corresp="note-0293-04a" n="*" anchored="true" place="margin">723</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Manente tubo ſi machina major detur, actio in operculum <lb />in eadem ratione cum operculo creſcet, ita ut minima aquæ <lb />quantitate pondus maximum ſuſtineatur, ac etiam elevetur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Follis hydrostaticus</hi>.</head>
        <p>
          <s xml:space="preserve">Duo orbes lignei AB, AB, diametri quindecim pollicum, <lb />
<ptr xml:id="note-0293-05a" corresp="note-0293-05" type="noteAnchor" />
corio circumdantur &amp; </s>
          <s xml:space="preserve">junguntur ita, ut formetur vas cylin-<lb />
<ptr xml:id="note-0293-06a" corresp="note-0293-06" type="noteAnchor" />
dricum folli aliquomodo ſimile, quod aquam continere poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0293-05" corresp="note-0293-05a" place="margin">729.</note>
              <note xml:space="preserve" xml:id="note-0293-06" corresp="note-0293-06a" place="margin"><hi rend="small caps">TAB. XXIX</hi>. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In orbe ſuperiori datur foramen in l, cui reſpondet cy-<lb />lindrus æneus, cum orbe cohærens, &amp; </s>
          <s xml:space="preserve">cochlea circumdatus, <lb />quo tubus D, ejusdem longitudinis cum tubo in præceden-<lb />ti Experimento, machinæ jungitur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Aqua machinæ per tubum infundatur, &amp; </s>
          <s xml:space="preserve">aqua in tubo <lb />
<ptr xml:id="note-0293-07a" corresp="note-0293-07" type="noteAnchor" />
ſuſtinebit pondera P,P,P,P,P,P, ſimul excedentia ducentas <lb />&amp; </s>
          <s xml:space="preserve">quinquagintâ libras. </s>
          <s xml:space="preserve">Pondera hæc infundendo aquam in <lb />tubum etiam elevari poterunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0293-07" corresp="note-0293-07a" place="margin">730.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc omnia quantumvis paradoxa ex natura fluiditatis ſe-<lb />
<ptr xml:id="note-0293-08a" corresp="note-0293-08" type="noteAnchor" />
quuntur; </s>
          <s xml:space="preserve">gutta quæcunque quæ quieſcit, omnes partes
</s>
          <pb facs="0294" n="210" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
verſus æquali cum vi conatur recedere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi ergo ab una
<ptr xml:id="note-0294-01a" corresp="note-0294-01" type="noteAnchor" />
parte prematur, illam partem verſus, propter æqualem a-<lb />ctioni reactionem, ipſa premet, &amp; </s>
          <s xml:space="preserve">hac eadem vi omnes par-<lb />tes verſus recedere conabitur. </s>
          <s xml:space="preserve">In primo Experimento, a-<lb />qua, quæ fundum tangit, &amp; </s>
          <s xml:space="preserve">tubo reſpondet, ſuſtinet pon-<lb />dus columnæ aqueæ in tubo contentæ, &amp; </s>
          <s xml:space="preserve">adfundum uſque <lb />continuatæ, &amp; </s>
          <s xml:space="preserve">tali cum vi fundum premit, ut &amp; </s>
          <s xml:space="preserve">aquam <lb />vicinam, quæ cum effluere non poſſit in fundum, &amp; </s>
          <s xml:space="preserve">aquam <lb />vicinam, hac eadem vi agit; </s>
          <s xml:space="preserve">quod &amp; </s>
          <s xml:space="preserve">ad aquam huic vici-<lb />nam applicari poteſt, quare in omnibus fundi punctis datur <lb />preſſio æqualis preſſioni in loco in quem aqua in tubo gra-<lb />vat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideo fundus hic gravatur eodem modo ac ſi aquæ <lb />columna, ejuſdem altitudinis cum aqua in tubo, &amp; </s>
          <s xml:space="preserve">cu us <lb />baſis eſſet ipſe fundus, huic imponeretur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0293-08" corresp="note-0293-08a" place="margin">731.</note>
              <note xml:space="preserve" xml:id="note-0294-01" corresp="note-0294-01a" n="*" anchored="true" place="margin">711.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simili ratiocinio dilucidantur Experimenta 5. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">Pa-<lb />tet enim ſingula operculi puncta ſurſum premi ab a-<lb />qua ea vi, qua aqua quæ in apertura operculi hæret à ſuperiori <lb />quæ in tubo hæret, deorſum premitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In ſecundo Experimento concipiatur, cylindrum A con-<lb />tinuari ita, ut ad aquæ ſuperficiem perveniat; </s>
          <s xml:space="preserve">eo aqua ex-<lb />terior ab aqua hoc cylindro contenta ſeparatur, hæcque <lb />ſola in fundum premit, funduſque hanc totam ſuſtinet. </s>
          <s xml:space="preserve">Aqua <lb />in cylindro premit in latera cylindri, aqua exterior premit <lb />in ſuperficiem exteriorem cylindri, &amp; </s>
          <s xml:space="preserve">ſuperficies exterior <lb />eodem modo premitur ac interior, preſſioneſque in puncta <lb />oppoſita ſunt æquales; </s>
          <s xml:space="preserve">ita ut, ſi ſuperficies tolleretur, preſ-<lb />ſiones hæ ſeſe mutuo deſtruerent; </s>
          <s xml:space="preserve">non intereſt igitur utrum <lb />talis ſuperficies detur an non, &amp; </s>
          <s xml:space="preserve">ea ſublata, id eſt, ſub-<lb />lata cylindri continuatione, non mutatur actio in fun-<lb />dum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Experimento tertio pondus lanci impoſitum non mo-<lb />do ſuſtinetur ab aqua in vaſe, ſed etiam ab actione ſuperfi-<lb />ciei inferioris cylindri D e in aquam, quæ actio æqualis eſt <lb />actioni aquæ in hanc ſuperficiem, in quam eodem modo pre-<lb />mit aqua ac in Exp. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">in operculum agit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Preſſionem lateralem, qualem in Exp. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">demonſtravi-
</s>
          <pb facs="0295" n="211" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP II.</fw>
mus, æqualem eſſe illi, quæ ſurſum aut deorſum dirigitur, <lb />ex æqualitate actionis fluidi omnes partes verſus facile de-<lb />ducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quamvis hæc omnia a gravitate fluidorum pendeant, <lb />
<ptr xml:id="note-0295-01a" corresp="note-0295-01" type="noteAnchor" />
horum actiones ab ipſorum pondere diſtingui debent, quod <lb />ſemper quantitati materiæ eſt proportionale <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0295-01" corresp="note-0295-01a" place="margin">732.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">704.</note>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT III. <lb />De Solidis fluidis immerſis.</head>
        <p>
          <s xml:space="preserve">DIverſa corporum, ſive ſolidorum, ſive fluidorum, pon-<lb />dera a diverſâ materiæ quantitate, quam continent, <lb />pendere, non a ſpatio quod hæc occupat, vidimus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">vo-
lumen enim, manente pondere, mutatis poris, variari <lb />poteſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Materiæ quantitas in corpore, conſiderata cum relatione <lb />
<ptr xml:id="note-0295-03a" corresp="note-0295-03" type="noteAnchor" />
ad volumen corporis, id eſt, ad ſpatium ab hoc occupatum, <lb />vocatur corporis Denſitas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0295-03" corresp="note-0295-03a" place="margin">733.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus dicitur habere denſitatem duplam, aut triplam, <lb />&amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">denſitatis alterius corporis, quando, poſitis volumini-<lb />bus æqualibus, materiæ quantitas dupla, aut tripla &amp;</s>
          <s xml:space="preserve">c. <lb /></s>
          <s xml:space="preserve">eſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Corpus homogeneum dicitur, quod in omnibus partibus eſt <lb />
<ptr xml:id="note-0295-04a" corresp="note-0295-04" type="noteAnchor" />
ejuſdem denſitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0295-04" corresp="note-0295-04a" place="margin">734.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Heterogeneum cujus non omnes partes æqualem denſi-<lb />
<ptr xml:id="note-0295-05a" corresp="note-0295-05" type="noteAnchor" />
tatem habent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0295-05" corresp="note-0295-05a" place="margin">735.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi> 4.</head>
        <p rend="italics">
          <s xml:space="preserve">Pondus corporis conſideratum cum relatione ad volumen <lb />
<ptr xml:id="note-0295-06a" corresp="note-0295-06" type="noteAnchor" />
vocatur corporis Gravitas ſpecifica.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0295-06" corresp="note-0295-06a" place="margin">736.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Gravitas ſpecifica dicitur dupla, quando manente volu-<lb />mine pondus eſt duplum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Gravitates ergo ſpecificæ &amp; </s>
          <s xml:space="preserve">denſitates corporum, in cor-<lb />
<ptr xml:id="note-0295-07a" corresp="note-0295-07" type="noteAnchor" />
</s>
          <pb facs="0296" n="212" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
poribus homogeneis, in eadem ſunt ratione; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſunt inter ſe <lb />ut pondera corporum æqualium quantum ad volumen.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0295-07" corresp="note-0295-07a" place="margin">737.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpora homogenea fuerint ejuſdem ponderis, vo-<lb />
<ptr xml:id="note-0296-01a" corresp="note-0296-01" type="noteAnchor" />
lumina eo ſunt minora quo denſitates ſunt majores, &amp; </s>
          <s xml:space="preserve">ma-<lb />nente pondere, minuitur volumen in eadem ratione, in <lb />qua denſitas augetur; </s>
          <s xml:space="preserve">ſunt ideo in hoc cafu volumina inver-<lb />ſe ut denſitates.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-01" corresp="note-0296-01a" place="margin">438.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In homogeneis corporibus, ſi duæ dentur ex tribus ra-<lb />tionibus, ponderum, voluminum, &amp; </s>
          <s xml:space="preserve">denſitatum, tertia <lb />detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Pondera enim ſunt in ratione compoſita voluminum &amp; </s>
          <s xml:space="preserve">denſi-<lb />
<ptr xml:id="note-0296-02a" corresp="note-0296-02" type="noteAnchor" />
tatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-02" corresp="note-0296-02a" place="margin">739.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Volumina idcirco ſunt directè ut pondera, &amp; </s>
          <s xml:space="preserve">inverſe ut <lb />
<ptr xml:id="note-0296-03a" corresp="note-0296-03" type="noteAnchor" />
denſitates.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-03" corresp="note-0296-03a" place="margin">740.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Tandem denſitates ſunt directè ut pondera, &amp; </s>
          <s xml:space="preserve">inverſè ut <lb />
<ptr xml:id="note-0296-04a" corresp="note-0296-04" type="noteAnchor" />
volumina.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-04" corresp="note-0296-04a" place="margin">741.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quando ſolidum fluido immergitur, a fluido ab omni par-<lb />
<ptr xml:id="note-0296-05a" corresp="note-0296-05" type="noteAnchor" />
te premitur, preſſioque hæc in ratione altitudinis fluidi ſu-<lb />pra ſolidum creſcit. </s>
          <s xml:space="preserve">Ut hoc ex dictis in capite præcedenti <lb />ſequitur, ac etiam directo Experimento probatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-05" corresp="note-0296-05a" place="margin">742.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Extremitati tubi vitrei B m alligatur ſaccus coriaceus S, <lb />
<ptr xml:id="note-0296-06a" corresp="note-0296-06" type="noteAnchor" />
mercurio plenus, veſica etiam poteſt adhiberi; </s>
          <s xml:space="preserve">immergitur <lb />
<ptr xml:id="note-0296-07a" corresp="note-0296-07" type="noteAnchor" />
ſaccus hic aquâ, ita, ut extremitas B tubi ſupra aquam <lb />perveniat.</s>
          <s xml:space="preserve">. Preſſione aquæ in ſuperficiem ſacci. </s>
          <s xml:space="preserve">adſcendit <lb />mercurius in tubum, ut perveniat ad m; </s>
          <s xml:space="preserve">adſcenſusque mer-<lb />curii ſequitur proportionem altitudinis aquæ ſupra ſaccum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-06" corresp="note-0296-06a" place="margin">743.</note>
              <note xml:space="preserve" xml:id="note-0296-07" corresp="note-0296-07a" place="margin">TAB. XXIX. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando ſolidum ad magnam profunditatem fluido im-<lb />mergitur, preſſio in ſuperiorem partem a preſſione in in-<lb />feriorem vix differt; </s>
          <s xml:space="preserve">unde corpora altè immerſa ab omni <lb />
<ptr xml:id="note-0296-08a" corresp="note-0296-08" type="noteAnchor" />
parte quaſi æqualiter premuntur; </s>
          <s xml:space="preserve">quæ preſſio a corporibus <lb />mollibus ſine figuræ mutatione, &amp; </s>
          <s xml:space="preserve">ab admodum fragilibus <lb />fine diſruptione, ſuſtineri poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-08" corresp="note-0296-08a" place="margin">744.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Fruſtum ceræ mollis, figuræ irregularis, &amp; </s>
          <s xml:space="preserve">ovum, ve-<lb />
<ptr xml:id="note-0296-09a" corresp="note-0296-09" type="noteAnchor" />
ſicæ aquâ repletæ includuntur, veſica exacte clauſa pyxidi <lb />
<ptr xml:id="note-0296-10a" corresp="note-0296-10" type="noteAnchor" />
</s>
          <pb facs="0297" n="213" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. III.</fw>
æneæ A inſeritur; </s>
          <s xml:space="preserve">operculo ligneo O hæc obtegitur, ita <lb />ut a veſica ſuſtineatur; </s>
          <s xml:space="preserve">pondus P centum, aut centum &amp; </s>
          <s xml:space="preserve"><lb />quinquaginta librarum, etiam majus abhiberi poteſt, ſuper-<lb />imponitur, quo neque ovum frangitur, neque ceræ figura <lb />ullo modo mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0296-09" corresp="note-0296-09a" place="margin">745.</note>
              <note xml:space="preserve" xml:id="note-0296-10" corresp="note-0296-10a" place="margin">TAB. XXVIII. <lb />fig 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ne quidem guttæ cujuſcunque fluidi figura, preſſione alte-<lb />
<ptr xml:id="note-0297-01a" corresp="note-0297-01" type="noteAnchor" />
rius fluidi ab omni parte æquali, mutari poteſt. </s>
          <s xml:space="preserve">Sit gutta fi-<lb />
<ptr xml:id="note-0297-02a" corresp="note-0297-02" type="noteAnchor" />
guræ irregularis A, quæ alio fluido ab omni parte æquali-<lb />ter prematur. </s>
          <s xml:space="preserve">Directio preſſionis in omnibus punctis eſt <lb />
<ptr xml:id="note-0297-03a" corresp="note-0297-03" type="noteAnchor" />
perpendicularis ad ſuperficiem; </s>
          <s xml:space="preserve">quod ſi negetur, reſolven-<lb />da erit preſſio in duas <ptr type="noteAnchor" />, quarum una perpendiculariter a-
<ptr xml:id="note-0297-04a" corresp="note-0297-04" type="noteAnchor" />
gat ad ſuperficiem, alia juxta directionem ſuperficiei paral-<lb />lelam, quæ ſecunda cum in ſuperficiem non agat, premitur <lb />gutta illâ ſolâ, cujus directio perpendicularis eſt ad ſuperfi-<lb />ciem. </s>
          <s xml:space="preserve">Prematur punctum B, guttula preſſa quaquaverſum <lb />æquali cum vi premit, &amp; </s>
          <s xml:space="preserve">guttæ minores ſingulæ preſſæ eo-<lb />dem modo premunt, ita ut preſſio ſtatim per integram gut-<lb />tam datam diſpergatur, quare particula ut D, quæ in gut-<lb />ta ab omni parte æqualiter premitur, conatur cedere per <lb />DE, cum vi qua premitur, id eſt, cum vi qua externe <lb />premitur particula B, ſed æquali vi ponimus per ED pre-<lb />mi particulam D; </s>
          <s xml:space="preserve">non poterit ergo hæc moveri; </s>
          <s xml:space="preserve">eadem <lb />demonſtratio poterit applicari puncto F, ut alii puncto cui-<lb />cunque ſuperficiei, ita ut nullibi gutta moveri poſ-<lb />ſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0297-01" corresp="note-0297-01a" place="margin">746.</note>
              <note xml:space="preserve" xml:id="note-0297-02" corresp="note-0297-02a" place="margin">TAB. XXVIII. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0297-03" corresp="note-0297-03a" place="margin">747.</note>
              <note xml:space="preserve" xml:id="note-0297-04" corresp="note-0297-04a" n="*" anchored="true" place="margin">229.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Solidum fluido ſpecifice gravius, ad quamcunque alti. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0297-05a" corresp="note-0297-05" type="noteAnchor" />
tudinem fluido immerſum, deorſum pellitur preſſione, quæ <lb />valet pondus columnæ quæ formatur ex ipſo corpore &amp; </s>
          <s xml:space="preserve">flui-<lb />do ſuperincumbenti. </s>
          <s xml:space="preserve">Pondus columoæ ſimilis, ſed quæ <lb />tota ex fluido conſtat, eſt vis cum qua corpus a fluido ſur-<lb />ſum premitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Cum vero ſolidum ponatur fluido ſpeci-
<ptr xml:id="note-0297-06a" corresp="note-0297-06" type="noteAnchor" />
fice gravius, vis hæc minor eſt illâ, &amp; </s>
          <s xml:space="preserve">ab eadem ſuperatur, <lb />&amp; </s>
          <s xml:space="preserve">corpus deſcendit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0297-05" corresp="note-0297-05a" place="margin">748.</note>
              <note xml:space="preserve" xml:id="note-0297-06" corresp="note-0297-06a" n="*" anchored="true" place="margin">742. 711.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simili ratiocinio, ſolidum fluido ſpecifice levius immer ſum, <lb />
<ptr xml:id="note-0297-07a" corresp="note-0297-07" type="noteAnchor" />
ad ſupremam fluidi ſuperficiem adſcendere debere, proba-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0297-07" corresp="note-0297-07a" place="margin">749.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0298" n="214" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Poſita verò eadem ſolidi cum fluido gravitate ſpecifica, <lb />
<ptr xml:id="note-0298-01a" corresp="note-0298-01" type="noteAnchor" />
neque adſcendet, neque deſcendet, ſed ad quamcunque al-<lb />titudinem in fluido ſuſpenſum manebit, &amp; </s>
          <s xml:space="preserve">fluidum inte-<lb />grum corpus ſuſtinebit; </s>
          <s xml:space="preserve">in quo caſu, propter æqualitatem <lb />gravitatum ſpecificarum, fluidum ſuſtinet pondus æquale <lb />ponderi fluidi, quod impleret ſpatium a corpore occupa-<lb />tum. </s>
          <s xml:space="preserve">Fluidum autem eodem modo agit in omnia ſolida <lb />æqualia ad eandem profunditatem immerſa, &amp; </s>
          <s xml:space="preserve">æqualiter <lb />hæc ſuſtinet; </s>
          <s xml:space="preserve">amittit ergo Corpus omne immerſum partem <lb />
<ptr xml:id="note-0298-02a" corresp="note-0298-02" type="noteAnchor" />
ponderis, æqualem ponderi fluidi quod æquale ſpatium cum <lb />corpore occupat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0298-01" corresp="note-0298-01a" place="margin">750.</note>
              <note xml:space="preserve" xml:id="note-0298-02" corresp="note-0298-02a" place="margin">751.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Proprie loquendo non quidem amittit corpus partem pon-<lb />deris quæ a fluido ſuſtinetur; </s>
          <s xml:space="preserve">ſed deſcendit in fluido aut <lb />trahit funem quo ſuſtinetur, quaſi revera pondus imminutum <lb />foret.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Ex unco lancis libræ ſuperius memoratæ <ptr type="noteAnchor" /> ſuſpendatur
<ptr xml:id="note-0298-03a" corresp="note-0298-03" type="noteAnchor" />
cylindrus æneus cavus E; </s>
          <s xml:space="preserve">unco, fundo hujus cohærenti, <lb />
<ptr xml:id="note-0298-04a" corresp="note-0298-04" type="noteAnchor" />
ope capilli equini, ſuſpenditur cylindrus ſolidus C, ex eo-<lb />
<ptr xml:id="note-0298-05a" corresp="note-0298-05" type="noteAnchor" />
dem metallo, qui ſi alteri E inſeratur, hunc exacte implet <lb />ita, ut in E, quando aquâ repletur, contineatur aquæ <lb />quantitas, quæ poteſt implere locum a Coccupatum. </s>
          <s xml:space="preserve">Lan-<lb />ci oppoſitæ pondus imponatur ut detur æquilibrium; </s>
          <s xml:space="preserve">de-<lb />ſcendat bilanx, ut cylindrus C aquâ, vaſe D contentâ, im-<lb />mergatur; </s>
          <s xml:space="preserve">eo æquilibrium deſtruitur, quia C pro parte ab <lb />aqua ſuſtinetur; </s>
          <s xml:space="preserve">ad hoc verò redit libra, ſi vas E aquâ im-<lb />pleatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0298-03" corresp="note-0298-03a" place="margin">752.</note>
              <note xml:space="preserve" xml:id="note-0298-04" corresp="note-0298-04a" place="margin">TAB. XXX. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0298-05" corresp="note-0298-05a" n="*" anchored="true" place="margin">705.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p rend="italics">
          <s xml:space="preserve">Pondus, quod corpus fluido immer ſum ſervat, vocatur il-<lb />
<ptr xml:id="note-0298-06a" corresp="note-0298-06" type="noteAnchor" />
lius gravitas reſpectiva.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0298-06" corresp="note-0298-06a" place="margin">753.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Hæcque gravitas reſpectiva eſt exceſſus gravitatis ſpeci-<lb />
<ptr xml:id="note-0298-07a" corresp="note-0298-07" type="noteAnchor" />
ficæ ſolidi ſuper gravitatem ſpecificam fluidi;</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0298-07" corresp="note-0298-07a" place="margin">754.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur, omnia ſolida æqualia, licet diver ſæ <lb />
<ptr xml:id="note-0298-08a" corresp="note-0298-08" type="noteAnchor" />
gravitatis ſpecificæ, quando eodem fluido immerguntur, pon-<lb />dus æquale amittere <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Experimentum ultimum eodem mo-
<ptr xml:id="note-0298-09a" corresp="note-0298-09" type="noteAnchor" />
do procedit cum cylindro ex quocunque alio metallo &amp; </s>
          <s xml:space="preserve">af-
</s>
          <pb facs="0299" />
          <s xml:space="preserve">
<pb facs="0299a" />
<ptr xml:id="fig-0299a-01a" corresp="fig-0299a-01" type="figureAnchor" />
<pb facs="0300" />
<pb facs="0301" n="215" /><fw type="head">MATHEMATICA. LIB. II. CAP. III.</fw>
fuſâ eâdem aquæ quantitate, quæ nempe implet vas E, æ-<lb />quilibrium ſemper inſtauratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0298-08" corresp="note-0298-08a" place="margin">755.</note>
              <note xml:space="preserve" xml:id="note-0298-09" corresp="note-0298-09a" n="*" anchored="true" place="margin">751.</note>
              <figure xml:id="fig-0299a-01" corresp="fig-0299a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0299a-01" />
                <label>0299a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex dictis ulterius ſequitur quomodocunque inter ſe diffe-<lb />
<ptr xml:id="note-0301-01a" corresp="note-0301-01" type="noteAnchor" />
rant denſitates corporum inæqualium, ſi eodem fluido im-<lb />mergantur, pondera ab iis amiſſa eſſe in ratione volu-<lb />minum. </s>
          <s xml:space="preserve">In ea enim ratione ſunt ſpatia ab iis in fluido occu-<lb />pata.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0301-01" corresp="note-0301-01a" place="margin">756.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Idcirco corpora ejuſdem ponderis, ſed diverſæ denſi-<lb />tatis, partes inæquales ponderis amittunt, quando eo-<lb />dem fluido immerguntur, propter voluminum inæqualita-<lb />tem.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Fruſta ejuſdem ponderis, unum auri, alterum plumbi, <lb />
<ptr xml:id="note-0301-02a" corresp="note-0301-02" type="noteAnchor" />
g, g, capillis equinis, uncis bilancis ſæpius memoratæ <ptr type="noteAnchor" /> ſuſ-
<ptr xml:id="note-0301-03a" corresp="note-0301-03" type="noteAnchor" />
penduntur, æquilibrium datur; </s>
          <s xml:space="preserve">deſcendat bilanx, &amp; </s>
          <s xml:space="preserve">corpo-<lb />
<ptr xml:id="note-0301-04a" corresp="note-0301-04" type="noteAnchor" />
ra g, g, aquâ, vaſis F, F contentâ, immergantur, æquilibri-<lb />um deſtruetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0301-02" corresp="note-0301-02a" place="margin">757.</note>
              <note xml:space="preserve" xml:id="note-0301-03" corresp="note-0301-03a" place="margin">TAB. XXIX. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0301-04" corresp="note-0301-04a" n="*" anchored="true" place="margin">701.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando ſolidum, fluido ſpecifice gravius, in fluido <lb />ſuſpenditur, fluidum, ab omni parte, in illud ſolidum, <lb />pro altitudine ſua, agit <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſolidum æqualiter in illud rea-
<ptr xml:id="note-0301-05a" corresp="note-0301-05" type="noteAnchor" />
git; </s>
          <s xml:space="preserve">actiones illæ ſunt igitur eædem, ac ſi ſpatium, a ſolido <lb />occupatum, ipſo fluido impleretur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita non intereſt, quo <lb />
<ptr xml:id="note-0301-06a" corresp="note-0301-06" type="noteAnchor" />
ad pondus totius fluidi, utrum in eo ſolidum ſpecifice gravius <lb />ſuſpendatur, an affundatur ejuſdem fluidi quantitas, quæ <lb />æquale ſpatium cum ſolido occupat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0301-05" corresp="note-0301-05a" n="*" anchored="true" place="margin">742.</note>
              <note xml:space="preserve" xml:id="note-0301-06" corresp="note-0301-06a" place="margin">758.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum.</hi> 5.</head>
        <p>
          <s xml:space="preserve">Vas A, aquam continens, brachio libræ ſuſpenditur, ei-<lb />
<ptr xml:id="note-0301-07a" corresp="note-0301-07" type="noteAnchor" />
que immergitur cylindrus æneus C, qui capillo equino ſuſti-<lb />
<ptr xml:id="note-0301-08a" corresp="note-0301-08" type="noteAnchor" />
netur, ne fundum vaſis tangat; </s>
          <s xml:space="preserve">pondere lanci oppoſitæ <lb />impoſito, datur æquilibrium. </s>
          <s xml:space="preserve">Extracto cylindro C deſtrui-<lb />tur æquilibrium, &amp; </s>
          <s xml:space="preserve">inſtauratur infundendo aquam, quæ cy-<lb />lindro cavo E contineri poteſt, in quo ſi inſeratur cylindrus <lb />ſolidus C, exacte ab hoc repletur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0301-07" corresp="note-0301-07a" place="margin">759.</note>
              <note xml:space="preserve" xml:id="note-0301-08" corresp="note-0301-08a" place="margin">TAB. XXX. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex collatione n. </s>
          <s xml:space="preserve">751. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">758.</s>
          <s xml:space="preserve">, ut &amp; </s>
          <s xml:space="preserve">Experimentorum 3. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0301-09a" corresp="note-0301-09" type="noteAnchor" />
5. </s>
          <s xml:space="preserve">quibus illi confirmantur, patet, fluidum acquirere pondus <lb />quod ſolidum immerſum amittit. </s>
          <s xml:space="preserve">Vis gravitatis ſemper pro-
</s>
          <pb facs="0302" n="216" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
portionalis eſt quantitati materiæ, &amp; </s>
          <s xml:space="preserve">non mutatur immerſio-<lb />ne ſolidi in fluidum; </s>
          <s xml:space="preserve">quare ſumma ponderum ſolidi &amp; </s>
          <s xml:space="preserve">flui-<lb />di, &amp; </s>
          <s xml:space="preserve">ante &amp; </s>
          <s xml:space="preserve">poſt immerſionem, non differt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0301-09" corresp="note-0301-09a" place="margin">760.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Unco Vlancis A libræ appendatur ſolidum C, &amp; </s>
          <s xml:space="preserve">detur æqui-<lb />
<ptr xml:id="note-0302-01a" corresp="note-0302-01" type="noteAnchor" />
librium, lanci B impoſitis ponderibus P &amp; </s>
          <s xml:space="preserve">p, quorum p va-<lb />
<ptr xml:id="note-0302-02a" corresp="note-0302-02" type="noteAnchor" />
let pondus quod corpus C in aqua amittit. </s>
          <s xml:space="preserve">Detur etiam <lb />vas D aquam continens, &amp; </s>
          <s xml:space="preserve">libræ EF, quæ pede ſuſtine-<lb />tur, appenſum; </s>
          <s xml:space="preserve">pondere lanci oppoſitæ impoſito, detur <lb />&amp; </s>
          <s xml:space="preserve">hìc æquilibrium; </s>
          <s xml:space="preserve">deſcendat bilanx cum corpore C, ut <lb />hoc aquâ, in vaſe D, contentâ immergatur, deſtruitur <lb />æquilibrium in ambabus libris, quæ ambæ ad ipſum rede-<lb />unt, transferendo pondus p ex lance B in lancem bra-<lb />chii F.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0302-01" corresp="note-0302-01a" place="margin">761.</note>
              <note xml:space="preserve" xml:id="note-0302-02" corresp="note-0302-02a" place="margin">TAB. XXIX. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus, fluido ſpecifice gravius, &amp; </s>
          <s xml:space="preserve">quod in hoc de-<lb />
<ptr xml:id="note-0302-03a" corresp="note-0302-03" type="noteAnchor" />
ſcendit, majori vi deorſum fertur quam ſurſum premitur, <lb />ut antea explicatum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quarum virium differentia eſt cor-
<ptr xml:id="note-0302-04a" corresp="note-0302-04" type="noteAnchor" />
poris gravitas reſpectiva. </s>
          <s xml:space="preserve">Vis prima pro parte conſtat ex <lb />pondere fluidi corpori ſuperincumbentis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">corpus ad ta-<lb />lem poteſt immergi profunditatem, ut hocce pondus æqua-<lb />le ſit memoratæ gravitati reſpectivæ; </s>
          <s xml:space="preserve">ſi in hoc caſu fluidum <lb />hoc ſuperincumbens tollatur, ſuſtinebitur corpus a preſſione <lb />fluidi inferioris. </s>
          <s xml:space="preserve">Si ad majorem profunditatem corpus im-<lb />
<ptr xml:id="note-0302-05a" corresp="note-0302-05" type="noteAnchor" />
mergatur, &amp; </s>
          <s xml:space="preserve">etiam fluidum cohibeatur ne in ſuperficiem <lb />corporis ſupremam premat, (cum preſſio, qua corpus ſur-<lb />ſum pellitur, cum profunditate ad quam immergitur cre-<lb />ſcat <ptr type="noteAnchor" />) majori vi in altum feretur corpus quam gravi-
<ptr xml:id="note-0302-06a" corresp="note-0302-06" type="noteAnchor" />
tate deſcendet, quare, ſi libere moveri poſſit, adſcen-<lb />det.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0302-03" corresp="note-0302-03a" place="margin">662.</note>
              <note xml:space="preserve" xml:id="note-0302-04" corresp="note-0302-04a" n="*" anchored="true" place="margin">748.</note>
              <note xml:space="preserve" xml:id="note-0302-05" corresp="note-0302-05a" place="margin">763.</note>
              <note xml:space="preserve" xml:id="note-0302-06" corresp="note-0302-06a" n="*" anchored="true" place="margin">742.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Cylindro C, ab utraque parte aperto, applicetur ab in-<lb />
<ptr xml:id="note-0302-07a" corresp="note-0302-07" type="noteAnchor" />
feriori parte lamina plumbea F, craſſitiei quartæ partis <lb />
<ptr xml:id="note-0302-08a" corresp="note-0302-08" type="noteAnchor" />
unius pollicis; </s>
          <s xml:space="preserve">ſi ita exacte cum cylindro congruat, ut aquam <lb />excludat, laminaque filo, unco V in centro laminæ alligato, <lb />ſuſtineatur, donec ad profunditatem circiter trium pollicum <lb />aquâ immergatur, ab aqua ſuſtinebitur, quod relicto filo pate-
</s>
          <pb facs="0303" n="217" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. III.</fw>
bit. </s>
          <s xml:space="preserve">Ad majorem profunditatem magis arcte cum cylindro <lb />cohærebit, ad minorem cadet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0302-07" corresp="note-0302-07a" place="margin">764.</note>
              <note xml:space="preserve" xml:id="note-0302-08" corresp="note-0302-08a" place="margin">TAB. XXX. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si cum lamina aurea hocce Experimentum inſtitueretur, <lb />ad majorem profunditatem immergenda eſſet; </s>
          <s xml:space="preserve">auri enim <lb />gravitas ſpecifica eſt ad aquæ gravitatem ſpecificam ut 19. <lb /></s>
          <s xml:space="preserve">ad 1; </s>
          <s xml:space="preserve">quare illius gravitas reſpectiva eſt ad aquæ gravita-<lb />tem ſpecificam ut 18. </s>
          <s xml:space="preserve">ad 1. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Columna idcirco aquea de-
<ptr xml:id="note-0303-01a" corresp="note-0303-01" type="noteAnchor" />
cies &amp; </s>
          <s xml:space="preserve">octies, altitudine ſua, craſſitiem laminæ aureæ ſupe-<lb />rare debet, ut valeat hujus gravitatem reſpectivam; </s>
          <s xml:space="preserve">requi-<lb />ritur ergo ut aquæ altitudo, ſupra ſuperficiem ſuperiorem <lb />laminæ aureæ, toties ad minimum valeat ipſius laminæ craſ-<lb />ſitiem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0303-01" corresp="note-0303-01a" n="*" anchored="true" place="margin">714.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Cylindrus A cum fundo mobili operculo obtectus &amp; </s>
          <s xml:space="preserve">cum <lb />
<ptr xml:id="note-0303-02a" corresp="note-0303-02" type="noteAnchor" />
tubo D conjunctus, ut ante expoſitum <ptr type="noteAnchor" />, aquâ immergitur,
<ptr xml:id="note-0303-03a" corresp="note-0303-03" type="noteAnchor" />
funduſque, quando ad profunditatem unius pedis infra aquæ <lb />
<ptr xml:id="note-0303-04a" corresp="note-0303-04" type="noteAnchor" />
ſuperficiem pervenit, adſcendit, licet ponderet integram <lb />libram cum quadrante, &amp; </s>
          <s xml:space="preserve">licet, ope cochleæ, in centro <lb />fundi ab inferiori parte cohærentis, conjungatur cum pon-<lb />dere P unius libræ, &amp; </s>
          <s xml:space="preserve">præter pondera quæ elevantur ſupe-<lb />ratur attritus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0303-02" corresp="note-0303-02a" place="margin">765.</note>
              <note xml:space="preserve" xml:id="note-0303-03" corresp="note-0303-03a" place="margin">TAB. XXX. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0303-04" corresp="note-0303-04a" n="*" anchored="true" place="margin">722.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Idem ſolidum, quod fluidis diverſæ denſitatis immergi-<lb />
<ptr xml:id="note-0303-05a" corresp="note-0303-05" type="noteAnchor" />
tur, diverſam ponderis ſui partem amittit <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ideò quan-
<ptr xml:id="note-0303-06a" corresp="note-0303-06" type="noteAnchor" />
do duo corpora, ejuſdem denſitatis &amp; </s>
          <s xml:space="preserve">ponderis, fluidis di-<lb />verſæ denſitatis immerguntur, deſtruitur inter illa æquili-<lb />brium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0303-05" corresp="note-0303-05a" place="margin">766.</note>
              <note xml:space="preserve" xml:id="note-0303-06" corresp="note-0303-06a" n="*" anchored="true" place="margin">751.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Duæ laminæ g, g ejuſdem metalli &amp; </s>
          <s xml:space="preserve">æ quales, uncislan-<lb />
<ptr xml:id="note-0303-07a" corresp="note-0303-07" type="noteAnchor" />
cium A &amp; </s>
          <s xml:space="preserve">B ſuſpenduntur; </s>
          <s xml:space="preserve">deſcenſu libræ fluidis, vaſis F, F <lb />
<ptr xml:id="note-0303-08a" corresp="note-0303-08" type="noteAnchor" />
contentis, immerguntur; </s>
          <s xml:space="preserve">una in aquam, altera in oleum <lb />terebinthinæ, æquilibrium deſtruitur, &amp; </s>
          <s xml:space="preserve">illa hac levior <lb />fit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0303-07" corresp="note-0303-07a" place="margin">767.</note>
              <note xml:space="preserve" xml:id="note-0303-08" corresp="note-0303-08a" place="margin">TAB. XXIX <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Solidum fluido levius, &amp; </s>
          <s xml:space="preserve">hoc immerſum, adſcendit, &amp; </s>
          <s xml:space="preserve">in <lb />
<ptr xml:id="note-0303-09a" corresp="note-0303-09" type="noteAnchor" />
ſuprema fluidi ſuperficie hæret <ptr type="noteAnchor" />, ita ut pro parte tantum
<ptr xml:id="note-0303-10a" corresp="note-0303-10" type="noteAnchor" />
immergatur; </s>
          <s xml:space="preserve">pro majori tamen gravitate ſpecifica in fluido <lb />magis deſcendit, &amp; </s>
          <s xml:space="preserve">corpus non quieſcit, niſi pars immerſa
</s>
          <pb facs="0304" n="218" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tale ſpatium in fluido occupet, ut fluidum, quod idem hocce <lb />ſpatium impleret, ejuſdem ponderis cum toto corpore ſit. <lb /></s>
          <s xml:space="preserve">In alio enim caſu ſolidum non eadem cum vi in partes vi-<lb />cinas fluidi agit, cum qua fluidum ageret, ſi corporis locum <lb />occuparet, in hoc tamen caſu ſolo quies fluidi <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">ipſius
<ptr xml:id="note-0304-01a" corresp="note-0304-01" type="noteAnchor" />
corporis dari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0303-09" corresp="note-0303-09a" place="margin">768.</note>
              <note xml:space="preserve" xml:id="note-0303-10" corresp="note-0303-10a" n="*" anchored="true" place="margin">749.</note>
              <note xml:space="preserve" xml:id="note-0304-01" corresp="note-0304-01a" n="*" anchored="true" place="margin">713.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sequitur ex hac propoſitione, corporum, in ſuperficie <lb />
<ptr xml:id="note-0304-02a" corresp="note-0304-02" type="noteAnchor" />
ejuſdem fluidi natantium, partes immerſas eſſe inter ſe <lb />ut corporum pondera. </s>
          <s xml:space="preserve">Idcirco ſi, ſuperaddito pondere, <lb />corporis gravitas mutetur, in eâdem ratione augetur pars <lb />immerſa; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">partes, quæ variis ponderibus in fluidum de-<lb />
<ptr xml:id="note-0304-03a" corresp="note-0304-03" type="noteAnchor" />
ſcendunt, ſunt inter ſe ut hæc pondera.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0304-02" corresp="note-0304-02a" place="margin">769.</note>
              <note xml:space="preserve" xml:id="note-0304-03" corresp="note-0304-03a" place="margin">770.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 10.</head>
        <p>
          <s xml:space="preserve">Detur vas aquam continens A; </s>
          <s xml:space="preserve">detur cylindrus cavus ex <lb />
<ptr xml:id="note-0304-04a" corresp="note-0304-04" type="noteAnchor" />
<ptr xml:id="note-0304-05a" corresp="note-0304-05" type="noteAnchor" />
quocunque metallo C; </s>
          <s xml:space="preserve">huic imponatur pondus p, ut parte <lb />b d in aquam deſcendat; </s>
          <s xml:space="preserve">ſuperaddito pondere ſemi libræ, <lb />menſuretur quantum deſcendat; </s>
          <s xml:space="preserve">addatur iterum atque ite-<lb />rum pondus æquale, &amp; </s>
          <s xml:space="preserve">ſingulis vicibus æqualiter deſcen-<lb />dit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0304-04" corresp="note-0304-04a" place="margin">771.</note>
              <note xml:space="preserve" xml:id="note-0304-05" corresp="note-0304-05a" place="margin">TAB. XXXI <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In n. </s>
          <s xml:space="preserve">762. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">763.</s>
          <s xml:space="preserve">, Experimentis 7. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">8. </s>
          <s xml:space="preserve">confirmatis, vi-<lb />
<ptr xml:id="note-0304-06a" corresp="note-0304-06" type="noteAnchor" />
dimus, quomodo corpus fluido gravius ab hoc ſuſtineatur <lb />&amp; </s>
          <s xml:space="preserve">quaſi natet; </s>
          <s xml:space="preserve">ſimili methodo corpus fluido levius in fundo <lb />retineri poteſt; </s>
          <s xml:space="preserve">in illo caſu preſſio fluidi ſuperincumbentis <lb />tollitur, hìc tollenda eſt preſſio fluidi inferioris qua corpus <lb />ſurſum pellitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0304-06" corresp="note-0304-06a" place="margin">772.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 11.</head>
        <p>
          <s xml:space="preserve">Lamina ænea b c, exacte plana, ſuſtentaculo D impoſi-<lb />
<ptr xml:id="note-0304-07a" corresp="note-0304-07" type="noteAnchor" />
<ptr xml:id="note-0304-08a" corresp="note-0304-08" type="noteAnchor" />
ta, in fundo vaſis A hæret; </s>
          <s xml:space="preserve">lamina ſimilis b c cum fruſto <lb />ſuberis E conjungitur, ita ut cum hoc conſtituat corpus <lb />aqua levius; </s>
          <s xml:space="preserve">congruant hæ laminæ, &amp; </s>
          <s xml:space="preserve">baculo ſuber retinea-<lb />tur dum aqua affunditur; </s>
          <s xml:space="preserve">relicto ſubere non adſcendet, <lb />donec, hoc è loco moto, laminæ ſeparentur, ut aqua in <lb />laminam cum ſubere conjunctam preſſionem ſuam exerere <lb />poſſit, illamque cum ſubere in altum ferre.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0304-07" corresp="note-0304-07a" place="margin">773.</note>
              <note xml:space="preserve" xml:id="note-0304-08" corresp="note-0304-08a" place="margin">TAB. XXXI <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0305" />
        <pb facs="0305a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0305a-01" />
          <label>0305a-01</label>
        </figure>
        <pb facs="0306" />
        <pb facs="0307" n="219" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. IV.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IV.</head>
        <head xml:space="preserve">De comparandis Fluidorum Denſitatibus.</head>
        <p>
          <s xml:space="preserve">CUm corporis denſitas ſequatur proportionem ponderis <lb />ipſius, dato volumine, comparando corporum æqua-<lb />
<ptr xml:id="note-0307-01a" corresp="note-0307-01" type="noteAnchor" />
lium pondera, detegimus ipſorum denſitates <ptr type="noteAnchor" />, Si ergo vas
<ptr xml:id="note-0307-02a" corresp="note-0307-02" type="noteAnchor" />
quodcunque exacte fluido repleatur, &amp; </s>
          <s xml:space="preserve">fluidum hoc ponde-<lb />retur, idemque alio fluido repleatur, quod etiam ponderetur, <lb />pondera erunt ut denſitates. </s>
          <s xml:space="preserve">Sed cum hæc methodus in <lb />praxi variis obnoxia ſit difficultatibus, in hac explicanda <lb />non inhæremus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0307-01" corresp="note-0307-01a" place="margin">774.</note>
              <note xml:space="preserve" xml:id="note-0307-02" corresp="note-0307-02a" n="*" anchored="true" place="margin">288.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando duorum fluidorum preſſiones ſunt æquales, mate-<lb />
<ptr xml:id="note-0307-03a" corresp="note-0307-03" type="noteAnchor" />
riæ quantitates, id eſt, pondera, in columnis, æquales ba-<lb />ſes habentibus, non differunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare volumina, quæ ſunt
<ptr xml:id="note-0307-04a" corresp="note-0307-04" type="noteAnchor" />
ut columnarum altitudines, ſunt inverſè ut denſitates <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0307-05a" corresp="note-0307-05" type="noteAnchor" />
ex quo deducitur methodus haſce comparandi in tubis com-<lb />municantibus; </s>
          <s xml:space="preserve">in quibus tamen non deſiderantur baſes co-<lb />lumnarum æquales, id eſt, non intereſt an tubi ſint inæqua-<lb />les nec ne, quod altitudinem non mutat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0307-03" corresp="note-0307-03a" place="margin">775.</note>
              <note xml:space="preserve" xml:id="note-0307-04" corresp="note-0307-04a" n="*" anchored="true" place="margin">708.</note>
              <note xml:space="preserve" xml:id="note-0307-05" corresp="note-0307-05a" n="*" anchored="true" place="margin">738.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">714.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Tubo vitreo curvo A infundatur mercurius, quo pars <lb />
<ptr xml:id="note-0307-07a" corresp="note-0307-07" type="noteAnchor" />
inferior tubi a b ad c impletur; </s>
          <s xml:space="preserve">infundatur aqua ab una par-<lb />
<ptr xml:id="note-0307-08a" corresp="note-0307-08" type="noteAnchor" />
te à b ad e; </s>
          <s xml:space="preserve">in crus oppoſitum infundatur oleum terebinthi-<lb />næ, donec ambæ ſuperficies b, c, mercurii ſint in eadem li-<lb />nea horizontali, ſitque altitudo olei c d; </s>
          <s xml:space="preserve">erunt hæ altitudi-<lb />nes ut 87. </s>
          <s xml:space="preserve">ad 100. </s>
          <s xml:space="preserve">in qua ratione inverſa eſt denſitas aquæ <lb />ad olei terebinthinæ denſitatem, ſunt ergo hæ ut {1/87} ad {1/100}, <lb />aut ut 100. </s>
          <s xml:space="preserve">ad 87.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0307-07" corresp="note-0307-07a" place="margin">776.</note>
              <note xml:space="preserve" xml:id="note-0307-08" corresp="note-0307-08a" place="margin">TAB. XXXI. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Mercurius infunditur, ne fluida in fundo tubi miſcean-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Adhibito ſolido immerſo etiam comparantur fluidorum <lb />denſitates, ſi enim ſolidum, fluidis comparandis levius, va-<lb />
<ptr xml:id="note-0307-09a" corresp="note-0307-09" type="noteAnchor" />
riis fluidis immergatur, partes immerſæ erunt inversè ut <lb />fluidorum denſitates; </s>
          <s xml:space="preserve">nam, quia idem ſolidum adhibetur, <lb />portiones variorum fluidorum, quæ ſingulis caſibus ſpatium
</s>
          <pb facs="0308" n="220" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
a parte immerſa occupatum poſſent implere, ſunt ejuſdem <lb />ponderis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo volumina illarum portionum immerſarum,
<ptr xml:id="note-0308-01a" corresp="note-0308-01" type="noteAnchor" />
ſunt inverſè ut denſitates <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0307-09" corresp="note-0307-09a" place="margin">777.</note>
              <note xml:space="preserve" xml:id="note-0308-01" corresp="note-0308-01a" n="*" anchored="true" place="margin">768.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">738.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head xml:space="preserve">Qua Fluidorum denſitates conferuntur.</head>
        <note xml:space="preserve" place="margin">778.</note>
        <p>
          <s xml:space="preserve">Machina hæc A vitrea eſt, conſtat ex globo cavo, cum <lb />
<ptr xml:id="note-0308-04a" corresp="note-0308-04" type="noteAnchor" />
tubo cylindrico in partes æquales diviſo Infra globum al-<lb />ter minor additur, qui pro parte mercurio aut globulis exi-<lb />guis plumbeis impletur, ut eo pondere tubus verticaliter <lb />in fluida deſcendat, &amp; </s>
          <s xml:space="preserve">in hoc ſitu retineatur; </s>
          <s xml:space="preserve">ne nimium <lb />ponderis in minori globo detur cavendum; </s>
          <s xml:space="preserve">nam ut machi-<lb />na fluidis comparandis levior ſit requiritur. </s>
          <s xml:space="preserve">In variis flui-<lb />dis ad varias profunditates deſcendit machina, &amp; </s>
          <s xml:space="preserve">denſitates <lb />horum, ſunt inversè ut partes immerſæ, quæ ergo inter ſe <lb />comparandæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0308-04" corresp="note-0308-04a" place="margin">TAB XXXI <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Filum machinæ alligatur, &amp; </s>
          <s xml:space="preserve">machina cum filo annexo <lb />exacte ponderatur, pondus noſtræ fuit gr. </s>
          <s xml:space="preserve">550.</s>
          <s xml:space="preserve">; machina <lb />aquâ immerſa ad b deſcendit; </s>
          <s xml:space="preserve">pondus ergo aquæ ejuſdem <lb />voluminis cum parte machinæ immerſa valet gr. </s>
          <s xml:space="preserve">550 <ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0308-05a" corresp="note-0308-05" type="noteAnchor" />
hocce volumen hoc numero poteſt exprimi. </s>
          <s xml:space="preserve">Filum memo-<lb />ratum unco lancis bilancis hydroſtaticæ <ptr type="noteAnchor" /> annectitur; </s>
          <s xml:space="preserve">ma-
<ptr xml:id="note-0308-06a" corresp="note-0308-06" type="noteAnchor" />
chinâ manente immerſâ, lanci oppoſitæ pondus viginti gr. <lb /></s>
          <s xml:space="preserve">imponitur, &amp; </s>
          <s xml:space="preserve">lente bilanx elevatur, (quo tubus pro parte <lb />aqua extrahitur,) donec detur æquilibrium, ſuperficieſque <lb />aquæ tunc pertingit ad punctum d. </s>
          <s xml:space="preserve">Aqua ſuſtinet pondus <lb />totius machinæ, demtis granis viginti, id eſt, ſuſtinet gr. </s>
          <s xml:space="preserve"><lb />530.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">pondus aquæ ejuſdem voluminis cum parte nunc <lb />immerſâ tot grana valet, &amp; </s>
          <s xml:space="preserve">hoc numero exprimitur, volu-<lb />menque partis d b tubi erit 20. </s>
          <s xml:space="preserve">Si fpatium d b dividatur <lb />in partes æquales 10. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">diviſiones continuentur adſcenden-<lb />do ultra b, &amp; </s>
          <s xml:space="preserve">deſcendendo infra d, ſingulæ valebunt 2; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />ex nota diviſione, ad quam mazhina in fluidum deſcendit, <lb />dabitur volumen partis immerſæ, Ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">ſi totus tubus ex-<lb />tra aquam hæreat, volumen immerſum erit 526. </s>
          <s xml:space="preserve">ſi ad ſu-<lb />premam hìc notatam diviſionem deſcendat, volumen im-<lb />merſum erit 556; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">denſitates fluidorum, in quibus hoc
</s>
          <pb facs="0309" />
          <s xml:space="preserve">
<pb facs="0309a" />
<ptr xml:id="fig-0309a-01a" corresp="fig-0309a-01" type="figureAnchor" />
<pb facs="0310" />
<pb facs="0311" n="221" /><fw type="head">MATHEMATICA. LIB. II. CAP. IV.</fw>
contingit, ſunt inverſè ut illi numeri, id eſt, ut 556. </s>
          <s xml:space="preserve">ad <lb />526. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſolæ denſitates intermediæ ope hujus machinæ <lb />comparari poſſunt. </s>
          <s xml:space="preserve">Si globus minorem ad tubum rationem <lb />haberet, fluida, quorum denſitates magis inter ſe differ-<lb />rent, comparari poſſent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0308-05" corresp="note-0308-05a" n="*" anchored="true" place="margin">768.</note>
              <note xml:space="preserve" xml:id="note-0308-06" corresp="note-0308-06a" n="*" anchored="true" place="margin">705.</note>
              <figure xml:id="fig-0309a-01" corresp="fig-0309a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0309a-01" />
                <label>0309a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando fluida varia comparantur, numeri, volumina <lb />partium immerſarum deſignantes, habentur pro denomina-<lb />toribus fractionum, unitatem in numeratore habentium, <lb />deſignantque hæ fractiones rationem denſitatum; </s>
          <s xml:space="preserve">ſunt enim <lb />inter ſe inverſè ut denominatores.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Sint comparandæ denſitates aquarum diverſas ſalis quan-<lb />
<ptr xml:id="note-0311-01a" corresp="note-0311-01" type="noteAnchor" />
titates continentium, in unam deſcendit machina ad divi-<lb />ſionem a; </s>
          <s xml:space="preserve">alterà ſi immergatur, deſcendit tantum ad divi-<lb />ſionem c; </s>
          <s xml:space="preserve">denſitates harum erunt inter ſe ut {1/546} ad {1/542}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0311-01" corresp="note-0311-01a" place="margin">779.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non poſſunt hac methodo inter ſe conferri fluidorum <lb />denſitates niſi quæ parum differunt, uſumque machinæ <lb />hæ habent ubi vina, aut cereviſiæ conferri debent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Methodus omnium optima eſt, adhibito ſolido fluidis <lb />graviore. </s>
          <s xml:space="preserve">Quando idem corpus variis fluidis immergitur, <lb />
<ptr xml:id="note-0311-02a" corresp="note-0311-02" type="noteAnchor" />
pondera ab illo, in his amiſſa, ſunt inter ſe ut horum den-<lb />
<ptr xml:id="note-0311-03a" corresp="note-0311-03" type="noteAnchor" />
ſitates <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0311-02" corresp="note-0311-02a" place="margin">780.</note>
              <note xml:space="preserve" xml:id="note-0311-03" corresp="note-0311-03a" n="*" anchored="true" place="margin">751. 737.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head xml:space="preserve">Alia qua Fluidorum Denſitates conferuntur.</head>
        <note xml:space="preserve" place="margin">781.</note>
        <p>
          <s xml:space="preserve">Utendum hìc bilance hydroſtatica <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">vitri fruſto ſolido
<ptr xml:id="note-0311-05a" corresp="note-0311-05" type="noteAnchor" />
cujuscunque figuræ ut C; </s>
          <s xml:space="preserve">hoc, capillo equino, unco lan-<lb />
<ptr xml:id="note-0311-06a" corresp="note-0311-06" type="noteAnchor" />
cis A ſuſpenditur. </s>
          <s xml:space="preserve">Deſideratur &amp; </s>
          <s xml:space="preserve">pondus æneum P, cujus no-<lb />ta eſt differentia cum pondere ipſius vitri C: </s>
          <s xml:space="preserve">quæ differen-<lb />tia in noſtrâ machinâ eſt 700. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ipſi ponderi inſcripta; <lb /></s>
          <s xml:space="preserve">pondus hoc alii lanci B annectitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0311-05" corresp="note-0311-05a" n="*" anchored="true" place="margin">705.</note>
              <note xml:space="preserve" xml:id="note-0311-06" corresp="note-0311-06a" place="margin">TAB. XXX. <lb />fig. 4. 5. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc vitrum C in fluido quocunque ſuſpendatur, &amp; </s>
          <s xml:space="preserve"><lb />æquilibrium detur, impoſito pondere lancium uni aut alteri, <lb />denſitas fluidi detegitur. </s>
          <s xml:space="preserve">Si lanci A, addatur numerus gr. <lb /></s>
          <s xml:space="preserve">impoſitorum differentiæ memoratæ gr. </s>
          <s xml:space="preserve">700.</s>
          <s xml:space="preserve">; ſi lanci B, <lb />ſubtrahatur numerus ille ex iiſdem 700. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in utroque caſu,
</s>
          <pb facs="0312" n="222" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ut patet, determinatur pondus a corpore amiſſum, id eſt, <lb />pondus denſitatem fluidi exprimens.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <note xml:space="preserve" place="margin">782.</note>
        <p>
          <s xml:space="preserve">Oleo Terebinthinæ immergatur vitrum C, lanci A ſuſ-<lb />penſum, dum pondus P lanci B adhæret; </s>
          <s xml:space="preserve">lanci B impoſi-<lb />tis gr. </s>
          <s xml:space="preserve">100. </s>
          <s xml:space="preserve">æquilibrium datur. </s>
          <s xml:space="preserve">Si aquâ idem vitrum im-<lb />mergatur 11. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">in eadem lance deſiderantur ut bilanx ſit <lb />in æquilibrio. </s>
          <s xml:space="preserve">Si verò de lacte agatur 10. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">lanci A impo-<lb />nenda ſunt. </s>
          <s xml:space="preserve">Subtractis numero primo &amp; </s>
          <s xml:space="preserve">ſecundo ex ſe-<lb />ptingentis, &amp; </s>
          <s xml:space="preserve">hiſce addito numero tertio, habemus 600, <lb />689, 710, denſitates memoratorum fluidorum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit nunc aliunde notum pedem cubicum aquæ ponde-<lb />
<ptr xml:id="note-0312-02a" corresp="note-0312-02" type="noteAnchor" />
rarelibras 63. </s>
          <s xml:space="preserve">cum unciis 7. </s>
          <s xml:space="preserve">drachmis 2. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſcrup. </s>
          <s xml:space="preserve">2.</s>
          <s xml:space="preserve">: quod de-<lb />tegimus determinando pondus in aqua amiſſum a corpore cu-<lb />jus capacitas nota eſt. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> Uſus ego ſum cylindro cupreo cavo cu-
<ptr xml:id="note-0312-03a" corresp="note-0312-03" type="noteAnchor" />
jus latera exacte erant ſex poll. </s>
          <s xml:space="preserve">Rhenolandicorum. </s>
          <s xml:space="preserve">Pondus hoc <lb />valet gr. </s>
          <s xml:space="preserve">487360. </s>
          <s xml:space="preserve">dum volumen aquæ æquale vitro noſtro C <lb />ponderat grana 689; </s>
          <s xml:space="preserve">unde conſtat volumen hoc debere <lb />multiplicari per 707 {1/3} ut habeamus pedem cubicum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />multiplicatis per hunc numerum 710. </s>
          <s xml:space="preserve">habebimus grana in <lb />pede cubico lactis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hac methodo pondus pedis cubi-<lb />ci fluidi cujuſcunque detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0312-02" corresp="note-0312-02a" place="margin">783.</note>
              <note xml:space="preserve" xml:id="note-0312-03" corresp="note-0312-03a" n="*" anchored="true" place="margin">751.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT V.</head>
        <head xml:space="preserve">De hydroſtatica Solidorum Comparatione.</head>
        <p>
          <s xml:space="preserve">IN omnibus corporibus homogeneis, denſitates ſunt in ra-<lb />tione compoſita, ex directa ponderum &amp; </s>
          <s xml:space="preserve">inverſa vo-<lb />luminum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò dividendo pondera per volumina dantur
<ptr xml:id="note-0312-04a" corresp="note-0312-04" type="noteAnchor" />
denſitates, id eſt, dantur numeri, qui ſunt inter ſe ut hæ <lb />
<ptr xml:id="note-0312-05a" corresp="note-0312-05" type="noteAnchor" />
denſitates.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0312-04" corresp="note-0312-04a" n="*" anchored="true" place="margin">741.</note>
              <note xml:space="preserve" xml:id="note-0312-05" corresp="note-0312-05a" place="margin">784.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In omnibus corporibus, adhibita libra, pondera compa-<lb />
<ptr xml:id="note-0312-06a" corresp="note-0312-06" type="noteAnchor" />
rantur; </s>
          <s xml:space="preserve">volumina deteguntur immergendo corpora eodem <lb />fluido; </s>
          <s xml:space="preserve">pondera enim ab iis amiſſa ſunt ut ipſorum volumi-<lb />na <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0312-06" corresp="note-0312-06a" place="margin">785.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">756.</note>
        <pb facs="0313" n="223" />
        <fw type="head">MATHEMATICA. LIB. II. CAP IV.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head xml:space="preserve">Qua ſolidorum Corporum Denſitates conferuntur.</head>
        <p>
          <s xml:space="preserve">Hìc iterum bilanx hydroſtatica uſu venit <ptr type="noteAnchor" />, ut &amp; </s>
          <s xml:space="preserve">vas vi-
<ptr xml:id="note-0313-01a" corresp="note-0313-01" type="noteAnchor" />
treum ut D, cui corpora comparanda imponi poſſunt; </s>
          <s xml:space="preserve">re-<lb />
<ptr xml:id="note-0313-02a" corresp="note-0313-02" type="noteAnchor" />
quiritur etiam pondus ut P (fig.</s>
          <s xml:space="preserve">6.) </s>
          <s xml:space="preserve">quod cum hoc vaſe in <lb />
<ptr xml:id="note-0313-03a" corresp="note-0313-03" type="noteAnchor" />
aqua ſuſpenſum æquiponderet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0313-01" corresp="note-0313-01a" place="margin">786.</note>
              <note xml:space="preserve" xml:id="note-0313-02" corresp="note-0313-02a" place="margin">TAB XXXI <lb />fig 7.</note>
              <note xml:space="preserve" xml:id="note-0313-03" corresp="note-0313-03a" n="*" anchored="true" place="margin">705.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Annectitur, ope capilli equini, vas D, loco corporis C <lb />(vide fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">lanci A, &amp; </s>
          <s xml:space="preserve">aquâ immergitur, pondere P <lb />lanci B appenſo, datur æquilibrium. </s>
          <s xml:space="preserve">Corpus, cujus den-<lb />ſitas quæritur lanci A imponitur, &amp; </s>
          <s xml:space="preserve">ponderatur: </s>
          <s xml:space="preserve">Idem hoc <lb />corpus, reliquis manentibus in vas D, aquâ ut dictum immer-<lb />ſum, transfertur, lancique A imponitur quantum ponderis <lb />requiritur ut æquilibrium detur; </s>
          <s xml:space="preserve">hocque eft pondus a cor-<lb />pore in aquâ amiſſum, per hoc ergo ipſius corporis pondus <lb />dividendum eſt, ut habeamus denſitatem <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">id eſt dividi-
<ptr xml:id="note-0313-04a" corresp="note-0313-04" type="noteAnchor" />
mus pondus in lance B per pondus in lance A.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0313-04" corresp="note-0313-04a" n="*" anchored="true" place="margin">784.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi></head>
        <p>
          <s xml:space="preserve">In ſubjecta tabella habemus quorundam corporum pon-<lb />
<ptr xml:id="note-0313-05a" corresp="note-0313-05" type="noteAnchor" />
dera, &amp; </s>
          <s xml:space="preserve">pondera in aqua amiſſa, indeque deductas denſitates.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0313-05" corresp="note-0313-05a" place="margin">787.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin"> <lb /># Pondera \\ corporum. # Pondera in \\ aqua amiſſa. # Denſitates. <lb />Plumbum # 582 {1/2} gr. # 51 {1/2} gr. # 11, 31. <lb />Argentum # 439 {1/2} gr. # 42 {1/2} gr. # 10, 34. <lb />Cuprum # 474. gr. # 54. gr. # 8, 78. <lb />Æs calamin. # 356. gr. # 43. gr. # 8, 28. <lb />Ferrum # 329. gr. # 43 {1/4} gr. # 7, 60. <lb />Stannum # 534 {1/4} gr. # 71 {2/2} gr. # 7, 47. <lb />### Aquæ denſitas cum reliquis collata. # 1, 00. <lb /></note>
        <p>
          <s xml:space="preserve">Talis enim detegitur denſitas corporis, quod cum aqua <lb />eandem gravitatem fpecificam habet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hac methodo denſitates etiam corporum aquâ ſpecificè <lb />leviorum deteguntur, ſi ita cum vaſe jungantur ut hujus <lb />pondere in aquam trahantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Annectendo corpus cujus denſitas quæritur, &amp; </s>
          <s xml:space="preserve">quod flui-<lb />do gravius eſt, corpori fluido leviori, etiam denſitas dete-<lb />gitur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0314" n="224" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi>2.</head>
        <head rend="italics" xml:space="preserve">Qua Corporum ſolidorum Denſitates conferuntur.</head>
        <p>
          <s xml:space="preserve">Sit machina A, ſimilis machinæ in capite præcedenti de-<lb />
<ptr xml:id="note-0314-01a" corresp="note-0314-01" type="noteAnchor" />
ſcriptæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in inferiori parte cum hac cohæret annulus DE;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0314-02a" corresp="note-0314-02" type="noteAnchor" />
proprio pondere globus pro parte tantum aquâ immergitur. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0314-03a" corresp="note-0314-03" type="noteAnchor" />
Uſui hæc Machina adaptari nequit, niſi, quantum ponde-<lb />ris corpus quodcunque in aqua amittat, alia quacunque me-<lb />thodo conſtet; </s>
          <s xml:space="preserve">notumque ideo ponimus 109 {7/10} gr. </s>
          <s xml:space="preserve">plumbi <lb />in aqua ponderare 100 gr.</s>
          <s xml:space="preserve">; imponantur ideo tot gr. </s>
          <s xml:space="preserve">an-<lb />nulo DE, quo machina, in aquam immiſſa, deſcendit ad <lb />a; </s>
          <s xml:space="preserve">adjiciatur aliud pondus ad libitum quod Ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">in aqua <lb />valet grana octo, &amp; </s>
          <s xml:space="preserve">machina deſcendet ad c; </s>
          <s xml:space="preserve">ſpatium a c divi-<lb />datur in partes octo, diviſionesque ſurſum &amp; </s>
          <s xml:space="preserve">deorſum conti-<lb />nuentur, diviſioque a pro centeſima habeatur, diviſio c e-<lb />rit centeſima octava, omnium infima in hac figura erit nona-<lb />geſima ſeptima. </s>
          <s xml:space="preserve">Clare patet, ſi n. </s>
          <s xml:space="preserve">770 conferatur cum <lb />præparatione memorata, diviſionem, ad quam machina in <lb />aquam deſcendit, indicare pondus granorum, quo machi-<lb />na gravatur; </s>
          <s xml:space="preserve">impoſito ideò corpore annulo DE, illius <lb />pondus in aquâ determinatur; </s>
          <s xml:space="preserve">ſubtrahendo hocce pondus <lb />ab illius pondere extra aquam, datur pondus in aqua amiſ-<lb />ſum; </s>
          <s xml:space="preserve">per quod, ſi pondus extra aquam dividatur, denſitas, <lb />ut in principio hujus capitis dictum, detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0314-01" corresp="note-0314-01a" place="margin">788.</note>
              <note xml:space="preserve" xml:id="note-0314-02" corresp="note-0314-02a" place="margin">TAB. XXXI. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0314-03" corresp="note-0314-03a" n="*" anchored="true" place="margin">778</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum vero præcedens methodus &amp; </s>
          <s xml:space="preserve">magis compendioſa, <lb />
<ptr xml:id="note-0314-04a" corresp="note-0314-04" type="noteAnchor" />
quia &amp; </s>
          <s xml:space="preserve">in hoc librâ indigemus, &amp; </s>
          <s xml:space="preserve">magis accurata ſit hæc <lb />negligi poſſet, &amp; </s>
          <s xml:space="preserve">machinam ipſam non indicaſſem, niſi uſu <lb />veniret, ubi determinandum generaliter utrum corpora æ-<lb />qualiter ponderantia denſitate differant, quod, ubi monetæ ex-<lb />plorandæ ſunt, plerumque quæritur: </s>
          <s xml:space="preserve">Machina autem hæc, <lb />neglecta omni prævia præparatione hoc indicat, ſi ſucceſ-<lb />ſive impoſitis corporibus annulo, machina ad profundi-<lb />tates diverſas immergatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0314-04" corresp="note-0314-04a" place="margin">789.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si pondus pedis cubici aquæ <ptr type="noteAnchor" /> multiplicemus per
<ptr xml:id="note-0314-05a" corresp="note-0314-05" type="noteAnchor" />
numerum, qui corporis denſitatem exprimit, habemus <lb />
<ptr xml:id="note-0314-06a" corresp="note-0314-06" type="noteAnchor" />
pondus pedis cubici ipſius corporis, quæ ponderis deter-<lb />minatio in multis occaſionibus uſum magnum habet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0314-05" corresp="note-0314-05a" place="margin">790.</note>
              <note xml:space="preserve" xml:id="note-0314-06" corresp="note-0314-06a" n="*" anchored="true" place="margin">783.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0315" />
        <pb facs="0315a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0315a-01" />
          <label>0315a-01</label>
        </figure>
        <pb facs="0316" />
        <pb facs="0317" n="225" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. V.</fw>
        <p>
          <s xml:space="preserve">Præter hunc &amp; </s>
          <s xml:space="preserve">alium uſum collationis denſitatum indi-<lb />cabo.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si ex metallis duobus notis mixtum detur, poterit deter-<lb />
<ptr xml:id="note-0317-01a" corresp="note-0317-01" type="noteAnchor" />
minari quantum utriuſque contineat, ſi metallorum &amp; </s>
          <s xml:space="preserve">mixti <lb />denſitates dentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0317-01" corresp="note-0317-01a" place="margin">791.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint metallorum denſitates AB, AD; </s>
          <s xml:space="preserve">mixti denſitas AC. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0317-02a" corresp="note-0317-02" type="noteAnchor" />
Sint etiam AL &amp; </s>
          <s xml:space="preserve">LI, ut volumina metallorum primi &amp; </s>
          <s xml:space="preserve">ſe-<lb />cundi in mixto. </s>
          <s xml:space="preserve">Ponamus formatum rectangulum ABEI, <lb />ductaſque lineas CG, DH, FL, lateribus parallelas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0317-02" corresp="note-0317-02a" place="margin">TAB. XXXI. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondus primi metalli in mixtura rectangulo AF repræ-<lb />ſentari poteſt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">repræſentatque in hoc caſu rectangulum
<ptr xml:id="note-0317-03a" corresp="note-0317-03" type="noteAnchor" />
LH pondus metalli ſecundi, eſtque gnomon ABFMHIA <lb />pondus integri mixti; </s>
          <s xml:space="preserve">hoc etiam rectangulo ACGI exhi-<lb />betur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod idcirco gnomoni memorato æquale eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0317-03" corresp="note-0317-03a" n="*" anchored="true" place="margin">739.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">739</note>
        <p>
          <s xml:space="preserve">Subtracto utrimque gnomone communi CNMHI, re-<lb />ſtant æqualia rectangula BN, NH, ductaque DE tranſibit <lb />hæc per punctum N <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ergo DH, aut AI, ad NG,
<ptr xml:id="note-0317-05a" corresp="note-0317-05" type="noteAnchor" />
aut LI, ut HE ad GE; </s>
          <s xml:space="preserve">id eſt volumen mixti ad volu-<lb />
<ptr xml:id="note-0317-06a" corresp="note-0317-06" type="noteAnchor" />
men ſecundi metalli in mixto, ut differentia denſitatum me-<lb />tallorum primi &amp; </s>
          <s xml:space="preserve">ſecundi ad differentiam denſitatum metal-<lb />li primi &amp; </s>
          <s xml:space="preserve">mixti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0317-05" corresp="note-0317-05a" n="*" anchored="true" place="margin">43. El. Id</note>
              <note xml:space="preserve" xml:id="note-0317-06" corresp="note-0317-06a" place="margin">792.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondus autem totius mixturæ eſt ad pondus metalli ſe-<lb />
<ptr xml:id="note-0317-07a" corresp="note-0317-07" type="noteAnchor" />
cundi in mixto, in ratione compoſita denſitatum mixti &amp; </s>
          <s xml:space="preserve"><lb />ſecundi metalli, &amp; </s>
          <s xml:space="preserve">ratione voluminis mixti &amp; </s>
          <s xml:space="preserve">voluminis <lb />ſecundi metalli in mixto <ptr type="noteAnchor" />, id eſt ut productum denſitatis
<ptr xml:id="note-0317-08a" corresp="note-0317-08" type="noteAnchor" />
mixti per differentiam denſitatum metallorum ad denſita-<lb />tem ſecundi metalli ductamin differentiam denſitatum primi <lb />metalli &amp; </s>
          <s xml:space="preserve">mixti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0317-07" corresp="note-0317-07a" place="margin">793.</note>
              <note xml:space="preserve" xml:id="note-0317-08" corresp="note-0317-08a" n="*" anchored="true" place="margin">739.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0318" n="226" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">LIBRI II. Pars II.</head>
        <head xml:space="preserve">De Motu &amp; Reſiſtentiâ Fluidorum.</head>
        <head xml:space="preserve">CAPUT VI.</head>
        <head rend="italics" xml:space="preserve">De celeritate fluidi, ex preſſione fluidi ſuperincum-<lb />bentis.</head>
        <p>
          <s xml:space="preserve">FLuidum inferius a ſuperiori premitur, &amp; </s>
          <s xml:space="preserve">quidem <lb />æqualiter omnes partes verſus hæc preſſio dirigitur, &amp; </s>
          <s xml:space="preserve"><lb />æqualiter omnes partes verſus fluidum conatur recedere; <lb /></s>
          <s xml:space="preserve">idcirco ſi preſſio ab una parte tollatur, ad illam partem <lb />
<ptr xml:id="note-0318-01a" corresp="note-0318-01" type="noteAnchor" />
movetur fluidum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">non intereſt a quacunque parte preſſio <lb />tollatur, eadem celeritate movetur; </s>
          <s xml:space="preserve">quod Experimentis <lb />in capite de fluidis proſilientibus memorandis confirma-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0318-01" corresp="note-0318-01a" place="margin">794.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ad eandem profunditatem celeritas eſt etiam ubique ea-<lb />dem, propter preſſionis æqualitatem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">mutata vero pro-
<ptr xml:id="note-0318-02a" corresp="note-0318-02" type="noteAnchor" />
funditate mutatur celeritas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0318-02" corresp="note-0318-02a" n="*" anchored="true" place="margin">707. 708.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hanc dicimus preſſione communicari velocitatem, non <lb />
<ptr xml:id="note-0318-03a" corresp="note-0318-03" type="noteAnchor" />
autem particulas hanc cadendo acquirere: </s>
          <s xml:space="preserve">primæ enim par-<lb />ticulæ quæ exeunt, non lentius illis, quæ ſequuntur, moven-<lb />tur. </s>
          <s xml:space="preserve">Præterea non tantum exeunt quæ deſcendunt, ſed &amp; </s>
          <s xml:space="preserve"><lb />quæ lateraliter adfluunt; </s>
          <s xml:space="preserve">moveturque particula preſſione <lb />omnium particularum circumambientium exceptis illis quæ <lb />in motu præcedunt, &amp; </s>
          <s xml:space="preserve">ita particula, quæ deſcendit, non <lb />tam a ſuperincumbentibus a quibus ſtatim ſeparatur, cum <lb />ipſis velocius debeat agitari, ſed præcipue lateralium preſ-<lb />ſione velocitatem acquirit, duratque preſſio hæc, donec <lb />particula a reliquis ſeparatur, &amp; </s>
          <s xml:space="preserve">aliæ locum quem occupabat <lb />impleverint, &amp; </s>
          <s xml:space="preserve">non ulterius; </s>
          <s xml:space="preserve">ab inſequentibus enim, eàdem <lb />velocitate agitatis, accelerari non poteſt. </s>
          <s xml:space="preserve">Unde ſequitur a-
</s>
          <pb facs="0319" n="227" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. VI.</fw>
ctionem fluidi in particulam, qua actione velocitas particulæ <lb />communicatur, pendere a tali deſcenſu particularum quo <lb />locus a particula occupatus impletur. </s>
          <s xml:space="preserve">Deſcenſus autem hic-<lb />
<ptr xml:id="note-0319-01a" corresp="note-0319-01" type="noteAnchor" />
ce, ſi A ſit particula mota, cujus diameter ſit d e, quo-<lb />modocunque concipiatur, valet deſcenſum totius colu-<lb />mnæ BC ad profunditatem d e, poſitâ C in ſuperficie fluidi; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vis in hoc deſcenſu acquiſita tota impenditur actione <lb />in particulam motam, cui ergo vis communicatur æqualis <lb />illi quam columna hæc BD in deſcenſu hoc per d e acquirit, <lb />eſtque hæc æqualis illi quam particula acquireret cadendo <lb />ab altitudine CB <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0318-03" corresp="note-0318-03a" place="margin">795.</note>
              <note xml:space="preserve" xml:id="note-0319-01" corresp="note-0319-01a" place="margin">TAB XXXIII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">471.</note>
        <p>
          <s xml:space="preserve">Hinc ſequitur fluidum preſſione fluidi ſuperincumbentis, <lb />
<ptr xml:id="note-0319-03a" corresp="note-0319-03" type="noteAnchor" />
(ab hac enim pendet etiam preſſio lateralis) ex foramine <lb />ea proſilire velocitate, quam corpus acquirit cadendo à ſupre-<lb />ma fluidi ſuperficie ad for amen uſque; </s>
          <s xml:space="preserve">ſepoſitâ nempe, ut <lb />in hac demonſtratione, partium cobæſione, quæ licet exi-<lb />gua ſit, in fluidis plerisque tamen obſervatur; </s>
          <s xml:space="preserve">qua cohæ-<lb />ſione particulæ exeuntes retinentur; </s>
          <s xml:space="preserve">ideoque retardantur. <lb /></s>
          <s xml:space="preserve">Sed &amp; </s>
          <s xml:space="preserve">præter hanc retardationem, quæ ab ipſo fluido pen-<lb />det, ex variis aliis cauſis extraneis velocitas fluidi minuitur, <lb />de quibus in capite ſequenti agam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0319-03" corresp="note-0319-03a" place="margin">796.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi></head>
        <head rend="italics" xml:space="preserve">Qua Experimenta de Fluidis proſilientibus inſti-<lb />tuuntur.</head>
        <p>
          <s xml:space="preserve">Parallelopipedum ligneum AB, longitudinis &amp; </s>
          <s xml:space="preserve">latitudi-<lb />
<ptr xml:id="note-0319-04a" corresp="note-0319-04" type="noteAnchor" />
nis quindecim pollicum, &amp; </s>
          <s xml:space="preserve">altitudinis duorum pedum, a-<lb />
<ptr xml:id="note-0319-05a" corresp="note-0319-05" type="noteAnchor" />
quâ impletur; </s>
          <s xml:space="preserve">ita diſponitur ut fundus ejus elevetur circi-<lb />ter decem pollicibus ſupra fundum horizontalem arcæ li-<lb />gneæ CD, cujus longitudo eſt fere quatuor pedum, latitu-<lb />do unius pedis cum ſemiſſe, profunditas quinque aut ſex <lb />pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0319-04" corresp="note-0319-04a" place="margin">797.</note>
              <note xml:space="preserve" xml:id="note-0319-05" corresp="note-0319-05a" place="margin">TAB. XXXIII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In F, ad altitudinem circiter ſedecim pollicum ſupra fun-<lb />dum arcæ CD, hæret tubus æneus horizontalis, cujus ca-<lb />vitatis diameter excedit ſemipollicem; </s>
          <s xml:space="preserve">pars anterior lami-<lb />nâ clauditur, in cujus medio foramen datur diametri par-<lb />tis duodecimæ unius pollicis: </s>
          <s xml:space="preserve">foramen hocce clauditur o-
</s>
          <pb facs="0320" n="228" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
perculo, quo pars tubi anterior obtegitur, &amp; </s>
          <s xml:space="preserve">quod cum <lb />hoc ope cochleæ jungitur: </s>
          <s xml:space="preserve">duo tubi ſimiles aptantur in E <lb />circa fundum vaſis AB, &amp; </s>
          <s xml:space="preserve">in G, hicque ſupra F elevatur <lb />quantum ille infra F deprimitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Circa fundum etiam ejuſdem machinæ firmatur epiſto-<lb />mium N, cochleâ inſtructum ut ipſi tubus jungatur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>1.</head>
        <p>
          <s xml:space="preserve">Vas AB aqua impletur ita, ut altitudo ſuperficiei ſu-<lb />
<ptr xml:id="note-0320-01a" corresp="note-0320-01" type="noteAnchor" />
premæ aquæ ſupra fundum vaſis CD foramine in F in duas <lb />partes æquales dividatur, quæ ſingulæ in noſtra machina <lb />ſunt 15 {3/4}. </s>
          <s xml:space="preserve">pol. </s>
          <s xml:space="preserve">Aqua ex hoc foramine ad M proſilit, ita <lb />ut diſtantia horizontalis puncti M à foramine ſit 29 {1/2}. </s>
          <s xml:space="preserve">poll. </s>
          <s xml:space="preserve">duo-<lb />bus poll. </s>
          <s xml:space="preserve">deficiens ab altitudine aquæ ſupra fundum va-<lb />ſis CD; </s>
          <s xml:space="preserve">ſi ad diſtantiam 31 {1/2} poll. </s>
          <s xml:space="preserve">pertingeret, percurret <lb />aqua, motu æquabili, celeritate cum qua exit, in tempore <lb />in quo corpus cadere poteſt ab F ad fundum arcæ CD, <lb />fpatium, duplum hujus altitudinis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ideo agitaretur ce-
<ptr xml:id="note-0320-02a" corresp="note-0320-02" type="noteAnchor" />
leritate quam corpus ab hac altitudine cadendo poteſt ac-<lb />quirere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hæc autem altitudo æqualis eſt altitudini ſuper-
<ptr xml:id="note-0320-03a" corresp="note-0320-03" type="noteAnchor" />
ficiei aquæ ſupra foramen. </s>
          <s xml:space="preserve">Cum vero tantum pertingat ad <lb />diſtantiam 29 {1/2} poll. </s>
          <s xml:space="preserve">deficit vera aquæ velocitas a velocita-<lb />te memorata decima ſexta circiter parte.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0320-01" corresp="note-0320-01a" place="margin">798.</note>
              <note xml:space="preserve" xml:id="note-0320-02" corresp="note-0320-02a" n="*" anchored="true" place="margin">327.</note>
              <note xml:space="preserve" xml:id="note-0320-03" corresp="note-0320-03a" n="*" anchored="true" place="margin">257.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sepoſitis retardationibus, quadrata velocitatum, quibus <lb />
<ptr xml:id="note-0320-04a" corresp="note-0320-04" type="noteAnchor" />
fluidum ex variis foraminibus exit, ſunt inter ſe ut altitu-<lb />dines fluidi ſupra foramina <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Experimentis etiam conſtat
<ptr xml:id="note-0320-05a" corresp="note-0320-05" type="noteAnchor" />
retardationes parum admodum hanc proportionem turba-<lb />re quamdiu altitudines non excedunt pedes 30. </s>
          <s xml:space="preserve">aut 35. <lb /></s>
          <s xml:space="preserve">In minoribus altitudinibus proportionem hanc ſequenti Ex-<lb />perimento ante oculos ponimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0320-04" corresp="note-0320-04a" place="margin">799.</note>
              <note xml:space="preserve" xml:id="note-0320-05" corresp="note-0320-05a" n="*" anchored="true" place="margin">796. 255.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>2.</head>
        <p>
          <s xml:space="preserve">Uſu hîc venit Machina ſuperius memorata <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">circa
<ptr xml:id="note-0320-06a" corresp="note-0320-06" type="noteAnchor" />
exp. </s>
          <s xml:space="preserve">hoc notamus, diſtantias, ad quas proſilit aqua in fundo <lb />
<ptr xml:id="note-0320-07a" corresp="note-0320-07" type="noteAnchor" />
<ptr xml:id="note-0320-08a" corresp="note-0320-08" type="noteAnchor" />
arcæ CD, dum horizontaliter exit ex foramine ut E, po-<lb />fitis diverſis ſuperficiei aquæ altitudinibus, eſſe ſpatia hori-<lb />zontaliter motu æquabili percurſa, in tempore in quo cor-<lb />pus cadendo poteſt percurrere IL æqualem altitudini fora-
</s>
          <pb facs="0321" n="229" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. VII.</fw>
minis ſupra fundum arcæ <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">hasque idcirco diſtantias eſſe
<ptr xml:id="note-0321-01a" corresp="note-0321-01" type="noteAnchor" />
ut velocitates <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0320-06" corresp="note-0320-06a" place="margin">800.</note>
              <note xml:space="preserve" xml:id="note-0320-07" corresp="note-0320-07a" place="margin">TAB. XXXIII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0320-08" corresp="note-0320-08a" n="*" anchored="true" place="margin">797.</note>
              <note xml:space="preserve" xml:id="note-0321-01" corresp="note-0321-01a" n="*" anchored="true" place="margin">327.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">94.</note>
        <p>
          <s xml:space="preserve">Si nunc detur aqua in vaſe AB, ad altitudinem octo <lb />pollicum ſupra foramen in E, &amp; </s>
          <s xml:space="preserve">menſuretur diſtantia ad <lb />quam proſilit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">infuſâ ulterius aquâ, donec altitudo ſit octo-<lb />decim pollicum, iterum menſuretur diſtantia; </s>
          <s xml:space="preserve">erunt hæ <lb />ut 2. </s>
          <s xml:space="preserve">ad 3. </s>
          <s xml:space="preserve">Quadrata diſtantiarum ſunt hîc ut aquæ alti-<lb />tudines, in qua ratione quadrata celeritatum.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VII.</head>
        <head rend="italics" xml:space="preserve">De Fluidis proſilientibus.</head>
        <p>
          <s xml:space="preserve">FLuidum verticaliter ex foramine proſiliens, ea velocita-<lb />
<ptr xml:id="note-0321-03a" corresp="note-0321-03" type="noteAnchor" />
te in altum adſcendit, qua ad altitudinem ſupre-<lb />mæ ſuperficiei fluidi pervenire poteſt, nunquam tamen ad <lb />hanc altitudinem pertingit, variis ex cauſis, præter par-<lb />tium cohæſionem ſupra memoratam <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0321-03" corresp="note-0321-03a" place="margin">801.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">796.</note>
        <p>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Celeritas, qua fluidum in altum adſcendit, omnibus <lb />
<ptr xml:id="note-0321-05a" corresp="note-0321-05" type="noteAnchor" />
momentis minuitur, &amp; </s>
          <s xml:space="preserve">columna fluidi proſilientis conſtat <lb />ex partibus, ad varias altitudines, celeritate diverſa motis: <lb /></s>
          <s xml:space="preserve">columnæ ubique ejuſdem craſſitiei partes omnes neceſſario <lb />eadem celeritate moventur; </s>
          <s xml:space="preserve">prædicta columna fit ergo la-<lb />tior omnibus momentis, dum fluidi celeritas minuitur; </s>
          <s xml:space="preserve"><lb />quod ex impetu fluidi inſequentis oritur, &amp; </s>
          <s xml:space="preserve">ex natura flui-<lb />di impreſſioni cuicunque cedentis, &amp; </s>
          <s xml:space="preserve">facile verſus omnes <lb />partes moti; </s>
          <s xml:space="preserve">ex hoc impetu motus ubique retardatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0321-05" corresp="note-0321-05a" place="margin">802.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Minuitur &amp; </s>
          <s xml:space="preserve">hicce motus ex fluido, quod, cum totum <lb />motum amiſit, hæret in ſuperiori parte columnæ, &amp; </s>
          <s xml:space="preserve">flui-<lb />do inſequenti ſuſtinetur per momentum temporis, ante-<lb />quam ad latera defluat, quo fluidum hoc in ſequens retar-<lb />datur, quæ retardatio toti columnæ communicatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Attritu juxta latera foraminis minor eſt fluidi proſili-<lb />entis celeritas; </s>
          <s xml:space="preserve">qui attritus augetur, quando per tubos &amp; </s>
          <s xml:space="preserve"><lb />epiſtomia fluidum deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Tandem aëris reſiſtentia motui fluidorum remoram facit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cauſam primam retardationis memoratam corrigi mini-<lb />me poſſe nemo eſt qui non videt.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0322" n="230" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Secunda corrigitur paululum inclinando fluidi directio-<lb />nem, ut per ſe patet; </s>
          <s xml:space="preserve">hac de cauſa, fluidum, directione paululum <lb />
<ptr xml:id="note-0322-01a" corresp="note-0322-01" type="noteAnchor" />
ad horizontem inclinata, altius quâm verticaliter adſcendit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0322-01" corresp="note-0322-01a" place="margin">803.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum i</hi>.</head>
        <p>
          <s xml:space="preserve">Machinæ ſuperius deſcriptæ <ptr type="noteAnchor" />, ope cochleæ in N jun-
<ptr xml:id="note-0322-02a" corresp="note-0322-02" type="noteAnchor" />
gitur tubus curvus NO, ex quo aqua per foramen exiguum <lb />
<ptr xml:id="note-0322-03a" corresp="note-0322-03" type="noteAnchor" />
in altum proſilit verticaliter; </s>
          <s xml:space="preserve">convertendo paululum tubum, <lb />
<ptr xml:id="note-0322-04a" corresp="note-0322-04" type="noteAnchor" />
quod facile fit propter cochleam in N, inclinatur directio <lb />motus aquæ, &amp; </s>
          <s xml:space="preserve">altius hæc adſcendit. </s>
          <s xml:space="preserve">Hac autem inclina-<lb />tione ſpectaculi amœnitas deſtruitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0322-02" corresp="note-0322-02a" place="margin">804.</note>
              <note xml:space="preserve" xml:id="note-0322-03" corresp="note-0322-03a" place="margin">TAB. XXXIII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0322-04" corresp="note-0322-04a" n="*" anchored="true" place="margin">797.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa tertiam cauſam retardationis notandum, eo majo-<lb />rem, ſervata proportione, dari attritum quo foramen mi-<lb />nus eſt; </s>
          <s xml:space="preserve">circumferentia enim, in qua attritus datur, creſcit <lb />ut diameter, &amp; </s>
          <s xml:space="preserve">ipſum foramen augetur ut quadratum dia-<lb />metri <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">augeturque magis fluidi proſilientis quantitas quàm
<ptr xml:id="note-0322-05a" corresp="note-0322-05" type="noteAnchor" />
attritus. </s>
          <s xml:space="preserve">Etiam auctâ celeritate attritum augeri clarum eſt, <lb />quare foramina cum altitudine aquæ proſilientis ſunt augenda, <lb />
<ptr xml:id="note-0322-06a" corresp="note-0322-06" type="noteAnchor" />
ut dum ex una cauſa attritus augetur, ex alia minua-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0322-05" corresp="note-0322-05a" n="*" anchored="true" place="margin">El. XII.</note>
              <note xml:space="preserve" xml:id="note-0322-06" corresp="note-0322-06a" place="margin">805.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Extremitates tuborum, ex quibus aqua proſilit, vulgo <lb />
<ptr xml:id="note-0322-07a" corresp="note-0322-07" type="noteAnchor" />
figuram coni truncati habent, ut in P repræſentatur; </s>
          <s xml:space="preserve">in <lb />qua extremitate magnum aqua attritum patitur &amp; </s>
          <s xml:space="preserve">irregula-<lb />riter movetur, motuque irregulari in altum exit. </s>
          <s xml:space="preserve">Corri-<lb />guntur hæc obtegendo extremitatem tubi laminâ planâ &amp; </s>
          <s xml:space="preserve">po-<lb />
<ptr xml:id="note-0322-08a" corresp="note-0322-08" type="noteAnchor" />
litâ, in qua foramen datur, cujus latera admodum polita <lb />etiam deſiderantur; </s>
          <s xml:space="preserve">altius tunc aqua proſilit; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, quia <lb />motu omnino regulari adſcendit, perfecte eſt transluci-<lb />da.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0322-07" corresp="note-0322-07a" place="margin">TAB. XXXIII. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0322-08" corresp="note-0322-08a" place="margin">806.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>2.</head>
        <p>
          <s xml:space="preserve">Detur tubus memoratus P, ut &amp; </s>
          <s xml:space="preserve">cylindrus Q, ab una <lb />
<ptr xml:id="note-0322-09a" corresp="note-0322-09" type="noteAnchor" />
parte, laminâ perforatâ, clauſus; </s>
          <s xml:space="preserve">hi ſeparatim ope cochleæ <lb />
<ptr xml:id="note-0322-10a" corresp="note-0322-10" type="noteAnchor" />
jungantur extremitati O tubi NO (fig. </s>
          <s xml:space="preserve">2.)</s>
          <s xml:space="preserve">; </s>
          <s xml:space="preserve">manente aqua <lb />ad eandem altitudinem in vaſe AB, ſi proſiliat ex tubo P, <lb />&amp; </s>
          <s xml:space="preserve">ex cylindro Q, duorum pollicum ad minimum in hac <lb />exigua altitudine differentia dabitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0322-09" corresp="note-0322-09a" place="margin">807.</note>
              <note xml:space="preserve" xml:id="note-0322-10" corresp="note-0322-10a" place="margin">TAB. XXXIII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tubi, per quos aqua ex receptaculo deducitur, latiſſi-<lb />
<ptr xml:id="note-0322-11a" corresp="note-0322-11" type="noteAnchor" />
</s>
          <pb facs="0323" n="231" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. VII.</fw>
mi, reſpectu foraminis, requiruntur; </s>
          <s xml:space="preserve">ut lente aqua in hiſ-<lb />ce tubis moveatur, &amp; </s>
          <s xml:space="preserve">ſenſibilis attritus non detur. </s>
          <s xml:space="preserve">Etiam <lb />epiſtomiorum aperturæ latiſſimæ deſiderantur, ut attritus mi-<lb />nuatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0322-11" corresp="note-0322-11a" place="margin">808.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>3.</head>
        <p>
          <s xml:space="preserve">Vaſi AB, ad eandem altitudinem cum tubo F, inſeri-<lb />
<ptr xml:id="note-0323-01a" corresp="note-0323-01" type="noteAnchor" />
tur epiſtomium H; </s>
          <s xml:space="preserve">tubus, in quo epiſtomium datur, lami-<lb />
<ptr xml:id="note-0323-02a" corresp="note-0323-02" type="noteAnchor" />
nâ clauditur eodem modo ac tubus F, &amp; </s>
          <s xml:space="preserve">ſimiliter hæc la-<lb />mina perforatur; </s>
          <s xml:space="preserve">ipſius epiſtomii apertura eſt quartæ partis <lb />unius pollicis. </s>
          <s xml:space="preserve">Aqua, quæ per hoc epiſtomium tranſit, in <lb />ſpatium magis anguſtum redigitur quàm quæ per tubum F <lb />movetur; </s>
          <s xml:space="preserve">hæc magis eſt tranſiucida, &amp; </s>
          <s xml:space="preserve">ad majorem diſtan-<lb />tiam proſilit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0323-01" corresp="note-0323-01a" place="margin">809.</note>
              <note xml:space="preserve" xml:id="note-0323-02" corresp="note-0323-02a" place="margin">TAB. XXXIII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reſiſtentia aëris ſenſibilem in motu fluidorum exerit effe-<lb />
<ptr xml:id="note-0323-03a" corresp="note-0323-03" type="noteAnchor" />
ctum. </s>
          <s xml:space="preserve">Ut corpora omnia motui reſiſtit, daturque fluidi <lb />proſilientis in particulas aëreas actio, &amp; </s>
          <s xml:space="preserve">harum reactione <ptr type="noteAnchor" />,
<ptr xml:id="note-0323-04a" corresp="note-0323-04" type="noteAnchor" />
minuitur fluidi motus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0323-03" corresp="note-0323-03a" place="margin">810.</note>
              <note xml:space="preserve" xml:id="note-0323-04" corresp="note-0323-04a" n="*" anchored="true" place="margin">478.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Præter hanc reſiſtentiam, datur &amp; </s>
          <s xml:space="preserve">alia minime conte-<lb />mnenda aëris actio in fluidum proſiliens. </s>
          <s xml:space="preserve">Fluidorum proprie-<lb />tates aërem habere, in Parte ſequenti videbimus. </s>
          <s xml:space="preserve">Circumdat <lb />fluidum hoc totam columnam fluidi ſalientis, motuique hu-<lb />jus, quo ad latera ſeſe expandit dum latior fit, reſiſtit, &amp; </s>
          <s xml:space="preserve"><lb />major vis fluidi inſequentis requiritur, quàm ſi reſiſtentia <lb />hæc ſublata eſſet; </s>
          <s xml:space="preserve">reſiſtit ergo aër etiam preſſione laterali.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Reſiſtentia ex fluidi ictu in aërem creſcit cum ſuperficie im-<lb />pingenti, id eſt, ſi maneat celeritas, augetur cum forami-<lb />ne, in qua etiam ratione creſcit quantitas materiæ motæ, <lb />&amp; </s>
          <s xml:space="preserve">hujus reſpectu non intereſt cujuſcunque magnitudinis <lb />fuerit foramen.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Preſſio lateralis ſequitur proportionem ſuperficiei colu-<lb />mnæ; </s>
          <s xml:space="preserve">materia mota, quæ manente celeritate ſequitur ra-<lb />tionem ipſius vis inſitæ <ptr type="noteAnchor" />, ad inſtar totius columnæ, id eſt,
<ptr xml:id="note-0323-05a" corresp="note-0323-05" type="noteAnchor" />
quadrati ſuperficiei hujus mutatur: </s>
          <s xml:space="preserve">magis ergo, ſi foramen <lb />augeatur, creſcit vis fluidi quàm ipſa cauſa retardans; <lb /></s>
          <s xml:space="preserve">in majoribus ideo fluidorum proſilientium altitudinibus, ut <lb />
<ptr xml:id="note-0323-06a" corresp="note-0323-06" type="noteAnchor" />
preſlio lateralis, quæ, cum diutius agat majorem actionem
</s>
          <pb facs="0324" n="232" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
exerit, melius ſuperari poſſit, major a deſiderantur foramina, <lb />quod &amp; </s>
          <s xml:space="preserve">in eodem caſu ex alia cauſa requiri antea diximus <ptr type="noteAnchor" />:</s>
          <s xml:space="preserve">
<ptr xml:id="note-0324-01a" corresp="note-0324-01" type="noteAnchor" />
in quo loco ut &amp; </s>
          <s xml:space="preserve">hìc majora foramina in majoribus tantum <lb />altitudinibus neceſſaria ponimus, licet demonſtrationes pro-<lb />bent hæc foramina, in majoribus altitudinibus maxime ne-<lb />ceſſaria, in genere eſſe anteponenda.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0323-05" corresp="note-0323-05a" n="*" anchored="true" place="margin">450.</note>
              <note xml:space="preserve" xml:id="note-0323-06" corresp="note-0323-06a" place="margin">811.</note>
              <note xml:space="preserve" xml:id="note-0324-01" corresp="note-0324-01a" n="*" anchored="true" place="margin">205.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magna foramina etiam motui obſtant; </s>
          <s xml:space="preserve">nam 1. </s>
          <s xml:space="preserve">Major da-<lb />
<ptr xml:id="note-0324-02a" corresp="note-0324-02" type="noteAnchor" />
tur ſuperficies, cui incumbit fluidum altiſſimum, quod to-<lb />tum motum amiſit, ibique diutius hæret antequam ad late-<lb />ra defluat. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Fluidum non tantum illud ex foramine exit, <lb />quod huic reſpondet, ſed, ut fluxus continuus detur, flui-<lb />dum vicinum continuo adfluit, quod oblique movetur, &amp; </s>
          <s xml:space="preserve"><lb />dum proſilit motu compoſito agitatur, quo motus fluidi <lb />proſilientis turbatur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in majoribus foraminibus major eſt <lb />perturbatio ex hac cauſa oriunda.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0324-02" corresp="note-0324-02a" place="margin">812.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In minoribus foraminibus prævalent retardationes, quæ, <lb />aucto foramine, corriguntur; </s>
          <s xml:space="preserve">ita tamen poteſt augeri fora-<lb />men, ut hæ prævaleant tardationes, quæ aucto foramine <lb />creſcunt. </s>
          <s xml:space="preserve">Quare datur in omnibus altitudinibus certa fora-<lb />
<ptr xml:id="note-0324-03a" corresp="note-0324-03" type="noteAnchor" />
minis menſura, per quod fluidum ad maximam quam poteſt <lb />adſcendit altitudinem. </s>
          <s xml:space="preserve">Regulæ tamen de determinando fora-<lb />mine dari nequeunt, quia latitudo tuborum, per quos aqua <lb />deducitur, horumque inflexiones illud mutant, ita ut va-<lb />riatio in infinitum detur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0324-03" corresp="note-0324-03a" place="margin">813.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Notandum autem altitudinem, ad quam fluidum adſcen-<lb />
<ptr xml:id="note-0324-04a" corresp="note-0324-04" type="noteAnchor" />
dere poteſt, ut &amp; </s>
          <s xml:space="preserve">for aminis magnitudinem, limites habere, <lb />quos excedere vetitum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0324-04" corresp="note-0324-04a" place="margin">814.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nam aucta nimium fluidi celeritate, tanta vi in aërem <lb />impingit, ut in guttas diſpergatur; </s>
          <s xml:space="preserve">in quo caſu minuendo <lb />celeritatem altitudo ad quam adſcendit fluidum augetur, <lb />&amp; </s>
          <s xml:space="preserve">altitudo omnium maxima ad quam fluidum adſcendere <lb />poteſt in diverſis fluidis differt; </s>
          <s xml:space="preserve">hæcque in aqua proſilien-<lb />ti, vix centum pedes ſuperat. </s>
          <s xml:space="preserve">Diameter foraminis, quod <lb />huic maximæ altitudini reſpondet, vix excedit pollicem cum <lb />quarta parte.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0325" n="233" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. VII.</fw>
        <p>
          <s xml:space="preserve">Fluida, quæ oblique proſiliunt, non ex tot cauſis, neque <lb />
<ptr xml:id="note-0325-01a" corresp="note-0325-01" type="noteAnchor" />
tantum, quàm verticaliter proſilientiaretardantur. </s>
          <s xml:space="preserve">Secun-<lb />da retardationis cauſa antea memorata <ptr type="noteAnchor" /> hîc locum non ha-
<ptr xml:id="note-0325-02a" corresp="note-0325-02" type="noteAnchor" />
bet, &amp; </s>
          <s xml:space="preserve">effectus primæ minor eſt. </s>
          <s xml:space="preserve">De cætero in his locum <lb />habent, quæ de ſolidis oblique projectis dicta ſunt in capite <lb />20. </s>
          <s xml:space="preserve">libri primi, &amp; </s>
          <s xml:space="preserve">fluidum ut innumera ſolida ſeſe mutuo <lb />
<ptr xml:id="note-0325-03a" corresp="note-0325-03" type="noteAnchor" />
inſequentia, &amp; </s>
          <s xml:space="preserve">eandem viam percurrentia, conſiderari <lb />poteſt. </s>
          <s xml:space="preserve">In motu fluidi via percurſa ſenſibilis eſt, &amp; </s>
          <s xml:space="preserve">quæ <lb />de ſolidis oblique projectis dicta ſunt ope fluidorum ad <lb />Experimentum vocantur; </s>
          <s xml:space="preserve">ad quod hydrargyro utendum, <lb />propter hujus fluidi, præ cæteris, gravitatem ſpecificam. <lb /></s>
          <s xml:space="preserve">Hæc autem Machinâ peculiari inſtituenda ſunt Experimen-<lb />ta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0325-01" corresp="note-0325-01a" place="margin">815.</note>
              <note xml:space="preserve" xml:id="note-0325-02" corresp="note-0325-02a" n="*" anchored="true" place="margin">802.</note>
              <note xml:space="preserve" xml:id="note-0325-03" corresp="note-0325-03a" place="margin">816.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi>,</head>
        <head rend="italics" xml:space="preserve">Qua inſtituuntur Experimenta de Fluidis oblique <lb />proſilientibus.</head>
        <p>
          <s xml:space="preserve">Arca lignea ABCDEFH longitudinis eſt quatuor pe-<lb />
<ptr xml:id="note-0325-04a" corresp="note-0325-04" type="noteAnchor" />
dum cum ſemiſſe, latitudinis octo aut decem pollicum, alti-<lb />
<ptr xml:id="note-0325-05a" corresp="note-0325-05" type="noteAnchor" />
tudinis ſex aut ſeptem pollicum. </s>
          <s xml:space="preserve">Fundus conſtat ex tabula <lb />lignea excavata ad profunditatem ſemi-pollicis, ut melius mer-<lb />curium contineat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0325-04" corresp="note-0325-04a" place="margin">817.</note>
              <note xml:space="preserve" xml:id="note-0325-05" corresp="note-0325-05a" place="margin">TAB. XXXII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In extremitate H, lateris EFH, datur aſſer, aut tabula, <lb />HI, latitudinis ſex pollicum, altitudinis duorum pedum, <lb />in qua datur ſciſſura o t. </s>
          <s xml:space="preserve">Hujus ope parallelopipedum li-<lb />gneum s, cuia poſteriori parte cochlea cohæret, ad altitu-<lb />dinem quamcunque firmatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Parallelopipedum hoc videtur in S (fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">huic additur <lb />pyxis buxea cylindrica P, quæ ſulco circumdatur, cui in-<lb />ſeruntur laminæ duæ æneæ, quarum una videtur in fe, ha-<lb />rum extremitates junguntur cochleâ g, qua pyxis immobilis <lb />redditur, hæc vero circa axem eſt volubilis, quando relaxa-<lb />tur paululum cochlea.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In fundo hujus pyxidis datur cavitas cylindrica ab, diame-<lb />tri quartæ partis unius pollicis. </s>
          <s xml:space="preserve">Habet hæc communicatio-<lb />nem cum ſimili cavitate b c, quæ terminatur in medio cavi-<lb />tatis majoris c d, cujus diameter ſemi-pollicem excedit, &amp;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0326" n="234" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cui inſeritur conus truncatus H (fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">buxeus, cujus exte-<lb />rior ſuperficies, cum interiori cavitatis ſuperficie congruit <lb />ita, ut conus circa axem in hac cavitate rotari poſſit, dum <lb />firmiter retinetur cochleâ R, laminam æneam QO trajici-<lb />ente.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ad angulos rectos cohæret conus truncatus H cum <lb />cylindro IL, conumque cum cylindro flexa trajicit <lb />cavitas b i l, ejuſdem diametri cum cavitate b c, &amp; </s>
          <s xml:space="preserve">huic <lb />reſpondens. </s>
          <s xml:space="preserve">Latior autem illa eſt in L, ut ipſi inſeratur tu-<lb />bus vitreus NM.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tubilongitudo eſt ſeſqui pedis, extremitas altera videtur <lb />in NM, (fig. </s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">quæ inſeritur cylindro buxeo LI ad for-<lb />mam gnomonis excavati in l i b; </s>
          <s xml:space="preserve">in b c datur cavitas ma-<lb />jor, cui inſeritur conus truncatus ED, quo hæc exacte re-<lb />pletur, &amp; </s>
          <s xml:space="preserve">qui in hac circa axem convertitur, ope manu-<lb />brii EA.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cavitas b i reſpondet cavitati d e, quæ communicatur cum <lb />f g; </s>
          <s xml:space="preserve">pars hæc buxi annulo ferreo BQ circumdatur, in quo <lb />exiguum admodum datur foramen g, quod, partibus ma-<lb />chinæ junctis, cum cavitate pyxidis P (fig. </s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">communica-<lb />tionem habet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ne tubus frangatur, extremitates L, L, cylindrorum bu-<lb />xeorum (fig. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">cum tubo applicantur regulæ ligneæ <lb />m n (fig. </s>
          <s xml:space="preserve">1.)</s>
          <s xml:space="preserve">. </s>
          <s xml:space="preserve">Cum hujus extremitate inferiori m jungitur <lb />lamina ferrea, (ut videtur in fig. </s>
          <s xml:space="preserve">6.) </s>
          <s xml:space="preserve">cujus extremitas LPBQ <lb />gnomonis duplicati ſpeciem fert: </s>
          <s xml:space="preserve">cum extremitas L (fig. <lb /></s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">cylindri buxei applicetur extremitati regulæ MN, I <lb />fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">cum I fig. </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">congruit, &amp; </s>
          <s xml:space="preserve">cochlea Q in o comprimit <lb />cylindrum BD fig. </s>
          <s xml:space="preserve">5.</s>
          <s xml:space="preserve">, huncque firmiter cum cylindro LI <lb />conjungit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Machinæ omnes partes conjunctæ videntur in fig. </s>
          <s xml:space="preserve">1.</s>
          <s xml:space="preserve">; hy-<lb />drargyrum pyxidi p infunditur, &amp; </s>
          <s xml:space="preserve">ex foramine g fig. </s>
          <s xml:space="preserve">5. <lb /></s>
          <s xml:space="preserve">proſilit. </s>
          <s xml:space="preserve">Manente mercurio ad eandem altitudinem in pyxi-<lb />de, &amp; </s>
          <s xml:space="preserve">non variata regulæ n m inclinatione, eadem cum ce-<lb />leritate, juxta directionem quamcunque, proſilit hydrargy-<lb />rum; </s>
          <s xml:space="preserve">variatur autem inclinatio directionis, motu manubrii
</s>
          <pb facs="0327" n="235" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. VII.</fw>
e a (EA in fig. </s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">Angulus a directione, juxta quam mer-<lb />curius ex foramine exit, cum horizonte formatus menſura-<lb />tur ope quadrantis circuli diviſi q, juxta quem movetur in-<lb />dex f b, qui pondere ſuo ſemper in ſitu verticali retinetur. <lb /></s>
          <s xml:space="preserve">Quadrans hicce videtur in fig. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">index eſt FH. </s>
          <s xml:space="preserve">A poſteriori <lb />parte duo dantur annuli, per quos tranſit manubrium EA <lb />fig. </s>
          <s xml:space="preserve">5.</s>
          <s xml:space="preserve">; quando manubrium hocce eſt in ſitu verticali, index <lb />cum diviſione anguli 45. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">congruit, &amp; </s>
          <s xml:space="preserve">directio motus mer-<lb />curii exeuntis in eo caſu angulum ſemi-rectum cum hori-<lb />zonte efficit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">proſilitiones mercurii juxta varias directiones re-<lb />præſentantur: </s>
          <s xml:space="preserve">ſenſibiles hæ redduntur ope tabulæ ligneæ G, <lb />nigro colore tinctæ, quam mercurius in motu ſuo fere ra-<lb />dit; </s>
          <s xml:space="preserve">in hac, quod hìc repræſentari non potuit, ſecundum di-<lb />cta in n. </s>
          <s xml:space="preserve">331.</s>
          <s xml:space="preserve">, delineantur viæ a corpore, eadem celeritate, <lb />juxta directiones varios angulos cum horizonte ſormantes, <lb />percurſæ; </s>
          <s xml:space="preserve">ſemi-circulus etiam AL fig. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">XIII. </s>
          <s xml:space="preserve">in <lb />hac tabula deſcribitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Variæ tales tabulæ dantur, in quibus hæc eadem pro <lb />diverſis celeritatibus repræſentantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tabula fere in medio arcæ erigitur, &amp; </s>
          <s xml:space="preserve">cohæret cum la-<lb />tere EFH, ita ut juxta longitudinem pyxidis moveri poſ-<lb />ſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Celeritas mercurii proſilientis variatur mutando inclina-<lb />tionem regulæ n m, &amp; </s>
          <s xml:space="preserve">deſcenſu pyxidis p; </s>
          <s xml:space="preserve">apertura, ex qua <lb />proſilit hydrargyrum, ad altitudinem delineationi in tabula <lb />congruentem diſponitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Siſtitur hydrargyri proſilitio obturando cavitatem a b (fig. <lb /></s>
          <s xml:space="preserve">2.) </s>
          <s xml:space="preserve">paxillo DE (fig. </s>
          <s xml:space="preserve">4.)</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Partibus Machinæ conjunctis, &amp; </s>
          <s xml:space="preserve">diſpoſitis, ut in deſcri-<lb />
<ptr xml:id="note-0327-01a" corresp="note-0327-01" type="noteAnchor" />
ptione dictum, inclinetur regula n m, donec altitudo, ad quam <lb />
<ptr xml:id="note-0327-02a" corresp="note-0327-02" type="noteAnchor" />
proſilit mercurius, quando directione, quæ a verticali pau-<lb />lulum admodum divergit, in altum adſcendit, fere æquet <lb />diametrum ſemi-circuli in tabula G delineati. </s>
          <s xml:space="preserve">Ad talem <lb />altitudinem pyxis p conſtituatur, &amp; </s>
          <s xml:space="preserve">tabula G diſponatur,
</s>
          <pb facs="0328" n="236" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ut axis circumvolutionis cylindri BD (fig. </s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">reſpondeat <lb />puncto infimo ſemi-circuli memorati. </s>
          <s xml:space="preserve">Quomodocunque in-<lb />clinetur jactus directio, hujus amplitudo ſemper erit fere <lb />quadruplum lineæ BM in ſemi-circulo ABL (Tab. </s>
          <s xml:space="preserve">XIII. <lb /></s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">Exigua quædam datur differentia, quæ præcipue <lb />ex aëris reſiſtentia oritur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0327-01" corresp="note-0327-01a" place="margin">818.</note>
              <note xml:space="preserve" xml:id="note-0327-02" corresp="note-0327-02a" place="margin">TAB. XXXII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Machinâ, ut in præcedenti Experimento, diſpoſitâ, ſi pro-<lb />
<ptr xml:id="note-0328-01a" corresp="note-0328-01" type="noteAnchor" />
ſiliat hydrargyrum per duas directiones, quarum unius incli-<lb />natio angulum ſemi-rectum excedit, quantum alterius incli-<lb />natio ab hoc deficit, mercurius in punctis, parum diſtanti-<lb />bus ſecabit lineam horizontalem, quæ per ſemi-circuli, in <lb />tabula G delineati, punctum infimum tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0328-01" corresp="note-0328-01a" place="margin">819.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Manente Machinæ diſpoſitione, ſi via pro quacunque mo-<lb />
<ptr xml:id="note-0328-02a" corresp="note-0328-02" type="noteAnchor" />
tus directione in tabula, ut in Machinæ deſcriptione dictum, <lb />delineata ſit, &amp; </s>
          <s xml:space="preserve">index f b cum diviſione quadrantis, hanc <lb />denotans inclinationem, congruat, hydrargyrum in motu <lb />ſuo a via delineata parum aberrabit. </s>
          <s xml:space="preserve">Si pro variis angulis viæ <lb />delineantur, motu manubrii a e ſucceſſive hoc idem in di-<lb />verſis hiſce viis obſervari poterit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0328-02" corresp="note-0328-02a" place="margin">820.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Si alia tabula ut G adhibeatur, in qua prædicta pro alia <lb />
<ptr xml:id="note-0328-03a" corresp="note-0328-03" type="noteAnchor" />
mercurii celeritate ſunt delineata, Experimenta eodem mo-<lb />do procedunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0328-03" corresp="note-0328-03a" place="margin">821.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simili methodo, qua per ſemi-circulum determinatur di-<lb />ſtantia, ad quam corpora oblique projecta cadunt, detegitur <lb />diſtantia, ad quam fluidum ex foramine in latere vaſis pro-<lb />ſilit, quando vas plano horizontali imponitur: </s>
          <s xml:space="preserve">diverſa eſt hæc <lb />diſtantia pro varia foraminis altitudine, manente ſuperficie <lb />ſuperiori fluidi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit AB vaſis fluido repleti altitudo; </s>
          <s xml:space="preserve">ſecetur hæc in duas <lb />
<ptr xml:id="note-0328-04a" corresp="note-0328-04" type="noteAnchor" />
partes æquales in C; </s>
          <s xml:space="preserve">centro C &amp; </s>
          <s xml:space="preserve">radio EA ſemi-circu-<lb />
<ptr xml:id="note-0328-05a" corresp="note-0328-05" type="noteAnchor" />
lus deſcribatur; </s>
          <s xml:space="preserve">detur foramen in E; </s>
          <s xml:space="preserve">tandem ducatur ad <lb />AB perpendicularis ED in ſemi circuli circumferentia ter-<lb />minata in D. </s>
          <s xml:space="preserve">Proſiliat fluidum ex E ad F in plano borizon-
</s>
          <pb facs="0329" />
          <s xml:space="preserve">
<pb facs="0329a" />
<ptr xml:id="fig-0329a-01a" corresp="fig-0329a-01" type="figureAnchor" />
<pb facs="0330" />
<pb facs="0331" n="237" /><fw type="head">MATHEMATICA. LIB. II. CAP. VII.</fw>
tali, diſtantia BF, ſepoſitis omnibus retardationibus, du-<lb />pla erit ipſius perpendicularis ED.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0328-04" corresp="note-0328-04a" place="margin">822.</note>
              <note xml:space="preserve" xml:id="note-0328-05" corresp="note-0328-05a" place="margin">TAB. XXXII. <lb />fig. 4.</note>
              <figure xml:id="fig-0329a-01" corresp="fig-0329a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0329a-01" />
                <label>0329a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quod ut demonſtretur, conſiderandum fluidum, mo-<lb />tu æquabili, celeritate qua ex foramine exit, in tempore <lb />in quo corpus cadere poteſt ab E ad B, percurrere ſpatium <lb />BF <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In omni motu, ſpatium percurſum ſequitur rationem
compoſitam celeritatis &amp; </s>
          <s xml:space="preserve">temporis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hoc per illam mul-
<ptr xml:id="note-0331-01a" corresp="note-0331-01" type="noteAnchor" />
tiplicando datur ſpatium percurſum; </s>
          <s xml:space="preserve">id eſt, ſi pro variis <lb />motibus hæc inſtituatur operatio, dantur quantitates, quæ <lb />ſpatiorum percurſorum proportionem exprimunt. </s>
          <s xml:space="preserve">Si cum <lb />quadratis celeritatum &amp; </s>
          <s xml:space="preserve">temporum computatio ineatur, da-<lb />bitur ratio quadratorum ſpatiorum percurſorum. </s>
          <s xml:space="preserve">AE hìc de-<lb />ſignat quadratum celeritatis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">EB autem quadratum tem-
poris <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">harum linearum productum exprimit ergo qua-
<ptr xml:id="note-0331-02a" corresp="note-0331-02" type="noteAnchor" />
dratum ſpatii percurſi BF. </s>
          <s xml:space="preserve">Hocce autem productum eſt <lb />
<ptr xml:id="note-0331-03a" corresp="note-0331-03" type="noteAnchor" />
quadratum lineæ ED; </s>
          <s xml:space="preserve">quæ idcirco, mutato foramine, <lb />creſcit &amp; </s>
          <s xml:space="preserve">minuitur in eadem ratione cum diſtantia BF. </s>
          <s xml:space="preserve">Po-<lb />ſito foramine in centro C, diſtantia BG, ad quam flui-<lb />dum proſilit, ſepoſitis omnibus retardationibus, ipſi BA <lb />æqualis eſt <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">eſt dupla perpendicularis, quæ in C ad
<ptr xml:id="note-0331-04a" corresp="note-0331-04" type="noteAnchor" />
AB in ſemi-circulo duci poteſt; </s>
          <s xml:space="preserve">quod ergo in omni-<lb />bus foraminibus obtinet, &amp; </s>
          <s xml:space="preserve">ED erit dimidium ipſius <lb />BF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0331-01" corresp="note-0331-01a" n="*" anchored="true" place="margin">95.</note>
              <note xml:space="preserve" xml:id="note-0331-02" corresp="note-0331-02a" n="*" anchored="true" place="margin">799.</note>
              <note xml:space="preserve" xml:id="note-0331-03" corresp="note-0331-03a" n="*" anchored="true" place="margin">255.</note>
              <note xml:space="preserve" xml:id="note-0331-04" corresp="note-0331-04a" n="*" anchored="true" place="margin">796. 798.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ex hiſce ſequitur fluidum ex foramine in centro C ad <lb />
<ptr xml:id="note-0331-05a" corresp="note-0331-05" type="noteAnchor" />
diſtantiam omnium maximam proſilire.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0331-05" corresp="note-0331-05a" place="margin">823.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Utendum hìc machina in capite præcedenti deſcri-<lb />
<ptr xml:id="note-0331-06a" corresp="note-0331-06" type="noteAnchor" />
pta <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Proſiliat aqua ex foramine F, ut in Expe-
<ptr xml:id="note-0331-07a" corresp="note-0331-07" type="noteAnchor" />
rimento 1. </s>
          <s xml:space="preserve">Capitis VI. </s>
          <s xml:space="preserve">proſiliat eodem tempore <lb />
<ptr xml:id="note-0331-08a" corresp="note-0331-08" type="noteAnchor" />
ex E, ut &amp; </s>
          <s xml:space="preserve">ex G; </s>
          <s xml:space="preserve">foramen G minus quam F, fo-<lb />ramen F, vero magis a ſuperficie aquæ diſtat, ex <lb />neutro pervenit aqua ad diſtantiam ad quam ex F pro-<lb />ſilit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0331-06" corresp="note-0331-06a" place="margin">824.</note>
              <note xml:space="preserve" xml:id="note-0331-07" corresp="note-0331-07a" place="margin">TAB. XXXIII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0331-08" corresp="note-0331-08a" n="*" anchored="true" place="margin">797.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ex dictis ulterius ſequitur ex foraminibus E &amp; </s>
          <s xml:space="preserve">e æque <lb />
<ptr xml:id="note-0331-09a" corresp="note-0331-09" type="noteAnchor" />
diſtantibus a centro C fluidum ad eandem proſilire diſtan-<lb />
<ptr xml:id="note-0331-10a" corresp="note-0331-10" type="noteAnchor" />
</s>
          <pb facs="0332" n="238" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tiam, quia in eo caſu perpendiculares ED, ed ſunt æ-<lb />quales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0331-09" corresp="note-0331-09a" place="margin">825.</note>
              <note xml:space="preserve" xml:id="note-0331-10" corresp="note-0331-10a" place="margin">TAB. XXXIII. <lb />fig 4.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Per F concipiatur linea horizontalis, quæ tranſit per H; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0332-01a" corresp="note-0332-01" type="noteAnchor" />
HG &amp; </s>
          <s xml:space="preserve">HE ſunt æquales, &amp; </s>
          <s xml:space="preserve">ex utroque foramine G <lb />
<ptr xml:id="note-0332-02a" corresp="note-0332-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">E aqua proſilit ad L.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0332-01" corresp="note-0332-01a" place="margin">826.</note>
              <note xml:space="preserve" xml:id="note-0332-02" corresp="note-0332-02a" place="margin">TAB. XXXIII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VIII.</head>
        <head rend="italics" xml:space="preserve">De Fluido ex vaſis profluente, &amp; Irregularitatibus <lb />in boc motu.</head>
        <p>
          <s xml:space="preserve">FLuidi quantitas, quæ in dato tempore, ex dato forami-<lb />
<ptr xml:id="note-0332-03a" corresp="note-0332-03" type="noteAnchor" />
ne, fluit, ad inſtar fluidi exeuntis velocitatis creſcit: <lb /></s>
          <s xml:space="preserve">pendet hæc ab altitudine fluidi ſupra foramen, &amp; </s>
          <s xml:space="preserve">non in-<lb />tereſt quamcunque partem verſus motus fluidi dirigatur <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0332-04a" corresp="note-0332-04" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">ſepoſitis retardationibus, quadrata quantitatum effluen-<lb />tium ſunt in ratione altitudinum fluidi ſupra foramina <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0332-03" corresp="note-0332-03a" place="margin">827.</note>
              <note xml:space="preserve" xml:id="note-0332-04" corresp="note-0332-04a" n="*" anchored="true" place="margin">794</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">799</note>
        <p>
          <s xml:space="preserve">In tempore in quo corpus libere cadendo percurrit alti-<lb />
<ptr xml:id="note-0332-06a" corresp="note-0332-06" type="noteAnchor" />
tudinem fluidi ſupra foramen, exit ex foramine, ſepoſitis <lb />retardationibus, fluidi columna longitudine duplum altitu-<lb />dinis hujus æquans <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Foramen ipſum eſt baſis columnæ,
<ptr xml:id="note-0332-07a" corresp="note-0332-07" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">datur: </s>
          <s xml:space="preserve">ſi altitudo fluidi ſupra foramen nota ſit, datur <lb />tota columna; </s>
          <s xml:space="preserve">tempus etiam facile Experimentis determi-<lb />natur <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">detecta autem quantitate, quæ in tempore
<ptr xml:id="note-0332-08a" corresp="note-0332-08" type="noteAnchor" />
noto exit, quid, in tempore quocunque dato effluat, <lb />non latet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0332-06" corresp="note-0332-06a" place="margin">828.</note>
              <note xml:space="preserve" xml:id="note-0332-07" corresp="note-0332-07a" n="*" anchored="true" place="margin">796. 257.</note>
              <note xml:space="preserve" xml:id="note-0332-08" corresp="note-0332-08a" n="*" anchored="true" place="margin">288.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quantitas autem fluidi, quæ hac computatione detegi-<lb />
<ptr xml:id="note-0332-09a" corresp="note-0332-09" type="noteAnchor" />
tur ſenſibiliter admodum excedit illam, quæ revera exit: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />quod maxime notabile eſt, Experimenta quæ circa has ve-<lb />
<ptr xml:id="note-0332-10a" corresp="note-0332-10" type="noteAnchor" />
locitates, &amp; </s>
          <s xml:space="preserve">illa, quæ de quantitatibus fluidorum, certo tem-<lb />pore ex foraminibus fluentium, inſtituuntur, minime reci-<lb />porcantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">non poteſt quantitas hæc ex nota velocitate <lb />determinari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0332-09" corresp="note-0332-09a" place="margin">829.</note>
              <note xml:space="preserve" xml:id="note-0332-10" corresp="note-0332-10a" place="margin">830.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fluidum quod juxta foraminis latera exit, attritum patitur &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0332-11a" corresp="note-0332-11" type="noteAnchor" />
</s>
          <pb facs="0333" n="239" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. VIII.</fw>
retardatur, quam retardationem non patitur fluidum illud <lb />quod ex foraminis centro irrumpit; </s>
          <s xml:space="preserve">retardatur quidem hoc <lb />a fluido laterali cum quo cohæret; </s>
          <s xml:space="preserve">ſed fluidi partes facile <lb />moventur inter ſe, &amp; </s>
          <s xml:space="preserve">retardatio hæc exigua eſt reſpectu <lb />alterius, idcirco parum etiam acceleratur fluidum laterale a <lb />medio, &amp; </s>
          <s xml:space="preserve">hoc continuo celerius illo movetur; </s>
          <s xml:space="preserve">non tamen <lb />a medio fluido ſeparatur laterale, nam quamvis facile juxta <lb />ſe invicem fluidorum partes moventur, difficilius à ſe invi-<lb />cem divelluntur; </s>
          <s xml:space="preserve">fluidum ergo medium, fluxu ſuo conti-<lb />nuo, ſecum fert laterale, quod licet lentius motum, ad e-<lb />andem diſtantiam aut altitudinem cum medio pertingit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0332-11" corresp="note-0332-11a" place="margin">831.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Judicium autem de velocitate, niſi ex diſtantia aut alti-<lb />tudine fertur; </s>
          <s xml:space="preserve">velocitas verò quæ ſic determinatur, pau-<lb />lulum deficit a velocitate qua fluidum ex medio foraminis <lb />exit, quia hoc in toto motu ſuo a laterali fluido, &amp; </s>
          <s xml:space="preserve">aliis cau-<lb />ſis, retardatur. </s>
          <s xml:space="preserve">Sed multo magis excedit velocitas hæc <lb />lateralis fluidi velocitatem, ut ex nunc explicatis ſequitur; <lb /></s>
          <s xml:space="preserve">ſi quis ergo toti fluido exeunti menſuratam tribuat veloci-<lb />tatem, quantitatem fluidi, certo tempore exeuntis, deter-<lb />minabit veram excedentem; </s>
          <s xml:space="preserve">minus tamen veram excedet <lb />quam ſi in determinanda velocitate omnes retardationes <lb />ſeponat, &amp; </s>
          <s xml:space="preserve">juxta regulam, in n. </s>
          <s xml:space="preserve">828. </s>
          <s xml:space="preserve">indicatam, compu-<lb />tationem ineat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Experimentis autem conſtat quantitates aquæ ex æquali-<lb />
<ptr xml:id="note-0333-01a" corresp="note-0333-01" type="noteAnchor" />
bus foraminibus, determinato tempore, exeuntes; </s>
          <s xml:space="preserve">ſi per <lb />latiores tubos aqua deducatur, &amp; </s>
          <s xml:space="preserve">per foramen in lamina <lb />exeat, rationem ſequi a ſubduplicata altitudinis aquæ ſupra <lb />foramen parum differentem; </s>
          <s xml:space="preserve">cum verò hæc ratio non ſit ex-<lb />acta, ſi nimium differant altitudines, regula locum non ha-<lb />bet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0333-01" corresp="note-0333-01a" place="margin">832.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ubi Computationes ineundæ erunt de aquæ quantitate, <lb />quæ effluit ex foramine dato, manente altitudine aquæ ſu-<lb />pra foramen, ſubjecta tabella uſu venire poterit, quæ ad al-<lb />titudines majores aut minores non producenda eſt. </s>
          <s xml:space="preserve">Quo <lb />Experimento nitatur hæc &amp; </s>
          <s xml:space="preserve">quæ in computatione hu-<lb />jus obſervanda fuere in ſcholio huic capiti ſubjecto dicam.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0334" n="240" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Pono aquam fluere ex foramine circulari, cujus diameter <lb />eſt ſemi pollicis Rhenolandici; </s>
          <s xml:space="preserve">agitur ulterius hìc de pe-<lb />dibus Rhenolandicis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">833.</note>
        <note xml:space="preserve" place="margin"> <lb />Altitudo \\ Aquæ # Tempus in quo \\ pes cylindricus aquæ effluit. <lb />
4 pedes # 52, 16. Min. S.
5 # 46, 60.
6 # 42, 59,
7 # 39, 43.
8 # 36, 89.
9 # 34, 78.
10 # 32, 99.
11 # 31, 55.
12 # 30, 12.
</note>
        <note xml:space="preserve" place="margin"> <lb />Altitudo \\ Aquæ. # Tempus in quo \\ pes cylindricus Aquæ effluit. <lb />13 pedes # 28, 94. Min. S. <lb />14 # 27. 88. <lb />15 # 26, 94. <lb />16 # 26, 08. <lb />17 # 25, 30 <lb />18 # 24, 59 <lb />19 # 23, 93. <lb />20 # 23, 33. <lb />21 # 22, 71. <lb /></note>
        <p>
          <s xml:space="preserve">Si foramina differant &amp; </s>
          <s xml:space="preserve">altitudo maneat, quantitas <lb />
<ptr xml:id="note-0334-04a" corresp="note-0334-04" type="noteAnchor" />
fluidi quæ determinato tempore exit, ipſius foraminis ra-<lb />tionem ſequitur, ſi in omnibus punctis foraminis æquali <lb />velocitate fluidum feratur; </s>
          <s xml:space="preserve">quod quamvis non obtineat, <lb />parum tamen a memorata ratione aberrare quantitates, quæ <lb />revera exeunt, experimentis cum aqua inſtitutis con-<lb />ſtat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0334-04" corresp="note-0334-04a" place="margin">834.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cæteris paribus, quantitates quæ effluunt, eſſe ut tempora <lb />
<ptr xml:id="note-0334-05a" corresp="note-0334-05" type="noteAnchor" />
clarum eſt: </s>
          <s xml:space="preserve">ſunt ergo quantitates hæ generaliter in ratio-<lb />ne compoſita temporis, foraminum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">radicum quadr atarum
<ptr xml:id="note-0334-06a" corresp="note-0334-06" type="noteAnchor" />
altitudinum fluidi ſupra foramina <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0334-05" corresp="note-0334-05a" place="margin">835.</note>
              <note xml:space="preserve" xml:id="note-0334-06" corresp="note-0334-06a" n="*" anchored="true" place="margin">834.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">832.</note>
        <p>
          <s xml:space="preserve">In vaſis, in quibus fluidi adfluxus non datur, hujus ce-<lb />
<ptr xml:id="note-0334-08a" corresp="note-0334-08" type="noteAnchor" />
leritas dum effluit continuo mutatur, ad quod attenden-<lb />dum in comparatione temporum in quibus vaſa diverſa e-<lb />vacuantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0334-08" corresp="note-0334-08a" place="margin">836.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vaſa cylindricâ hìc conſideramus, &amp; </s>
          <s xml:space="preserve">dicta, ad vaſa quæ-<lb />cunque eandem juxta integram altitudinem capacitatem <lb />ſervantia, referri poterunt; </s>
          <s xml:space="preserve">ponimus fluidum per foramen <lb />in fundo effluere.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Tempora, in quibus vaſa cylindrica, ejuſdem diametri <lb />
<ptr xml:id="note-0334-09a" corresp="note-0334-09" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">altitudinis, evacuantur, fluido ex foraminibus in-<lb />æqualibus fluente, ſunt inter ſe inverſe ut bæc fo-<lb />ramina.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0334-09" corresp="note-0334-09a" place="margin">837.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0335" n="241" />
        <fw type="head">MATHEMATICA. LIB. II. CAP VIII.</fw>
        <p>
          <s xml:space="preserve">Vaſa hæc, planis ad baſin parallelis, concipiantur diviſa <lb />in partes æquales minimas; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">diviſiones utriuſque vaſis <lb />non differant inter ſe; </s>
          <s xml:space="preserve">cum agatur de partibus minimis, <lb />concipi poteſt celeritatem in evacuatione unius partis non <lb />mutari. </s>
          <s xml:space="preserve">Fluidi quantitas, quæ ex foramine fluit, ſi alti-<lb />tudo non mutetur, creſcit cum foramine &amp; </s>
          <s xml:space="preserve">eo breviori <lb />tempore evacuatur determinata fluidi quantitas, quo fora-<lb />men majus eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">minuitur tempus hoc in ratione qua fo-<lb />ramen augetur. </s>
          <s xml:space="preserve">Dum partes reſpondentes in vaſis e-<lb />vacuantur altitudines ſunt æquales; </s>
          <s xml:space="preserve">partes etiam i-<lb />pſæ, &amp; </s>
          <s xml:space="preserve">ideo quantitates fluidi quæ effluunt, ſunt æ-<lb />quales, ergo tempora in inverſa ratione foraminum; <lb /></s>
          <s xml:space="preserve">quod cùm in ſingulis partibus reſpondentibus locum ha-<lb />beat, ad tempora evacuationum integrorum vaſorum etiam <lb />referri debet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando vaſa cylindrica ſunt inæqualia &amp; </s>
          <s xml:space="preserve">æque alta, per <lb />
<ptr xml:id="note-0335-01a" corresp="note-0335-01" type="noteAnchor" />
foramina æqualia, in temporibus, quæ ſunt ut cylindrorum <lb />baſes, evacuantur. </s>
          <s xml:space="preserve">Vaſa iterum in partes minimas, &amp; </s>
          <s xml:space="preserve">nu-<lb />mero æquali in utroque vaſe, diviſa concipiantur: </s>
          <s xml:space="preserve">ex par-<lb />tibus reſpondentibus per foramina æqualia, liquidum fluit, <lb />elevato hoc ad eandem altitudinem in utroque vaſe; </s>
          <s xml:space="preserve">quan-<lb />titates ergo quæ effluunt ſunt ut tempora; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò in hac <lb />temporum ratione ſunt ipſæ partes reſpondentes, quæ ſunt <lb />ut cylindrorum baſes: </s>
          <s xml:space="preserve">tempora autem integrarum evacua-<lb />tionum ſunt ut tempora in quibus partes reſpondentes e-<lb />vacuantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0335-01" corresp="note-0335-01a" place="margin">838.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dentur tandem duo vaſa cylindrica EI, AD, quorum <lb />
<ptr xml:id="note-0335-02a" corresp="note-0335-02" type="noteAnchor" />
baſes ſunt æquales, altitudines vero diverſæ, ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">ut 1. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0335-03a" corresp="note-0335-03" type="noteAnchor" />
ad 4. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">evacuentur bæc per foramina æqualia: </s>
          <s xml:space="preserve">concipiantur <lb />etiam hæc vaſa planis ad baſin parallelis in partes minimas <lb />diviſa, quales ſunt Hi, Cd; </s>
          <s xml:space="preserve">ſitqueidem numerus partium in u-<lb />troque vaſe, &amp; </s>
          <s xml:space="preserve">ſint partes inter ſe ut ipſa vaſa, id eſt, ut <lb />1. </s>
          <s xml:space="preserve">ad 4. </s>
          <s xml:space="preserve">Partes ſingulæ motu æquabili evacuantur, quia de <lb />minimis agitur: </s>
          <s xml:space="preserve">celeritates in partibus reſpondentibus ſunt <lb />ubique ut 1. </s>
          <s xml:space="preserve">ad 2. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, quia altitudines harum partium ſu-
<ptr xml:id="note-0335-04a" corresp="note-0335-04" type="noteAnchor" />
pra baſes ſunt ut vaſorum altitudines, quæ ſunt ut horum
</s>
          <pb facs="0336" n="242" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
numerorum quadrata. </s>
          <s xml:space="preserve">Unde ſequitur tempora, in qui-<lb />bus partes reſpondentes evacuantur, etiam eſſe inter ſe ut <lb />unum ad duo; </s>
          <s xml:space="preserve">quia in tempore duplo, celeritate dupla, <lb />quantitas quadrupla evacuatur. </s>
          <s xml:space="preserve">Cum autem tempora ſint <lb />in eadem ratione pro ſingulis partibus reſpondentibus, tem-<lb />pora, in quibus integra vaſa evacuantur, ſunt etiam ut <lb />unum ad duo. </s>
          <s xml:space="preserve">Si vaſa ſint ut 1 ad 9. </s>
          <s xml:space="preserve">tempora, ut de-<lb />monſtratione ſimili evincitur, erunt ut 1. </s>
          <s xml:space="preserve">ad 3; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in gene-<lb />re tempora ſunt ut celeritates, quibus partes reſpondentes <lb />evacuantur, quarum celeritatum quadrata ſunt ut vaſorum <lb />altitudines, <ptr type="noteAnchor" /> in qua ratione ergo etiam ſunt quadratatem-
<ptr xml:id="note-0336-01a" corresp="note-0336-01" type="noteAnchor" />
porum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0335-02" corresp="note-0335-02a" place="margin">839.</note>
              <note xml:space="preserve" xml:id="note-0335-03" corresp="note-0335-03a" place="margin">TAB. XXXIII. <lb />fig. 5. 6.</note>
              <note xml:space="preserve" xml:id="note-0335-04" corresp="note-0335-04a" n="*" anchored="true" place="margin">799.</note>
              <note xml:space="preserve" xml:id="note-0336-01" corresp="note-0336-01a" n="*" anchored="true" place="margin">799.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum i.</hi></head>
        <p>
          <s xml:space="preserve">Dentur ex metallo tenui tria vaſa cylindrica A, C, B, <lb />
<ptr xml:id="note-0336-02a" corresp="note-0336-02" type="noteAnchor" />
diametros æquales habentia, &amp; </s>
          <s xml:space="preserve">quorum altitudines ſunt ut <lb />
<ptr xml:id="note-0336-03a" corresp="note-0336-03" type="noteAnchor" />
unum, tria, &amp; </s>
          <s xml:space="preserve">quatuor; </s>
          <s xml:space="preserve">unumquodque inciſionem in ora ha-<lb />beat, qua effluit aqua certam ſuperans altitudinem, quæ pro <lb />vaſis altitudine habetur; </s>
          <s xml:space="preserve">in fundis vaſorum A &amp; </s>
          <s xml:space="preserve">B, quæ <lb />ſunt ut unum &amp; </s>
          <s xml:space="preserve">quatuor, foramina æqualia dentur, &amp; </s>
          <s xml:space="preserve">a-<lb />quà impleantur; </s>
          <s xml:space="preserve">eodem momento foramina aperiantur; </s>
          <s xml:space="preserve">ſi <lb />aqua ex B fluens vaſe C recipiatur, impletur hoc in tem-<lb />pore in quo A evacuatur: </s>
          <s xml:space="preserve">C continet tres partes quartas <lb />vaſis B; </s>
          <s xml:space="preserve">partem quartam, quæ ſupereſt, æquali etiamtem-<lb />pore cum vaſe A evacuari, a nemine in dubium vocari po-<lb />teſt; </s>
          <s xml:space="preserve">bis ergo evacuatur A, dum B ſemel.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0336-02" corresp="note-0336-02a" place="margin">840.</note>
              <note xml:space="preserve" xml:id="note-0336-03" corresp="note-0336-03a" place="margin">TAB. XXXIII. <lb />fig 7.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Tempora, in quibus vaſa cylindrica quæcunque evacuan-<lb />
<ptr xml:id="note-0336-04a" corresp="note-0336-04" type="noteAnchor" />
tur, ſunt in ratione compoſita baſium <ptr type="noteAnchor" />, inverſa forami-
<ptr xml:id="note-0336-05a" corresp="note-0336-05" type="noteAnchor" />
num <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">radicum quadratarum altitudinum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0336-04" corresp="note-0336-04a" place="margin">841.</note>
              <note xml:space="preserve" xml:id="note-0336-05" corresp="note-0336-05a" n="*" anchored="true" place="margin">838.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">837.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">839.</note>
        <p>
          <s xml:space="preserve">Dividi ita poteſt, vas cylindricum, ut partes inter diviſio-<lb />
<ptr xml:id="note-0336-08a" corresp="note-0336-08" type="noteAnchor" />
nes interceptæ æqualibus temporibus evacuentur, quod <lb />
<ptr xml:id="note-0336-09a" corresp="note-0336-09" type="noteAnchor" />
fiet, ſi diviſionum a baſi diſtantiæ fuerint ut numerorum na-<lb />turalium quadrata; </s>
          <s xml:space="preserve">tempora enim evacuationum vaſorum, <lb />quorum altitudines hanc ſequuntur proportionem, ſunt <lb />ut numeri naturales <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">temporum differentiæ æqua-
<ptr xml:id="note-0336-10a" corresp="note-0336-10" type="noteAnchor" />
les.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0336-08" corresp="note-0336-08a" place="margin">842.</note>
              <note xml:space="preserve" xml:id="note-0336-09" corresp="note-0336-09a" place="margin">TAB. XXXIII. <lb />fig 6.</note>
              <note xml:space="preserve" xml:id="note-0336-10" corresp="note-0336-10a" n="*" anchored="true" place="margin">839.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tempus in quo vas cylindricum evacuatur eſt ut celeri-
</s>
          <pb facs="0337" n="243" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. VIII.</fw>
tas cum qua fluidum effluere inchoat <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">celeritas ergo,
<ptr xml:id="note-0337-01a" corresp="note-0337-01" type="noteAnchor" />
dum fluidum in vaſe deſcendit, in eadem ratione minui-<lb />tur, cum tempore evacuationis fluidi in vaſe ſuperſtitis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />motus fluidi, ex vaſe cylindrico fluentis, eſt retardatus æqua-<lb />
<ptr xml:id="note-0337-02a" corresp="note-0337-02" type="noteAnchor" />
liter in temporibus æqualibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0337-01" corresp="note-0337-01a" n="*" anchored="true" place="margin">839. 792.</note>
              <note xml:space="preserve" xml:id="note-0337-02" corresp="note-0337-02a" place="margin">843.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ex cylindro, &amp; </s>
          <s xml:space="preserve">alio vaſe ejuſdem altitudinis, &amp; </s>
          <s xml:space="preserve">flui-<lb />
<ptr xml:id="note-0337-03a" corresp="note-0337-03" type="noteAnchor" />
dum ſemper ad eandem altitudinem continenti, per for amina <lb />æqualia fluat fluidum, in tempore in quo evacuatur cylin-<lb />drus, ex vaſe memorato fluit dupla fluidi quantitas quàm ex <lb />cylindro. </s>
          <s xml:space="preserve">Nam, propter altitudines vaſorum æquales, ce-<lb />leritates in principio ſunt æquales; </s>
          <s xml:space="preserve">fluidi, quod ex vaſe ſem-<lb />per repleto exit, celeritas eſt æquabilis; </s>
          <s xml:space="preserve">celeritas fluidi, ex <lb />cylindro fluentis, eſt æquabiliter retardata <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Idcirco ex
<ptr xml:id="note-0337-04a" corresp="note-0337-04" type="noteAnchor" />
iſto vaſe, dum cylindrus evacuatur, fluet dupla aquæ <lb />quantitas quàm ex cylindro. </s>
          <s xml:space="preserve">Si enim duo corpora eadem <lb />celeritate propellantur, &amp; </s>
          <s xml:space="preserve">primum motu æquabili progre-<lb />diatur, ſecundum autem motu æquabiliter retardato, &amp; </s>
          <s xml:space="preserve"><lb />moveantur donec hoc totum motum amiſerit, primum in eo <lb />tempore percurret ſpatium duplum ſpatii a ſecundo percur-<lb />ſi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hìc fluidum, quod effluit, pro ſpatio percurſo haberi
<ptr xml:id="note-0337-05a" corresp="note-0337-05" type="noteAnchor" />
poteſt, quia foramina ſunt æqualia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0337-03" corresp="note-0337-03a" place="margin">844.</note>
              <note xml:space="preserve" xml:id="note-0337-04" corresp="note-0337-04a" n="*" anchored="true" place="margin">843.</note>
              <note xml:space="preserve" xml:id="note-0337-05" corresp="note-0337-05a" n="*" anchored="true" place="margin">258. 259. <lb />257.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Notavimus ſupra partium cohæſionem motum fluidorum <lb />
<ptr xml:id="note-0337-06a" corresp="note-0337-06" type="noteAnchor" />
retardare, contrarium etiam in multis occaſionibus obſer-<lb />vamus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">licet velocitas ex preſſione oriunda, quaſcunque <lb />partes verſus eadem ſit, omnium tamen celerrime movetur <lb />fluidum, dum verticaliter deſcendit; </s>
          <s xml:space="preserve">hoc in motu ſuo ca-<lb />dendo continuo acceleratur, cum inſequenti cohæret &amp; </s>
          <s xml:space="preserve">ſe-<lb />cum quaſi trahit, velocitatemque fluidi ex vaſe profluentis <lb />auget.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0337-06" corresp="note-0337-06a" place="margin">845.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa aquam quædam obſervabo, quia cum hac experi-<lb />menta fuere ſumta, quamvis hæc ipſa etiam ad alia fluida <lb />applicari poſſint, magiſque in fluidis glutinoſis hæc ſenſi-<lb />bilia forent de quibus tamen hìc non agitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Motus ex vaſe, cum quo in inferiori parte tubus con-<lb />
<ptr xml:id="note-0337-07a" corresp="note-0337-07" type="noteAnchor" />
jungitur, etiam acceleratur. </s>
          <s xml:space="preserve">Sit vas tale E æquale &amp; </s>
          <s xml:space="preserve">ſi-<lb />
<ptr xml:id="note-0337-08a" corresp="note-0337-08" type="noteAnchor" />
mile vaſi A, &amp; </s>
          <s xml:space="preserve">quod cum tubo altitudinem habeat vaſis B;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0338" n="244" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
habeat tubus aperturas ambas æquales foraminibus in fundis <lb />vaſorum A &amp; </s>
          <s xml:space="preserve">B; </s>
          <s xml:space="preserve">impleantur aquâ vaſa <hi rend="small caps">A</hi>, E, &amp; </s>
          <s xml:space="preserve">B. </s>
          <s xml:space="preserve">In <lb />principio motus, ex vaſis A &amp; </s>
          <s xml:space="preserve">E æquali celeritate aqua <lb />fluit, quia ex tubo non major fluere poteſt aquæ quantitas, <lb />quam quæ tubum per aperturam ſuperiorem intrat, quem <lb />major aquæ quantitas ingredi nequit, quam quæ ex vaſe A <lb />fluere poteſt. </s>
          <s xml:space="preserve">Sed aqua quæ per tubum deſcendit accele-<lb />ratur, &amp; </s>
          <s xml:space="preserve">cum integram tubi capacitatem repleat; </s>
          <s xml:space="preserve">magis a-<lb />quam inſequentem ſecum trahit quàm ſublato tubo, tunc <lb />enim tenuior fit continuò columna aquæ effluentis. </s>
          <s xml:space="preserve">Aqua <lb />autem quæ per tubum fluit, dum inſequentem accelerat, ab <lb />hac retardatur; </s>
          <s xml:space="preserve">quare aquæ quantitas, quæ certo tempore ex <lb />vaſe E effluit, eſt media inter aquæ quantitates, quæ ex vaſis <lb /><hi rend="small caps">A</hi> &amp; </s>
          <s xml:space="preserve">B, eodem tempore fluere poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0337-07" corresp="note-0337-07a" place="margin">846.</note>
              <note xml:space="preserve" xml:id="note-0337-08" corresp="note-0337-08a" place="margin">TAB. XXXIX. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Vaſis A, E, &amp; </s>
          <s xml:space="preserve">B, ſecundum proportiones memoratas, ex <lb />
<ptr xml:id="note-0338-01a" corresp="note-0338-01" type="noteAnchor" />
metallo tenui conſtructis; </s>
          <s xml:space="preserve">aquâ impleantur A &amp; </s>
          <s xml:space="preserve">E; </s>
          <s xml:space="preserve">eodem <lb />momento apertis foraminibus, celerius deſcendet aquæ ſu-<lb />perficies in E quàm in A: </s>
          <s xml:space="preserve">contra adhibitis vaſis E &amp; </s>
          <s xml:space="preserve">B, ce-<lb />lerius deſcendit in hoc quàm in illo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0338-01" corresp="note-0338-01a" place="margin">847.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Maneat apertura ſuperior tubi, qua cum vaſe tubus com-<lb />
<ptr xml:id="note-0338-02a" corresp="note-0338-02" type="noteAnchor" />
municationem babet; </s>
          <s xml:space="preserve">augeatur apertura inferior; </s>
          <s xml:space="preserve">major a-<lb />quæ quantitas effluet, &amp; </s>
          <s xml:space="preserve">magis accelerabitur aqua, quæ tu-<lb />bum intrat; </s>
          <s xml:space="preserve">ſatiſque poteſt augeri hæc apertura, non mu-<lb />tata tubi longitudine, ut ex ipſa major aquæ quantitas fluat <lb />quam ex vaſe B. </s>
          <s xml:space="preserve">In hoc caſu, per aperturam tubi ſupe-<lb />riorem ad parvam infra aquæ ſuperficiem profunditatem, <lb />major fluit aquæ quantitas quàm ex apertura æquali ad <lb />profunditatem quadruplam. </s>
          <s xml:space="preserve">Adhibito longiori tubo, 1-<lb />dem præſtari poterit, licet non augeatur tubi apertura in-<lb />ferior.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0338-02" corresp="note-0338-02a" place="margin">848.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Sit vas F, a vaſe E in eo ſolo differens, quod apertura <lb />
<ptr xml:id="note-0338-03a" corresp="note-0338-03" type="noteAnchor" />
tubi inferior in illo major ſit; </s>
          <s xml:space="preserve">ſit etiam vas antea memoratum <lb />
<ptr xml:id="note-0338-04a" corresp="note-0338-04" type="noteAnchor" />
B. </s>
          <s xml:space="preserve">Diametri foraminis in hujus fundo, &amp; </s>
          <s xml:space="preserve">aperturæ ſuperio-<lb />ris tubi cum vaſe P conjuncti, ſunt 4. </s>
          <s xml:space="preserve">lin.</s>
          <s xml:space="preserve">; apertura inferior
</s>
          <pb facs="0339" n="245" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. VIII.</fw>
hujus tubi eſt 5. </s>
          <s xml:space="preserve">lin. </s>
          <s xml:space="preserve">Aquâ vaſa impleantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eodem mo-<lb />mento fluat ex utroque; </s>
          <s xml:space="preserve">citius aquæ ſuperficies in vaſe F <lb />quàm in B deſcendet. </s>
          <s xml:space="preserve">Altitudo vaſis B eſt circiter ſede-<lb />cim pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0338-03" corresp="note-0338-03a" place="margin">849.</note>
              <note xml:space="preserve" xml:id="note-0338-04" corresp="note-0338-04a" place="margin">TAB. XXXIII. <lb />fig 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">His Experimentis duo alia notabilia admodum circa par-<lb />tium cohæ ſionem ſubjungam, quibus effectus hujus cohæ-<lb />ſionis dilucidantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Antliæ, duæ æquales A, B, junguntur fruſto æneo G; </s>
          <s xml:space="preserve">huic <lb />
<ptr xml:id="note-0339-01a" corresp="note-0339-01" type="noteAnchor" />
tubi duo E da, F db inſeruntur, quorum hic cum antlia <lb />
<ptr xml:id="note-0339-02a" corresp="note-0339-02" type="noteAnchor" />
B, ille cum A communicatur. </s>
          <s xml:space="preserve">Tuborum horum axes in eo-<lb />dem plano dantur, &amp; </s>
          <s xml:space="preserve">ſeſe mutuo ad angulos rectos ſecant, <lb />confundunturque tubi in d.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0339-01" corresp="note-0339-01a" place="margin">850.</note>
              <note xml:space="preserve" xml:id="note-0339-02" corresp="note-0339-02a" place="margin">TAB. XXXV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Antlia A repletur aquâ rubro, aut alio colore, tinctâ, B <lb />repletur aquâ purâ; </s>
          <s xml:space="preserve">emboli junguntur laminâ L, quæ con-<lb />chleis firmatur &amp; </s>
          <s xml:space="preserve">ſimul intruduntur. </s>
          <s xml:space="preserve">Tincta aqua viam ſe-<lb />quitur E db, alia viam F da, &amp; </s>
          <s xml:space="preserve">vix ſenſibilis aquarum per <lb />mixtio datur, dum in d juxta ſe invicem tranſeunt, &amp; </s>
          <s xml:space="preserve">vias <lb />flectunt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Differt Experimentum hoc a præcedenti in unicâ circum-<lb />
<ptr xml:id="note-0339-03a" corresp="note-0339-03" type="noteAnchor" />
ſtantia, effectus tamen diverſus omnino eſt. </s>
          <s xml:space="preserve">Tuborum <lb />
<ptr xml:id="note-0339-04a" corresp="note-0339-04" type="noteAnchor" />
E da, F db, axes non in eodem dantur plano, ſed unius axis <lb />alterius cavitatem quaſi tangit ita, ut pro parte tantum tu-<lb />bi confundantur in d. </s>
          <s xml:space="preserve">Intruſis nunc embolis, colorata a-<lb />qua, quæ pro parte libere tranſit per E da omnem aliam <lb />coloratam ſecum trahit; </s>
          <s xml:space="preserve">dum eodem modo aqua pura per <lb />F db fertur; </s>
          <s xml:space="preserve">his vix ſenſibiliter permixtis quamvis juxta ſe <lb />invicem aquæ in d tranſeant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0339-03" corresp="note-0339-03a" place="margin">851.</note>
              <note xml:space="preserve" xml:id="note-0339-04" corresp="note-0339-04a" place="margin">TAB. XXXV. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Experimentum hoc celebrem auctorem in errorem indu-<lb />xit, qui hoc ipſum inſtituit experimentum, cum in animum <lb />haberet præcedens tentare, concluſionemque deduxit am-<lb />bobus experimentis contrariam; </s>
          <s xml:space="preserve">fluidi particulas liberrime <lb />ſine confuſione inter alîus fluidi particulas viam continuare, <lb />agitato licet hoc fluido juxta aliam directionem.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0340" n="246" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM.</head>
        <p>
          <s xml:space="preserve">DIxi me in hoc ſcholio explicaturum, ex quo experimento, &amp; </s>
          <s xml:space="preserve">quomodo, <lb />computatio tabulæ n. </s>
          <s xml:space="preserve">833. </s>
          <s xml:space="preserve">fuerit inita.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Mariotte Experimento, variis vicibus repetito, obſervatisque cautelis ne-<lb />
<ptr xml:id="note-0340-01a" corresp="note-0340-01" type="noteAnchor" />
ceſſariis, determinavit ex foramine, cujus diameter erat {1/4} poll.</s>
          <s xml:space="preserve">, ſervatâ aquæ <lb />altitudine ſupra hoc 13. </s>
          <s xml:space="preserve">ped.</s>
          <s xml:space="preserve">, ſingulis vicibus effluxiſſe, in uno minuto pri-<lb />mo, pintas 28.</s>
          <s xml:space="preserve">, quarum pes cubicus continet 70. </s>
          <s xml:space="preserve">Agitur hîc de pede regio <lb />Gallico, qui ad pedem Rhenolandicum ſe habet ut 144. </s>
          <s xml:space="preserve">ad 139.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0340-01" corresp="note-0340-01a" place="margin">852.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dato hoc experimento detegendum in quo tempore pes cylindricus eva-<lb />cuari poteſt, per foramen cujus diameter eſt ſemi poll.</s>
          <s xml:space="preserve">, poſitâ etiam aquæ <lb />altitudine ſupra hoc 13. </s>
          <s xml:space="preserve">pedum, # dum # menſura # Rhenolandica ad-<lb />hibetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tempus quo certa aquæ quantitas evacuatur, eo brevius eſt quo major <lb />
<ptr xml:id="note-0340-02a" corresp="note-0340-02" type="noteAnchor" />
quantitas determinato tempore exit; </s>
          <s xml:space="preserve">tempora ergo ſunt inverſe ut hæ quanti-<lb />tates, quæ cæteris paribus ſunt in ratione ſubduplicata altitudinum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0340-02" corresp="note-0340-02a" place="margin">853.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">832.</note>
        <p>
          <s xml:space="preserve">Tempora etiam ſunt eo minora quo foramina majora, id eſt, cæteris pa-<lb />ribus ſunt in ratione inverſa quadratorum diametrorum foraminum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tandem, cæteris paribus, tempora ſunt directe ut quantitates quæ effiuunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In experimento à Mariotte inſtituto, altitudo tredecim pedum Gallicorum <lb />eſt ad altitudinem totidem pedum Rhenolandicorum in caſu de quo agitur, <lb />ut 144. </s>
          <s xml:space="preserve">ad. </s>
          <s xml:space="preserve">139.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quadrata diametrorum foraminum ſunt ut 1. </s>
          <s xml:space="preserve">ad 4. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ut <hi rend="overline">144.</hi><hi rend="superscript">q</hi> ad <hi rend="overline">132.</hi><hi rend="superscript">q</hi></s>
        </p>
        <p>
          <s xml:space="preserve">Quantitates aquæ ſunt, ut pintæ 28. </s>
          <s xml:space="preserve">ad pedem cylindricum Rhenolandi-<lb />cum; </s>
          <s xml:space="preserve">quæ quantitates ſunt in ratione compoſita, rationis 28. </s>
          <s xml:space="preserve">ad 70. </s>
          <s xml:space="preserve">aut 14. <lb /></s>
          <s xml:space="preserve">ad 35, id eſt, quantitatis quæ effluxit ad pedem cubicum Gallicum, rationis pe-<lb />dis cubici Gallici ad pedem cubicum Rhenolandicum, &amp; </s>
          <s xml:space="preserve">rationis pedis cu-<lb />bici ad pedem cylindricum, aut 452. </s>
          <s xml:space="preserve">ad 355.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Idcirco tempus unius minuti primi, aut 60. </s>
          <s xml:space="preserve">m. </s>
          <s xml:space="preserve">ſ.</s>
          <s xml:space="preserve">, ad tempus quæſi-<lb />tum, in ratione compoſita ex hiſce ſex rationibus, √139.</s>
          <s xml:space="preserve">\x{0020} ad √144\x{0020}, 4. </s>
          <s xml:space="preserve">ad 1.</s>
          <s xml:space="preserve">, <lb /><hi rend="overline">139.</hi><hi rend="superscript">q</hi> ad <hi rend="overline">144.</hi><hi rend="superscript">q</hi>, 14. </s>
          <s xml:space="preserve">ad 35.</s>
          <s xml:space="preserve">, <hi rend="overline">144.</hi><hi rend="superscript">c</hi> ad <hi rend="overline">139.</hi><hi rend="superscript">c</hi>, &amp; </s>
          <s xml:space="preserve">452. </s>
          <s xml:space="preserve">ad. </s>
          <s xml:space="preserve">355.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Rationes prima, tertia, &amp; </s>
          <s xml:space="preserve">quinta, reducuntur ad rationem, √144.</s>
          <s xml:space="preserve">\x{0020} ad <lb />√139\x{0020}; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſunt 60. </s>
          <s xml:space="preserve">m. </s>
          <s xml:space="preserve">ſ. </s>
          <s xml:space="preserve">ad tempus quæſitum, ut 4 x 14 x 452 x 12. </s>
          <s xml:space="preserve">ad <lb />
<ptr xml:id="note-0340-04a" corresp="note-0340-04" type="noteAnchor" />
1 x 35 x 355 x √139.</s>
          <s xml:space="preserve">\x{0020} quod tempus detegitur 28, 94. </s>
          <s xml:space="preserve">m. </s>
          <s xml:space="preserve">ſ. </s>
          <s xml:space="preserve">Quo tempore dato <lb />reliqua quæ notantur in tabella n. </s>
          <s xml:space="preserve">833. </s>
          <s xml:space="preserve">deteguntur quærendo numeros in ra-<lb />tione inverſa ſubduplicata altitudinum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0340-04" corresp="note-0340-04a" place="margin">854.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IX.</head>
        <head rend="italics" xml:space="preserve">De Curſu Fluminum.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">FLumen vocamus aquam, in canali ſuperius aperto, pro-<lb />
<ptr xml:id="note-0340-05a" corresp="note-0340-05" type="noteAnchor" />
pria gravitate fluentem, ut A E. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0340-06a" corresp="note-0340-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0340-05" corresp="note-0340-05a" place="margin">855.</note>
              <note xml:space="preserve" xml:id="note-0340-06" corresp="note-0340-06a" place="margin">TAB XXXIV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0341" />
        <pb facs="0341a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0341a-01" />
          <label>0341a-01</label>
        </figure>
        <pb facs="0342" />
        <pb facs="0343" n="247" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. IX.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Flumen in eodem ſtatu manere, aut in ſtatu manente, <lb />
<ptr xml:id="note-0343-01a" corresp="note-0343-01" type="noteAnchor" />
dicitur, quando aqua uniformiter fluit, ita ut in eodem lo-<lb />co ſemper ſit ad eandem altitudinem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0343-01" corresp="note-0343-01a" place="margin">856.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio.</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Sectio Fluminis vocatur planum Flumen ſecans perpen-<lb />
<ptr xml:id="note-0343-02a" corresp="note-0343-02" type="noteAnchor" />
diculariter ad fundum, &amp; </s>
          <s xml:space="preserve">ad quæ directionem in medio, ut <lb />ponq.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0343-02" corresp="note-0343-02a" place="margin">857.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando Flumen a lateribus terminatur, planis inter ſe pa-<lb />rallelis, &amp; </s>
          <s xml:space="preserve">ad horizontem normalibus, &amp; </s>
          <s xml:space="preserve">fundus etiam eſt <lb />planum, ſive horizontale, ſive inclinatum, ſectio Fluminis <lb />cum tribus hiſce planis angulos rectos efficit, &amp; </s>
          <s xml:space="preserve">eſt paralle-<lb />logrammum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In omni Flumine in ſtatu manente, eadem aquæ quantitas <lb />
<ptr xml:id="note-0343-03a" corresp="note-0343-03" type="noteAnchor" />
per ſingulas ſectiones eodem tempore fluit. </s>
          <s xml:space="preserve">Niſi enim in lo-<lb />co quocunque eadem aquæ quantitas adfluat, quæ ex eo <lb />defluit, in eodem ſtatu Flumen non manebit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">demon-<lb />ſtratio hæc locum habet, quæcunque fuerit alvei irregula-<lb />ritas, ex qua, alio reſpectu, multæ in Fluminis motu mu-<lb />tationes oriuntur; </s>
          <s xml:space="preserve">attritus ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">major eſt pro majore al-<lb />vei inæqualitate.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0343-03" corresp="note-0343-03a" place="margin">858.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Irregularitates in Fluminis motu in infinitum variari <lb />poſſunt, &amp; </s>
          <s xml:space="preserve">regulæ circa illas tradi nequeunt; </s>
          <s xml:space="preserve">ſepoſitis <lb />ergo irregularitatibus omnibus Fluminum curſus exami-<lb />nandus eſt; </s>
          <s xml:space="preserve">niſi enim in hoc caſu motus leges notæ fue-<lb />rint, de nullo judicium, vero fundamento nixum, ferri <lb />poterit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponimus ergo aquam fluere per canalem regularem, ſi-<lb />
<ptr xml:id="note-0343-04a" corresp="note-0343-04" type="noteAnchor" />
ne ſenſibili attritu; </s>
          <s xml:space="preserve">canalem terminari ad latera planis pa-<lb />rallelis inter ſe &amp; </s>
          <s xml:space="preserve">verticalibus; </s>
          <s xml:space="preserve">fundumque etiam planum <lb />eſſe &amp; </s>
          <s xml:space="preserve">ad horizontem inclinari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0343-04" corresp="note-0343-04a" place="margin">859.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit canalis A E; </s>
          <s xml:space="preserve">ex receptaculo majori aqua in illum <lb />fluat, maneatque in receptaculo ſemper ad eandem altitu-<lb />dinem, ut Flumen ſit in ſtatu manenti. </s>
          <s xml:space="preserve">Aqua juxta pla-<lb />num inclinatum deſcendit &amp; </s>
          <s xml:space="preserve">acceleratur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quo, propter
<ptr xml:id="note-0343-05a" corresp="note-0343-05" type="noteAnchor" />
æqualem aquæ quantitatem per ſingulas ſectiones fluen-
</s>
          <pb facs="0344" n="248" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tem <ptr type="noteAnchor" />, altitudo aquæ, recedendo a Fluminis initio.</s>
          <s xml:space="preserve">, con-
<ptr xml:id="note-0344-01a" corresp="note-0344-01" type="noteAnchor" />
tinuo minuitur, &amp; </s>
          <s xml:space="preserve">aquæ ſuperſicies adipiſcitur figuram iqs.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0343-05" corresp="note-0343-05a" n="*" anchored="true" place="margin">263.</note>
              <note xml:space="preserve" xml:id="note-0344-01" corresp="note-0344-01a" n="*" anchored="true" place="margin">858.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">860.</note>
        <p>
          <s xml:space="preserve">Ad determinandam aquæ in variis locis velocitatem, con-<lb />
<ptr xml:id="note-0344-03a" corresp="note-0344-03" type="noteAnchor" />
cipiamus canalis aperturam ADCB plano claudi; </s>
          <s xml:space="preserve">ſi perfo-<lb />retur planum, eo celerius ex foramine proſiliet aqua, quo <lb />magis hoc diſtabit a ſuperficie aquæ bi; </s>
          <s xml:space="preserve">eandemque habe-<lb />bit aqua celeritatem, quam corpus, cadendo a ſuperficie <lb />aquæ ad profunditatem foraminis infra illam, acquirit <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0344-04a" corresp="note-0344-04" type="noteAnchor" />
quod ex preſſione aquæ ſuperincumbentis oritur. </s>
          <s xml:space="preserve">Datur <lb />eadem preſſio, id eſt, eadem vis motrix, quando impedi-<lb />mentum in AC tollitur; </s>
          <s xml:space="preserve">ponimus enim capax adeo rece-<lb />ptaculum, ut &amp; </s>
          <s xml:space="preserve">in hoc caſu preſſio lateralis agat in aquam <lb />quæ canalem intrat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0344-03" corresp="note-0344-03a" place="margin">861.</note>
              <note xml:space="preserve" xml:id="note-0344-04" corresp="note-0344-04a" n="*" anchored="true" place="margin">796.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hunc nunc ingreditur unaquæque particula aquæ ea <lb />celeritate, quam corpus acquirit, cadendo ab aquæ ſuperfi-<lb />cie ad particulæ profunditatem. </s>
          <s xml:space="preserve">Particula hæc, juxta pla-<lb />num inclinatum, in canale movetur, &amp; </s>
          <s xml:space="preserve">hujus motus acce-<lb />leratur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quidem eodem modo ac ſi verticaliter cadendo <lb />motum continuaſſet ad eandem profunditatem infra ſuper-<lb />ficiem aquæ in origine Fluminis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">271.</note>
        <p>
          <s xml:space="preserve">Si ducatur horizontalis linea it, particula in r habebit <lb />celeritatem quam corpus cadendo per i C &amp; </s>
          <s xml:space="preserve">devolvendo <lb />per Cr poteſt acquirere; </s>
          <s xml:space="preserve">quæ eſt celeritas, caſu per tr, a <lb />corpore acquiſita. </s>
          <s xml:space="preserve">Vbique ergo menſuratur particulæ cele-<lb />
<ptr xml:id="note-0344-06a" corresp="note-0344-06" type="noteAnchor" />
ritas, ducendo ab hac perpendicularem ad planum horizon-<lb />tale, quod per ſuperficiem aquæ in origine Fluminis concipi-<lb />tur, &amp; </s>
          <s xml:space="preserve">velocitas, quam corpus per hanc perpendicularem ca-<lb />dendo acquirit, erit particulæ celeritas, quæ major eſt pro <lb />majori perpendicularis longitudine, &amp; </s>
          <s xml:space="preserve">non augetur preſſione <lb />
<ptr xml:id="note-0344-07a" corresp="note-0344-07" type="noteAnchor" />
aquæ ſuper incumbentis, quæ non poteſt augere celeritatem <lb />aquæ, quæ aliunde majorem habet quam quæ ex hac preſ-<lb />ſione oriri poteſt: </s>
          <s xml:space="preserve">eodem modo ac corpus inſequens in an-<lb />tecedens celerius motum agere non poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0344-06" corresp="note-0344-06a" place="margin">862.</note>
              <note xml:space="preserve" xml:id="note-0344-07" corresp="note-0344-07a" place="margin">863.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In puncto quocunque r ad Fluminis fundum ducatur per-<lb />pendicularis rs, Fluminis altitudinem menſurans; </s>
          <s xml:space="preserve">cum non <lb />horizontalis ſit rs, ſi a variis hujus lineæ punctis ad it per-
</s>
          <pb facs="0345" n="249" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. IX.</fw>
pendiculares ducantur, eo hæ breviores erunt, quo magis <lb />ab r diſtabunt, omniumque breviſſima erit sv; </s>
          <s xml:space="preserve">ideoque <lb />particularum, in linea rs, celeritates eo minores ſunt, quo <lb />magis hæ ad ſuperficiem Fluminis accedunt, &amp; </s>
          <s xml:space="preserve">aqua infe-<lb />
<ptr xml:id="note-0345-01a" corresp="note-0345-01" type="noteAnchor" />
rior celerius ſuperiori movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0345-01" corresp="note-0345-01a" place="margin">864.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Harum tamen aquarum in progreſſu fluminis ad æqualita-<lb />
<ptr xml:id="note-0345-02a" corresp="note-0345-02" type="noteAnchor" />
tem continuo magis accedunt celeritates. </s>
          <s xml:space="preserve">Nam celeritatum <lb />harum quadrata ſunt ut rt ad sv, quarum linearum dif-<lb />ferentia, recedendo a fluminis origine, continuo minuitur, <lb />propter imminutam altitudinem rs<ptr type="noteAnchor" />, dum lineæ ipſæ au-
<ptr xml:id="note-0345-03a" corresp="note-0345-03" type="noteAnchor" />
gentur. </s>
          <s xml:space="preserve">Quod cum in quadratis obtineat, multo magis in <lb />ipſis celeritatibus locum habet, quarum differentia ergo et-<lb />iam minuitur, dum ipſæ creſcunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0345-02" corresp="note-0345-02a" place="margin">865.</note>
              <note xml:space="preserve" xml:id="note-0345-03" corresp="note-0345-03a" n="*" anchored="true" place="margin">860.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si fundi inclinatio in principio fluminis mutetur ut ſit <lb />
<ptr xml:id="note-0345-04a" corresp="note-0345-04" type="noteAnchor" />
yZ, &amp; </s>
          <s xml:space="preserve">major aquæ quantitas in canalem fluat, altior erit <lb />ubique in flumine, ſed non mutatur celeritas aquæ in loco quo-<lb />cunque. </s>
          <s xml:space="preserve">Hæc enim celeritas non ab altitudine aquæ in flu-<lb />mine pendet, ſed, ut demonſtratum, a diſtantia inter par-<lb />riculam motam &amp; </s>
          <s xml:space="preserve">planum horizontale per aquæ ſu-<lb />perficiem in origine fluminis tranſiens; </s>
          <s xml:space="preserve">quæ diſtantia per-<lb />pendiculari ut rt aut sv menſuratur; </s>
          <s xml:space="preserve">hæ autem adfluxu a-<lb />quæ non variantur, ſi modo maneat aquæ ſuperficies in re-<lb />ceptaculo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0345-04" corresp="note-0345-04a" place="margin">866.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Claudatur canalis pars ſuperior obſtaculo ut X, quod quan-<lb />
<ptr xml:id="note-0345-05a" corresp="note-0345-05" type="noteAnchor" />
tumvis parum infra aquæ ſuperficiem deſcendat; </s>
          <s xml:space="preserve">aqua o-<lb />mnis quæ adfluit perfluere non poterit, adſcendet idcirco; <lb /></s>
          <s xml:space="preserve">ſed eo celeritas aquæ infra cataractam non augetur <ptr type="noteAnchor" />, con-
<ptr xml:id="note-0345-06a" corresp="note-0345-06" type="noteAnchor" />
tinuoque accumulatur aqua adfluens; </s>
          <s xml:space="preserve">quæ ergo ita <lb />adſcendit ut ſupra impedimentum aut ripas fluminis de-<lb />fluat. </s>
          <s xml:space="preserve">Si vero ripæ eleventur &amp; </s>
          <s xml:space="preserve">impedimentum continue-<lb />tur, ſupra lineam it aquæ altitudo excreſcet, antea enim <lb />hujus celeritas augeri nequit: </s>
          <s xml:space="preserve">in quo caſu totius aquæ in <lb />receptaculo altitudo augebitur; </s>
          <s xml:space="preserve">cum enim ponamus <lb />flumen in ſtatu manenti neceſſe eſt ut aliunde continuo in <lb />receptaculum tantum aquæ adfluat, quantum ex illo in flu-<lb />men defluit; </s>
          <s xml:space="preserve">imminuta verò aquæ defluentis quantitate,
</s>
          <pb facs="0346" n="250" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
neceſſario altitudo in receptaculo augetur, donec celeritas <lb />aquæ infra obſtaculum fluentis ita augeatur, ut eadem <lb />aquæ quantitas infra hocce obſtaculum tranſeat, quæ <lb />ante poſitam cataractam per hanc fluminis ſectionem flu-<lb />xit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0345-05" corresp="note-0345-05a" place="margin">867.</note>
              <note xml:space="preserve" xml:id="note-0345-06" corresp="note-0345-06a" n="*" anchored="true" place="margin">866.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc omnia, ut jam monuimus, ſepoſitis irregularitati-<lb />bus omnibus, vera ſunt, &amp; </s>
          <s xml:space="preserve">quo irregularitates ſunt mino-<lb />res, eo magis cum dictis motus veri congruunt; </s>
          <s xml:space="preserve">de qui-<lb />bus ut judicium feratur, neceſſe eſt ut Experimentis velo-<lb />citates aquarum poſſimus comparare, &amp; </s>
          <s xml:space="preserve">ipſas velocitates i-<lb />ta determinare, ut ſpatia in certo tempore percurſa dete-<lb />gantur; </s>
          <s xml:space="preserve">hæc autem detegere poterimus ſi in ſubſidium vo-<lb />cemus, quæ in Capite <hi rend="small caps">XI</hi>. </s>
          <s xml:space="preserve">de fluidorum actionibus demon-<lb />ſtrantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit circuli quadrans ACB in gradus diviſus; </s>
          <s xml:space="preserve">in centro <lb />
<ptr xml:id="note-0346-01a" corresp="note-0346-01" type="noteAnchor" />
ei annectitur filum, cujus extremitas altera cum globo P, <lb />
<ptr xml:id="note-0346-02a" corresp="note-0346-02" type="noteAnchor" />
aquâ graviori, cohæret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0346-01" corresp="note-0346-01a" place="margin">868.</note>
              <note xml:space="preserve" xml:id="note-0346-02" corresp="note-0346-02a" place="margin">TAB. XXXIV. <lb />fig 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aquâ fluenti globus immergitur, ſervato latere CA qua-<lb />
<ptr xml:id="note-0346-03a" corresp="note-0346-03" type="noteAnchor" />
drantis in ſitu verticali; </s>
          <s xml:space="preserve">globus actione aquæ ita ſuſtinetur, <lb />ut filum PC cum latere CA angulum PCA conſtituat, <lb />cujus ope aquæ in globum impingentis celeritas detegi-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0346-03" corresp="note-0346-03a" place="margin">869.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus in aqua quieſcens tribus potentiis trahitur; </s>
          <s xml:space="preserve">gra-<lb />vitate ſua verticaliter deſcendere conatur; </s>
          <s xml:space="preserve">ex fluidi actio-<lb />ne juxta motus aquæ directionem fertur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tandem filo per <lb />PC trahitur, Formetur triangulum EFG, in quo EF <lb />lineam verticalem deſignat, cum hac conſtituat linea FG <lb />angulum EFG, æqualem angulo a directione motus flu-<lb />minis cum linea verticali formato, tandem ſit angulus GEF <lb />æqualis angulo PCA. </s>
          <s xml:space="preserve">Trianguli EFG latera parallela <lb />ſunt directionibus trium memoratarum potentiarum, po-<lb />tentiæ ipſæ idcirco ſunt ut hæc latera <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi ergo EF globi
<ptr xml:id="note-0346-04a" corresp="note-0346-04" type="noteAnchor" />
gravitatem reſpectivam deſignat, FG exprimet actionem <lb />aquæ in globum. </s>
          <s xml:space="preserve">Si pro variis Experimentis, eodem adhi-<lb />bito globo, variis in locis inſtitutis, talia triangula deline-<lb />antur, latere EF manente, (gravitatem globi reſpectivam,
</s>
          <pb facs="0347" n="251" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. IX.</fw>
quæ non mutatur, deſignante) latera ut FG inter ſe pro-<lb />portionem actionum aquæ in globum ſervabunt. </s>
          <s xml:space="preserve">Hæ au-<lb />tem ſunt ut quadrata velocitatum aquarum in locis <lb />in quibus Experimenta inſtituta ſunt ut in cap. </s>
          <s xml:space="preserve"><hi rend="small caps">XI</hi>. </s>
          <s xml:space="preserve">videbi-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0346-04" corresp="note-0346-04a" n="*" anchored="true" place="margin">210</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Actio aquæ in globum cum pondere conferri poteſt, eſt <lb />
<ptr xml:id="note-0347-01a" corresp="note-0347-01" type="noteAnchor" />
enim ad globi pondus reſpectivum ut FG ad EF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0347-01" corresp="note-0347-01a" place="margin">870.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondusque hac proportione detectum eſt pondus cy-<lb />lindri aquei, cujusbaſeos diameter eſt globi diameter, &amp; </s>
          <s xml:space="preserve">cujus <lb />altitudo illa eſt, a qua cadendo in vacuo corpus acquirit ve-<lb />locitatem qua aqua in globum incurrit; </s>
          <s xml:space="preserve">ut hoc etiam in cap. <lb /></s>
          <s xml:space="preserve"><hi rend="small caps">XI</hi>. </s>
          <s xml:space="preserve">demonſtramus. </s>
          <s xml:space="preserve">Data nunc hac altitudine, dabitur (ſi du-<lb />ratio vibrationis penduli cujuſcunque, cujus longitudo no-<lb />ta eſt, determinata fuerit) ſpatium, quod ab aqua in tem-<lb />pore noto poteſt percurri<ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſicetiam aquæ quantitas quæ
<ptr xml:id="note-0347-02a" corresp="note-0347-02" type="noteAnchor" />
per locum magnitudine datum, in fluminis ſectione, in <lb />dato tempore, fluit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0347-02" corresp="note-0347-02a" n="*" anchored="true" place="margin">288. 255. 257.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Notandum hanc velocitatis aquæ determinationem non <lb />bene procedere in aquæ ſuperficie; </s>
          <s xml:space="preserve">quia actio aquæ <lb />in globum ibi irregularis eſt. </s>
          <s xml:space="preserve">Poteſt hæc celeri-<lb />
<ptr xml:id="note-0347-03a" corresp="note-0347-03" type="noteAnchor" />
tas detegi immergendo aquâ corpus, aquâ paululum levius, <lb />quod verſus ſuperficiem hæreat, &amp; </s>
          <s xml:space="preserve">non ſatis hanc excedat <lb />ut motu venti affici poſſit; </s>
          <s xml:space="preserve">cum gravitates ſpecificæ aquæ <lb />&amp; </s>
          <s xml:space="preserve">corporis vix differant, &amp; </s>
          <s xml:space="preserve">hoc pro toto immerſo haberi <lb />poſſit, eadem celeritate cum aqua movebitur, &amp; </s>
          <s xml:space="preserve">menſura-<lb />ri tempus, ope penduli, poterit, dum corpus ſpatium an-<lb />te menſuratum percurrit. </s>
          <s xml:space="preserve">Quando vento aquæ ſuperfi-<lb />cies agitatur, non bene Experimentum procedet, pro-<lb />pter motum undarum, quo in corporis motu irregularitas <lb />datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0347-03" corresp="note-0347-03a" place="margin">871.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0348" n="252" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT X.</head>
        <head rend="italics" xml:space="preserve">De Motu Undarum.</head>
        <p>
          <s xml:space="preserve">AQuæ quieſcentis ſuperficies plana eſt &amp; </s>
          <s xml:space="preserve">ad horizontem <lb />
<ptr xml:id="note-0348-01a" corresp="note-0348-01" type="noteAnchor" />
parallela <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi aliqua ex cauſa hæc cava fiat in A, cir-
<ptr xml:id="note-0348-02a" corresp="note-0348-02" type="noteAnchor" />
cumdatur hæc cavitas elevatione BB; </s>
          <s xml:space="preserve">elevata hæc aqua <lb />
<ptr xml:id="note-0348-03a" corresp="note-0348-03" type="noteAnchor" />
gravitate deſcendit, &amp; </s>
          <s xml:space="preserve">celeritate deſcendendo acquiſita ca-<lb />vitatem novam format, quo motu aqua ad latera hujus ca-<lb />vitatis adſcendit, &amp; </s>
          <s xml:space="preserve">implet cavitatem A, dum nova ele-<lb />vatio C verſus formatur; </s>
          <s xml:space="preserve">hæc dum deprimitur de novo a-<lb />qua eandem partem verſus adſcendit; </s>
          <s xml:space="preserve">unde motus in aquæ <lb />ſuperficie oritur, &amp; </s>
          <s xml:space="preserve">cavitas, præ ſe elevationem ferens, <lb />ab A ad C movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0348-01" corresp="note-0348-01a" place="margin">872.</note>
              <note xml:space="preserve" xml:id="note-0348-02" corresp="note-0348-02a" place="margin">TAB XXXIV. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0348-03" corresp="note-0348-03a" n="*" anchored="true" place="margin">707.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Cavitas hæc cum conjuncta elevatione vocatur unda</s>
        </p>
        <note xml:space="preserve" place="margin">873.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Latitudo undæ eſt ſpatium ab unda in ſuperficie aquæ <lb />
<ptr xml:id="note-0348-05a" corresp="note-0348-05" type="noteAnchor" />
occupatum &amp; </s>
          <s xml:space="preserve">menſuratum juxta motus undæ directionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0348-05" corresp="note-0348-05a" place="margin">874.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cavitas ut A ab omni parte elevatione circumdatur, &amp; </s>
          <s xml:space="preserve"><lb />motus memoratus omnes partes verſus ſeſe expandit; </s>
          <s xml:space="preserve">un-<lb />
<ptr xml:id="note-0348-06a" corresp="note-0348-06" type="noteAnchor" />
dæ ideo per circulum moventur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0348-06" corresp="note-0348-06a" place="margin">875.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur obſtaculum AB, in quod unda, cujus origo eſt <lb />
<ptr xml:id="note-0348-07a" corresp="note-0348-07" type="noteAnchor" />
in C, incurrat; </s>
          <s xml:space="preserve">examinandum quam in puncto quocunque <lb />
<ptr xml:id="note-0348-08a" corresp="note-0348-08" type="noteAnchor" />
ut E mutationem patiatur unda, quando in hoc puncto ad <lb />obſtaculum pervenit. </s>
          <s xml:space="preserve">In omnibus locis, per quæ unda tranſ-<lb />it, dum hæc latitudinem ſuam percurrit, aqua elevatur, <lb />cavitas deinde formatur, quæ iterum impletur; </s>
          <s xml:space="preserve">quam mu-<lb />tationem dum ſuperficies aquæ ſubit, hujus particulæ per <lb />parvum ſpatium eunt &amp; </s>
          <s xml:space="preserve">redeunt. </s>
          <s xml:space="preserve">Directio hujus motus <lb />eſt per CE, celeritaſque per hanc lineam repræſentari po-<lb />teſt; </s>
          <s xml:space="preserve">concipiatur hicce motus in duos alios reſolutus per <lb />GE &amp; </s>
          <s xml:space="preserve">DE, quorum celeritates per haſce lineas reſpecti-<lb />ve repræſentantur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Motu per DE particulæ in obſtacu-
<ptr xml:id="note-0348-09a" corresp="note-0348-09" type="noteAnchor" />
lum non agunt, &amp; </s>
          <s xml:space="preserve">eadem celeritate, poſt impactum, jux-<lb />ta hanc directionem motum continuant; </s>
          <s xml:space="preserve">motuſque hic re-
</s>
          <pb facs="0349" n="253" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. X.</fw>
præſentatur per EF, poſit is EF &amp; </s>
          <s xml:space="preserve">ED inter ſe æqualibus. </s>
          <s xml:space="preserve">Mo-<lb />tu per GE particulæ directe ad obſtaculum accedunt, &amp; </s>
          <s xml:space="preserve">aqua, <lb />quæ ultra obſtaculum progredi nequit, &amp; </s>
          <s xml:space="preserve">ab inſequenti <lb />propellitur, cedit illam partem verſus in qua minima reſi-<lb />ſtentia datur, id eſt, adſcendit; </s>
          <s xml:space="preserve">hæcque major quam in <lb />cæteris locis elevatio ex motu per GE oritur; </s>
          <s xml:space="preserve">quia hoc <lb />motu ſolo ad obſtaculum particulæ accedunt. </s>
          <s xml:space="preserve">Deſcenſu a-<lb />qua eam acquirit velocitatem cum qua fuit elevata, &amp; </s>
          <s xml:space="preserve">ea-<lb />dem cum vi particulæ aqueæ ab obſtaculo juxta directio-<lb />nem EG repelluntur cum qua ad obſtaculum acceſſere. <lb /></s>
          <s xml:space="preserve">Ex hoc motu &amp; </s>
          <s xml:space="preserve">motu memorato per EF oritur motus <lb />per EH, cujus celeritas per lineam EH, æqualem <lb />lineæ CE, deſignatur, &amp; </s>
          <s xml:space="preserve">reflexione celeritas undæ non <lb />mutatur; </s>
          <s xml:space="preserve">reditque hæc per EH, eodem modo ac ſublato <lb />obſtaculo per Eb motum continuaſſet. </s>
          <s xml:space="preserve">Si a C perpendi-<lb />cularis CD ducatur ad obſtaculum, &amp; </s>
          <s xml:space="preserve">hæc producatur, <lb />fiatque Dc æqualis CD, linea HE continuata tranſibit per <lb />c; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cum hæc demonſtratio in omnibus punctis obſtaculi <lb />procedat, ſequitur undam reflexam eandem habere figuram <lb />
<ptr xml:id="note-0349-01a" corresp="note-0349-01" type="noteAnchor" />
ab hac parte obſtaculi, quam, ſublato obſtaculo, ultra hoc <lb />habuiſſet. </s>
          <s xml:space="preserve">Si obſtaculum ad horizontem inclinetur, aqua <lb />
<ptr xml:id="note-0349-02a" corresp="note-0349-02" type="noteAnchor" />
ſuper illo adſcendit &amp; </s>
          <s xml:space="preserve">deſcendit, &amp; </s>
          <s xml:space="preserve">attritum patitur, quo <lb />undæ reflexio turbatur, &amp; </s>
          <s xml:space="preserve">ſæpiſſime in totum deſtruitur. <lb /></s>
          <s xml:space="preserve">Hæc eſt ratio quare plerumque fluminum ripæ undas non <lb />reflectant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0348-07" corresp="note-0348-07a" place="margin">876.</note>
              <note xml:space="preserve" xml:id="note-0348-08" corresp="note-0348-08a" place="margin">TAB. XXXIV. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0348-09" corresp="note-0348-09a" n="*" anchored="true" place="margin">604.</note>
              <note xml:space="preserve" xml:id="note-0349-01" corresp="note-0349-01a" place="margin">877.</note>
              <note xml:space="preserve" xml:id="note-0349-02" corresp="note-0349-02a" place="margin">878.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando in obſtaculo ut BL foramen datur ut I, pars un-<lb />
<ptr xml:id="note-0349-03a" corresp="note-0349-03" type="noteAnchor" />
dæ, quæ per hoc tranſit, motum directe continuat, &amp; </s>
          <s xml:space="preserve"><lb />QQ verſus ſeſe expandit, &amp; </s>
          <s xml:space="preserve">nova unda formatur, quæ <lb />per ſemicirculum movetur, cujus centrum eſt ipſum fora-<lb />men. </s>
          <s xml:space="preserve">Nam pars undæ elevata, quæ primo transgreditur <lb />foramen, ſtatim paululumad latera defluit, &amp; </s>
          <s xml:space="preserve">deinde deſcen-<lb />dendo cavitatem format, quæ ab omni parte ultra ſoramen <lb />elevatione circumdatur, quæ ad omnes partes, eodem mo-<lb />do, ac de geneſi primæ undæ dictum <ptr type="noteAnchor" />, ſeſe expandit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0349-03" corresp="note-0349-03a" place="margin">879.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">872.</note>
        <p>
          <s xml:space="preserve">Unda, cui opponitur obſtaculum ut AO, inter <lb />
<ptr xml:id="note-0349-05a" corresp="note-0349-05" type="noteAnchor" />
O &amp; </s>
          <s xml:space="preserve">N motum continuat; </s>
          <s xml:space="preserve">ſed R verſus per portio-
</s>
          <pb facs="0350" n="254" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
nem circuli, cujus centrum non multum ab O diſtat, ſeſe <lb />expandit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0349-05" corresp="note-0349-05a" place="margin">880.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce ſacile deducitur motus undæ ponè obſtaculum <lb />
<ptr xml:id="note-0350-01a" corresp="note-0350-01" type="noteAnchor" />
ut MN.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0350-01" corresp="note-0350-01a" place="margin">881.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Undæ ſæpe producuntur ex motu corporis tremulo, quæ <lb />
<ptr xml:id="note-0350-02a" corresp="note-0350-02" type="noteAnchor" />
etiam per circulum ſeſe expandunt, licet per lineam rectam <lb />corpus eat &amp; </s>
          <s xml:space="preserve">redeat; </s>
          <s xml:space="preserve">aqua enim agitatione elevata deſcen-<lb />dendo cavitatem format, quæ ab omni parte elevatione cir-<lb />cumdatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0350-02" corresp="note-0350-02a" place="margin">882.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Undæ variæ ſeſe mutuo non perturbant, dum juxta va-<lb />
<ptr xml:id="note-0350-03a" corresp="note-0350-03" type="noteAnchor" />
rias directiones moventur. </s>
          <s xml:space="preserve">Cujus effectus ratio hæc eſt; <lb /></s>
          <s xml:space="preserve">quamcunque ex motu undæ figuram adepta fuerit aquæ ſu-<lb />perficies, in hac elevatio &amp; </s>
          <s xml:space="preserve">depreſſio dari poſſunt, ut &amp; </s>
          <s xml:space="preserve"><lb />motus qualis in undæ motu requiritur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0350-03" corresp="note-0350-03a" place="margin">883.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Qui unquam undarum motum attente conſideravit, hæc <lb />omnia cum Experimentis congruere vidit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Celeritas undarum ut determinetur, motus alius cum ha-<lb />rum motu analogus examinandus eſt. </s>
          <s xml:space="preserve">Detur fluidum in <lb />
<ptr xml:id="note-0350-04a" corresp="note-0350-04" type="noteAnchor" />
tubo cylindrico curvo EH, ſuperetque altitudo fluidi in <lb />
<ptr xml:id="note-0350-05a" corresp="note-0350-05" type="noteAnchor" />
crure EF altitudinem in alio crure quantitate lE, quæ <lb />differentia in duas partes æquales ſecanda eſt in i. </s>
          <s xml:space="preserve">Gravi-<lb />tate ſua deſcendit fluidum in crure EH, dum æqualiter in <lb />tubo EH adſcendit, &amp; </s>
          <s xml:space="preserve">ita quando ſuperficies fluidi perve-<lb />nit ad i, ad eandem in utroque crure datur altitudinem, &amp; </s>
          <s xml:space="preserve"><lb />in hoc ſitu ſolo fluidum poteſt quieſcere: </s>
          <s xml:space="preserve">ſed celeritate de-<lb />ſcendendo acquiſita motum continuat, magisque adſcendit <lb />in tubo GH, &amp; </s>
          <s xml:space="preserve">in EF deprimitur ad l uſque, niſi qua-<lb />tenus ab attritu tubi motus minuitur. </s>
          <s xml:space="preserve">Fluidum in tubo <lb />GH magis elevatum etiam gravitate deſcendit, &amp; </s>
          <s xml:space="preserve">fluidum <lb />in tubo it &amp; </s>
          <s xml:space="preserve">redit, donec ex attritu totum motum amiſe-<lb />rit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0350-04" corresp="note-0350-04a" place="margin">884.</note>
              <note xml:space="preserve" xml:id="note-0350-05" corresp="note-0350-05a" place="margin">TAB. XXXIV. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quantitas materiæ movendæ eſt totum fluidum in tubo; <lb /></s>
          <s xml:space="preserve">vis motrix eſt pondus columnæ lE; </s>
          <s xml:space="preserve">hoc fluidum premens <lb />eodem motu cum reliquo fluido in tubo agitatur &amp; </s>
          <s xml:space="preserve">reſpe-<lb />ctu hujus quieſcit; </s>
          <s xml:space="preserve">agit ergo in fluidum motum ut in quie-<lb />ſcens &amp; </s>
          <s xml:space="preserve">toto ſuo pondere premit in inferius fluidum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Al-
<ptr xml:id="note-0350-06a" corresp="note-0350-06" type="noteAnchor" />
</s>
          <pb facs="0351" n="255" />
          <s xml:space="preserve"><fw type="head">MATHEMATIC A. LIB. II. CAP. X.</fw>
titudo autem hujus fluidi prementis ſemper eſt duplum di-<lb />ſtantiæ Ei, quæ ergo diſtantia cum hac vi motrice in ea-<lb />dem ratione creſcit &amp; </s>
          <s xml:space="preserve">minuitur. </s>
          <s xml:space="preserve">Diſtantia autem Ei eſt <lb />ſpatium a fluido percurrendum, ut a ſitu EH perveniat <lb />ad ſitum quietis; </s>
          <s xml:space="preserve">quod ergo ſpatium ſemper eſt ut vis quæ <lb />continuo in fluidum agit: </s>
          <s xml:space="preserve">ſed tali ex cauſa demonſtravi-<lb />mus penduli in cycloide oſcillati vibrationes omnes eſſe æ-<lb />que diuturnas <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideo &amp; </s>
          <s xml:space="preserve">hîc quæcunque fuerit agitationum
<ptr xml:id="note-0351-01a" corresp="note-0351-01" type="noteAnchor" />
inæqualitas, æquali ſemper tempore fluidum it aut redit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0350-06" corresp="note-0350-06a" n="*" anchored="true" place="margin">252.</note>
              <note xml:space="preserve" xml:id="note-0351-01" corresp="note-0351-01a" n="*" anchored="true" place="margin">287.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tempus in quo fluidum ſic agitatum adſcendit aut de-<lb />
<ptr xml:id="note-0351-02a" corresp="note-0351-02" type="noteAnchor" />
ſcendit, eſt tempus in quo vibratur pendulum, cujus longi-<lb />tudo, id eſt, diſtantia inter centra oſcillationis &amp; </s>
          <s xml:space="preserve">ſuſpen-<lb />ſionis, æqualis eſt ſemi-longitudini fluidi in tubo, ſive ſe-<lb />mi-ſummæ linearum EE, FG, &amp; </s>
          <s xml:space="preserve">GH: </s>
          <s xml:space="preserve">longitudo hæc <lb />in axe tubi menſuranda eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0351-02" corresp="note-0351-02a" place="margin">885.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vibretur hocce pendulum in cycloïde methodo ſuperius <lb />
<ptr xml:id="note-0351-03a" corresp="note-0351-03" type="noteAnchor" />
explicata <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Pendulum PC &amp; </s>
          <s xml:space="preserve">arcus AD ejuſdem ſunt
<ptr xml:id="note-0351-04a" corresp="note-0351-04" type="noteAnchor" />
longitudinis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in puncto A directio curvæ ad horizontem
<ptr xml:id="note-0351-05a" corresp="note-0351-05" type="noteAnchor" />
<ptr xml:id="note-0351-06a" corresp="note-0351-06" type="noteAnchor" />
perpendicularis eſt, &amp; </s>
          <s xml:space="preserve">corpus toto ſuo pondere juxta cur-<lb />vam deſcendere conatur: </s>
          <s xml:space="preserve">hoc autem pondus eſt ad vim in <lb />corpus agens, poſito hoc in P, ut AD, aut PC ad PD<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0351-07a" corresp="note-0351-07" type="noteAnchor" />
Sit nunc fluidum in eo ſitu, ut iE (fig. </s>
          <s xml:space="preserve">5.) </s>
          <s xml:space="preserve">æqualis ſit PD; <lb /></s>
          <s xml:space="preserve">pondus totius materiæ movendæ, id eſt, totius fluidi, eſt <lb />ad pondus lE, quod eſt vis in hoc ſitu in fluidum agens <lb />ut longitudo fluidi in tubo ad lineam lE, in qua ratione <lb />etiam ſunt harum quantitatum ſemiſſes, id eſt PC ad PD <lb />(fig. </s>
          <s xml:space="preserve">6.)</s>
          <s xml:space="preserve">. </s>
          <s xml:space="preserve">In pendulo ergo pondus materiæ movendæ eſt <lb />ad vim in hanc agentem in P, ut in tubo pondus materiæ mo-<lb />vendæ ad vim in hanc agentem in ſitu EH. </s>
          <s xml:space="preserve">Æqualibus viribus <lb />ideo corpus pendulum &amp; </s>
          <s xml:space="preserve">fluidum in hac occaſione propel-<lb />luntur, &amp; </s>
          <s xml:space="preserve">hoc ubique obtinet ubi ſpatia, a fluido in agi-<lb />tatione &amp; </s>
          <s xml:space="preserve">a corpore in vibratione percurſa, ſunt æqualia; </s>
          <s xml:space="preserve"><lb />idcirco in hoc caſu agitatio &amp; </s>
          <s xml:space="preserve">vibratio eodem tempore per-<lb />aguntur, &amp; </s>
          <s xml:space="preserve">non modo in hoc caſu, ſed ſemper <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Cum
<ptr xml:id="note-0351-08a" corresp="note-0351-08" type="noteAnchor" />
vero vibrationes exiguæ in circulo a vibrationibus in cy-
</s>
          <pb facs="0352" n="256" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cloïde non differant, etiam ad illas demonſtratio referri <lb />debet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0351-03" corresp="note-0351-03a" place="margin">886.</note>
              <note xml:space="preserve" xml:id="note-0351-04" corresp="note-0351-04a" place="margin">TAB. XXXIV. <lb />fig 6.</note>
              <note xml:space="preserve" xml:id="note-0351-05" corresp="note-0351-05a" n="*" anchored="true" place="margin">283.</note>
              <note xml:space="preserve" xml:id="note-0351-06" corresp="note-0351-06a" n="*" anchored="true" place="margin">284.</note>
              <note xml:space="preserve" xml:id="note-0351-07" corresp="note-0351-07a" n="*" anchored="true" place="margin">287.</note>
              <note xml:space="preserve" xml:id="note-0351-08" corresp="note-0351-08a" n="*" anchored="true" place="margin">884.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>.</head>
        <p>
          <s xml:space="preserve">Detur tubus vitreus cylindricus curvus ut EFGH; </s>
          <s xml:space="preserve">ſit <lb />
<ptr xml:id="note-0352-01a" corresp="note-0352-01" type="noteAnchor" />
crurum longitudo unius pedis, &amp; </s>
          <s xml:space="preserve">cylindri diameter ſemi-<lb />pollicis; </s>
          <s xml:space="preserve">tubo mercurius infundatur, &amp; </s>
          <s xml:space="preserve">conſtitato pendu-<lb />lo, cujus longitudo æquet dimidium longitudinis cylindri <lb />mercurii in tubo, ſi mercurius in tubo agitetur, iiſdem <lb />temporibus adſcendit &amp; </s>
          <s xml:space="preserve">deſcendit hic, in quibus pendu-<lb />lum oſcillando it &amp; </s>
          <s xml:space="preserve">redit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0352-01" corresp="note-0352-01a" place="margin">887.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut ex dictis determinemus undarum celeritatem, variæ <lb />
<ptr xml:id="note-0352-02a" corresp="note-0352-02" type="noteAnchor" />
undæ æquales &amp; </s>
          <s xml:space="preserve">ſeſe mutuo immediate inſequentes con-<lb />
<ptr xml:id="note-0352-03a" corresp="note-0352-03" type="noteAnchor" />
ſiderandæ ſunt ut AB, CD, EF, quæ ab A ad F <lb />moventur. </s>
          <s xml:space="preserve">Unda AB percurrit latitudinem ſuam, quan-<lb />do cavitas A pervenit ad C; </s>
          <s xml:space="preserve">quod fieri non poteſt, niſi a-<lb />qua in C ad altitudinem undarum culminum adſcendat, i-<lb />terumque ad profunditatem C deſcendat; </s>
          <s xml:space="preserve">in quo motu aqua <lb />infra lineam hi ſenſibiliter non agitatur: </s>
          <s xml:space="preserve">congruit ergo hic-<lb />ce motus cum motu memorato in tubo, &amp; </s>
          <s xml:space="preserve">aqua adſcendit <lb />&amp; </s>
          <s xml:space="preserve">deſcendit, id eſt, unda latitudinem ſuam percurrit, dum <lb />pendulum longitudinis dimidii BC duas peragit oſcillatio-<lb />nes <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">aut dum pendulum longitudinis BCD, prioris qua-
<ptr xml:id="note-0352-04a" corresp="note-0352-04" type="noteAnchor" />
druplæ, ſemel vibratur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0352-02" corresp="note-0352-02a" place="margin">888.</note>
              <note xml:space="preserve" xml:id="note-0352-03" corresp="note-0352-03a" place="margin">TAB. XXXIV. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0352-04" corresp="note-0352-04a" n="*" anchored="true" place="margin">885.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">290.</note>
        <p>
          <s xml:space="preserve">Pendet igitur celeritas undæ à longitudine lineæ BCD, <lb />quæ pro majori undarum latitudine, &amp; </s>
          <s xml:space="preserve">pro majori profun-<lb />ditate ad quam in motu undarum aqua deſcendit, major <lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In undis latioribus, quæ non alte elevantur, linea ut <lb />BCD a latitudine undæ vix differt, &amp; </s>
          <s xml:space="preserve">in eo caſu unda <lb />
<ptr xml:id="note-0352-06a" corresp="note-0352-06" type="noteAnchor" />
latitudinem ſuam percurrit, dum pendulum huic latitudi-<lb />ni æquale ſemel oſcillatur. </s>
          <s xml:space="preserve">In omni motu æquabili mul-<lb />tiplicando tempus per celeritatem datur ſpatium percur-<lb />ſum <ptr type="noteAnchor" />, unde ſequitur celeritates undarum eſſe ut radices
<ptr xml:id="note-0352-07a" corresp="note-0352-07" type="noteAnchor" />
<ptr xml:id="note-0352-08a" corresp="note-0352-08" type="noteAnchor" />
quadratas latitudinum: </s>
          <s xml:space="preserve">nam cum in hac ratione ſint tem-<lb />pora quibus latitudines ſuas percurrunt <ptr type="noteAnchor" />, eadem in harum
<ptr xml:id="note-0352-09a" corresp="note-0352-09" type="noteAnchor" />
</s>
          <pb facs="0353" />
          <s xml:space="preserve">
<pb facs="0353a" />
<ptr xml:id="fig-0353a-01a" corresp="fig-0353a-01" type="figureAnchor" />
<pb facs="0354" />
<pb facs="0355" n="257" /><fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
celeritatibus ratio requiritur, ut producta temporum per <lb />celeritates ſint ut undarum latitudines, quæ ſunt ſpatia <lb />percurſa.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0352-06" corresp="note-0352-06a" place="margin">889.</note>
              <note xml:space="preserve" xml:id="note-0352-07" corresp="note-0352-07a" n="*" anchored="true" place="margin">95.</note>
              <note xml:space="preserve" xml:id="note-0352-08" corresp="note-0352-08a" place="margin">890.</note>
              <note xml:space="preserve" xml:id="note-0352-09" corresp="note-0352-09a" n="*" anchored="true" place="margin">290. 889.</note>
              <figure xml:id="fig-0353a-01" corresp="fig-0353a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0353a-01" />
                <label>0353a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc omnia tantum pro quamproxime veris habenda <lb />ſunt, quia undarum motus a motu in tubo paululum dif-<lb />fert; </s>
          <s xml:space="preserve">qui error pro parte tamen compenſatur ex eo quod <lb />penduli longitudo menſuretur juxta lineas inclinatas BC &amp; </s>
          <s xml:space="preserve"><lb />CD.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XI.</head>
        <head rend="italics" xml:space="preserve">De Reſiſtentia Fluidorum.</head>
        <p>
          <s xml:space="preserve">OMne corpus quod in fluido movetur reſiſtentiam patitur, <lb />
<ptr xml:id="note-0355-01a" corresp="note-0355-01" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">quidem ex duplici cauſa.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0355-01" corresp="note-0355-01a" place="margin">891.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quamvis fluidorum partes parum admodum cohæreant <lb />illas tamen vi quadam cohærere extra dubium eſt <ptr type="noteAnchor" />, hanc
<ptr xml:id="note-0355-02a" corresp="note-0355-02" type="noteAnchor" />
autem, dum corpus in motu ſuo ſeparat fluidorum particu-<lb />
<ptr xml:id="note-0355-03a" corresp="note-0355-03" type="noteAnchor" />
las, ſuperare debet cobæſionem; </s>
          <s xml:space="preserve">bæcque eſt prima reſiſten-<lb />tiæ cauſa.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0355-02" corresp="note-0355-02a" n="*" anchored="true" place="margin">54. 55.</note>
              <note xml:space="preserve" xml:id="note-0355-03" corresp="note-0355-03a" place="margin">892.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Actio bæc ſimilis eſt illi qua corporum mollium partes ſe-<lb />
<ptr xml:id="note-0355-04a" corresp="note-0355-04" type="noteAnchor" />
parantur, dum in ipſis cavitas formatur, quam formari vi-<lb />dimus actione, quæ ſequitur proportionem ipſius cavitatis <lb />
<ptr xml:id="note-0355-05a" corresp="note-0355-05" type="noteAnchor" />
formatæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quam demonſtrationem ad corpus in fluido mo-
tum etiam poſſumus applicare; </s>
          <s xml:space="preserve">in hoc autem motu corpus <lb />cavitatem format proportionalem ſpatio percurſo, quamvis <lb />cavitas hæc ſingulis momentis affluxu fluidi iterum implea-<lb />tur. </s>
          <s xml:space="preserve">Unde deducimus corpus ex hac prima cauſa, reſi-<lb />
<ptr xml:id="note-0355-06a" corresp="note-0355-06" type="noteAnchor" />
ſtentiam pati proportionalem huic ſpatio percurſo; </s>
          <s xml:space="preserve">quæid-<lb />circo ad inſtar velocitatis augetur &amp; </s>
          <s xml:space="preserve">minuitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0355-04" corresp="note-0355-04a" place="margin">893.</note>
              <note xml:space="preserve" xml:id="note-0355-05" corresp="note-0355-05a" n="*" anchored="true" place="margin">464.</note>
              <note xml:space="preserve" xml:id="note-0355-06" corresp="note-0355-06a" place="margin">894.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">94</note>
        <p>
          <s xml:space="preserve">Dum corpus in corpore molli cavitatem format, partes <lb />
<ptr xml:id="note-0355-08a" corresp="note-0355-08" type="noteAnchor" />
immediata tantum actione corporum in ſe mutuo transfe-<lb />runtur, qua ceſſante actione ceſſat particularum <lb />motus; </s>
          <s xml:space="preserve">hac de cauſa in formanda cavitate tantum <lb />conſumitur vis qua partium cohæſio ſuperatur, poſ-
</s>
          <pb facs="0356" n="258" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſuntque corpora integras in formandis cavitatibus vires in-<lb />ſitas amittere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0355-08" corresp="note-0355-08a" place="margin">895.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus autem in motu per fluidum non tantum trans-<lb />fert particulas actione immediata, dum ſibi viam in-<lb />ter has aperit, in qua translatione immediata cohæſionem <lb />ſuperat; </s>
          <s xml:space="preserve">ſed &amp; </s>
          <s xml:space="preserve">præterea ipſis particulis vim communicat, <lb />qua poſt ceſlatam corporis actionem inter ſe moventur: <lb /></s>
          <s xml:space="preserve">reactio verò particularum, dum ipſis motus hicce impri-<lb />
<ptr xml:id="note-0356-01a" corresp="note-0356-01" type="noteAnchor" />
mitur, ex harum inertia oriunda, eſt ſecunda cauſa reſi-<lb />ſtentiæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0356-01" corresp="note-0356-01a" place="margin">896.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut clarius concipiamus quæ reſiſtentias has ſpectant, ad <lb />hoc attendere debemus. </s>
          <s xml:space="preserve">Mutuam actionem corporis &amp; </s>
          <s xml:space="preserve">fluidi <lb />
<ptr xml:id="note-0356-02a" corresp="note-0356-02" type="noteAnchor" />
eandem eſſe, ſive corpus certa velocitate in fluido quieſcente <lb />moveatur, ſive, quieſcente corpore, eâdem velocitate flui-<lb />dum in hoc incurrat. </s>
          <s xml:space="preserve">Actio enim hæc a motu reſpectivo <lb />pendet, qui in hiſce caſibus non variat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0356-02" corresp="note-0356-02a" place="margin">897.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc ſepoſitâ partium cohæſione ad motum fluidi at-<lb />tendamus, &amp; </s>
          <s xml:space="preserve">hoc conſideremus dum in corpus quieſcens <lb />incurrit, facile videbimus fluidi actionem eſſe preſſionem, <lb />
<ptr xml:id="note-0356-03a" corresp="note-0356-03" type="noteAnchor" />
particulaſque non impingere in corpus ſed juxta hoc, aut <lb />juxta particulas fluidi, quæ corpus tangunt, moveri &amp; </s>
          <s xml:space="preserve">inter-<lb />ea illas premere corpus, eodem modo ac corpus premit <lb />planum ſuper quo movetur, quales preſſiones ex viribus <lb />oriundas ſuperius <ptr type="noteAnchor" /> indicavimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0356-03" corresp="note-0356-03a" place="margin">898.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">120. 321. 522.</note>
        <p>
          <s xml:space="preserve">Preſſio hæc a vi inſitâ particularum oriunda, eſt ut hæc <lb />
<ptr xml:id="note-0356-05a" corresp="note-0356-05" type="noteAnchor" />
vis, id eſt ut quadratum velocitatis <ptr type="noteAnchor" />, augetur etiam ut nu-
<ptr xml:id="note-0356-06a" corresp="note-0356-06" type="noteAnchor" />
merus particularum determinato tempore incurrentium, <lb />qui numerus velocitatis ſequitur proportionem: </s>
          <s xml:space="preserve">tandem <lb />preſſio de qua agimus ſequitur rationem temporis per quod <lb />ſingulæ particulæ in determinatam partem ſuperficiei pre-<lb />munt, quod tempus eo minus eſt quo velocitas eſt major, <lb />ſequiturque rationem inverſam velocitatis; </s>
          <s xml:space="preserve">quare ultimæ duæ <lb />rationes ſeſe mutuo deſtruunt ſuperſtitemque habemus ſo-<lb />
<ptr xml:id="note-0356-07a" corresp="note-0356-07" type="noteAnchor" />
lam rationem quadrati velocitatis; </s>
          <s xml:space="preserve">quam idcirco ſequitur <lb />reſiſtentia ex ſecunda cauſa.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0356-05" corresp="note-0356-05a" place="margin">899.</note>
              <note xml:space="preserve" xml:id="note-0356-06" corresp="note-0356-06a" n="*" anchored="true" place="margin">477.</note>
              <note xml:space="preserve" xml:id="note-0356-07" corresp="note-0356-07a" place="margin">900.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quomodo autem ambæ reſiſtentiæ cauſæ ſimul agant <lb />
<ptr xml:id="note-0356-08a" corresp="note-0356-08" type="noteAnchor" />
</s>
          <pb facs="0357" n="259" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
concipimus, ſi ad hoc attendamus, particulas quæ in cor-<lb />
<ptr xml:id="note-0357-01a" corresp="note-0357-01" type="noteAnchor" />
pus, ut A agunt, ad latera defluere in B &amp; </s>
          <s xml:space="preserve">D, ibique, <lb />ſepoſitâ cohæſione, nullam exerere actionem, poſitâ autem <lb />cohæſione hac, particulæ hæ laterales ſecum trahunt, &amp; </s>
          <s xml:space="preserve"><lb />actione ſua inſequentes ſeparant, quæ deſideratur ſeparatio <lb />ut fluidum ab omni parte defluat: </s>
          <s xml:space="preserve">cohæſio autem ſuperari <lb />minime poterit niſi corpus reſiſtat, &amp; </s>
          <s xml:space="preserve">actio in hoc detur <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0357-02a" corresp="note-0357-02" type="noteAnchor" />
quæ actioni ex inertia oriundæ ſuperaddenda eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0356-08" corresp="note-0356-08a" place="margin">901.</note>
              <note xml:space="preserve" xml:id="note-0357-01" corresp="note-0357-01a" place="margin">TAB. XXXVI. <lb />fg. 5.</note>
              <note xml:space="preserve" xml:id="note-0357-02" corresp="note-0357-02a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina,</hi></head>
        <p rend="italics">
          <s xml:space="preserve">Qua Experimenta de Fluidorum Reſiſtentiis inſtituuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Arca lignea AB longitudinem habet quinque pedum, <lb />
<ptr xml:id="note-0357-03a" corresp="note-0357-03" type="noteAnchor" />
latitudinem duorum pedum cum ſemiſſe, altitudinem o-<lb />
<ptr xml:id="note-0357-04a" corresp="note-0357-04" type="noteAnchor" />
cto aut decem pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0357-03" corresp="note-0357-03a" place="margin">902.</note>
              <note xml:space="preserve" xml:id="note-0357-04" corresp="note-0357-04a" place="margin">TAB. XXXV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quatuor hæc ſuſtinetur columnis ligneis, altitudinis quin-<lb />que pedum, qui minori arcæ CD imponuntur, quæ ipſa <lb />pedibus gaudet quatuor, altitudinis circiter decem pollicum; <lb /></s>
          <s xml:space="preserve">non autem minorem hiſce pedibus tribuimus altitudinem, <lb />ut ex epiſtomio Eaqua in ſitulam, fere hujus altitudinis, re-<lb />cipiatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Parallelopipedum cavum ligneum F longitudinem ha-<lb />bet trium pedum cum ſemiſſe à g ad b; </s>
          <s xml:space="preserve">hujus cavitatis ba-<lb />ſis eſt quadratum quinque pollicum. </s>
          <s xml:space="preserve">In figura repræſenta-<lb />tur quomodo verticaliter regulis ligneis firmetur Parallelo-<lb />pipedum. </s>
          <s xml:space="preserve">Diſtantia inter hujus ſuperficiem ſuperiorem &amp; </s>
          <s xml:space="preserve"><lb />arcæ AB fundum eſt quindecim pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hoc ipſo fundo, in medio reſpectu longitudinis, fora-<lb />men datur rotundum, diametri circiter quatuor pollicum <lb />cum ſemiſſe, quod paulo minus diſtat ab uno latere quàm <lb />ab alio, ut magis commode experimenta inſtituantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Huic foramini reſpondet foramen, quod parum cum <lb />præcedenti differt, ſed tamen minus eſt, in medio ligni ſu-<lb />perioris parallelopipedi F.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hiſce foraminibus tubus plumbeus T verticaliter fir-<lb />matur, quo communicatio datur inter arcam AB &amp; </s>
          <s xml:space="preserve">pa-<lb />rallelopipedum F. </s>
          <s xml:space="preserve">Tubi longitudo eſt octodecim polli-
</s>
          <pb facs="0358" n="260" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cum; </s>
          <s xml:space="preserve">ipſius cavitas eſt cylindrica, bene lævigata, diametrum-<lb />que habet quatuor pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Probe firmatur tubus, &amp; </s>
          <s xml:space="preserve">aquæ effluxus, inter hunc &amp; </s>
          <s xml:space="preserve">li-<lb />gnum, interpoſitis lini filamentis, cohibetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Et tubi anguſtiores ſæpe adhibentur, in quo caſu annu-<lb />lis ligneis extremitates circumdantur, ut eodem modo fir-<lb />mentur in foraminibus memoratis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In inferiori parte Parallelopipedi F epiſtomia dantur qua-<lb />tuor I, L, M, N. </s>
          <s xml:space="preserve">Horum aperturæ in laminis dantur <lb />horizontalibus, quæ omnes in eodem poſitæ ſunt plano ho-<lb />rizontali; </s>
          <s xml:space="preserve">ſuntque hæ aperturæ ipſis epiſtomiorum capaci-<lb />tatibus multo minores, ut aqua ſine ſenſibili attritu effluat. <lb /></s>
          <s xml:space="preserve">Minorum duorum epiſtomiorum, quæ æqualia ſunt, aper-<lb />turæ æquales ſunt, alîus dupla eſt, &amp; </s>
          <s xml:space="preserve">maximi tripla. </s>
          <s xml:space="preserve">Dia-<lb />meter aperturæ mediæ ſemi poll. </s>
          <s xml:space="preserve">æqualis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quantumvis exacte hæ menſurentur aperturæ, non o-<lb />mnis error vitari poteſt, qui quomodo corrigatur, ſtatim di-<lb />cam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Oris arcæ AB in medio imponitur tabula P, cujus lon-<lb />gitudo arcæ latitudinem paululum excedit &amp; </s>
          <s xml:space="preserve">cujus latitu-<lb />do ſedecim aut octodecim eſt poll. </s>
          <s xml:space="preserve">Hæc, ne impoſita <lb />caſu in aquam cadat, oris, ſemipollicem altis, circumdatur. <lb /></s>
          <s xml:space="preserve">Firmatur tabula regulis ligneis quatuor, quarum duæ viden-<lb />tur in o &amp; </s>
          <s xml:space="preserve">q, cum ipſa cohærentibus, &amp; </s>
          <s xml:space="preserve">inter quas promi-<lb />nentia lignea r, cum arca cohærens, recipitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tabulæ huic ſuperimponitur crux lignea S, infra tabu-<lb />lam penetrans, ut cochleâ firmetur. </s>
          <s xml:space="preserve">Cruci appenditur bi-<lb />lanx V, quâ in aliis experimentis utimur, &amp; </s>
          <s xml:space="preserve">de qua antea <lb />egimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">703</note>
        <p>
          <s xml:space="preserve">Ita ſuſpenditur hæc, ut, quando eſt in æquilibrio, lan-<lb />cium pedes ſupra tabulam ad altitudinem, quæ paululum <lb />excedit quartam partem pollicis, tantum eleventur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Uncus autem lancis k reſpondet foramini in tabula, quod <lb />diametrum habet trium partium quartarum pollicis, &amp; </s>
          <s xml:space="preserve">cu-<lb />jus centrum datur in axe continuato tubi T.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0359" n="261" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
        <p>
          <s xml:space="preserve">Uſu veniunt in experimentis, quæ hac Machinâ inſtituun-<lb />tur, globi, cylindri, &amp; </s>
          <s xml:space="preserve">coni varii, qui ſinguli capillis equi-<lb />nis ſuſpenduntur; </s>
          <s xml:space="preserve">in qua ſuſpenſione reſpectu cylindrorum <lb />&amp; </s>
          <s xml:space="preserve">conorum attendendum, ut axem habeant verticalem, &amp; </s>
          <s xml:space="preserve"><lb />conorum vertices ſurſum dirigantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">An aperturæ epiſtomiorum eſſent exactæ, ut explorarem, <lb />&amp; </s>
          <s xml:space="preserve">errores corrigerem, methodo uſus ſum, quam nunc <lb />exponam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Rebus ut explicavi diſpoſitis, in T applicato tubo, cujus <lb />
<ptr xml:id="note-0359-01a" corresp="note-0359-01" type="noteAnchor" />
diameter erat hypotenuſa trianguli rectanguli iſoſceles, cu-<lb />jus latera ſuntduorum pollicum, arcam AB aquâ replevi ita, <lb />ut oræ arcæ duobus tantum pollicibus aquam ſuperarent, <lb />quo etiam F &amp; </s>
          <s xml:space="preserve">T repleta fuere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0359-01" corresp="note-0359-01a" place="margin">903.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In tubo T, capillo equino cylindrum ſuſpendi æneum, cujus <lb />diameter pollicem fere quartâ parte excedit, &amp; </s>
          <s xml:space="preserve">cujus altitudo <lb />eſt ſeſqui pollicis, ſuprema ſuperficies paululum convexa eſt, <lb />&amp; </s>
          <s xml:space="preserve">cavus ipſe eſt, ut minusgravet libram, &amp; </s>
          <s xml:space="preserve">exacte clauſus, <lb />ne aqua in ipſum penetrare poſſit: </s>
          <s xml:space="preserve">capillus equinus cum unco k <lb />lancis libræ V cohærebat, &amp; </s>
          <s xml:space="preserve">pondere lanci oppoſitæ <lb />impoſito dabatur æquilibrium.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæſivi quodnam pondus adjiciendum eſſet, ut æqui-<lb />librium daretur, aperto uno ex epiſtomiis minoribus; </s>
          <s xml:space="preserve">de-<lb />tegitur pondus hoc tentando; </s>
          <s xml:space="preserve">Primo pondus ad libitum <lb />imponitur, libraque manu in ſitu æquilibrii retinetur, &amp;</s>
          <s xml:space="preserve">, <lb />poſt apertum epiſtomium, relinquitur; </s>
          <s xml:space="preserve">ſi libra moveatur, <lb />pro diverſo motu augetur, aut minuitur, pondus, &amp; </s>
          <s xml:space="preserve">eadem <lb />operatio repetitur, donec, relictâ bilance, hæc in æqui-<lb />librio maneat, habemuſque tunc pondus quod valet actio-<lb />nem quam aqua, dum per tubum movetur, in corpus exerit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hac methodo detexi, apertis ſucceſſive epiſtomiis mino-<lb />ribus, parum actiones differre; </s>
          <s xml:space="preserve">ideoque non exactiſſime æ-<lb />quales eſſe aquæ quantitates per ſingula effluentes, qui er-<lb />ror facillime paululum admodum aucto foramine uno cor-<lb />rectus fuit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Apertis tunc ambobus his epiſtomiis I, L, ſimul, ut a-
</s>
          <pb facs="0360" n="262" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
quæ quantitas dupla efflueret, quæſivi aquæ actionem in cy-<lb />lindrum, curavique ut actio eadem foret aperto unico epi-<lb />ſtomio M.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tandem eâdem methodo eo reduxi epiſtomium N, ut <lb />ex hoc ea flueret aquæ quantitas, quæ ex epiſtomio M &amp; </s>
          <s xml:space="preserve"><lb />uno ex epiſtomiis I, aut L, ſimul, æquali tempore, <lb />fluit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In his omnibus obſervavi, &amp; </s>
          <s xml:space="preserve">hoc in omnibus experi-<lb />mentis, quæ hac machinâ inſtituuntur, obſervandum, ut <lb />aqua in arca ſervetur ad eandem altitudinem, quare, ubi <lb />uno pollice depreſſa eſt ſuperficies, de novo aqua infundenda <lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Poteſt nunc machina experimentis inſervire. </s>
          <s xml:space="preserve">Aperto e-<lb />
<ptr xml:id="note-0360-01a" corresp="note-0360-01" type="noteAnchor" />
piſtomio I, aut L, certa aquæ quantitas effluit, determi-<lb />natâque velocitate movetur aqua in tubo T, &amp; </s>
          <s xml:space="preserve">uniformem <lb />velocitatem habet in toto tubo; </s>
          <s xml:space="preserve">in hunc enim continuo in-<lb />trat &amp; </s>
          <s xml:space="preserve">eodem tempore exit aquæ quantitas, æqualis illi, quæ <lb />ex epiſtomio deſluit. </s>
          <s xml:space="preserve">Dupla eſt aquæ velocitas in tubo, ſi <lb />dupla aquæ quantitas defluat, id eſt, ſi ambo epiſtomia I &amp; </s>
          <s xml:space="preserve"><lb />L, aut ſolum M, aperiantur. </s>
          <s xml:space="preserve">Tripla eſtaperto M &amp; </s>
          <s xml:space="preserve">I vel <lb />L ſimul, aut N ſolo. </s>
          <s xml:space="preserve">Quadrupla eſt velocitas apertis tri-<lb />bus epiſtomiis I, L, &amp; </s>
          <s xml:space="preserve">M, aut N &amp; </s>
          <s xml:space="preserve">uno ex I &amp; </s>
          <s xml:space="preserve">L. </s>
          <s xml:space="preserve">Quin-<lb />tupla eſt apertis ſimul M &amp; </s>
          <s xml:space="preserve">N. </s>
          <s xml:space="preserve">Sextupla apertis N, M, <lb />&amp; </s>
          <s xml:space="preserve">uno ex I &amp; </s>
          <s xml:space="preserve">L. </s>
          <s xml:space="preserve">Septupla tandem apertis omnibus ſi-<lb />mul.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0360-01" corresp="note-0360-01a" place="margin">904.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In his omnibus motibus nunquam acceleratio aquæ in <lb />tubo T dari poteſt ex cohæſione oriunda, qualem alio lo-<lb />co <ptr type="noteAnchor" /> memoravimus; </s>
          <s xml:space="preserve">quæ ſi daretur non hæc procederet
<ptr xml:id="note-0360-02a" corresp="note-0360-02" type="noteAnchor" />
concluſio, æqualem certo tempore per epiſtomium fluere <lb />aquæ quantitatem; </s>
          <s xml:space="preserve">ſive ſolum, ſive cum aliis aperiatur, quod <lb />hìc extra dubium eſt; </s>
          <s xml:space="preserve">quia ex ſola preſſione aquæ ſupra ori-<lb />ficium tubi incumbentis dari poteſt velocitas quæ variis <lb />vicibus maximam ſuperat quâ in hiſce aqua in tubo gau-<lb />det.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0360-02" corresp="note-0360-02a" n="*" anchored="true" place="margin">246.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0361" n="263" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum 1.</hi></head>
        <p>
          <s xml:space="preserve">Rebus, ut in machinæ deſcriptione expoſitum, diſpo-<lb />
<ptr xml:id="note-0361-01a" corresp="note-0361-01" type="noteAnchor" />
ſitis, adhibitoque tubo T, ſuperius memorato, cujus dia-<lb />
<ptr xml:id="note-0361-02a" corresp="note-0361-02" type="noteAnchor" />
meter eſt hypotenuſa trianguli rectanguli iſoſceles, cujus <lb />ſingula latera ſunt duorum pollicum, globus æneus G, cujus <lb />diameter eſt ſemi poll.</s>
          <s xml:space="preserve">, ſuſpenditur ad profunditatem, non <lb />intereſt quamcunque, ſex, octo, aut decem pollicum, in tu-<lb />bo, in cujus axe datur globus; </s>
          <s xml:space="preserve">quia capillus equinus, cui <lb />cohæret, cum unco lancis E conjungitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0361-01" corresp="note-0361-01a" place="margin">905.</note>
              <note xml:space="preserve" xml:id="note-0361-02" corresp="note-0361-02a" place="margin">TAB. XXXV. <lb />fig. 1.2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Methodo in n. </s>
          <s xml:space="preserve">903. </s>
          <s xml:space="preserve">tradita quæruntur actiones aquæ in <lb />globum, dum ſucceſſive, diverſis velocitatibus, aqua per tu-<lb />bum tranſit, quæ actiones valent reſiſtentias corporis, quan-<lb />do hoc, quieſcente aquâ, iisdem velocitatibus, in hac movetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pondera minima quibus utor in his actionibus determi-<lb />nandis, quartam partem grani valent; </s>
          <s xml:space="preserve">ſuntque actiones quæ <lb />ſquuntur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">906.</note>
        <note xml:space="preserve" place="margin"> <lb />Velocitates # Reſiſtentiæ <lb />
1. # gr. {3/4}.
2. # gr. 1 {1/2}.
3. # gr. 3.
4. # gr. 4 {3/4}.
5. # gr. 7 {3/4}.
6. # gr. 10 {1/2}.
7. # gr. 14.
</note>
        <p>
          <s xml:space="preserve">In tribus primis velocitatibus deficiebant paululum a-<lb />ctiones a ponderibus notatis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Experimenta hæc, adhibitâ admodum exactâ bilance, fue-<lb />
<ptr xml:id="note-0361-05a" corresp="note-0361-05" type="noteAnchor" />
re inſtituta, maximâ cum curâ, non tamen nullum omni-<lb />no errorem quantumvis exiguum dari aſlerere non auſim.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0361-05" corresp="note-0361-05a" place="margin">907</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fateor potius exiguos, quarta parte grani minores, vitari <lb />non potuiſſe, &amp; </s>
          <s xml:space="preserve">non credo ab experimento recedi, quando <lb />tale quid ſuppletur, ubi regularis ſeries hoc poſtulat,</s>
        </p>
        <p>
          <s xml:space="preserve">Errorem talem dari in prima actione, hîc determinatâ, <lb />quæ parum deficit a {3/4} gr.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">qui reſpectu hujus ponderis ſen-
</s>
          <pb facs="0362" n="264" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſiblis eſt, non tantum indicat regularis ſeries ex reliquis ex-<lb />perimentis deducenda, ſed &amp; </s>
          <s xml:space="preserve">hoc confirmat Experimen-<lb />tum ſequens.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Experimenta hìc traduntur, ut ante initam ullam compu-<lb />tationem a me fuere inſtituta.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Diviſo nunc grano in centum partes, patet in ſequenti <lb />ſerie reſiſtentiam pro parte ſequi rationem velocitatis, pro <lb />parte rationem quadrati velocitatis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">908.</note>
        <note xml:space="preserve" place="margin"> <lb />Velocitates # Reſiſtentiæ \\ ex primacauſa. # Reſiſtentiæ \\ exſecunda cauſa. # Summæ \\ ambarum. # Reſiſtentiæ \\ In Exp. <lb />
1. # 1 X 20 = 20. # 1 X 26 = 26. # 46. # 75.
2. # 2 X 20 = 40, # 4 X 26 = 104. # 144. # 150.
3. # 3 X 20 = 60, # 9 X 26 = 234. # 294. # 300.
4. # 4 X 20 = 80, # 16 X 26 = 416. # 496. # 475.
5. # 5 X 20 = 100, # 25 X 26 = 650. # 750. # 775.
6. # 6 X 20 = 120, # 36 X 26 = 936. # 1056. # 1050.
7. # 7 X 20 = 140, # 49 X 26 = 1274. # 1414. # 1400.
</note>
        <p>
          <s xml:space="preserve">Quando corpora ſimilia, ſimiliter, &amp; </s>
          <s xml:space="preserve">velocitatibus æqua-<lb />
<ptr xml:id="note-0362-03a" corresp="note-0362-03" type="noteAnchor" />
libus, per idem fluidum, moventur, deducitur ex ante de-<lb />
<ptr xml:id="note-0362-04a" corresp="note-0362-04" type="noteAnchor" />
monſtratis <ptr type="noteAnchor" />, reſiſtentiam utramque augeri &amp; </s>
          <s xml:space="preserve">minui, ut au-
getur &amp; </s>
          <s xml:space="preserve">minuitur numerus particularum fluidi ex loco mota-<lb />rum eodem tempore, id eſt, ſequitur reſiſtentia integra ra-<lb />
<ptr xml:id="note-0362-05a" corresp="note-0362-05" type="noteAnchor" />
tionem quadratorum laterum homologorum <ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">, ſi de glo-
bis, cylindris, aut conis, agatur, rationem quadratorum dia-<lb />metrorum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0362-03" corresp="note-0362-03a" place="margin">909.</note>
              <note xml:space="preserve" xml:id="note-0362-04" corresp="note-0362-04a" n="*" anchored="true" place="margin">893. 899.</note>
              <note xml:space="preserve" xml:id="note-0362-05" corresp="note-0362-05a" n="*" anchored="true" place="margin">20. El. VI.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">2 El. XII.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum 2.</hi></head>
        <p>
          <s xml:space="preserve">Differt hoc cum præcedenti tantum reſpectu magnitudi-<lb />
<ptr xml:id="note-0362-07a" corresp="note-0362-07" type="noteAnchor" />
nis globi, qui in tubo T ſuſpenditur. </s>
          <s xml:space="preserve">In hoc adhibemus <lb />
<ptr xml:id="note-0362-08a" corresp="note-0362-08" type="noteAnchor" />
globum H, cujus diameter eſt hypotenuſa trianguli rectan-<lb />guli iſoſceles, cujus latera ſunt ſemipoll.</s>
          <s xml:space="preserve">, æqualia nempe <lb />diametro globi Gin experimento I. </s>
          <s xml:space="preserve">adhibito; </s>
          <s xml:space="preserve">quare qua-<lb />drata diametrorum ſunt ut unum ad duo <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in qua ratione
<ptr xml:id="note-0362-09a" corresp="note-0362-09" type="noteAnchor" />
etiam detectæ fuere reſiſtentiæ, ut ſequenti tabella patet, in <lb />qua + denotat exceſlum, &amp; </s>
          <s xml:space="preserve">- defectum exprimit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0362-07" corresp="note-0362-07a" place="margin">910.</note>
              <note xml:space="preserve" xml:id="note-0362-08" corresp="note-0362-08a" place="margin">TAB. XXXV. <lb />fig. 1.2.</note>
              <note xml:space="preserve" xml:id="note-0362-09" corresp="note-0362-09a" n="*" anchored="true" place="margin">47. El. I.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0363" n="265" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
        <note xml:space="preserve" place="margin">911.</note>
        <note xml:space="preserve" place="margin"> <lb />Velocitates # Reſiſtentiæ globi H. # Reſiſtentiæ globi G in exp. I. <lb />
1 # {3/4} + # {3/4} -
2 # 2 {3/4} # 1 {1/2} -
3 # 6 -- # 3 --
4 # 9 {3/4} + # 4 {3/4}
5 # 15 {1/4} # 7 {3/4}
6 # 21 # 10 {1/2}
7 # 28 # 14.
</note>
        <p>
          <s xml:space="preserve">Reſiſtentiæ in minori velocitate ſolæ ſunt quæ cum propo-<lb />ſitione non congruunt; </s>
          <s xml:space="preserve">ſed jam in experimento præcedenti <lb />vidimus illam corrigendam eſſe, quæ in illo experimento <lb />fuit detecta; </s>
          <s xml:space="preserve">reſiſtentia verò ibi in regulari ſerie poſita, <lb />dimidium eſt illius, quæ, in eadem velocitate, in hoc ulti-<lb />mo experimento, fuit determinata.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Reſiſtentia ex prima cauſa non mutatur pro diverſa cor-<lb />
<ptr xml:id="note-0363-03a" corresp="note-0363-03" type="noteAnchor" />
poris figura, ſi modo cavitas formata in motu eadem ſit <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0363-04a" corresp="note-0363-04" type="noteAnchor" />
quare in cono &amp; </s>
          <s xml:space="preserve">cylindro juxta axeos directionem motis, <lb />ut &amp; </s>
          <s xml:space="preserve">in globo, ſi horum corporum diametri fuerint æqua-<lb />les, &amp; </s>
          <s xml:space="preserve">agatur de eodem fluido, &amp; </s>
          <s xml:space="preserve">eadem velocitate, re-<lb />ſiſtentia eadem eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0363-03" corresp="note-0363-03a" place="margin">912.</note>
              <note xml:space="preserve" xml:id="note-0363-04" corresp="note-0363-04a" n="*" anchored="true" place="margin">893 464.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reſiſtentia autem ex ſecunda cauſa variat pro diverſa <lb />
<ptr xml:id="note-0363-05a" corresp="note-0363-05" type="noteAnchor" />
corporis figura; </s>
          <s xml:space="preserve">nam licet ſluidum quieſcens quaqua ver ſum æ-<lb />quali vi premat, hoc ad preſſionem ex motu oriundam non <lb />debere referri facile patet, quæ juxta unicam tantum dire-<lb />ctionem agit, &amp; </s>
          <s xml:space="preserve">non tota ſuſtinetur niſi a plano ad hanc di-<lb />ctionem perpendiculari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0363-05" corresp="note-0363-05a" place="margin">913.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Demonſtramus in ſcholio ſequenti reſiſtentiam cylindri <lb />
<ptr xml:id="note-0363-06a" corresp="note-0363-06" type="noteAnchor" />
ſe babere ad coni reſiſtentiam, ſi ambo fuerint recti, &amp; </s>
          <s xml:space="preserve">eâ-<lb />dem velocitate, juxta axium directiones, in eodem fluido, mo-<lb />ti, ut linea in coni ſuperficie, à vertice ad punctum quod-<lb />cunque baſeos ducta, ad ſemidiametrum baſeos.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0363-06" corresp="note-0363-06a" place="margin">914.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Cylindri autem recti &amp; </s>
          <s xml:space="preserve">globi reſiſtentias eſſe inter ſe ut <lb />
<ptr xml:id="note-0363-07a" corresp="note-0363-07" type="noteAnchor" />
tria ad duo, ſi diametri fuerint æquales, &amp; </s>
          <s xml:space="preserve">ille juxta a-
</s>
          <pb facs="0364" n="266" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
xeos directionem feratur, in eodem ſcholio demonſtra-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0363-07" corresp="note-0363-07a" place="margin">915.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Unde ſequitur reſiſtentiam globi ſe babere ad reſiſtentiam <lb />
<ptr xml:id="note-0364-01a" corresp="note-0364-01" type="noteAnchor" />
conirecti, juxta axeos directionem moti, &amp; </s>
          <s xml:space="preserve">cujus baſeos dia-<lb />meter æqualis eſt diametro globi, ut duæ tertiæ partes li-<lb />neæ, in ſuperficie coni ad punctum baſeos ductæ, ſe babent ad <lb />ſemidiametrum baſeos.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0364-01" corresp="note-0364-01a" place="margin">916.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Obſervandum coni verticem in motibus hiſce præcede-<lb />re; </s>
          <s xml:space="preserve">ſienim baſis reſiſtentiam pateretur, clarum eſſet hanc a <lb />reſiſtentia cylindri ejuſdem diametri non differre.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Experimentum hoc ut præcedentia inſtituitur, differt <lb />
<ptr xml:id="note-0364-02a" corresp="note-0364-02" type="noteAnchor" />
tantum corpus in quod aqua agit. </s>
          <s xml:space="preserve">Uſus ſum cono in O <lb />
<ptr xml:id="note-0364-03a" corresp="note-0364-03" type="noteAnchor" />
delineato, baſis diameter eſt ſemipollicis, altitudo ſemipol-<lb />licis a vertice v ad centrum circuli qui figuram conicam <lb />terminat, infra quam figuram conicam cylindricum erat <lb />corpus, eratque partis cylindricæ altitudo circiter octavæ <lb />partis pollicis. </s>
          <s xml:space="preserve">Hæc vero inferior pars corporis conſide-<lb />randa non eſt, quia in hanc aqua, juxta axeos corporis dire-<lb />ctionem mota, incurrere non poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0364-02" corresp="note-0364-02a" place="margin">917</note>
              <note xml:space="preserve" xml:id="note-0364-03" corresp="note-0364-03a" place="margin">TAB. XXXV. <lb />fig. 1. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Actiones aquæ in corpus tabellâ ſequenti continen-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">918.</note>
        <note xml:space="preserve" place="margin"> <lb />Velocitates # Reſiſtentiæ <lb />
1. # gr. {1/2}. -
2. # gr. 1 {1/4} +
3. # gr. 2 {1/2} -
4. # gr. 4.
5. # gr. 6. -
6. # gr. 8 {1/2}
7. # gr. 11.
</note>
        <p>
          <s xml:space="preserve">Diviſo grano in centum partes, in tabella ſequentiſe-<lb />paramus reſiſtentias ex utraque cauſa.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0365" n="267" />
        <fw type="head">MATHEMATICA. LIB. II. CAP XI.</fw>
        <note xml:space="preserve" place="margin">919.</note>
        <note xml:space="preserve" place="margin"> <lb />Velocitates. # Reſiſtentiæ # Reſiſtentiæ # Summæ # Reſiſtentiæ <lb />
exprimâcauſâ. # ex 2<hi rend="superscript">2</hi>. cauſâ # ambarum. # in Exp.
1. # 1 x 20 = 20. # 1 x 20 = 20 # 40 # 50 -
2. # 2 x 20 = 40. # 4 x 20 = 80 # 120 # 125 +
3. # 3 x 20 = 60. # 9 x 20 = 180 # 240 # 250 -
4. # 4 x 20 = 80. # 16 x 20 = 320 # 400 # 400
5. # 5 x 20 = 100. # 25 x 20 = 500 # 600 # 600 -
6. # 6 x 20 = 120. # 36 x 20 = 720 # 840 # 850
7. # 7 x 20 = 140. # 49 x 20 = 980 # 1120 # 1100
</note>
        <p>
          <s xml:space="preserve">Qui tabellam hanc examinaverit, vix quicquam magis ac-<lb />curatum in talibus experimentis poſſe ſperari, facile vide-<lb />bit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Conferendo hoc Experimentum cum primo <ptr type="noteAnchor" />, confirma-
<ptr xml:id="note-0365-03a" corresp="note-0365-03" type="noteAnchor" />
tur n. </s>
          <s xml:space="preserve">912.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0365-03" corresp="note-0365-03a" n="*" anchored="true" place="margin">908. 919.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Liquet etiam quoad reſiſtentiam ex ſecunda cauſa, hanc <lb />in hoc caſu ſe habere ad reſiſtentiam globiejuſdem diame-<lb />tri ut 26. </s>
          <s xml:space="preserve">ad 20 <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">908. 919.</note>
        <p>
          <s xml:space="preserve">Ut nunc computationem ineamus de hiſce reſiſtentiis; </s>
          <s xml:space="preserve">ſunt <lb />
<ptr xml:id="note-0365-05a" corresp="note-0365-05" type="noteAnchor" />
hæ inter ſe ut {2/3} v b ad ſemidiametrum baſis <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ſi hæc ſemidi
<ptr xml:id="note-0365-06a" corresp="note-0365-06" type="noteAnchor" />
ameter dicatur 1.</s>
          <s xml:space="preserve">, erit coni altitudo 2.</s>
          <s xml:space="preserve">; &amp; </s>
          <s xml:space="preserve">valebit vb radicem <lb />quadratam numeri 5 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſunt ergo reſiſtentiæ ut {2/3}√5. </s>
          <s xml:space="preserve">ad I.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0365-07a" corresp="note-0365-07" type="noteAnchor" />
Sed in ſuperiori parte, ut in vertice conus ſuſpendi poſſit, <lb />figura conica non ſervatur, quare reſiſtentia augenda <lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0365-05" corresp="note-0365-05a" place="margin">920.</note>
              <note xml:space="preserve" xml:id="note-0365-06" corresp="note-0365-06a" n="*" anchored="true" place="margin">916.</note>
              <note xml:space="preserve" xml:id="note-0365-07" corresp="note-0365-07a" n="*" anchored="true" place="margin">47. El. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ad latera foraminis per quod filum transmittitur, duæ <lb />exiguæ dantur ſuperficies planæ, quæ ſimul circiter valent <lb />{1/25} ſuperficiei circuli cujus diameter eſt bd, quare vigeſi-<lb />ma quinta pars reſiſtentiæ coni augenda in ratione reſiſten-<lb />tiæ coni hujus ad reſiſtentiam cylindri, id eſt, in ratione I <lb />ad √5 <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sunt ergo reſiſtentiæ quæſitæ ut {25 x 2/3} √5. </s>
          <s xml:space="preserve">ad
<ptr xml:id="note-0365-08a" corresp="note-0365-08" type="noteAnchor" />
</s>
          <pb facs="0366" n="268" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
24 + √ 5. </s>
          <s xml:space="preserve">quæ ratio vix differt a ratione 26. </s>
          <s xml:space="preserve">ad 19. </s>
          <s xml:space="preserve">In <lb />qua computatione negleximus conſiderationem figuræ i-<lb />pſius verticis cui filum fuit alligatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0365-08" corresp="note-0365-08a" n="*" anchored="true" place="margin">915.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Differt hæc reſiſtentia ex computatione a reſiſtentia in <lb />exp. </s>
          <s xml:space="preserve">vigeſima parte, quomodocunque mutetur velocitas, <lb />unde patet differentiam hanc figuræ ipſi tribuendam eſſe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cum autem non admodum magna ſit hæc differentia, &amp; </s>
          <s xml:space="preserve"><lb />cum non commode ad computum potuerit revocari pars <lb />quædam figuræ, facile patet experimento hoc propoſitionem <lb />n. </s>
          <s xml:space="preserve">916. </s>
          <s xml:space="preserve">confirmari.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Experimentis cum cylindris inſtitutis non uſus ſum ad <lb />
<ptr xml:id="note-0366-01a" corresp="note-0366-01" type="noteAnchor" />
demonſtrata confirmanda; </s>
          <s xml:space="preserve">difficultas horum experimento-<lb />rum in cauſa eſt; </s>
          <s xml:space="preserve">vix enim poteſt ſuſpendi cylindrus quin <lb />agitetur, dum aqua juxta hunc movetur; </s>
          <s xml:space="preserve">unde irregularis <lb />eſt ſeries reſiſtentiarum, &amp; </s>
          <s xml:space="preserve">in majoribus velocitatibus ad-<lb />modum incerta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0366-01" corresp="note-0366-01a" place="margin">921.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diverſaſque detexi reſiſtentias cylindrorum, quorum dia-<lb />metri erant æquales, ſed altitudines diverſæ; </s>
          <s xml:space="preserve">quod clarum <lb />eſt indicium agitationis cujuſdam, cum extra dubium ſit, <lb />reſiſtentiam cylindri juxta axeos directionem moti ab ipſius <lb />altitudine non pendere. </s>
          <s xml:space="preserve">Cum vero facile ſphæræ coni ita <lb />fuſpendantur, ut agitatio nulla timenda ſit, hæc corpora ad-<lb />hibenda credidi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hoc tamen de experimentis cum cylindris inſtitutis addam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Inter quatuor cylindros cum quibus experimenta tentavi <lb />unum datur, cujus diameter eſt ſemipollicis, &amp; </s>
          <s xml:space="preserve">altitudo <lb />{2/3} poll.</s>
          <s xml:space="preserve">, cujus reſiſtentiæ dant ſeriem regularem, quæ cum <lb />ante demonſtratis exacte ſatis congruit; </s>
          <s xml:space="preserve">ſi illam excipiamus <lb />reſiſtentiam, quæ reſpondet velocitati ſex, quæ 1 {1/4} gr. </s>
          <s xml:space="preserve">id <lb />eſt circiter duodecima parte in exp. </s>
          <s xml:space="preserve">deſicit ab illa quæ <lb />in ſerie deſideratur, quæ differentia certè notabilis eſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Hoc ut præcedentia fuit inſtitutum, ſuſpenſo cylindro <lb />
<ptr xml:id="note-0366-02a" corresp="note-0366-02" type="noteAnchor" />
K, cujus diameter erat ſemi pollicis; </s>
          <s xml:space="preserve">motus aquæ e-<lb />
<ptr xml:id="note-0366-03a" corresp="note-0366-03" type="noteAnchor" />
</s>
          <pb facs="0367" />
          <s xml:space="preserve">
<pb facs="0367a" />
<ptr xml:id="fig-0367a-01a" corresp="fig-0367a-01" type="figureAnchor" />
<pb facs="0368" />
<pb facs="0369" n="269" /><fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
rat juxta directionem axeos cylindri. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0369-01a" corresp="note-0369-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0366-02" corresp="note-0366-02a" place="margin">922.</note>
              <note xml:space="preserve" xml:id="note-0366-03" corresp="note-0366-03a" place="margin">TAB. XXXV <lb />fig 1. 4.</note>
              <figure xml:id="fig-0367a-01" corresp="fig-0367a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0367a-01" />
                <label>0367a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0369-01" corresp="note-0369-01a" place="margin"> <lb />Velocitates # Reſiſtentiæ <lb />1. # gr. {3/4}. <lb />2. # gr. 2. <lb />3. # gr. 4. <lb />4. # gr. 7 {1/2}. <lb />5. # gr. 11. <lb />6. # gr. 14. <lb />7. # gr. 20 {1/2}. <lb /></note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diviſo grano in centum partes ſeparantur reſiſtentiæ ex <lb />duabus cauſis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">923.</note>
        <note xml:space="preserve" place="margin"> <lb />Velocitates # Reſiſtentiæ # Reſiſtentiæ # Summæ # Reſiſtentiæ <lb />ex 1<hi rend="superscript">2</hi> cauſa # ex 2<hi rend="superscript">2</hi>. cauſa # ambarum # in exper. <lb />
1. # 1 x 20 = 20. # 1 x 39 = 39. # 59. # 75.
2. # 2 x 20 = 40. # 4 x 39 = 156. # 196. # 200.
3. # 3 x 20 = 60. # 9 x 39 = 351. # 411. # 400.
4. # 4 x 20 = 80. # 16 x 39 = 624. # 704. # 750.
5. # 5 x 20 = 100. # 25 x 39 = 975. # 1075. # 1100.
6. # 6 x 20 = 120. # 36 x 39 = 1404. # 1524. # 1400.
7. # 7 x 20 = 140. # 49 x 39 = 1911. # 2051. # 2050.
</note>
        <p>
          <s xml:space="preserve">Unde patet reſiſtentiam ex prima cauſa in hoc caſu illam <lb />eſſe, quæ obſervata fuit, in experimentis cum globo &amp; </s>
          <s xml:space="preserve">co-<lb />no inſtitutis ejuſdem diametri cum hoc cylindro, juxta <lb />demonſtrata in n. </s>
          <s xml:space="preserve">912. </s>
          <s xml:space="preserve">Patet etiam reſiſtentiam ex ſe-<lb />cunda cauſa in hoc experimento ſe habere ad reſiſtentiam <lb />globi ut 39 ad 26. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, id eſt ut 3. </s>
          <s xml:space="preserve">ad 2, ut monui in n.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0369-04a" corresp="note-0369-04" type="noteAnchor" />
915.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0369-04" corresp="note-0369-04a" n="*" anchored="true" place="margin">923. 908.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reſiſtentia ex prima cauſa in variis fluidis differt, hanc-<lb />
<ptr xml:id="note-0369-05a" corresp="note-0369-05" type="noteAnchor" />
que differentiam niſi experimentis determinari non poſſe <lb />facile etiam patet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0369-05" corresp="note-0369-05a" place="margin">924.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In motibus velocioribus, ſi fluida glutinoſa excipiamus <lb />
<ptr xml:id="note-0369-06a" corresp="note-0369-06" type="noteAnchor" />
exigua eſt reſiſtentia ex cobæſione partium, collata cum re, <lb />ſiſtentia ex ſecunda cauſa; </s>
          <s xml:space="preserve">quod ex diverſis rationibus, ſe-<lb />cundum quas augentur, ſequitur. </s>
          <s xml:space="preserve">Centies ex gr. </s>
          <s xml:space="preserve">auctâ ve-
</s>
          <pb facs="0370" n="270" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
locitate in qua æquales ſunt reſiſtentiæ hæ, prima erit ad <lb />ſecundam ut unum ad centum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0369-06" corresp="note-0369-06a" place="margin">925.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reſiſtentia autem ex ſecundâ caujâ in variis fluidis ſe-<lb />
<ptr xml:id="note-0370-01a" corresp="note-0370-01" type="noteAnchor" />
quitur rationem particularum ex loco motarum; </s>
          <s xml:space="preserve">pendete-<lb />nim a materiæ inertia, quæ materiæ quantitatis rationem <lb />ſequitur <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">eſt ergo reſiſtentia hæc ceteris paribus ut fluidi
<ptr xml:id="note-0370-02a" corresp="note-0370-02" type="noteAnchor" />
denſitas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0370-01" corresp="note-0370-01a" place="margin">926.</note>
              <note xml:space="preserve" xml:id="note-0370-02" corresp="note-0370-02a" n="*" anchored="true" place="margin">13.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Computatio de reſiſtentia ex ſecunda cauſâ iniri poteſt, <lb />nullo inſtituto experimento, determinando pondus quod <lb />hanc reſiſtentiam valet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit corpus cujus ſuperficies AB reſiſtentiam patitur, dum <lb />
<ptr xml:id="note-0370-03a" corresp="note-0370-03" type="noteAnchor" />
motus directio ad hanc ſuperſiciem perpendicularis eſt; </s>
          <s xml:space="preserve">po-<lb />
<ptr xml:id="note-0370-04a" corresp="note-0370-04" type="noteAnchor" />
nimus autem ut ſuperius, corpus quieſcere, dum fluidum <lb />movetur, quo actio fluidi in corpus non mutatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0370-03" corresp="note-0370-03a" place="margin">927.</note>
              <note xml:space="preserve" xml:id="note-0370-04" corresp="note-0370-04a" place="margin">TAB. XXXVI. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">897.</note>
        <p>
          <s xml:space="preserve">Sit ſuperficiei AB æqualis ſuperficies CD in fundo vaſis, <lb />continentis ſimile fluidum ad altitudinem EF; </s>
          <s xml:space="preserve">ponamus præ-<lb />terea preſſionem quam patitur pars CD fundi, æqualem eſſe <lb />actioni, quam patitur AB, ſepoſita partium cohæſio-<lb />ne.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Plana hæc duo æqualia, cohibent ſingula motum fluidi; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">propter actionum ſuarum æqualitatem, æquales motus <lb />cohibent. </s>
          <s xml:space="preserve">Ideoque ſublatis ipſis planis, fluidum in locis in <lb />quibus plana agebant eâdem velocitate fertur, id eſt, flui-<lb />dum, quod in fuperficiem AB agit, movetur velocitate qua <lb />fluidum per foramen in CD exire poteſt, id eſt veloci-<lb />tate, quam corpus acquirit in vacuo cadendo ab altitudine <lb />EC <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſeponimus enim cohæſionem partium &amp; </s>
          <s xml:space="preserve">omnem at-
<ptr xml:id="note-0370-06a" corresp="note-0370-06" type="noteAnchor" />
tritum. </s>
          <s xml:space="preserve">Ergo actio, quam patitur ſuperficies AB, dum <lb />fluidum in hancagit, valet pondus columnæ fluidi, cujus ba-<lb />ſis eſt CD, aut AB, &amp; </s>
          <s xml:space="preserve">altitudo EF; </s>
          <s xml:space="preserve">hæc eſt enim preſſio <lb />quam patitur CD <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0370-06" corresp="note-0370-06a" n="*" anchored="true" place="margin">796.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">721.</note>
        <p rend="italics">
          <s xml:space="preserve">Unde patet Priſmatis recti, juxta directionem ad baſim <lb />
<ptr xml:id="note-0370-08a" corresp="note-0370-08" type="noteAnchor" />
perpendicularem, in fluido moti, reſiſtentiam valere pondus <lb />columnæ ejuſdem fluidi, cujus baſis æqualis eſt baſi priſma-<lb />tis, &amp; </s>
          <s xml:space="preserve">cujus altitudo illa eſt, à qua corpus in vacuo ca-
</s>
          <pb facs="0371" n="271" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
dendo acquirit velocitatem qua priſma in fluido fer-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0370-08" corresp="note-0370-08a" place="margin">928.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Demonſtratio hæc tantum locum habet ubi ſuperficies, <lb />
<ptr xml:id="note-0371-01a" corresp="note-0371-01" type="noteAnchor" />
quæ reſiſtentiam patitur, ad motus directionem perpendicu-<lb />laris eſt <ptr type="noteAnchor" />, ubi de aliis ſuperficiebus agitur ad demonſtrata
<ptr xml:id="note-0371-02a" corresp="note-0371-02" type="noteAnchor" />
de his <ptr type="noteAnchor" /> attendendum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0371-01" corresp="note-0371-01a" place="margin">929.</note>
              <note xml:space="preserve" xml:id="note-0371-02" corresp="note-0371-02a" n="*" anchored="true" place="margin">913.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">214. 915.</note>
        <p>
          <s xml:space="preserve">Quare ſi de globo agatur, reſiſtentia valebit duas tertias <lb />partes ponderis cylindri ex fluido cujus diameter æqualis <lb />eſt diametro globi, &amp; </s>
          <s xml:space="preserve">cujus altitudo illa eſt a qua caden-<lb />do in vacuo corpus acquirit velocitatem, cum qua in fluido <lb />movetur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">928. 915.</note>
        <p rend="italics">
          <s xml:space="preserve">Altitudo a qua corpus cadendo acquirit velocitatem, qua <lb />
<ptr xml:id="note-0371-05a" corresp="note-0371-05" type="noteAnchor" />
ſi in fluido feratur, reſiſtentia ex ſecunda cauſa ponderi i-<lb />pſius corporis æqualis ſit, ex his facile detegitur. </s>
          <s xml:space="preserve">Si de pri-<lb />ſmate agatur, denſitas fluidi ſe babebit ad priſmatis denſi-<lb />tatem, ut bujus altitudo ad altitudinem quæſitam <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0371-05" corresp="note-0371-05a" place="margin">930.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">928. 732.</note>
        <p>
          <s xml:space="preserve">Si de globo agatur denſitas fluidi ſe babebit ad globi den-<lb />
<ptr xml:id="note-0371-07a" corresp="note-0371-07" type="noteAnchor" />
ſitatem, ut altitudo cylindri ejuſdem ponderis cum globo <lb />&amp; </s>
          <s xml:space="preserve">diametrum æqualem globi diametro habentis, quæ alti-<lb />tudo valet duas tertias partes diametri, ad duas tertias par-<lb />tes altitudinis quæſitæ <ptr type="noteAnchor" />, id eſt ut diameter ad altitudinem
<ptr xml:id="note-0371-08a" corresp="note-0371-08" type="noteAnchor" />
quæſitam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0371-07" corresp="note-0371-07a" place="margin">931.</note>
              <note xml:space="preserve" xml:id="note-0371-08" corresp="note-0371-08a" n="*" anchored="true" place="margin">928. 915. <lb />738.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pondus quod reſiſtentiam valet, ideoque ipſa reſiſten-<lb />
<ptr xml:id="note-0371-09a" corresp="note-0371-09" type="noteAnchor" />
tia ex ſecunda cauſa, ſequitur rationem baſeos priſmatis, <lb />denſitatis fluidi &amp; </s>
          <s xml:space="preserve">quadrati velocitatis corporis <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quod
<ptr xml:id="note-0371-10a" corresp="note-0371-10" type="noteAnchor" />
cum ante demonſtratis <ptr type="noteAnchor" /> congruit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0371-09" corresp="note-0371-09a" place="margin">932.</note>
              <note xml:space="preserve" xml:id="note-0371-10" corresp="note-0371-10a" n="*" anchored="true" place="margin">928 255.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">908. 926. <lb />900.</note>
        <p>
          <s xml:space="preserve">Quæ de pondere reſiſtentiam valenti dicta ſunt <ptr type="noteAnchor" /> etiam cum
<ptr xml:id="note-0371-12a" corresp="note-0371-12" type="noteAnchor" />
experimentis congruunt, ut patebit ſi computatio ineatur <lb />
<ptr xml:id="note-0371-13a" corresp="note-0371-13" type="noteAnchor" />
de pondere quod valet reſiſtentiam, data velocitate qua-<lb />cunque ex illis quas in experimentis aqua habuit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0371-12" corresp="note-0371-12a" place="margin">933.</note>
              <note xml:space="preserve" xml:id="note-0371-13" corresp="note-0371-13a" n="*" anchored="true" place="margin">928.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Velocitatem aquæ diximus 2. </s>
          <s xml:space="preserve">aperto epiſtomio cujus a-<lb />
<ptr xml:id="note-0371-14a" corresp="note-0371-14" type="noteAnchor" />
pertura erat circulus diametri ſemi pollicis, &amp; </s>
          <s xml:space="preserve">ſupra quod <lb />foramen aquæ altitudo erat quinque pedum; </s>
          <s xml:space="preserve">ita ut pes cy-<lb />lindricus aquæ effluere potuerit in tempore 46, 66. </s>
          <s xml:space="preserve">minu-<lb />torum ſecundorum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Pes cylindricus in tubo, in quo ex-
<ptr xml:id="note-0371-15a" corresp="note-0371-15" type="noteAnchor" />
</s>
          <pb facs="0372" n="272" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
perimenta fuere inſtituta, ſi hicce continuatus foret occu-<lb />paret pedes 18 <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ergo aqua per tubum tranſivit velocita-
<ptr xml:id="note-0372-01a" corresp="note-0372-01" type="noteAnchor" />
te qua pédes 18, percurruntur, in tempore minutorum <lb />ſecundorum 46, 66. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ubi velocitas in Exp. </s>
          <s xml:space="preserve">fuit 6.</s>
          <s xml:space="preserve">, hoc <lb />idem ſpatium 18. </s>
          <s xml:space="preserve">pedum potuit percurri in min. </s>
          <s xml:space="preserve">ſec. </s>
          <s xml:space="preserve">15, <lb />55. </s>
          <s xml:space="preserve">Experimentis cum pendulis inſtitutis, &amp; </s>
          <s xml:space="preserve">computatio-<lb />ne, juxta regulam ante memoratam <ptr type="noteAnchor" />, initâ, conſtat, cor-
<ptr xml:id="note-0372-02a" corresp="note-0372-02" type="noteAnchor" />
pus in uno minuto ſecundo cadere ab altitudine 15, 626. <lb /></s>
          <s xml:space="preserve">pedum Rhenolandicorum, quales ubique in menſuris noſtris <lb />adhibemus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">velocitate ab hac altitudine cadendo acqui-<lb />ſita corpus in uno minuto ſecundo percurrit pedes 31, 252. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
&amp; </s>
          <s xml:space="preserve">in minutis ſec. </s>
          <s xml:space="preserve">15, 55. </s>
          <s xml:space="preserve">percurret pedes 486, 06.</s>
          <s xml:space="preserve">; ergo ve-<lb />locitas 6. </s>
          <s xml:space="preserve">in exp. </s>
          <s xml:space="preserve">ad velocitatem acquiſitam cadendo ab al-<lb />titudine 15, 626. </s>
          <s xml:space="preserve">pedum, ut 18. </s>
          <s xml:space="preserve">ad 486, 06. </s>
          <s xml:space="preserve">Idcirco acqui-<lb />rit corpus velocitatem hanc exp.</s>
          <s xml:space="preserve">, cadendo in vacuo ab alti-<lb />tudine o, 257. </s>
          <s xml:space="preserve">poll. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, quæ vix excedit quartam pollicis par-
<ptr xml:id="note-0372-03a" corresp="note-0372-03" type="noteAnchor" />
tem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0371-14" corresp="note-0371-14a" place="margin">934.</note>
              <note xml:space="preserve" xml:id="note-0371-15" corresp="note-0371-15a" n="*" anchored="true" place="margin">833.</note>
              <note xml:space="preserve" xml:id="note-0372-01" corresp="note-0372-01a" place="margin">15 El. XII.</note>
              <note xml:space="preserve" xml:id="note-0372-02" corresp="note-0372-02a" n="*" anchored="true" place="margin">288.</note>
              <note xml:space="preserve" xml:id="note-0372-03" corresp="note-0372-03a" n="*" anchored="true" place="margin">255.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pes cubicus aquæ ponderat grana 487360 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pondus
<ptr xml:id="note-0372-04a" corresp="note-0372-04" type="noteAnchor" />
pedis cylindrici eſt gran. </s>
          <s xml:space="preserve">382772. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">poll. </s>
          <s xml:space="preserve">cylindrici <lb />gran. </s>
          <s xml:space="preserve">221 {1/2}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0372-04" corresp="note-0372-04a" n="*" anchored="true" place="margin">783.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reſiſtentia cylindri cujus diameter eſt ſemi poll. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ve-<lb />locitas illa quæ in experimentis dicitur 6. </s>
          <s xml:space="preserve">eſt pondus cylin-<lb />dri aquei cujus diameter eſt ſemi poll. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">altitudo æqualis <lb />o, 257. </s>
          <s xml:space="preserve">poll. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, valet ergo gr. </s>
          <s xml:space="preserve">14, 23.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">928.</note>
        <p>
          <s xml:space="preserve">Ponendo nunc reſiſtentiam hanc in ratione duplicata ve-<lb />locitatum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">globi reſiſtentiam duas tertias partes reſi-
<ptr xml:id="note-0372-06a" corresp="note-0372-06" type="noteAnchor" />
ſtentiæ cylindri <ptr type="noteAnchor" />, tabellam ſequentem formamus, in qua
<ptr xml:id="note-0372-07a" corresp="note-0372-07" type="noteAnchor" />
partes, centeſimâ grani parte minores, negliguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0372-06" corresp="note-0372-06a" n="*" anchored="true" place="margin">932.</note>
              <note xml:space="preserve" xml:id="note-0372-07" corresp="note-0372-07a" n="*" anchored="true" place="margin">915</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0373" n="273" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XI.</fw>
        <note xml:space="preserve" place="margin">935.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">923.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">908.</note>
        <note xml:space="preserve" place="margin"> <lb />Velocitates. # # Reſiſtentiæ # ex # ſecundâ # cauſâ. <lb />
# # Cylindri ## Globi
# comp. # Exp.<ptr type="noteAnchor" /> # comp. # Exp.<ptr type="noteAnchor" />
1. # 39. # 39. # 26. # 26.
2. # 158. # 156. # 105. # 104.
3. # 356. # 351. # 237. # 234.
4. # 632. # 624. # 421. # 416.
5. # 988. # 975. # 659. # 650.
6. # 1423. # 1404. # 949. # 936.
7. # 1937. # 1911. # 1291. # 1274.
</note>
        <p>
          <s xml:space="preserve">Exiguam dari differentiam inter has reſiſtentias, compu-<lb />
<ptr xml:id="note-0373-05a" corresp="note-0373-05" type="noteAnchor" />
tatione detectas, &amp; </s>
          <s xml:space="preserve">illas, quæ experimentis deteguntur, non <lb />mirum; </s>
          <s xml:space="preserve">cum pendeat collatio hæc, 1. </s>
          <s xml:space="preserve">à menſura aquæ ef-<lb />fluentis certo tempore, 2. </s>
          <s xml:space="preserve">à menſura ſpatii percurſi certo <lb />tempore a corpore cadente, 3. </s>
          <s xml:space="preserve">à menſura ponderis pedis <lb />cubici aquæ, &amp; </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">tandem à menſura ipſarum reſiſtentiarum. <lb /></s>
          <s xml:space="preserve">In ſingulis harum quatuor menſurarum errores exigui vitari <lb />minime poſſunt; </s>
          <s xml:space="preserve">non tamen tales ſunt ut ſcrupulus ullus <lb />circa experimenta ſupereſſe poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0373-05" corresp="note-0373-05a" place="margin">936.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In cap. </s>
          <s xml:space="preserve">22. </s>
          <s xml:space="preserve">lib. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">diximus, nos in hoc capite tradituros de-<lb />
<ptr xml:id="note-0373-06a" corresp="note-0373-06" type="noteAnchor" />
monſtrationem ab illa diverſam, quæ in n. </s>
          <s xml:space="preserve">446. </s>
          <s xml:space="preserve">datur, de <lb />virium menſura, quas in eodem corpore quadratis veloci-<lb />tatum ſtatuimus proportionales <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hac ergo caput hoc
<ptr xml:id="note-0373-07a" corresp="note-0373-07" type="noteAnchor" />
terminabo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0373-06" corresp="note-0373-06a" place="margin">937.</note>
              <note xml:space="preserve" xml:id="note-0373-07" corresp="note-0373-07a" n="*" anchored="true" place="margin">447.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">A nemine in dubium vocatur fluidi velocitatem, ex preſ-<lb />ſione fluidi ſuperincumbentis oriundam, ſequi rationem ſub-<lb />duplicatam altitudinis fluidi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">demonſtravimus in hoc ca-
<ptr xml:id="note-0373-08a" corresp="note-0373-08" type="noteAnchor" />
pite <ptr type="noteAnchor" />, reſiſtentiam ex ſecunda cauſa ſequi hujus altitudinis
<ptr xml:id="note-0373-09a" corresp="note-0373-09" type="noteAnchor" />
rationem; </s>
          <s xml:space="preserve">ideoque rationem duplicatam velocitatis; </s>
          <s xml:space="preserve">ſed <lb />etiam vidimus reſiſtentiam eandem ſequi rationem cum vi in-<lb />ſita particulis ſingulis fluidi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare vis hæc etiam eſt ut
<ptr xml:id="note-0373-10a" corresp="note-0373-10" type="noteAnchor" />
quadratum velocitatis. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0373-08" corresp="note-0373-08a" n="*" anchored="true" place="margin">799.</note>
              <note xml:space="preserve" xml:id="note-0373-09" corresp="note-0373-09a" n="*" anchored="true" place="margin">928.</note>
              <note xml:space="preserve" xml:id="note-0373-10" corresp="note-0373-10a" n="*" anchored="true" place="margin">899.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0374" n="274" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM, <lb />Demonſtrationes n. 914. &amp; 915.</head>
        <p>
          <s xml:space="preserve">Sint ABCD, EFG, ſectiones per axes cylindri &amp; </s>
          <s xml:space="preserve">coni, quorum ba-<lb />
<ptr xml:id="note-0374-01a" corresp="note-0374-01" type="noteAnchor" />
ſium diametri ſunt æquales; </s>
          <s xml:space="preserve">moveatur fluidum juxta directiones axium. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0374-02a" corresp="note-0374-02" type="noteAnchor" />
Planum AB integram fluidi actionem ſuſtinet, dum hoc juxta hanc ſuperfi-<lb />ciem ab omni parte continuo defluit. </s>
          <s xml:space="preserve">Superficies autem FE minorem ſuſti-<lb />net preſſionem &amp; </s>
          <s xml:space="preserve">eo minorem quo ipſius obliquitas ad motus directionem <lb />major eſt <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">revocaturque preſſio, in punctum quodcunque M, ad preſſio-
<ptr xml:id="note-0374-03a" corresp="note-0374-03" type="noteAnchor" />
nem perpendicularem ad ſuperficiem, ſi poſita IM, juxta motus directio-<lb />nem, ipſi FE æqualem, detur in M perpendicularis ML ad FE, &amp; </s>
          <s xml:space="preserve">duca-<lb />tur huic parallela IL. </s>
          <s xml:space="preserve">Tunc preſſio ex motu oriunda ſe habet ad preſſionem <lb />quam ſuperficies patitur ut IM ad ML <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">talemque preſſionem ſuperficies FE
<ptr xml:id="note-0374-04a" corresp="note-0374-04" type="noteAnchor" />
in omnibus punctis patitur, fluidum enim, quod in omnibus punctis tangit <lb />ſuperficiem, a continuo accedente fluido talem patitur actionem. </s>
          <s xml:space="preserve">Ita res ſe-<lb />ſe non haberet, ſi de motu corporum ſeparatorum ageretur; </s>
          <s xml:space="preserve">tuncenim nu-<lb />merus corporum in ſuperficiem EF incurrentium, æqualis eſſet numero cor-<lb />porum, quæ, ſublata ſuperficie EF, in ſuperficiem EH impingi poſſent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0374-01" corresp="note-0374-01a" place="margin">938.</note>
              <note xml:space="preserve" xml:id="note-0374-02" corresp="note-0374-02a" place="margin">TAB. XXXVI. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0374-03" corresp="note-0374-03a" n="*" anchored="true" place="margin">913.</note>
              <note xml:space="preserve" xml:id="note-0374-04" corresp="note-0374-04a" n="*" anchored="true" place="margin">229.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si preſſio per LM in duas ſolvatur ducta LN perpendiculari ad IM, deſi-<lb />gnabit NM actionem qua corpus juxta directionem motus fluidi propellitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Actio nunc tota in conumad actionem in cylindrum, ut coni ſuperficies <lb />convexa ad cylindri baſin; </s>
          <s xml:space="preserve">tales enim ſunt ſuperficies in quas preſſiones a-<lb />gunt; </s>
          <s xml:space="preserve">id eſt ut EF ad EH: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ut actio, quæ in ſingulis punctis in conum agit, <lb />juxta directionem motus fluidi, ad actionem, quæ in ſingulis punctis cylindrum <lb />propellit, id eſt, ut NM ad IM. </s>
          <s xml:space="preserve">Ratio ex his compoſita eſt ratio pro-<lb />ducti EF per NM ad productum EH per IM.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quæ producta propter æquales EF, IM, ſunt ut NM ad EH, aut <lb />ML; </s>
          <s xml:space="preserve">ſunt enim æquales hæ lineæ; </s>
          <s xml:space="preserve">propter æqualia &amp; </s>
          <s xml:space="preserve">ſimilia trian-<lb />gula IML, EFH. </s>
          <s xml:space="preserve">Sunt etiam ſimilia triangula LMN, LMI <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">qua-
<ptr xml:id="note-0374-05a" corresp="note-0374-05" type="noteAnchor" />
re MN ad ML, ut ML ad MI, aut ut EH ad EF. </s>
          <s xml:space="preserve">Ergo reſiſtentia <lb />coni ſe habet ad cylindri reſiſtentiam, poſitis ambobus rectis, habentibus ba-<lb />ſes æquales, &amp; </s>
          <s xml:space="preserve">velocitatibus æqualibus, juxta axium directiones, in eodem <lb />fluido, agitatis, ut ſemidiameter baſis ad rectam in coni ſuperficie a ver-<lb />tice ad punctum baſeos ducta, ut diximus in n. </s>
          <s xml:space="preserve">914.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0374-05" corresp="note-0374-05a" n="*" anchored="true" place="margin">8. El. VI.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus nunc cylindrum cum ſphæra, diametros æquales habentes, eâ-<lb />
<ptr xml:id="note-0374-06a" corresp="note-0374-06" type="noteAnchor" />
dem velocitate, in eodem fluido, moveri, cylindrumque juxta axcos dire-<lb />ctionem transferri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0374-06" corresp="note-0374-06a" place="margin">939.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit hic ABLM, dum ſphæra repræſentatur per DFEG; </s>
          <s xml:space="preserve">eſtque C cen-<lb />
<ptr xml:id="note-0374-07a" corresp="note-0374-07" type="noteAnchor" />
trum. </s>
          <s xml:space="preserve">Reſiſtentia quam patitur pars baſeos cylindri, infinitè exigua, I i, ſe <lb />habet ad reſiſtentiam quam patitur pars reſpondens F f ſuperficiei ſphæræ <lb />ductis IH, ih, ad axem cylindri, ideoque ad directionem motus, paralle-<lb />lis, ut F f ad F g, quæ ad AB parallela ducitur; </s>
          <s xml:space="preserve">quod patet hìc applicando <lb />demonſtrationem datam in numero præcedenti. </s>
          <s xml:space="preserve">Triangula F fg, FHC, <lb />ambo rectangula, &amp; </s>
          <s xml:space="preserve">habentia angulos æquales f F g, CFH, quorum ſin-<lb />gulorum defectus ab angulo recto eſt angulus g FC, ſunt ſimilia: </s>
          <s xml:space="preserve">ergo</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0374-07" corresp="note-0374-07a" place="margin">TAB. XXXVI. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">F f, F g :: FC aut IH, FH</head>
        <p>
          <s xml:space="preserve">Idcirco ſi IH repræſentat reſiſtentiam quam patitur pars ſuperficiei I i, <lb />FH ipſam repræſentabit quam patitur pars reſpondens F f ſuperficiei globi.</s>
          <s xml:space="preserve">
</s>
          <pb facs="0375" n="275" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
Et cum hæc demonſtratio ad ſingula ſuperficiei hemiſphærii DFE puncta <lb />poſſit applicari; </s>
          <s xml:space="preserve">ſequitur, cylindrum ADEB, hemiſphærio circumſcriptum, <lb />ſe habere ad ipſum hemiſphærium, ut integra reſiſtentia cylindri ad inte-<lb />gram ſpheræ reſiſtentiam; </s>
          <s xml:space="preserve">quæ ergo reſiſtentiæ ſunt ut tria ad duo, ut monui <lb />in n. </s>
          <s xml:space="preserve">115.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex iiſdem hiſce principiis quæ corporum quorumcunque reſiſtentias ſpe-<lb />
<ptr xml:id="note-0375-01a" corresp="note-0375-01" type="noteAnchor" />
ctant deducuntur. </s>
          <s xml:space="preserve">Ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">facile ex his probatur, cylindri recti, cujus altitudo <lb />
<ptr xml:id="note-0375-02a" corresp="note-0375-02" type="noteAnchor" />
diametro æqualis eſt, reſiſtentiam ex ſecunda cauſa eandem eſſe, ſi velocitas ea-<lb />dem fuerit, juxta quamcunque directionem feratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0375-01" corresp="note-0375-01a" place="margin">940.</note>
              <note xml:space="preserve" xml:id="note-0375-02" corresp="note-0375-02a" place="margin">941.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XII. <lb />De Retardatione Corporum in Fluidis motorum.</head>
        <p>
          <s xml:space="preserve">VIdimus ſuperius corpus in fluido motum reſiſtentiam pa-<lb />
<ptr xml:id="note-0375-03a" corresp="note-0375-03" type="noteAnchor" />
ti <ptr type="noteAnchor" />, darique preſſionem motui contrariam, qua corpus
<ptr xml:id="note-0375-04a" corresp="note-0375-04" type="noteAnchor" />
retardari manifeſtum eſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0375-03" corresp="note-0375-03a" place="margin">942.</note>
              <note xml:space="preserve" xml:id="note-0375-04" corresp="note-0375-04a" n="*" anchored="true" place="margin">891.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">436.</note>
        <p>
          <s xml:space="preserve">Cum duplex detur reſiſtentia, corpus etiam ex duplici <lb />cauſa a motu ſuo amittit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Natura utriuſque reſiſtentiæ cum diverſa ſit, generant hæ <lb />
<ptr xml:id="note-0375-06a" corresp="note-0375-06" type="noteAnchor" />
retardationes diverſas, in ipſis illis caſibus, in quibus preſſio-<lb />nes, quas in corpus exerunt, ſunt æquales, ſed preſſiones <lb />non ſunt ejuſdem generis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0375-06" corresp="note-0375-06a" place="margin">943.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In caſu in quo corpus quieſcit dum fluidum movetur cau-<lb />
<ptr xml:id="note-0375-07a" corresp="note-0375-07" type="noteAnchor" />
ſæ quæ, moto corpore, hoc retardant, nunc ipſi motum <lb />communicant &amp; </s>
          <s xml:space="preserve">eſt hæc velocitas acquiſita, æqualis ipſi re-<lb />tardationi, quam patitur corpus quando, quieſcentefluido, corpus <lb />movetur, ea velocitate, quam in caſu primo fluidum babuit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0375-07" corresp="note-0375-07a" place="margin">944.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">897.</note>
        <p>
          <s xml:space="preserve">In caſu autem hoc in quo fluidum movetur, cobæſio par-<lb />
<ptr xml:id="note-0375-09a" corresp="note-0375-09" type="noteAnchor" />
tium immediate nunquam motum corporipoteſt communicare, <lb />ſed tantum mediante motu aliarum particularum, ut ex-<lb />plicavimus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod non itidem ad ſecundam cauſam reſi-
<ptr xml:id="note-0375-10a" corresp="note-0375-10" type="noteAnchor" />
ſtentiæ applicari poteſt, quæ immediate corpori motum com-<lb />municat: </s>
          <s xml:space="preserve">quare ex principiis omnino diverſis, quæ retarda-<lb />
<ptr xml:id="note-0375-11a" corresp="note-0375-11" type="noteAnchor" />
tiones ex hiſce diverſis reſiſtentiis oriundas ſpectant, dedu-<lb />cenda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0375-09" corresp="note-0375-09a" place="margin">945.</note>
              <note xml:space="preserve" xml:id="note-0375-10" corresp="note-0375-10a" n="*" anchored="true" place="margin">901.</note>
              <note xml:space="preserve" xml:id="note-0375-11" corresp="note-0375-11a" place="margin">946.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando corpus quieſcit, &amp; </s>
          <s xml:space="preserve">fluidum movetur, particulæ <lb />
<ptr xml:id="note-0375-12a" corresp="note-0375-12" type="noteAnchor" />
quæ ad latera defluunt cohæſionem ſuperant, &amp; </s>
          <s xml:space="preserve">hæ ex vi ſua
</s>
          <pb facs="0376" n="276" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
amittunt, quæ actio conſideranda foret ad determinandam <lb />velocitatem ex hac corpori communicatam, &amp; </s>
          <s xml:space="preserve">difficilior eſt <lb />hujus celeritatis determinatio, quam tamen in ſcholio hujus <lb />cap. </s>
          <s xml:space="preserve">ultimo explicabo. </s>
          <s xml:space="preserve">In quo etiam ſcrupulos quof-<lb />dam tollam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0375-12" corresp="note-0375-12a" place="margin">947.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Præſtabit hic retardationem determinare quam patitur <lb />corpus in caſu, in quo hoc movetur, &amp; </s>
          <s xml:space="preserve">fluidum quieſcit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vidimus reſiſtentiam ex prima cauſa ejuſdem eſſe naturæ <lb />
<ptr xml:id="note-0376-01a" corresp="note-0376-01" type="noteAnchor" />
cum reſiſtentia corporum mollium, dum in his cavitas for-<lb />matur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0376-01" corresp="note-0376-01a" place="margin">948.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">893.</note>
        <p>
          <s xml:space="preserve">Vidimus etiam cavitatem hanc proportionem ſequi ipſi-<lb />us vis amiſſæ in hac formanda <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">cavitas autem quam cor-
<ptr xml:id="note-0376-03a" corresp="note-0376-03" type="noteAnchor" />
pus in fluido format, dum per hoc movetur, ſpatio per-<lb />
<ptr xml:id="note-0376-04a" corresp="note-0376-04" type="noteAnchor" />
curſo proportionalis eſt: </s>
          <s xml:space="preserve">ergo &amp; </s>
          <s xml:space="preserve">huic ſpatio vis, ex hac re-<lb />ſiſtentia ex primâ cauſâ amiſſa, proportionalis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0376-03" corresp="note-0376-03a" n="*" anchored="true" place="margin">464.</note>
              <note xml:space="preserve" xml:id="note-0376-04" corresp="note-0376-04a" place="margin">949.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus quod in vacuo verticaliter in altum projicitur, in <lb />adſcenſu ſuo amittit continuo vim proportionalem ſpatio <lb />percurſo <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſequitur igitur retardatio in hoc adſcenſu ean-
<ptr xml:id="note-0376-05a" corresp="note-0376-05" type="noteAnchor" />
dem rationem quam ſequitur retardatio corporis oriunda ex <lb />
<ptr xml:id="note-0376-06a" corresp="note-0376-06" type="noteAnchor" />
reſiſtentia de qua agimus; </s>
          <s xml:space="preserve">ſed retardatio corporis adſcen-<lb />dentis eſt æquabilis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo &amp; </s>
          <s xml:space="preserve">talis eſt retardatio quam
<ptr xml:id="note-0376-07a" corresp="note-0376-07" type="noteAnchor" />
examinamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0376-05" corresp="note-0376-05a" n="*" anchored="true" place="margin">448, 261.</note>
              <note xml:space="preserve" xml:id="note-0376-06" corresp="note-0376-06a" place="margin">950.</note>
              <note xml:space="preserve" xml:id="note-0376-07" corresp="note-0376-07a" n="*" anchored="true" place="margin">258.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quamdiu ergo idem corpus, eodem modo, per idem flui-<lb />
<ptr xml:id="note-0376-08a" corresp="note-0376-08" type="noteAnchor" />
dum movetur, quacunque velocitate feratur, ſepoſit â reſi-<lb />ſtentiâ ex ſecundâ cauſâ, æqualibus temporibus, æquales <lb />gradus velocitatis amittit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">percurrendo ſpatium deter-<lb />minatum <ptr type="noteAnchor" />, quod quadrato velocitatis initio proportionale
<ptr xml:id="note-0376-09a" corresp="note-0376-09" type="noteAnchor" />
erit <ptr type="noteAnchor" />, in tempore ipſi velocitati huic proportionale <ptr type="noteAnchor" />, in-
<ptr xml:id="note-0376-10a" corresp="note-0376-10" type="noteAnchor" />
tegrum amittet motum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0376-08" corresp="note-0376-08a" place="margin">951.</note>
              <note xml:space="preserve" xml:id="note-0376-09" corresp="note-0376-09a" n="*" anchored="true" place="margin">949.</note>
              <note xml:space="preserve" xml:id="note-0376-10" corresp="note-0376-10a" n="*" anchored="true" place="margin">950. 258. <lb />262.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">950. 258. <lb />259 255.</note>
        <p>
          <s xml:space="preserve">Hinc videmus corpora in fluido mota tandem quieſcere, <lb />
<ptr xml:id="note-0376-12a" corresp="note-0376-12" type="noteAnchor" />
quod communi admiſſà opinione, de viribus ipſis velocitati-<lb />bus proportionalibus, difficulter admodum explicari poterit, <lb />ſi queat; </s>
          <s xml:space="preserve">nam niſi tempore infinito tota velocitas conſumi <lb />poſſet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0376-12" corresp="note-0376-12a" place="margin">952.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Retardatio ex ſecunda cauſa determinatur, ponendo cor-<lb />pus quieſcens, &amp; </s>
          <s xml:space="preserve">fluidum in hoc incurrens; </s>
          <s xml:space="preserve">quia facilius de-
</s>
          <pb facs="0377" n="277" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
terminatur velocitas, quæ corpori quieſcenti a fluido com-<lb />municatur, quàm retardatio quam corpus patitur; </s>
          <s xml:space="preserve">præſtabit <lb />ergo velocitatem hanc conſiderare, quæ ab ipſa retardatione, <lb />corporis agitati per fluidum quieſcens, non differt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">944.</note>
        <p>
          <s xml:space="preserve">Preſſio, quam in corpus quieſcens exerit fluidum, im-<lb />
<ptr xml:id="note-0377-02a" corresp="note-0377-02" type="noteAnchor" />
mediate corpus poteſt transferre, ſequitur igitur velocitatem <lb />infinite exiguam, momento infinite exiguo conſtanti, com-<lb />municari, proportionalem ipſi ſpatio, per quod corpus hoc <lb />quieſcens actione fluidi immediate transfertur, quod ſpa-<lb />tium ipſi preſſioni proportionale eſt <ptr type="noteAnchor" />, quæ ipſa rationem
<ptr xml:id="note-0377-03a" corresp="note-0377-03" type="noteAnchor" />
ſequitur quadrati velocitatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0377-02" corresp="note-0377-02a" place="margin">953.</note>
              <note xml:space="preserve" xml:id="note-0377-03" corresp="note-0377-03a" n="*" anchored="true" place="margin">107.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">500.</note>
        <p rend="italics">
          <s xml:space="preserve">Diminutiones idcirco velocitatis, quas corpus in fluido mo-<lb />
<ptr xml:id="note-0377-05a" corresp="note-0377-05" type="noteAnchor" />
tum, momentis infinite exiguis, æqualibus, ex reſiſtentiâ <lb />ex ſecundâ cauſâ, patitur, ſunt ut quadrata velocitatum <lb />ipſius corporis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0377-05" corresp="note-0377-05a" place="margin">954.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ex qua demonſtratione ſequitur nunquam corpus ex ſolâ <lb />
<ptr xml:id="note-0377-06a" corresp="note-0377-06" type="noteAnchor" />
reſiſtentiâ ex ſecundâ cauſâ integram poſſe amittere veloci-<lb />tatem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0377-06" corresp="note-0377-06a" place="margin">955.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Patet etiam in omni caſu retardationem, ex bacreſiſten-<lb />
<ptr xml:id="note-0377-07a" corresp="note-0377-07" type="noteAnchor" />
tia, eandem cum ipſa rationem ſequi, quamdiu corpus mo-<lb />tum eandem materiæ quantitatem continet, ubi autem hæc <lb />eſt diverſa, retardatio eſt cæteris paribus, inverſe ut hæc <lb />
<ptr xml:id="note-0377-08a" corresp="note-0377-08" type="noteAnchor" />
materiæ quantitas <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ex quibus facile videmus, quomodo
<ptr xml:id="note-0377-09a" corresp="note-0377-09" type="noteAnchor" />
poſitis demonſtratis in capite præcedenti retardationes pro <lb />variis corporibus, &amp; </s>
          <s xml:space="preserve">variis fluidis, inter ſe conferri poſ-<lb />ſint.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0377-07" corresp="note-0377-07a" place="margin">956.</note>
              <note xml:space="preserve" xml:id="note-0377-08" corresp="note-0377-08a" place="margin">957.</note>
              <note xml:space="preserve" xml:id="note-0377-09" corresp="note-0377-09a" n="*" anchored="true" place="margin">112.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si de ſphæris, cylindris, aut conis ſimilibus, Ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">a-<lb />
<ptr xml:id="note-0377-10a" corresp="note-0377-10" type="noteAnchor" />
gatur, poſitis cylindris, &amp; </s>
          <s xml:space="preserve">conis, juxta axium directiones <lb />motis, erunt retardationes ex ſecunda cauſa directè ut qua-<lb />
<ptr xml:id="note-0377-11a" corresp="note-0377-11" type="noteAnchor" />
drata diametrorum <ptr type="noteAnchor" />, ut quadrata velocitatum <ptr type="noteAnchor" />, ut denſi-
<ptr xml:id="note-0377-12a" corresp="note-0377-12" type="noteAnchor" />
tates fluidorum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">inverſe ut denſitates corporum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">cu-
<ptr xml:id="note-0377-13a" corresp="note-0377-13" type="noteAnchor" />
<ptr xml:id="note-0377-14a" corresp="note-0377-14" type="noteAnchor" />
bi diametrorum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">ſed ratio directa quadratorum, &amp; </s>
          <s xml:space="preserve">inver-
<ptr xml:id="note-0377-15a" corresp="note-0377-15" type="noteAnchor" />
ſa cuborum diametrorum, ad inverſam ipſarum diametro-<lb />rum reducitur; </s>
          <s xml:space="preserve">Idcirco, junctis rationibus ultimâ &amp; </s>
          <s xml:space="preserve">primâ, <lb />ſunt retardationes inverſe ut diametri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0377-10" corresp="note-0377-10a" place="margin">958.</note>
              <note xml:space="preserve" xml:id="note-0377-11" corresp="note-0377-11a" n="*" anchored="true" place="margin">956. 909.</note>
              <note xml:space="preserve" xml:id="note-0377-12" corresp="note-0377-12a" n="*" anchored="true" place="margin">954.</note>
              <note xml:space="preserve" xml:id="note-0377-13" corresp="note-0377-13a" n="*" anchored="true" place="margin">956 926.</note>
              <note xml:space="preserve" xml:id="note-0377-14" corresp="note-0377-14a" n="*" anchored="true" place="margin">957.</note>
              <note xml:space="preserve" xml:id="note-0377-15" corresp="note-0377-15a" n="*" anchored="true" place="margin">957.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Numeri in harum rationum ratione compoſita detegun-<lb />
<ptr xml:id="note-0377-16a" corresp="note-0377-16" type="noteAnchor" />
</s>
          <pb facs="0378" n="278" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tur, multiplicando pro ſingulis corporibus fluidi denſitatem <lb />per quadratum velocitatis corporis, &amp; </s>
          <s xml:space="preserve">dividendo pro-<lb />ductum hoc per diametrum ductam in denſitatem corporis, <lb />diviſionumque quotientes exprimunt retardationum rela-<lb />tiones.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0377-16" corresp="note-0377-16a" place="margin">959.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæ etiam deteguntur ſi pro ſingulis corporibus pondus, <lb />
<ptr xml:id="note-0378-01a" corresp="note-0378-01" type="noteAnchor" />
quod valet reſiſtentiam <ptr type="noteAnchor" />, dividatur per corporis pondus;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0378-02a" corresp="note-0378-02" type="noteAnchor" />
quotientes enim ſunt ut retardationes <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0378-01" corresp="note-0378-01a" place="margin">960.</note>
              <note xml:space="preserve" xml:id="note-0378-02" corresp="note-0378-02a" n="*" anchored="true" place="margin">928.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">956 957. <lb />121.</note>
        <p>
          <s xml:space="preserve">Dum corpus in fluido retardatur, ſingulis momentis, cum <lb />mutata velocitate, mutatur retardatio, unde varia circa mo-<lb />tum corporis, in fluido continuatum, deducuntur, quorum <lb />quædam in ſcholiis, huic capiti ſubjunctis, demonſtramus; <lb /></s>
          <s xml:space="preserve">horum pauca hîc indicabo.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Sepoſitâ, ut in ultimis propoſitionibus, reſiſtentiâ ex <lb />
<ptr xml:id="note-0378-04a" corresp="note-0378-04" type="noteAnchor" />
partium cobæſione, moveatur corpus per ſluidum, percur-<lb />ret boc ſpatia æqualia, temporibus inæqualibus, quæ erunt <lb />in progreſſione geometrica; </s>
          <s xml:space="preserve">in qua eadem progreſſione, ſed <lb />inverſâ, ſunt velocitates in initiis borum momento-<lb />rum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0378-04" corresp="note-0378-04a" place="margin">961.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si globus aut cylindrus rectus, juxta axeos directionem <lb />
<ptr xml:id="note-0378-05a" corresp="note-0378-05" type="noteAnchor" />
moveantur per fluidum, cylindri longitudo, &amp; </s>
          <s xml:space="preserve">globi diame-<lb />ter, ſe babebunt ad ſpatia, quibus percurrendo corpora hæc <lb />reſpectivè dimidium velocitatis amittunt, in ratione compo-<lb />ſita denſitatis fluidi ad denſitatem corporis, &amp; </s>
          <s xml:space="preserve">numeri 10000. <lb /></s>
          <s xml:space="preserve">ad 13863.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0378-05" corresp="note-0378-05a" place="margin">962.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Corporis autem, quod in fluido movetur, retardatio ab <lb />
<ptr xml:id="note-0378-06a" corresp="note-0378-06" type="noteAnchor" />
utraque cauſa reſiſtentiæ pendet, &amp; </s>
          <s xml:space="preserve">eſt pro parte æquabi-<lb />lis <ptr type="noteAnchor" />, pro parte ut quadratum velocitatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0378-06" corresp="note-0378-06a" place="margin">963.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">950.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">954.</note>
        <p>
          <s xml:space="preserve">Quod etiam ad corpora adſcendentia &amp; </s>
          <s xml:space="preserve">deſcendentia ap-<lb />plicari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus fluido ſpecificè gravius, quod adſcendit, aut fluido <lb />
<ptr xml:id="note-0378-09a" corresp="note-0378-09" type="noteAnchor" />
ſpecificè levius quod deſcendit, præter retardationem ex in-<lb />ertia fluidi oriundam <ptr type="noteAnchor" />, aliam æquabilem patitur, non modo ex
<ptr xml:id="note-0378-10a" corresp="note-0378-10" type="noteAnchor" />
cohæſione <ptr type="noteAnchor" />, ſed eſt præterea, in primo caſu, ex gravitate
<ptr xml:id="note-0378-11a" corresp="note-0378-11" type="noteAnchor" />
reſpectiva <ptr type="noteAnchor" />, in ſecundo, ex vi qua in fluido ſurſum pelli-
<ptr xml:id="note-0378-12a" corresp="note-0378-12" type="noteAnchor" />
tur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0378-09" corresp="note-0378-09a" place="margin">964.</note>
              <note xml:space="preserve" xml:id="note-0378-10" corresp="note-0378-10a" n="*" anchored="true" place="margin">954.</note>
              <note xml:space="preserve" xml:id="note-0378-11" corresp="note-0378-11a" n="*" anchored="true" place="margin">951</note>
              <note xml:space="preserve" xml:id="note-0378-12" corresp="note-0378-12a" n="*" anchored="true" place="margin">251.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">749.</note>
        <pb facs="0379" n="279" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
        <p>
          <s xml:space="preserve">E contra Si corpus, ſpecifice fluido quo immergitur gra-<lb />
<ptr xml:id="note-0379-01a" corresp="note-0379-01" type="noteAnchor" />
vius, deſcendat, aut fluido levius adſcendat, continuo ac-<lb />celeratur vi quæ valet differentiam gravitatum ſpecificarum <lb />corporis &amp; </s>
          <s xml:space="preserve">fluidi <ptr type="noteAnchor" />, quæ acceleratio, à gravitate oriunda,
<ptr xml:id="note-0379-02a" corresp="note-0379-02" type="noteAnchor" />
æquabilis eſt <ptr type="noteAnchor" />, minuitur hæc retardatione a cohæſione o-
<ptr xml:id="note-0379-03a" corresp="note-0379-03" type="noteAnchor" />
riundà, ſed æquabiliter <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">eſt adhucdum æquabilis ac-
<ptr xml:id="note-0379-04a" corresp="note-0379-04" type="noteAnchor" />
celeratio. </s>
          <s xml:space="preserve">Cum autem retardatio ex ſecundâ caufâ cum <lb />velocitate creſcat, minuitur continuò acceleratio; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cor-<lb />
<ptr xml:id="note-0379-05a" corresp="note-0379-05" type="noteAnchor" />
pus magis ac magis accedit ad velocitatem quandam maxi-<lb />mam determinatam, ad quam tamen nunquam pertingere po-<lb />teſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0379-01" corresp="note-0379-01a" place="margin">965.</note>
              <note xml:space="preserve" xml:id="note-0379-02" corresp="note-0379-02a" n="*" anchored="true" place="margin">751.</note>
              <note xml:space="preserve" xml:id="note-0379-03" corresp="note-0379-03a" n="*" anchored="true" place="margin">251.</note>
              <note xml:space="preserve" xml:id="note-0379-04" corresp="note-0379-04a" n="*" anchored="true" place="margin">951.</note>
              <note xml:space="preserve" xml:id="note-0379-05" corresp="note-0379-05a" place="margin">966.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Illa verò eſt velocitas maxima in qua retardatio accele-<lb />
<ptr xml:id="note-0379-06a" corresp="note-0379-06" type="noteAnchor" />
rationi æqualis eſt; </s>
          <s xml:space="preserve">ſi enim ad hanc pertingeret corpus, <lb />æquabiliter motum continuaret, preſſionibus oppoſitis ſeſe <lb />mutuo deſtruentibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0379-06" corresp="note-0379-06a" place="margin">967.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Corpus cylindricum banc acquirit velocitatem maximam <lb />
<ptr xml:id="note-0379-07a" corresp="note-0379-07" type="noteAnchor" />
in vacuo cadendo ab altitudine quæ ſe babet ad cylindri lon-<lb />gitudinem, ſi bic juxta axeos directionem in fluido deſcendat, <lb />aut ſi de globo agatur, ad hujus diametrum, ut differentia <lb />denſitatis corporis in fluido moti cum fluidi denſitate ad hanc <lb />fluidi denſitatem <ptr type="noteAnchor" />, ſinempe ſeponamus retardationem ex par-
<ptr xml:id="note-0379-08a" corresp="note-0379-08" type="noteAnchor" />
tium cobæſione oriundam, qua autem poſita minor erit al-<lb />titudo aqua in vacuo cadendo corpus acquirit velocitatem <lb />de qua agimus maximam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0379-07" corresp="note-0379-07a" place="margin">968.</note>
              <note xml:space="preserve" xml:id="note-0379-08" corresp="note-0379-08a" n="*" anchored="true" place="margin">928.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Relictis nunc motibus, in lineis rectis pauca etiam ad-<lb />dam de motu pendulorum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit ABD arcus cycloidis in quo pendulum vibratur; </s>
          <s xml:space="preserve">B pun-<lb />
<ptr xml:id="note-0379-09a" corresp="note-0379-09" type="noteAnchor" />
ctum infimum. </s>
          <s xml:space="preserve">Acceleratio ex gravitate in puncto quocunque <lb />
<ptr xml:id="note-0379-10a" corresp="note-0379-10" type="noteAnchor" />
ut E eſt ut EB <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſed hæc a cohæſione minuiter æquabili-
<ptr xml:id="note-0379-11a" corresp="note-0379-11" type="noteAnchor" />
ter <ptr type="noteAnchor" />, ſit hæc diminutio ut BF, acceleratio erit nunc ut
<ptr xml:id="note-0379-12a" corresp="note-0379-12" type="noteAnchor" />
EF, &amp; </s>
          <s xml:space="preserve">in A erit ut AF. </s>
          <s xml:space="preserve">Adſcenſu corporis, retardatio in <lb />G a gravitate oriunda, erit ut GB, a cohæſione erit ut BF <lb />&amp; </s>
          <s xml:space="preserve">ex his cauſis conjunctis eſt ut GF; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in tota vibratio-<lb />ne ſepoſitâ aliâ reſiſtentiâ, corpus reſpectu puncti F move-<lb />tur ut in vacuo agitatur reſpectu B.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0379-09" corresp="note-0379-09a" place="margin">969.</note>
              <note xml:space="preserve" xml:id="note-0379-10" corresp="note-0379-10a" place="margin">TAB. XXXVI. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0379-11" corresp="note-0379-11a" n="*" anchored="true" place="margin">287.</note>
              <note xml:space="preserve" xml:id="note-0379-12" corresp="note-0379-12a" n="*" anchored="true" place="margin">951.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vocabimus ideo deſcenſum motum penduli uſque ad F,
</s>
          <pb facs="0380" n="280" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
&amp; </s>
          <s xml:space="preserve">adſcenſum motum ultra punctum hoc; </s>
          <s xml:space="preserve">agam enim depen-<lb />dulis a parte A deſcendentibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut autem demonſtremus quæ obtinent, quando pendulum <lb />
<ptr xml:id="note-0380-01a" corresp="note-0380-01" type="noteAnchor" />
etiam reſiſtentiâ ex ſecunda cauſa retardatur, fingam re-<lb />ſiſtentiam quæ retardationem generat in ratione velocitatis, <lb />quaſdamque, hac poſitâ, propoſitiones demonſtrabo, qui-<lb />bus expoſitis facilius patebunt quæ locum habent quando <lb />retardatio eſt ut quadratum velocitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0380-01" corresp="note-0380-01a" place="margin">970.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitâ nunc retardatione in ratione ipſius velocitatis, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0380-02a" corresp="note-0380-02" type="noteAnchor" />
pendula duo, omnino ſimilia, in cycloide oſcillata, inæquales <lb />peragant vibrationes, eodemque momento cadere incipiant; <lb /></s>
          <s xml:space="preserve">moveri inchoant velocitatibus quæ ſunt ut arcus deſcenſu <lb />deſcribendi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi hæ impreſſiones primi momenti ſolæ con-
<ptr xml:id="note-0380-03a" corresp="note-0380-03" type="noteAnchor" />
ſiderantur, poſt tempus quodcunque celeritates erunt in <lb />eadem ratione ac in principio; </s>
          <s xml:space="preserve">nam retardationes, quæ <lb />ſunt ut ipſæ velocitates, harum proportionem immutare <lb />nequeunt; </s>
          <s xml:space="preserve">ratio enim inter quantitates non mutatur, addi-<lb />tione, aut ſubtractione, quantitatum in eadem ratione. </s>
          <s xml:space="preserve">Tem-<lb />poribus igitur æqualibus, utcunque inter movendum ex <lb />reſiſtentia mutetur corporis celeritas, ſpatia percurruntur <lb />quæ ſunt ut velocitates in principio <ptr type="noteAnchor" />, id eſt, ut arcus de-
<ptr xml:id="note-0380-04a" corresp="note-0380-04" type="noteAnchor" />
ſcenſu deſcribendi; </s>
          <s xml:space="preserve">idcirco poſt tempus quodcunque cor-<lb />pora ſunt in horum arcuum punctis reſpondentibus. </s>
          <s xml:space="preserve">In <lb />hiſce autem punctis accelerationes ſunt in eadem ratione <lb />quàm in principio <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ratio inter celeritates, quæ ex
<ptr xml:id="note-0380-05a" corresp="note-0380-05" type="noteAnchor" />
reſiſtentia non variatur, ex acceleratione etiam nullam muta-<lb />tionem patitur. </s>
          <s xml:space="preserve">In adſcenſu motus corporum retardatur, ſed in <lb />punctis reſpondentibus retardationes ſunt in eadem ratione in <lb />qua ſunt in deſcenſu accelerationes. </s>
          <s xml:space="preserve">Ubique ergo in punctis re-<lb />ſpondentibus celeritates ſunt in eadem ratione. </s>
          <s xml:space="preserve">Cum autem <lb />iiſdem momentis corpora ſint in hiſce punctis reſpon-<lb />dentibus, ſequitur motum amborum eodem momento de-<lb />ſtrui, id eſt, iiſdem temporibus vibrationes abſolvi. </s>
          <s xml:space="preserve">Spa-<lb />tia in integris vibrationibus percurſa, cum æqualibus tem-<lb />poribus percurrantur, &amp; </s>
          <s xml:space="preserve">cum in ſingulis momentis veloci-<lb />tates ſint inter ſe eadem ratione, ſunt quoque in hac ra-
</s>
          <pb facs="0381" n="281" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
tione; </s>
          <s xml:space="preserve">id eſt, arcus integrarum vibrationum ſunt ut arcus <lb />
<ptr xml:id="note-0381-01a" corresp="note-0381-01" type="noteAnchor" />
deſcenſu deſcripti, quorum dupla ſunt arcus in vacuo de-<lb />ſcribendi. </s>
          <s xml:space="preserve">Ergo Defectus arcuum in fluido deſcriptorum <lb />
<ptr xml:id="note-0381-02a" corresp="note-0381-02" type="noteAnchor" />
ab arcubus in vacuo deſcribendorum ſunt differentiæ quan-<lb />titatum in eadem ratione, &amp; </s>
          <s xml:space="preserve">ſunt ut arcus deſcenſu deſcri-<lb />pti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0380-02" corresp="note-0380-02a" place="margin">971.</note>
              <note xml:space="preserve" xml:id="note-0380-03" corresp="note-0380-03a" n="*" anchored="true" place="margin">287.</note>
              <note xml:space="preserve" xml:id="note-0380-04" corresp="note-0380-04a" n="*" anchored="true" place="margin">94.</note>
              <note xml:space="preserve" xml:id="note-0380-05" corresp="note-0380-05a" n="*" anchored="true" place="margin">287.</note>
              <note xml:space="preserve" xml:id="note-0381-01" corresp="note-0381-01a" place="margin">972.</note>
              <note xml:space="preserve" xml:id="note-0381-02" corresp="note-0381-02a" place="margin">973.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Creſcat nunc retardatio in ratione duplicata velocitatis, <lb />
<ptr xml:id="note-0381-03a" corresp="note-0381-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">vibrationes inæquales peragat corpus pendulum; </s>
          <s xml:space="preserve">majores <lb />erunt magis diuturnæ, propter reſiſtentiam magis creſcen-<lb />tem quàm in caſu n. </s>
          <s xml:space="preserve">971.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0381-03" corresp="note-0381-03a" place="margin">974.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Celeritates tamen, poſitis arcubus non admodum inæqua-<lb />
<ptr xml:id="note-0381-04a" corresp="note-0381-04" type="noteAnchor" />
libus, in arcuum deſcriptorum punctis reſpondentibus, ſunt <lb />ubique quam proximè in eadem ratione, &amp; </s>
          <s xml:space="preserve">quidem ratione <lb />arcuum deſcenſu deſcriptorum. </s>
          <s xml:space="preserve">Si retardatio eſſet in ratio-<lb />ne celeritatis, hæc proportio obtineret, nunc vero turba-<lb />tur propter majorem reſiſtentiam in majori vibratione, qua <lb />motus in hac magis minuitur. </s>
          <s xml:space="preserve">Sed duplici ex cauſa magis <lb />acceleratur. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Vibratio hæc major diutius durat <ptr type="noteAnchor" />, cor-
<ptr xml:id="note-0381-05a" corresp="note-0381-05" type="noteAnchor" />
puſque diutius hæret in certo ſpatio quàm in ſpatio reſpon-<lb />denti in vibratione minori, &amp; </s>
          <s xml:space="preserve">per longius tempus accele-<lb />ratur. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Defectus arcus deſcripti, ab arcu in vacuo deſcri-<lb />bendo, major eſt, ſervata proportione, in vibratione ma-<lb />jori; </s>
          <s xml:space="preserve">quia in hac retardatio magis differt a retardatione in mi-<lb />nori vibratione, quam in n. </s>
          <s xml:space="preserve">973. </s>
          <s xml:space="preserve">Puncta ergo reſponden-<lb />tia, ſervata proportione, magis a puncto F in arcu majori <lb />quam in minori diſtant, quamdiu in hoc corpus deſcendit; <lb /></s>
          <s xml:space="preserve">major ideo, ſervata proportione, in illo datur acceleratio, <lb />quia acceleratio eſt ut corporis diſtantia a puncto F. </s>
          <s xml:space="preserve">Datur er-<lb />go compenſatio, &amp; </s>
          <s xml:space="preserve">memorata proportio inſtauratur. </s>
          <s xml:space="preserve">In <lb />adſcenſu corporis, duratio retardationis concurrit cum ipſa <lb />retardatione ad hanc turbandam proportionem, ſed nunc mi-<lb />nus in majori arcu puncta reſpondentia, ſervata proportio-<lb />ne, a puncto F diſtant, quàm in minori, &amp; </s>
          <s xml:space="preserve">ex gravitate <lb />minor, ſervata proportione, retardatio datur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita jam, <lb />ſervatâ proportione, crevit differentia diſtantiæ punctorum
</s>
          <pb facs="0382" n="282" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
reſpondentium a puncto infimo, ut ex hoc ſolo facile com-<lb />penſatio detur,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0381-04" corresp="note-0381-04a" place="margin">975.</note>
              <note xml:space="preserve" xml:id="note-0381-05" corresp="note-0381-05a" n="*" anchored="true" place="margin">974.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Retardationes quæ ſunt ut quadrata celeritatum, ſunt <lb />igitur ubique in punctis reſpondentibus, ut quadrata ar-<lb />cuum deſcenſu deſcriptorum; </s>
          <s xml:space="preserve">cùm harum ſingulæ in punctis <lb />reſpondentibus eandem ſervent rationem, in ea etiam e-<lb />runt ratione ſummæ omnium, id eſt, retardationes integræ, <lb />quæ ſunt differentiæ inter arcus deſcenſu &amp; </s>
          <s xml:space="preserve">adſcenſu pro-<lb />
<ptr xml:id="note-0382-01a" corresp="note-0382-01" type="noteAnchor" />
ximo deſcriptos. </s>
          <s xml:space="preserve">Hæ ergo differentiæ, ſi vibrationes non <lb />fuerint admodum inæquales, ſunt quam proxime ut quadra-<lb />ta arcuum deſcenſu deſcriptorum. </s>
          <s xml:space="preserve">Hoc etiam cum Expe-<lb />rimentis ſatis exacte congruit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0382-01" corresp="note-0382-01a" place="margin">976.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi>, <lb />Qua Experimenta de Pendulorum Retardationibus <lb />inſtituuntur.</head>
        <p>
          <s xml:space="preserve">Arca ABFCD, longitudinis trium pedum, latitudinis <lb />
<ptr xml:id="note-0382-02a" corresp="note-0382-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">altitudinis unius pedis, aquâ impletur; </s>
          <s xml:space="preserve">unco V, medio <lb />
<ptr xml:id="note-0382-03a" corresp="note-0382-03" type="noteAnchor" />
Arcæ reſpondenti, pendulum V p ſuſpenditur; </s>
          <s xml:space="preserve">conſtat <lb />hoc ex filo æneo longitudinis ſeptem aut octo pedum, &amp; </s>
          <s xml:space="preserve"><lb />ex globo plumbeo p diametri unius pollicis cum ſemiſſe; <lb /></s>
          <s xml:space="preserve">quando pendulum quieſcit, diſtat globus ab Arcæ fundo <lb />tribus pollicibus In P globus major plumbeus, diametri <lb />trium pollicum, cum memorato filo jungitur, ut globus p <lb />in aqua minus retardetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0382-02" corresp="note-0382-02a" place="margin">977.</note>
              <note xml:space="preserve" xml:id="note-0382-03" corresp="note-0382-03a" place="margin">TAB. XXXI. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Juxta latitudinem Arcæ, ſuper hujus ora, moveri po-<lb />teſt tabula lignea altitudinis circiter quinque pollicum, cui <lb />applicantur regulæ diviſæ æneæ, EG, EG, &amp; </s>
          <s xml:space="preserve">indices <lb />MM, ad angulos, a pendulo deſcenſu &amp; </s>
          <s xml:space="preserve">adſcenſu deſcriptos, <lb />menſurandos, methodo in n. </s>
          <s xml:space="preserve">490. </s>
          <s xml:space="preserve">p. </s>
          <s xml:space="preserve">123. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">124. </s>
          <s xml:space="preserve">tradita.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>.</head>
        <p>
          <s xml:space="preserve">Regulæ EG, EG, ita diſponantur, ut extremitates G, G <lb />
<ptr xml:id="note-0382-04a" corresp="note-0382-04" type="noteAnchor" />
pendulo reſpondeant quando hoc quieſcit, &amp; </s>
          <s xml:space="preserve">ut inter il-<lb />las extremitates diſtantia detur æqualis diametro fili ænei <lb />cui corpora P, p, cohærent. </s>
          <s xml:space="preserve">Dimittatur pendulum ſucceſſi-<lb />vè a variis altitudinibus quæ in ſingulis occaſionibus indi-
</s>
          <pb facs="0383" n="283" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP XII.</fw>
ce notantur, deteguntur altitudines ad quas pendulum ad-<lb />ſcendit, ſi variis vicibus ab eadem altitudine dimittatur, <lb />&amp; </s>
          <s xml:space="preserve">index alter mutetur, donec ad hunc pendulum in adſcen-<lb />ſu appellat, ſed remoto indice ad ipſum non pertingat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0382-04" corresp="note-0382-04a" place="margin">978.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Differentiæ arcuum adſcenſu &amp; </s>
          <s xml:space="preserve">deſcenſu deſcriptorum <lb />erunt proxime inter ſe ut quadrata arcuum deſcenſu de-<lb />ſcriptorum, ſi ad hoc attendamus æqualiter vibrationes ſin-<lb />gulas eſſe minuendas, propter reſiſtentiam ex partium <lb />cohæſione.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Notandum autem pendulum non eſſe dimittendum niſi <lb />quieſcente aquæ ſuperficie.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 1. <lb />De Logarithmica.</head>
        <p>
          <s xml:space="preserve">QUæ in ſcholiis ſequentibus de retardationibus corporum, in fluidis mo-<lb />torum, demonſtrantur, lineæ logarithmicæ proprietates profundamen-<lb />to habent. </s>
          <s xml:space="preserve">Formationem ideò hujus curvæ, proprietatesque quibus in ſe-<lb />quentibus indigemus, in hocſcholio exponam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit AB recta, &amp; </s>
          <s xml:space="preserve">in hac partes infinite exiguæ AD, DF, FH, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">æ-<lb />
<ptr xml:id="note-0383-01a" corresp="note-0383-01" type="noteAnchor" />
quales inter ſe. </s>
          <s xml:space="preserve">Sint præterea ad AB, perpendiculares AC, DE, FG, <lb />
<ptr xml:id="note-0383-02a" corresp="note-0383-02" type="noteAnchor" />
HI, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">infinite parum differentes, &amp; </s>
          <s xml:space="preserve">quæ ſint progreſſione continua ge-<lb />ometrica. </s>
          <s xml:space="preserve">Si nunc curva tranſeat per extremitates C, E, G, I, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">erit hæc <lb />logarithmica, cujus Aſymtotos erit AB, ad quam continuo curva acce-<lb />dit, &amp; </s>
          <s xml:space="preserve">ad quam nunquam pertingere poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0383-01" corresp="note-0383-01a" place="margin">979.</note>
              <note xml:space="preserve" xml:id="note-0383-02" corresp="note-0383-02a" place="margin">TAB, XXXVII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eadem datur ratio inter ordinatas duas quaſcunque, ſi inter ipſas eadem detur <lb />
<ptr xml:id="note-0383-03a" corresp="note-0383-03" type="noteAnchor" />
diſtantia. </s>
          <s xml:space="preserve">AB ſe habet HI, ut LM ad RS, ſi diſtantia AH diſtantiæ LR <lb />fuerit æqualis. </s>
          <s xml:space="preserve">Ratio enim quæ datur inter AC &amp; </s>
          <s xml:space="preserve">HI componitur ex ra-<lb />tionibus AC ad DE, DE ad FG, &amp; </s>
          <s xml:space="preserve">FG ad HI; </s>
          <s xml:space="preserve">ratio LM ad RS, <lb />componitur ex rationibus LM ad NO, NO ad PQ, &amp; </s>
          <s xml:space="preserve">PQ ad RS: </s>
          <s xml:space="preserve">ra-<lb />tiones componentes ſingulæ ſunt æquales inter ſe <ptr type="noteAnchor" />, numeruſquerationum
<ptr xml:id="note-0383-04a" corresp="note-0383-04" type="noteAnchor" />
componentium in utroque caſu idem eſt, propter æquales diſtantias AH, <lb />LR; </s>
          <s xml:space="preserve">ergo &amp; </s>
          <s xml:space="preserve">æquales ſunt rationes compoſitæ. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">D. </s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0383-03" corresp="note-0383-03a" place="margin">983.</note>
              <note xml:space="preserve" xml:id="note-0383-04" corresp="note-0383-04a" n="*" anchored="true" place="margin">979.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Logarithmus ordinatæ cujuſcunque dicitur abſciſſa ipſi reſpondens, ubicunque ini-<lb />
<ptr xml:id="note-0383-05a" corresp="note-0383-05" type="noteAnchor" />
tium abſciſſarum ponatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0383-05" corresp="note-0383-05a" place="margin">981.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Diſtantia inter duas ordinatas vocatur logarithmus rationis quæ inter ipſas da-<lb />
<ptr xml:id="note-0383-06a" corresp="note-0383-06" type="noteAnchor" />
tur. </s>
          <s xml:space="preserve">Eſtque differentia logarithmorum ipſarum ordinatarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0383-06" corresp="note-0383-06a" place="margin">982.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitis iterum AH &amp; </s>
          <s xml:space="preserve">LR æqualibus habemus</s>
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">AC, HI :: LM, RS <ptr type="noteAnchor" />; &amp; dividendo</head>
        <note xml:space="preserve" n="*" anchored="true" place="margin">982.</note>
        <p>
          <s xml:space="preserve">AC - HI = TC, AC :</s>
          <s xml:space="preserve">: LM - RS = VM, LM. </s>
          <s xml:space="preserve">Quare eſt</s>
        </p>
        <pb facs="0384" n="284" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">TC, VM:: AC, LM.</head>
        <p>
          <s xml:space="preserve">Id eſt ordinatæ ſunt inter ſe, ut harum ſingularum differentiæ cum aliis or dina-<lb />
<ptr xml:id="note-0384-01a" corresp="note-0384-01" type="noteAnchor" />
tis æqualiter ab his diſtantibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-01" corresp="note-0384-01a" place="margin">983.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In puncto quocunque C logarithmicæ CM, ductâ tangente CT, quæ a-<lb />
<ptr xml:id="note-0384-02a" corresp="note-0384-02" type="noteAnchor" />
ſymtoton ſecat in T, habetur ſubtangens AT; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eſt hæc conſtans in omnibus <lb />curvæ punctis, ductâque in M tangente MV, erunt æquales AT, LV. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0384-03a" corresp="note-0384-03" type="noteAnchor" />
Ut hoc pateat ſint AD, LN infinitæ exiguæ &amp; </s>
          <s xml:space="preserve">æquales, ductiſque ordina-<lb />tis DE, NO, ſint E c, O m, ipſi AB parallelæ. </s>
          <s xml:space="preserve">Triangula C c E, CAT, <lb />ſunt ſimilia, ut &amp; </s>
          <s xml:space="preserve">M m O &amp; </s>
          <s xml:space="preserve">MLV; </s>
          <s xml:space="preserve">ergo</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-02" corresp="note-0384-02a" place="margin">TAB. XXXVII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0384-03" corresp="note-0384-03a" place="margin">984.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">C c, c E:: CA, AT, &amp; <lb />M m, m O :: ML, LV.</head>
        <p>
          <s xml:space="preserve">Sunt autem proportionalia antecedentia, in hiſce proportionibus <lb />Cc, M m :</s>
          <s xml:space="preserve">: CA, ML <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo &amp; </s>
          <s xml:space="preserve">conſequentia c E, m O :</s>
          <s xml:space="preserve">: AT, LV:</s>
          <s xml:space="preserve">
<ptr xml:id="note-0384-04a" corresp="note-0384-04" type="noteAnchor" />
ſed ſunt æquales c E, m O; </s>
          <s xml:space="preserve">idcirco &amp; </s>
          <s xml:space="preserve">AT, LV.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-04" corresp="note-0384-04a" n="*" anchored="true" place="margin">983.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſervatis ordinatis AC, DE, FG, HI &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">ſervataque æqualitate di-<lb />
<ptr xml:id="note-0384-05a" corresp="note-0384-05" type="noteAnchor" />
ſtantiarum AD, DF, FH, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">diſtantiæ hæ augeantur, aut minuantur, <lb />
<ptr xml:id="note-0384-06a" corresp="note-0384-06" type="noteAnchor" />
manifeſtum eſt logarithmicam mutari, ſubtangentemque etiam mutari in <lb />eadem ratione in qua diſtantiæ hæ mutantur; </s>
          <s xml:space="preserve">nam in triangulo C c E, ſervato <lb />
<ptr xml:id="note-0384-07a" corresp="note-0384-07" type="noteAnchor" />
latere C c, ſi mutetur c E, in triangulo ſimili CAT, cujus latus CA ſerva-<lb />tur, in eadem ratione cum c E mutabitur AT.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-05" corresp="note-0384-05a" place="margin">985.</note>
              <note xml:space="preserve" xml:id="note-0384-06" corresp="note-0384-06a" place="margin">TAB. XXXVII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0384-07" corresp="note-0384-07a" place="margin">TAB. XXXVII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Etiam in eadem ratione in qua ſingulæ diſtantiæ minores mutantur, mu-<lb />
<ptr xml:id="note-0384-08a" corresp="note-0384-08" type="noteAnchor" />
tantur ſummæ diſtantiarum quatumcunque: </s>
          <s xml:space="preserve">id eſt ut mutatur AD ſic &amp; </s>
          <s xml:space="preserve"><lb />mutatur AH, log. </s>
          <s xml:space="preserve">rationis AC ad HI; </s>
          <s xml:space="preserve">unde ſequitur, in diverſis logari-<lb />
<ptr xml:id="note-0384-09a" corresp="note-0384-09" type="noteAnchor" />
tbmicis ſubtangentes eſſe inter ſe, ut ſunt logarithmi ear undem rationum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-08" corresp="note-0384-08a" place="margin">TAB. XXXVII. <lb />fig 2.</note>
              <note xml:space="preserve" xml:id="note-0384-09" corresp="note-0384-09a" place="margin">986.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Tabulis logarithmorum quas editas habemus, logarithmus rationis u-<lb />
<ptr xml:id="note-0384-10a" corresp="note-0384-10" type="noteAnchor" />
nius ad decem eſt ipſa unitas, &amp; </s>
          <s xml:space="preserve">logarithmi rationum intermediarum per <lb />fractiones decimales exprimuntur, eſtque ſubtangens logarithmicæ tabularum <lb />o, 43429. </s>
          <s xml:space="preserve">44819.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-10" corresp="note-0384-10a" place="margin">987.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">De Retardatione in genere.</head>
        <p>
          <s xml:space="preserve">REtardatio, &amp; </s>
          <s xml:space="preserve">acceleratio, menſuratur, poſitis momentis infinitè exiguis æqua-<lb />
<ptr xml:id="note-0384-11a" corresp="note-0384-11" type="noteAnchor" />
libus; </s>
          <s xml:space="preserve">retardatio quæ a prima cauſa pendet æquabilis dicitur, quia di-<lb />minutiones velocitatis æqualibus temporibus ſunt æquales <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Retardatio ex
<ptr xml:id="note-0384-12a" corresp="note-0384-12" type="noteAnchor" />
ſecunda cauſa dicitur ut quadratum velocitatis, quia diminutiones, in mo-<lb />mentis infinitè exiguis æqualibus, ſunt ut hæc quadrata. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /></s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-11" corresp="note-0384-11a" place="margin">988.</note>
              <note xml:space="preserve" xml:id="note-0384-12" corresp="note-0384-12a" n="*" anchored="true" place="margin">951.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">954.</note>
        <p>
          <s xml:space="preserve">In ſingulis autem momentis infinitè exiguis retardationes, &amp; </s>
          <s xml:space="preserve">accelerationes, ſunt <lb />
<ptr xml:id="note-0384-14a" corresp="note-0384-14" type="noteAnchor" />
æquabiles, nam in tali momento mutatio in actione reſpectiva pro nulla ha-<lb />beri poteſt; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, durante integro momento eodem modo variat motus relativus <lb />fluidi &amp; </s>
          <s xml:space="preserve">corporis: </s>
          <s xml:space="preserve">ergo ſi momenta differant erunt retardationes, &amp; </s>
          <s xml:space="preserve">accelerationes <lb />
<ptr xml:id="note-0384-15a" corresp="note-0384-15" type="noteAnchor" />
ut ipſa momenta; </s>
          <s xml:space="preserve">id eſt ſunt hæ in momentis infinitè exiguis inæqualibus, in <lb />ratione compoſita rationis retar dationum, &amp; </s>
          <s xml:space="preserve">accelerationum, poſitis momentis æ-<lb />
<ptr xml:id="note-0384-16a" corresp="note-0384-16" type="noteAnchor" />
qualibus <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">rationis ipſorum momentorum inæqualium <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-14" corresp="note-0384-14a" place="margin">989.</note>
              <note xml:space="preserve" xml:id="note-0384-15" corresp="note-0384-15a" place="margin">990.</note>
              <note xml:space="preserve" xml:id="note-0384-16" corresp="note-0384-16a" n="*" anchored="true" place="margin">988.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">989.</note>
        <p>
          <s xml:space="preserve">Quando ſpatiola infinite exigua ſunt æqualia, momenta quibus ſingula <lb />
<ptr xml:id="note-0384-18a" corresp="note-0384-18" type="noteAnchor" />
ſpatiola percurruntur ſunt inverſè ut velocitates <ptr type="noteAnchor" />, ergo retardationes, &amp; </s>
          <s xml:space="preserve">acce-
<ptr xml:id="note-0384-19a" corresp="note-0384-19" type="noteAnchor" />
</s>
          <pb facs="0385" n="285" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
lerationes, quas corpus patitur, percurrendo ſingula talia ſpatiola æqualia, ſunt di-<lb />rectè ut retardationes, poſitis momentis æqualibus, &amp; </s>
          <s xml:space="preserve">inverſè ut velocita-<lb />tes <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0384-18" corresp="note-0384-18a" place="margin">991.</note>
              <note xml:space="preserve" xml:id="note-0384-19" corresp="note-0384-19a" n="*" anchored="true" place="margin">95.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">990.</note>
        <p>
          <s xml:space="preserve">Ideo in retardatione ex prima cauſa, ſi ſpatiola infinitè exigua fuerint æqualia, <lb />
<ptr xml:id="note-0385-02a" corresp="note-0385-02" type="noteAnchor" />
ſunt velocitatis diminutiones inverſè ut velocitates <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0385-02" corresp="note-0385-02a" place="margin">992.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">951.</note>
        <p>
          <s xml:space="preserve">In retardatione ex ſecunda cauſa, ſunt velocitatis diminutiones, in ſpatiolis æqua-<lb />
<ptr xml:id="note-0385-04a" corresp="note-0385-04" type="noteAnchor" />
libus, directè ut quadrata velocitatum, &amp; </s>
          <s xml:space="preserve">inverſè ut ipſæ velocitates <ptr type="noteAnchor" />, id eſt
<ptr xml:id="note-0385-05a" corresp="note-0385-05" type="noteAnchor" />
directe ut velocitates.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0385-04" corresp="note-0385-04a" place="margin">993.</note>
              <note xml:space="preserve" xml:id="note-0385-05" corresp="note-0385-05a" n="*" anchored="true" place="margin">954. 990.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 3.</head>
        <head rend="italics" xml:space="preserve">De Retardatione ex prima Cauſa.</head>
        <p>
          <s xml:space="preserve">SIt AC ſpatium, in quo corpus totam amittit velocitatem, quando ex pri-<lb />
<ptr xml:id="note-0385-06a" corresp="note-0385-06" type="noteAnchor" />
ma cauſa ſola retardatur, dum velocitas in initio repræſentatur lineâ <lb />
<ptr xml:id="note-0385-07a" corresp="note-0385-07" type="noteAnchor" />
AD.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0385-06" corresp="note-0385-06a" place="margin">994.</note>
              <note xml:space="preserve" xml:id="note-0385-07" corresp="note-0385-07a" place="margin">TAB. XXXVI. <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum ſpatium hoc AC a corpore percurritur, patitur hoc eaſdem muta-<lb />tiones, quibus ſubjicitur corpus adſcendens, quod ſola retardaretur gravitate, <lb />&amp; </s>
          <s xml:space="preserve">quod ad altitudinem AC adſcendendo totam amitteret velocitatem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0385-08a" corresp="note-0385-08" type="noteAnchor" />
Quadratum igitur velocitatis in A, ſe habet ad quadratum velocitatis in alio <lb />
<ptr xml:id="note-0385-09a" corresp="note-0385-09" type="noteAnchor" />
puncto quocunque B, ut AC ad BC <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si ergo fuerit AD ad BE, in ra-
<ptr xml:id="note-0385-10a" corresp="note-0385-10" type="noteAnchor" />
tione ſubduplicata AC ad BC, repræſentabit BE velocitatem in B. </s>
          <s xml:space="preserve">Datur <lb />autem ratio hæc inter ordinatas parabolæ quæ tranſit per C &amp; </s>
          <s xml:space="preserve">D, poſita <lb />C extremitate diametri AC †.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0385-08" corresp="note-0385-08a" n="*" anchored="true" place="margin">258. 951.</note>
              <note xml:space="preserve" xml:id="note-0385-09" corresp="note-0385-09a" n="*" anchored="true" place="margin">261. 255.</note>
              <note xml:space="preserve" xml:id="note-0385-10" corresp="note-0385-10a" place="margin">† la Hire <lb />fect. con. <lb />lib. 3. <lb />prop. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Idcirco ſi parabolæ diameter repræſentat ſpatium percurſum, ordinatæ ad dia-<lb />
<ptr xml:id="note-0385-11a" corresp="note-0385-11" type="noteAnchor" />
metrum velocitates, in punctis quibuſcunque, deſignabunt, ſi corpus ex ſola prima <lb />cauſa retardetur, aut aliam quamcunque retardationem æquabilem patiatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0385-11" corresp="note-0385-11a" place="margin">995.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſpatiola A a &amp; </s>
          <s xml:space="preserve">B b, infinitè exigua, fuerint æqualia, diminutiones velo-<lb />citatum DF, GE, erunt inverſè ut ipſæ velocitates AD, BE <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Si A a aut
<ptr xml:id="note-0385-12a" corresp="note-0385-12" type="noteAnchor" />
B b mutetur, mutatur in eadem ratione DF aut GE; </s>
          <s xml:space="preserve">ergo in Parabola, <lb />
<ptr xml:id="note-0385-13a" corresp="note-0385-13" type="noteAnchor" />
differentiæ infinitè exiguæ or dinatarum vicinarum ſunt directe ut differentiæ ab-<lb />ſciſſarum reſpondentium, &amp; </s>
          <s xml:space="preserve">inverſe ut ipſæ ordinatæ. </s>
          <s xml:space="preserve">Quod etiam ex ſola con-<lb />ſideratione parabolæ deduci potuiſſet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0385-12" corresp="note-0385-12a" n="*" anchored="true" place="margin">992.</note>
              <note xml:space="preserve" xml:id="note-0385-13" corresp="note-0385-13a" place="margin">996.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si duo dentur corpora, æqualibus velocitatibus mota, quæ diverſas patiuntur re-<lb />
<ptr xml:id="note-0385-14a" corresp="note-0385-14" type="noteAnchor" />
tardationes ex prima cauſa, aut in genere retardationes diverſas æquabiles, ſunt <lb />ſpatia, quibus percurrendo integræ velocitates tolluntur, inverſè ut retardationes <lb />in momentis æqualibus, ut hoc facile deducitur ex demonſtratis de adſcenſu <lb />ſuper planis inclinatis. </s>
          <s xml:space="preserve">Nam velocitatibus æqualibus corpora ad eandem ad-<lb />ſcendunt altitudinem ſuper planis diverſis <ptr type="noteAnchor" />, id eſt ſpatia, quibus percurren-
do integras amittunt velocitates, ſunt ut planorum longitudines, poſitis alti-<lb />
<ptr xml:id="note-0385-15a" corresp="note-0385-15" type="noteAnchor" />
dinibus æqualibus: </s>
          <s xml:space="preserve">ſed in hoc caſu ſunt preſſiones, quibus corpora ſuper his <lb />planis deſcendere conantur, quæ ſunt ut velocitates eodem tempore com-<lb />municatæ, aut ſublatæ, in ratione inverſâ longitudinum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Q. </s>
          <s xml:space="preserve">D, E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0385-14" corresp="note-0385-14a" place="margin">997.</note>
              <note xml:space="preserve" xml:id="note-0385-15" corresp="note-0385-15a" n="*" anchored="true" place="margin">274.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">238.</note>
        <pb facs="0386" n="286" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 4.</head>
        <head rend="italics" xml:space="preserve">De Retardatione ex ſecunda Cauſâ.</head>
        <p>
          <s xml:space="preserve">SIAB, logarithmicæ aſymtotos, ſpatium a corpore in fluido percurſum repræſentat, <lb />
<ptr xml:id="note-0386-01a" corresp="note-0386-01" type="noteAnchor" />
poterunt velocitates in ſingulis punctis ordinatis repræſentari; </s>
          <s xml:space="preserve">ſunt enim velo-<lb />
<ptr xml:id="note-0386-02a" corresp="note-0386-02" type="noteAnchor" />
citatum decrementa, in ſpatiis infinite exiguis æqualibus, AD, DF, <lb />FH, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">ut ipſæ velocitates <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">decrementa ordinatarum AC, DE,
<ptr xml:id="note-0386-03a" corresp="note-0386-03" type="noteAnchor" />
FG, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">ut ipſæ ordinatæ<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-01" corresp="note-0386-01a" place="margin">998.</note>
              <note xml:space="preserve" xml:id="note-0386-02" corresp="note-0386-02a" place="margin">TAB. XXXVII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0386-03" corresp="note-0386-03a" n="*" anchored="true" place="margin">993.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">983.</note>
        <p>
          <s xml:space="preserve">Unde ſequitur ſi ſpatia fuerint æqualia, ut AL, LX, XB, velocitates <lb />
<ptr xml:id="note-0386-05a" corresp="note-0386-05" type="noteAnchor" />
in punctis A, L, X, B, quæ deſignantur ordinatis AC, LM, XZ, BK, <lb />eſſe in progreſſione geometrica <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ut notavimus in n. </s>
          <s xml:space="preserve">961.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-05" corresp="note-0386-05a" place="margin">999.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">980.</note>
        <p>
          <s xml:space="preserve">Sit A T logarithmicæ aſymtos; </s>
          <s xml:space="preserve">BY logarithmica; </s>
          <s xml:space="preserve">BM ejuſdem conti-<lb />
<ptr xml:id="note-0386-07a" corresp="note-0386-07" type="noteAnchor" />
nuatio in ſitu contrario poſita.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-07" corresp="note-0386-07a" place="margin">1000.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XXXVII. <lb />fig. 3.</note>
        <p>
          <s xml:space="preserve">Si nunc ſumamus ordinatam quamcunque ut TYM; </s>
          <s xml:space="preserve">Logarithmus ra-<lb />tionis TM ad AB eſt AT<ptr type="noteAnchor" />, qui etiam eſt logarithmus rationis AB ad TY;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0386-09a" corresp="note-0386-09" type="noteAnchor" />
ſunt ergo in continua proportione TM, AB, TY <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quadratum AB
<ptr xml:id="note-0386-10a" corresp="note-0386-10" type="noteAnchor" />
valet TM x TY: </s>
          <s xml:space="preserve">ſuntque æqualia eidem quadrato AB, ideoque inter ſe, <lb />rectangula omnia ut TM x TY, SX x SL; </s>
          <s xml:space="preserve">PE x PG, &amp;</s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-09" corresp="note-0386-09a" n="*" anchored="true" place="margin">982.</note>
              <note xml:space="preserve" xml:id="note-0386-10" corresp="note-0386-10a" n="*" anchored="true" place="margin">980.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Idcirco creſcunt ordinatæ, quæ curvâ BM terminantur, ut minuuntur <lb />
<ptr xml:id="note-0386-11a" corresp="note-0386-11" type="noteAnchor" />
reſpondentes, quæ curva BY terminantur, ſuntque primæ inverſè ut ſe-<lb />cundæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-11" corresp="note-0386-11a" place="margin">1001.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Spatiola infinite exigua velocitate æquabili ſingula percurruntur; </s>
          <s xml:space="preserve">ſunt ergo <lb />
<ptr xml:id="note-0386-12a" corresp="note-0386-12" type="noteAnchor" />
momenta quibus talia ſpatiola æqualia AC, CP, PQ, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">percurruntur <lb />inverſè ut velocitates quibus percurruntur <ptr type="noteAnchor" />, id eſt inverſè ut AB, CD,
<ptr xml:id="note-0386-13a" corresp="note-0386-13" type="noteAnchor" />
PE, &amp; </s>
          <s xml:space="preserve">c <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">aut directe ut AB, CF, PG &amp;</s>
          <s xml:space="preserve">c <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ ſunt ut differentiæ,
<ptr xml:id="note-0386-14a" corresp="note-0386-14" type="noteAnchor" />
B b, F f. </s>
          <s xml:space="preserve">G g &amp;</s>
          <s xml:space="preserve">c <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-12" corresp="note-0386-12a" place="margin">1002.</note>
              <note xml:space="preserve" xml:id="note-0386-13" corresp="note-0386-13a" n="*" anchored="true" place="margin">95.</note>
              <note xml:space="preserve" xml:id="note-0386-14" corresp="note-0386-14a" n="*" anchored="true" place="margin">998.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1001.</note>
        <p>
          <s xml:space="preserve">Totum igitur tempus quo linea ut AQ percurritur, omnibus hiſce diffe-<lb />
<ptr xml:id="note-0386-16a" corresp="note-0386-16" type="noteAnchor" />
rentiis conjunctim repræſentatur, id eſt, lineâ NH; </s>
          <s xml:space="preserve">eodem modo OM <lb />repræſentat tempus quo QT percurritur: </s>
          <s xml:space="preserve">ſi vero ſpatia AQ, QT, fue-<lb />
<ptr xml:id="note-0386-17a" corresp="note-0386-17" type="noteAnchor" />
rint æqualia, erit NH ad OM, ut QH ad TM <ptr type="noteAnchor" />, id eſt inverſè ut QK
<ptr xml:id="note-0386-18a" corresp="note-0386-18" type="noteAnchor" />
ad TY <ptr type="noteAnchor" />, aut AB ad QK <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-16" corresp="note-0386-16a" n="*" anchored="true" place="margin">983.</note>
              <note xml:space="preserve" xml:id="note-0386-17" corresp="note-0386-17a" n="*" anchored="true" place="margin">983.</note>
              <note xml:space="preserve" xml:id="note-0386-18" corresp="note-0386-18a" n="*" anchored="true" place="margin">1001.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">980.</note>
        <p>
          <s xml:space="preserve">Tempora ergo, quibus ſpatia æqualia ſucceſſivè percurruntur, ſunt inverſè <lb />
<ptr xml:id="note-0386-20a" corresp="note-0386-20" type="noteAnchor" />
ut velocitates in fine, aut inverſè ut velocitates in initiis ſpatiorum; </s>
          <s xml:space="preserve">ut mo-<lb />nuimus in n. </s>
          <s xml:space="preserve">961.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-20" corresp="note-0386-20a" place="margin">1003.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus iterum corpus quod in linea AB movetur, &amp; </s>
          <s xml:space="preserve">ex ſecunda cauſa <lb />
<ptr xml:id="note-0386-21a" corresp="note-0386-21" type="noteAnchor" />
ſola retardatur, ſit AC velocitas in A, &amp; </s>
          <s xml:space="preserve">CM logarithmica, quæ in aliis pun-<lb />
<ptr xml:id="note-0386-22a" corresp="note-0386-22" type="noteAnchor" />
ctis velocitates determinat <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ut hac curvâ, &amp; </s>
          <s xml:space="preserve">tabulis utamur in computa-
tionibus neceſſe eſt, ut determinemus magnitudinem ſubtangentis logarithmi-<lb />
<ptr xml:id="note-0386-23a" corresp="note-0386-23" type="noteAnchor" />
cæ, quæ uſu venire poteſt in caſu quocunque propoſito, aut quod idem eſt, <lb />debemus determinare, in figura data quacunque, quodnam ſpatium ſubtan-<lb />gente repræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-21" corresp="note-0386-21a" place="margin">1004.</note>
              <note xml:space="preserve" xml:id="note-0386-22" corresp="note-0386-22a" place="margin">TAB. XXXVII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0386-23" corresp="note-0386-23a" n="*" anchored="true" place="margin">998.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus AC eſſe velocitatem, qua ſi corpus in fluido feratur, reſiſtentia <lb />ex ſecunda cauſa ipſi ponderi corporis æqualis ſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ergo Corporis pondus, id eſt, preſſio ex gravitate quæ corpus adſcendens retar-<lb />
<ptr xml:id="note-0386-24a" corresp="note-0386-24" type="noteAnchor" />
dat, æqualis eſt preſſioni quam corpus de quo agimus ex reſiſtentia ex ſecunda <lb />cauſa patitur. </s>
          <s xml:space="preserve">Preſſiones hæ ambæ immediate corpus transferunt, quando in
</s>
          <pb facs="0387" />
          <s xml:space="preserve">
<pb facs="0387a" />
<ptr xml:id="fig-0387a-01a" corresp="fig-0387a-01" type="figureAnchor" />
<pb facs="0388" />
<pb facs="0389" n="287" /><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
hoc agunt: </s>
          <s xml:space="preserve">ergo æqualiter eundem motum ejuſdem corporis mutare poſſunt; </s>
          <s xml:space="preserve">eſt-<lb />que retardatio, quam corpus in fluido patitur in primo momento, æqualis <lb />velocitati, quam in momento æquali corpus adſcendens, &amp; </s>
          <s xml:space="preserve">quod gravitas <lb />retardat, amittit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0386-24" corresp="note-0386-24a" place="margin">1005.</note>
              <figure xml:id="fig-0387a-01" corresp="fig-0387a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0387a-01" />
                <label>0387a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit nunc C c retardatio quam corpus patitur percurrendo AD, erit C c <lb />velocitas quam corpus amittit, adſcendendo ad altitudinem AD, quando gra-<lb />vitate retardatur. </s>
          <s xml:space="preserve">Concipiamus nunc parabolam deſcriptam, cujus axis ſit <lb />AB, &amp; </s>
          <s xml:space="preserve">quæ per puncta C &amp; </s>
          <s xml:space="preserve">E tranſeat, id eſt eandem habeat tangentem <lb />AT cum logarithmica, quæ per C &amp; </s>
          <s xml:space="preserve">E tranſit, &amp; </s>
          <s xml:space="preserve">cujus Aſymtos eſt <lb />AB.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ordinatæ logarithmicæ hujus deſignabunt velocitates corporis in fluido mo-<lb />ti, cujus velocitas in A eſt AC<ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">AX axis parabolæ, cujus vertex eſt X,
<ptr xml:id="note-0389-01a" corresp="note-0389-01" type="noteAnchor" />
demonſtrabit altitudinem ad quam corpus, velocitate AC in altum proje-<lb />
<ptr xml:id="note-0389-02a" corresp="note-0389-02" type="noteAnchor" />
ctum, &amp; </s>
          <s xml:space="preserve">ſola gravitate retardatum, poteſt adſcendere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">igitur XA, dimi-
<ptr xml:id="note-0389-03a" corresp="note-0389-03" type="noteAnchor" />
dium ſubtangentis AT<ptr type="noteAnchor" />, deſignat altitudinem a qua corpus in vacuo cadendo ac-
<ptr xml:id="note-0389-04a" corresp="note-0389-04" type="noteAnchor" />
quirit velocitatem, qua ſi corpus per fluidum moveatur, reſiſtentiam patitur pon-<lb />deri ipſius corporis æqualem, quæ altitudo datur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0389-01" corresp="note-0389-01a" n="*" anchored="true" place="margin">998.</note>
              <note xml:space="preserve" xml:id="note-0389-02" corresp="note-0389-02a" n="*" anchored="true" place="margin">995.</note>
              <note xml:space="preserve" xml:id="note-0389-03" corresp="note-0389-03a" place="margin">1006.</note>
              <note xml:space="preserve" xml:id="note-0389-04" corresp="note-0389-04a" n="*" anchored="true" place="margin">la Hire <lb />ſect. con. <lb />lib. 2. <lb />prop 20.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">930.</note>
        <p>
          <s xml:space="preserve">Hiſce poſitis ſequentia ſponte ſequuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut altitudo, à qua corpus in vacuo cadendo, acquirit velocitatem, quæ dat re-<lb />
<ptr xml:id="note-0389-06a" corresp="note-0389-06" type="noteAnchor" />
ſiſtentiam pondericorporis æqualem, ad ſpatium à corpore in fluido percurſum, ita <lb />dimidium ſubtangentis tabularum, 0, 21714. </s>
          <s xml:space="preserve">72409. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, ad logarihtmum rationis in-
<ptr xml:id="note-0389-07a" corresp="note-0389-07" type="noteAnchor" />
ter velocitates in initio &amp; </s>
          <s xml:space="preserve">in fine ſpatii <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0389-06" corresp="note-0389-06a" place="margin">1007.</note>
              <note xml:space="preserve" xml:id="note-0389-07" corresp="note-0389-07a" n="*" anchored="true" place="margin">987.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">938.</note>
        <p>
          <s xml:space="preserve">Numeri quicunque in tabulis, quorum logarihtmorum differentia eſt lo-<lb />
<ptr xml:id="note-0389-09a" corresp="note-0389-09" type="noteAnchor" />
garithmus rationis detectus, ſunt inter ſe ut hæ velocitates <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0389-09" corresp="note-0389-09a" place="margin">1008.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">982. 980.</note>
        <p>
          <s xml:space="preserve">Eâdem hac regulâ, data ratione inter velocitates in initio &amp; </s>
          <s xml:space="preserve">fine ſpatii per-<lb />
<ptr xml:id="note-0389-11a" corresp="note-0389-11" type="noteAnchor" />
curſi, detegitur ſpatium hoc.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0389-11" corresp="note-0389-11a" place="margin">1009.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Logarihtmus rationis 2. </s>
          <s xml:space="preserve">ad I. </s>
          <s xml:space="preserve">habetur, ſubtrahendo ex log. </s>
          <s xml:space="preserve">numeri duo <lb />
<ptr xml:id="note-0389-12a" corresp="note-0389-12" type="noteAnchor" />
0, 30102. </s>
          <s xml:space="preserve">99957. </s>
          <s xml:space="preserve">log. </s>
          <s xml:space="preserve">o. </s>
          <s xml:space="preserve">unitatis, ergo ut o, 21714. </s>
          <s xml:space="preserve">72409, ad 0, 30102. </s>
          <s xml:space="preserve">99957, <lb />id eſt, ut 10000000000. </s>
          <s xml:space="preserve">ad 13862945972.</s>
          <s xml:space="preserve">, ita altitudo, a qua in vacuo caden-<lb />do corpus acquirit velocitatem, quæ dat reſiſtentiam ponderi æqualem, ad <lb />ſpatium in quo corpus dimidium velocitatis amittit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Congruit hoc cum
<ptr xml:id="note-0389-13a" corresp="note-0389-13" type="noteAnchor" />
indicatis in n. </s>
          <s xml:space="preserve">962.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0389-12" corresp="note-0389-12a" place="margin">1010.</note>
              <note xml:space="preserve" xml:id="note-0389-13" corresp="note-0389-13a" n="*" anchored="true" place="margin">1007.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si in puncto quocunque retardatio ex ſecunda cauſa fiat æquabilis, ſpatium <lb />
<ptr xml:id="note-0389-14a" corresp="note-0389-14" type="noteAnchor" />
in quo tota deſtruitur velocitas dimidiata ſubtangente repræſentatur, ut ſequi-<lb />tur ex demonſtratione n. </s>
          <s xml:space="preserve">1005, quæ &amp; </s>
          <s xml:space="preserve">hîc applicari poteſt; </s>
          <s xml:space="preserve">cum autem ſub-<lb />tangens conſtans ſit <ptr type="noteAnchor" />, ſequitur etiam in fluido homogeneo, quale in his ubi-
<ptr xml:id="note-0389-15a" corresp="note-0389-15" type="noteAnchor" />
que ponimus, ſpatium illud non mutari, quomodocunque varietur veloci-<lb />tas, &amp; </s>
          <s xml:space="preserve">æquari altitudini a qua in vacuo cadendo corpus acquirit velocitatem, qua <lb />poſitâ, reſiſtentia ponderi æqualis eſt<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0389-14" corresp="note-0389-14a" place="margin">1011.</note>
              <note xml:space="preserve" xml:id="note-0389-15" corresp="note-0389-15a" n="*" anchored="true" place="margin">984.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1006.</note>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 5.</head>
        <head rend="italics" xml:space="preserve">De ambabus Retardationibus conjunctim.</head>
        <p>
          <s xml:space="preserve">Sit A M linea, quam corpus in fluido percurrit; </s>
          <s xml:space="preserve">ſit hæc Aſymtos loga-<lb />
<ptr xml:id="note-0389-17a" corresp="note-0389-17" type="noteAnchor" />
rithmicæ ISP; </s>
          <s xml:space="preserve">cujus AI eſt ordinata; </s>
          <s xml:space="preserve">ſit præterea GFB parabola cu-<lb />
<ptr xml:id="note-0389-18a" corresp="note-0389-18" type="noteAnchor" />
jus axis eſt IB; </s>
          <s xml:space="preserve">vertex B; </s>
          <s xml:space="preserve">ordinata GI, parallela AM; </s>
          <s xml:space="preserve">Parameter BI: </s>
          <s xml:space="preserve">Si <lb />AB fuerit ad BI, ut retardatio ex prima cauſa ad retardationem ex ſecun-
</s>
          <pb facs="0390" n="288" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
da in puncto A, poterit velocitas in puncto quocunque, ut C, determina-<lb />ri. </s>
          <s xml:space="preserve">Nam ſi in hoc puncto detur CD, ad AM perpendicularis, ordinata <lb />logarithmicæ, &amp; </s>
          <s xml:space="preserve">per D ducta ſit DF ad IG &amp; </s>
          <s xml:space="preserve">AM parallela, erunt GI <lb />&amp; </s>
          <s xml:space="preserve">FE, ut velocitates in punctis A &amp; </s>
          <s xml:space="preserve">C.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0389-17" corresp="note-0389-17a" place="margin">1012.</note>
              <note xml:space="preserve" xml:id="note-0389-18" corresp="note-0389-18a" place="margin">TAB. XXXVII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut hoc demonſtremus ponimus A a &amp; </s>
          <s xml:space="preserve">C c infinite exiguas, &amp; </s>
          <s xml:space="preserve">æquales; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0390-01a" corresp="note-0390-01" type="noteAnchor" />
velocitates in punctis a &amp; </s>
          <s xml:space="preserve">c, ſi ut in puncto C determinentur, erunt KH &amp; </s>
          <s xml:space="preserve"><lb />e f; </s>
          <s xml:space="preserve">decrementa ergo velocitatum, dum ſpatia æqualia A a, C c percurrun-<lb />tur, ſunt G g &amp; </s>
          <s xml:space="preserve">FL; </s>
          <s xml:space="preserve">demonſtrandum, ſi G g reſolvatur in duas partes quæ <lb />ſint ut AB ad BI, FL poſſe reſolvi in duas ita, ut partes primæ utriuſque <lb />decrementi ſint inverſè ut GI ad FE <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſecundæ directe in eadem ra-
<ptr xml:id="note-0390-02a" corresp="note-0390-02" type="noteAnchor" />
tione GI aut BI, (quia hæc eſt parabolæ parameter †) ad FE <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">id eſt
<ptr xml:id="note-0390-03a" corresp="note-0390-03" type="noteAnchor" />
debemus probare G g ſe habere ad FL, ut {AB/GI} + {BI/GI} ad {AB/FE} + {FE/GI}. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0390-04a" corresp="note-0390-04" type="noteAnchor" />
Hæc eſt autem demonſtratio; </s>
          <s xml:space="preserve">G g, FL :</s>
          <s xml:space="preserve">:{IK/GI}, {Ee/FE} <ptr type="noteAnchor" /> :</s>
          <s xml:space="preserve">: {AI/GI} = {AB/GI} + {BI/GI},
<ptr xml:id="note-0390-05a" corresp="note-0390-05" type="noteAnchor" />
{AE/FE} = {AB/FE} + {BE/FE} <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0390-01" corresp="note-0390-01a" place="margin">1013.</note>
              <note xml:space="preserve" xml:id="note-0390-02" corresp="note-0390-02a" n="*" anchored="true" place="margin">992</note>
              <note xml:space="preserve" xml:id="note-0390-03" corresp="note-0390-03a" place="margin">4 la Hire ſect con. lib 3. prop. 2.</note>
              <note xml:space="preserve" xml:id="note-0390-04" corresp="note-0390-04a" n="*" anchored="true" place="margin">993.</note>
              <note xml:space="preserve" xml:id="note-0390-05" corresp="note-0390-05a" n="*" anchored="true" place="margin">996.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">983.</note>
        <p>
          <s xml:space="preserve">Sed {BE/FE} = {BE x FE/FE x FE} = {BE x FE/BE x BI} <ptr type="noteAnchor" /> = {FE/BI} = {FE/GI} propter æquales BI,
<ptr xml:id="note-0390-07a" corresp="note-0390-07" type="noteAnchor" />
GI: </s>
          <s xml:space="preserve">Ergo G g, FL :</s>
          <s xml:space="preserve">: {AB/GI} + {BI/GI}, {AB/FE} + {FE/GI}. </s>
          <s xml:space="preserve">Quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0390-07" corresp="note-0390-07a" n="*" anchored="true" place="margin">la Hire <lb />ſect. con. <lb />lib. 3. <lb />prop. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Spatium in quo corpus totam amittit velocitatem eſt BP, aut AQ; </s>
          <s xml:space="preserve">in <lb />puncto enim Q velocitas nulla eſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1012.</note>
        <p>
          <s xml:space="preserve">Ut nunc hæc figura computationi inſerviat, ſpatium, datâ lineâ repræ-<lb />
<ptr xml:id="note-0390-09a" corresp="note-0390-09" type="noteAnchor" />
ſentatum, determinandum eſt, ut &amp; </s>
          <s xml:space="preserve">ratio quæ datur inter IB &amp; </s>
          <s xml:space="preserve">BA, ad quæ <lb />ſine experimentis, circa ipſas retardationes inſtitutis, pervenire non poſſu-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0390-09" corresp="note-0390-09a" place="margin">1014.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponimus ergo experimento detectum fuiſſe ſpatium AQ, in quo corpus <lb />totam amittit velocitatem, quo ſpatio dato, ratio inter AB &amp; </s>
          <s xml:space="preserve">BI, quæ eſt <lb />ratio retardationum in puncto A, detegi poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Velocitas in A lineâ GI, aut BI ipſi æquali, repræſentatur, &amp; </s>
          <s xml:space="preserve">retarda-<lb />tio dum ſpatium A a percurritur eſt G g, ut vidimus, quæ (propter ſubtan-<lb />gentem duplam abſciſſæ BI <ptr type="noteAnchor" />, ideoque duplam GI) dimidium eſt ipſius
<ptr xml:id="note-0390-10a" corresp="note-0390-10" type="noteAnchor" />
g H, aut i k.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0390-10" corresp="note-0390-10a" n="*" anchored="true" place="margin">la Hire <lb />ſect. con. <lb />lib. 2. <lb />prop. 20.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Logarithmicam ISP tangit linea I k O; </s>
          <s xml:space="preserve">ſumtâ AM duplà AO, ductâ-<lb />que IM, quæ ſecat k i in m, erit k i dupla m i, quæ ergo G g æqualis eſt, <lb />retardationemque repræſentat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit ad A I parallela MT; </s>
          <s xml:space="preserve">quam in N ſecat BP producta; </s>
          <s xml:space="preserve">ita ut æqua-<lb />les ſint AB, MN, ut &amp; </s>
          <s xml:space="preserve">BI, NT; </s>
          <s xml:space="preserve">ductâ ergo IN, quæ m i ſecat in n <lb />erit AB, ad BI, id eſt prima retardatio ad ſecundam in puncto A, ut m n, <lb />ad n i; </s>
          <s xml:space="preserve">repræſentant idcirco hæ ſeparatim utramque retardationem; </s>
          <s xml:space="preserve">nam <lb />ſumma retardationes conjunctim deſignat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Eſt nunc n i retardatio, quam corpus dum BI, quæ GI æqualis eſt, veloci-
</s>
          <pb facs="0391" n="289" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
tatem in A exprimit ex ſecunda cauſa ſola patitur. </s>
          <s xml:space="preserve">Si igitur concipia-<lb />mus logarithmicam IR cujus aſymtos ſit BN, &amp; </s>
          <s xml:space="preserve">quæ tranſeat per I &amp; </s>
          <s xml:space="preserve">n, <lb />deſignabit PR velocitatem quam corpus, ſi ex ſola ſecunda cauſa retarda-<lb />retur ſuperſtitem haberet, percurrendo ſpatium experimento detectum AQ, <lb />
<ptr xml:id="note-0391-01a" corresp="note-0391-01" type="noteAnchor" />
aut BP <ptr type="noteAnchor" />, poteſtque ratio inter BI &amp; </s>
          <s xml:space="preserve">PR detegi <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-01" corresp="note-0391-01a" n="*" anchored="true" place="margin">998.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1007.</note>
        <p>
          <s xml:space="preserve">Subtangens logarithmicæ IR eſt BN, aut AM dupla AO, quæ eſt ſub-<lb />tangens logarithmicæ IP.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si ergo AQ, æqualis BP, logarithmo rationis BI ad PR, in duas partes <lb />æquales dividatur in V, &amp; </s>
          <s xml:space="preserve">VS detur perpendicularis ad AQ, erit BI ad PR, <lb />
<ptr xml:id="note-0391-03a" corresp="note-0391-03" type="noteAnchor" />
ut AI ad VS <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sunt autem in continuâ proportione AI, VS, QP <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">er-
<ptr xml:id="note-0391-04a" corresp="note-0391-04" type="noteAnchor" />
go A I<hi rend="superscript">q</hi> ad V S<hi rend="superscript">q</hi>, id eſt B I<hi rend="superscript">q</hi> ad P R<hi rend="superscript">q</hi>, ut AI ad QP, aut AB; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">divi-<lb />dendo</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-03" corresp="note-0391-03a" n="*" anchored="true" place="margin">986.</note>
              <note xml:space="preserve" xml:id="note-0391-04" corresp="note-0391-04a" n="*" anchored="true" place="margin">980.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">B I<hi rend="superscript">q</hi> - PR<hi rend="superscript">q</hi>, PR<hi rend="superscript">q</hi> :: AI-AB = BI, AB.</head>
        <p>
          <s xml:space="preserve">Quod ſic enuntiari poteſt: </s>
          <s xml:space="preserve">Quadratum velocitatis corporis ininitio minus qua-<lb />
<ptr xml:id="note-0391-05a" corresp="note-0391-05" type="noteAnchor" />
drato velocitatis, quam, ſi corpus ex ſola ſecunda cauſa retardaretur, ſuperſtitem ha-<lb />beret, poſt percurſum ſpatium, in quo, dum ex ambabus cauſis retardatur, totum <lb />motum amittit, ad hoc ultimum quadrarum, ita retardatio ex ſecunda ad retar-<lb />dationem ex prima, in primo momento motus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-05" corresp="note-0391-05a" place="margin">1015.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">His præmiſſis, computatione detegimus velocitatem in puncto quocunque <lb />
<ptr xml:id="note-0391-06a" corresp="note-0391-06" type="noteAnchor" />
dato lineæ AQ, ut C.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-06" corresp="note-0391-06a" place="margin">1016.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quærimus in numeris tabularum logarithmum rationis BI ad PR <ptr type="noteAnchor" />, qui
<ptr xml:id="note-0391-07a" corresp="note-0391-07" type="noteAnchor" />
eſt logarithmus rationis AI ad VS; </s>
          <s xml:space="preserve">ſi hic duplicetur habemus numerum <lb />qui repræſentat AQ, ſi ponamus ISP eſſe logarithmicam tabularum; <lb /></s>
          <s xml:space="preserve">demonſtrata enim ad logarithmicam quamcunque applicari poſſunt; </s>
          <s xml:space="preserve">Dica-<lb />tur hic numerus L.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-07" corresp="note-0391-07a" n="*" anchored="true" place="margin">1007.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut ſpatium AQ, in quo corpus totum motum amittit, ad ſpatium da-<lb />tum AC, id eſt AQ ad AC, ita L ad logarithmum rationis AI ad CD aut <lb />AI ad AE: </s>
          <s xml:space="preserve">qui ergo datur, poteſtque deſignari littera M.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sumto nunc ad libitum numero qui deſignat AI, Log. </s>
          <s xml:space="preserve">AI - M erit <lb />log. </s>
          <s xml:space="preserve">numeri qui deſignat CD <ptr type="noteAnchor" />, aut AE. </s>
          <s xml:space="preserve">Log. </s>
          <s xml:space="preserve">A I - L eſt log.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0391-08a" corresp="note-0391-08" type="noteAnchor" />
numeri qui deſignat QP, aut AB: </s>
          <s xml:space="preserve">quos numeros determinamus: <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0391-09a" corresp="note-0391-09" type="noteAnchor" />
dantur ergo tres numeri, qui ſunt inter ſe ut AI, AE, AB; </s>
          <s xml:space="preserve">quare ex <lb />
<ptr xml:id="note-0391-10a" corresp="note-0391-10" type="noteAnchor" />
primis duobus ſubtracto ultimo, reſtant numeri, qui ſunt ut BI <lb />ad BE, ut id eſt quadrata velocitatum in A &amp; </s>
          <s xml:space="preserve">C <ptr type="noteAnchor" />, in initio &amp; </s>
          <s xml:space="preserve">puncto dato.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-08" corresp="note-0391-08a" n="*" anchored="true" place="margin">982.</note>
              <note xml:space="preserve" xml:id="note-0391-09" corresp="note-0391-09a" n="*" anchored="true" place="margin">1012.</note>
              <note xml:space="preserve" xml:id="note-0391-10" corresp="note-0391-10a" place="margin">la Hire <lb />ſect. con. <lb />lib. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Operatione contraria, datis velocitatibus GI &amp; </s>
          <s xml:space="preserve">FE, &amp; </s>
          <s xml:space="preserve">ſpa-<lb />tio AQ, in quo corpus totam amittit velocitatem, detegi-<lb />
<ptr xml:id="note-0391-11a" corresp="note-0391-11" type="noteAnchor" />
tur punctum C. </s>
          <s xml:space="preserve">Nam data AQ detegitur ratio inter BI &amp; </s>
          <s xml:space="preserve">BA <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſumto-
<ptr xml:id="note-0391-12a" corresp="note-0391-12" type="noteAnchor" />
que numero qui velocitatem GI, æqualem BI, exprimit datur BA; <lb /></s>
          <s xml:space="preserve">ſed ut GI<hi rend="superscript">q</hi> ad FE<hi rend="superscript">q</hi> ita BI ad BE, datur ergo numerus qui lineam hanc ex-<lb />primit; </s>
          <s xml:space="preserve">ideoque numeros determinamus, qui ſunt inter ſe ut AB, AE, <lb />AI. </s>
          <s xml:space="preserve">Ex demonſtratis autem conſtat <ptr type="noteAnchor" /> differentiam log. </s>
          <s xml:space="preserve">AI, AB, ad dif-
<ptr xml:id="note-0391-13a" corresp="note-0391-13" type="noteAnchor" />
ferentiam log. </s>
          <s xml:space="preserve">AI, AE, ita AQ ad AC, ſpatium percurſum, quod ergo <lb />detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-11" corresp="note-0391-11a" place="margin">1017.</note>
              <note xml:space="preserve" xml:id="note-0391-12" corresp="note-0391-12a" n="*" anchored="true" place="margin">1015.</note>
              <note xml:space="preserve" xml:id="note-0391-13" corresp="note-0391-13a" n="*" anchored="true" place="margin">1013.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Determinatur etiam CQ ſpatium in quo corpus amittit totum motum da-<lb />
<ptr xml:id="note-0391-14a" corresp="note-0391-14" type="noteAnchor" />
ta velocitate FE in initio, ſubtrahendo nempe AC ex AQ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0391-14" corresp="note-0391-14a" place="margin">1018.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc concipiamus, datâ velocitate GI, ſolam locum habere retarda-
</s>
          <pb facs="0392" n="290" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tionem ex ſecunda cauſâ hancque æquabilem fieri, datur ſpatium in quo tota <lb />
<ptr xml:id="note-0392-01a" corresp="note-0392-01" type="noteAnchor" />
deſtruitur velocitas <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hoc autem ſpatium ſe habet ad ſpatium in quo, ſolâ reſi-
<ptr xml:id="note-0392-02a" corresp="note-0392-02" type="noteAnchor" />
ſtentiâ ex primâ cauſâ, tota velocitas deſtruitur, ut AB ad BI <ptr type="noteAnchor" />, quæ ratio
<ptr xml:id="note-0392-03a" corresp="note-0392-03" type="noteAnchor" />
cum detur <ptr type="noteAnchor" />, etiam determinamus ſpatium hoc. </s>
          <s xml:space="preserve">Spatia autem hæc, in diverſis
<ptr xml:id="note-0392-04a" corresp="note-0392-04" type="noteAnchor" />
fluidis, ſunt inverſe ut partium cohæſiones.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-01" corresp="note-0392-01a" n="*" anchored="true" place="margin">1011.</note>
              <note xml:space="preserve" xml:id="note-0392-02" corresp="note-0392-02a" place="margin">1019.</note>
              <note xml:space="preserve" xml:id="note-0392-03" corresp="note-0392-03a" n="*" anchored="true" place="margin">997.</note>
              <note xml:space="preserve" xml:id="note-0392-04" corresp="note-0392-04a" n="*" anchored="true" place="margin">1015.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">1020.</note>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM. 6</head>
        <head rend="italics" xml:space="preserve">De Corporibus in altum projectis.</head>
        <p>
          <s xml:space="preserve">Corpus, fluido ſpecificè gravius, quod in boc in altum projicitur, tribus ex cau <lb />
<ptr xml:id="note-0392-06a" corresp="note-0392-06" type="noteAnchor" />
ſis retardatur, ex gravitate &amp; </s>
          <s xml:space="preserve">ambabus cauſis in hoc capite explicatis. <lb /></s>
          <s xml:space="preserve">Retardatio ex gravitate &amp; </s>
          <s xml:space="preserve">ex prima cauſa ſunt ambæ æquabiles <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">conjun-
<ptr xml:id="note-0392-07a" corresp="note-0392-07" type="noteAnchor" />
ctæ æquabilem tantum efficiunt retardationem; </s>
          <s xml:space="preserve">quare &amp; </s>
          <s xml:space="preserve">hîc applicari poſ-<lb />ſunt quæ in ſuperiori ſcholio demonſtrata ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-06" corresp="note-0392-06a" place="margin">1021.</note>
              <note xml:space="preserve" xml:id="note-0392-07" corresp="note-0392-07a" n="*" anchored="true" place="margin">258. 950.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ergo unico experimento conſtet ad quam altitudinem corpus in fluido, datâ ve-<lb />
<ptr xml:id="note-0392-08a" corresp="note-0392-08" type="noteAnchor" />
locitate, adſcendit, ſequentia problemata ſolvuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-08" corresp="note-0392-08a" place="margin">1022.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Detegitur altitudo ad quam, datâ aliâ velocitate quacunque, corpus adſcendere <lb />poteſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1018.</note>
        <p>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Datâ velocitate in initio, detegitur velocitas in puncto dato <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1023.</note>
        <p>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Detegitur data velocitate, ſpatium in quo, ſepoſitâ reſiſtentiâ ex ſecundâ <lb />
<ptr xml:id="note-0392-11a" corresp="note-0392-11" type="noteAnchor" />
cauſâ, id eſt gravitate reſpectivâ &amp; </s>
          <s xml:space="preserve">cobæſione conjunctim, corpus motum ſuum <lb />
<ptr xml:id="note-0392-12a" corresp="note-0392-12" type="noteAnchor" />
amitteret <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-11" corresp="note-0392-11a" n="*" anchored="true" place="margin">1016.</note>
              <note xml:space="preserve" xml:id="note-0392-12" corresp="note-0392-12a" place="margin">1024.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1019.</note>
        <p>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Detegitur ſpatium in quo corpus, data velocitate motum, ex ſola cobæſione mo-<lb />
<ptr xml:id="note-0392-14a" corresp="note-0392-14" type="noteAnchor" />
tum amitteret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-14" corresp="note-0392-14a" place="margin">1025.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum velocitas detur, datur altitudo ad quam corpus in vacuo adſcendere <lb />poteſt; </s>
          <s xml:space="preserve">eſt hæc ad altitudinem ad quam in fluido corpus, dum ſolâ gravi-<lb />tate reſpectiva retardatur, adſcendit, ut gravitas hæc reſpectiva eſt ad pon-<lb />dus integrum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">997.</note>
        <p>
          <s xml:space="preserve">Eſt vero altitudo hæc ultima, ad altitudinem ad quam adſcendit corpus <lb />dum gravitate reſpectiva &amp; </s>
          <s xml:space="preserve">cohæſione retardatur, quæ altitudo etiam datur <ptr type="noteAnchor" />,
<ptr xml:id="note-0392-16a" corresp="note-0392-16" type="noteAnchor" />
ut retardatio ex his ambabus cauſis ad retardationem ex ſola gravitate reſpe-<lb />ctiva <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-16" corresp="note-0392-16a" n="*" anchored="true" place="margin">1024.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">997.</note>
        <p>
          <s xml:space="preserve">Idcirco dividendo; </s>
          <s xml:space="preserve">ut differentia barum altitudinum ad ultimam, ita retar-<lb />
<ptr xml:id="note-0392-18a" corresp="note-0392-18" type="noteAnchor" />
datio ex cohæſione ad retar dationem ex gravitate reſpectiva &amp; </s>
          <s xml:space="preserve">in eadem ratione <lb />altitudo dum ſola gravitas reſpectiva retardat ad ſpatium in quo ſola cohæ-<lb />ſione motus perit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-18" corresp="note-0392-18a" place="margin">1026.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">997.</note>
        <p>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">Tandem, data velocitate, detegimus ſpatium, in quo corpus in motu bori-<lb />
<ptr xml:id="note-0392-20a" corresp="note-0392-20" type="noteAnchor" />
zontali, dum cohæſione &amp; </s>
          <s xml:space="preserve">inertiâ retardatur, motum amitteret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-20" corresp="note-0392-20a" place="margin">1027.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datur in præcedenti computatione ratio inter retardationem ex cohæſio-<lb />ne &amp; </s>
          <s xml:space="preserve">retardationem ex gravitate reſpectiva <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Datur altitudo a qua caden-
<ptr xml:id="note-0392-21a" corresp="note-0392-21" type="noteAnchor" />
do corpus acquirit velocitatem, qua ſi agitaretur, retardatio ex inertia æqua-<lb />lis eſſet retardationi ex pondere reſpectivo <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Altitudo autem hæc ſe habet
<ptr xml:id="note-0392-22a" corresp="note-0392-22" type="noteAnchor" />
ad altitudinem, à qua cadendo corpus acquirit velocitatem de qua agitur, <lb />ut retardatio ex inertia, quando retardationi ex pondere reſpectivo æqua-<lb />lis eſt, ad retardationem ex inertia in velocitate data quam examinamus, <lb />id eſt altitudines ſunt ut retardationes; </s>
          <s xml:space="preserve">nam hæ &amp; </s>
          <s xml:space="preserve">illæ ſunt ut quadrata ve-<lb />locitatum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0392-21" corresp="note-0392-21a" n="*" anchored="true" place="margin">1026.</note>
              <note xml:space="preserve" xml:id="note-0392-22" corresp="note-0392-22a" n="*" anchored="true" place="margin">928. 1005.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">255. 954.</note>
        <pb facs="0393" n="291" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
        <p>
          <s xml:space="preserve">Ratio retardationis ex cohæſione, quæ æquabilis eſt <ptr type="noteAnchor" />, ad retardationem ex
<ptr xml:id="note-0393-01a" corresp="note-0393-01" type="noteAnchor" />
inertia, in velocitate data, eſt compoſita ex ratione retardationis primæ ad <lb />retardationem ex pondere reſpectivo, &amp; </s>
          <s xml:space="preserve">ratione retardationis hujus ad ſe-<lb />cundam. </s>
          <s xml:space="preserve">Vidimus rationes componentes dari, datur ergo &amp; </s>
          <s xml:space="preserve">compoſita, id <lb />
<ptr xml:id="note-0393-02a" corresp="note-0393-02" type="noteAnchor" />
eſt ſi hoc applicemus ad demonſtrata in ſcholio præcedenti <ptr type="noteAnchor" />, datur ratio
AB ad BI; </s>
          <s xml:space="preserve">unde deducitur ratio BI ad PR <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">qua data detegitur BP <ptr type="noteAnchor" />
<ptr xml:id="note-0393-03a" corresp="note-0393-03" type="noteAnchor" />
ſpatium quæſitum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0393-01" corresp="note-0393-01a" n="*" anchored="true" place="margin">950.</note>
              <note xml:space="preserve" xml:id="note-0393-02" corresp="note-0393-02a" place="margin">TAB. XXXVII. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0393-03" corresp="note-0393-03a" n="*" anchored="true" place="margin"> 1013. 1014.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1015. 1014.</note>
        <p>
          <s xml:space="preserve">Corpus fluido ſpecifice levius, eodem modo in hoc ſurſum fertur, acgra-<lb />
<ptr xml:id="note-0393-05a" corresp="note-0393-05" type="noteAnchor" />
vius fundum petit; </s>
          <s xml:space="preserve">quare demonſtrata in hoc ſcholio, ad corpora fluidis ſpe-<lb />
<ptr xml:id="note-0393-06a" corresp="note-0393-06" type="noteAnchor" />
cifice leviora, &amp; </s>
          <s xml:space="preserve">in his motu impreſſo deſcendentia referri debent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0393-05" corresp="note-0393-05a" n="*" anchored="true" place="margin">1009.</note>
              <note xml:space="preserve" xml:id="note-0393-06" corresp="note-0393-06a" place="margin">1028.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM. 7.</head>
        <head rend="italics" xml:space="preserve">De Corporibus in Fluidis cadentibus.</head>
        <p>
          <s xml:space="preserve">COrpus quod in fluido ſponte cadit, continuo æquabiliter acceleratur <ptr type="noteAnchor" />, dum re-
<ptr xml:id="note-0393-07a" corresp="note-0393-07" type="noteAnchor" />
ſiſtentiam patitur, quæ eſt ut quadratum velocitatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0393-07" corresp="note-0393-07a" place="margin">1029.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">251. 950.</note>
        <p>
          <s xml:space="preserve">Quæ motum hunc ſpectant etiam parabolâ, &amp; </s>
          <s xml:space="preserve">logarithmicâ exhiben-<lb />
<ptr xml:id="note-0393-09a" corresp="note-0393-09" type="noteAnchor" />
tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0393-09" corresp="note-0393-09a" n="*" anchored="true" place="margin">954.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit QAR logarithmicæ BDH aſymtos; </s>
          <s xml:space="preserve">ordinata hujus curvæ ad Aſymto-<lb />
<ptr xml:id="note-0393-10a" corresp="note-0393-10" type="noteAnchor" />
ton perpendicularis AB; </s>
          <s xml:space="preserve">quæ etiam eſt axis parabolæ BFQ, cujus para-<lb />
<ptr xml:id="note-0393-11a" corresp="note-0393-11" type="noteAnchor" />
metrum ponimus AB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0393-10" corresp="note-0393-10a" place="margin">1030.</note>
              <note xml:space="preserve" xml:id="note-0393-11" corresp="note-0393-11a" place="margin">TAB. XXXVII. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si AR repræſentat ſpatium cadendo percurſum, poſito in A puncto ex <lb />quo corpus dimittitur, determinatur velocitas in puncto quocunque ut C, <lb />ductâ CD ad AB parallelâ, &amp;</s>
          <s xml:space="preserve">per D ad RAQ parallelâ DEF, velocitatem <lb />quæſitam deſignabit parabolæ ordinata EF, dum AQ velocitatem maxi-<lb />mam exprimit, ad quam corpus non pertingit, niſi poſt percurſum ſpatium <lb />AR in infinitum productum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hæc patebunt ſi, ſumtis ad libitum ſpatiolis æqualibus infinite exiguis, <lb />C c, G g demonſtremus augmenta velocitatum, quæ hìc f L &amp; </s>
          <s xml:space="preserve">k M expri-<lb />munt, eſſe inter ſe inverſè ut lineæ FE &amp; </s>
          <s xml:space="preserve">KI, quas velocitates exprimere <lb />dicimus, ſublatis partibus quæ ſunt ut ipſæ hæ lineæ FE &amp; </s>
          <s xml:space="preserve">KI <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">991. 993. <lb />1029.</note>
      </div>
      <div type="section">
        <head xml:space="preserve">f L, k M :: {E e/FE}, {Ii/KI}<ptr type="noteAnchor" /> :: {CD/FE} = {BA/FE} -{BE/FE}, {GH/KI} = {BA/KI} - {BI/KI}<ptr type="noteAnchor" /></head>
        <note xml:space="preserve" n="*" anchored="true" place="margin">995.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">983.</note>
        <p>
          <s xml:space="preserve">Sed BE x BA = FE x FE<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ergo {BE/FE} = {FE/BA}. </s>
          <s xml:space="preserve">Eodem modo {BI/KI}
<ptr xml:id="note-0393-15a" corresp="note-0393-15" type="noteAnchor" />
= KI/BA}. </s>
          <s xml:space="preserve">Idcirco</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0393-15" corresp="note-0393-15a" n="*" anchored="true" place="margin">la Hire <lb />ſect. con. <lb />lib. 3. <lb />prop. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">fL, kM :: {BA/FE}-{FE/BA}, {BA/KI} = {KI/BA}</head>
        <p>
          <s xml:space="preserve">Quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut figurâ hac in computatione utamur, velocitas maxima ad quam corpus <lb />
<ptr xml:id="note-0393-16a" corresp="note-0393-16" type="noteAnchor" />
pertingere poteſt, &amp; </s>
          <s xml:space="preserve">quæ QA repræſentatur, determinanda eſt:</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0393-16" corresp="note-0393-16a" place="margin">1031.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quærimus igitur velocitatem, qua conceſſa, retardatio ex ſecunda cauſa
</s>
          <pb facs="0394" n="292" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
accelerationi, ex pondere reſpectivo, demta retardatione ex prima cauſa, <lb />æqualis eſt; </s>
          <s xml:space="preserve">hæc enim eſt uniformis acceleratio quæ retardatione ex ſecuu-<lb />da cauſa deſtruenda eſt, ut acceleratio ceſſet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">967.</note>
        <p>
          <s xml:space="preserve">Hic iterum experimento indigemus; </s>
          <s xml:space="preserve">detur idcirco altitudo, ad quam in flui-<lb />do corpus data velocitate quacunque adſcendit; </s>
          <s xml:space="preserve">ex hac notâ, elicimus ratio-<lb />nem inter accelerationem ex pondere reſpectivo &amp; </s>
          <s xml:space="preserve">retardationem ex cohæſio-<lb />
<ptr xml:id="note-0394-02a" corresp="note-0394-02" type="noteAnchor" />
ne <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideoque rationem accelerationis hujus ad hanc ipſam, demtâ retardatione
ex cohæſione: </s>
          <s xml:space="preserve">eſt quæ hæc ratio ipſa quæ datur inter altitudinem, a qua cor-<lb />pus in vacuo cadendo acquirit velocitatem, quæ dat reſiſtentiam ponderi <lb />reſpectivo æqualem, quæ altitudo datur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">altitudinem a qua corpus in va-
<ptr xml:id="note-0394-03a" corresp="note-0394-03" type="noteAnchor" />
cuo cadendo acquirit velocitatem quæſitam QA <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0394-02" corresp="note-0394-02a" n="*" anchored="true" place="margin">1026.</note>
              <note xml:space="preserve" xml:id="note-0394-03" corresp="note-0394-03a" n="*" anchored="true" place="margin">928. 929.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">255. 954.</note>
        <p>
          <s xml:space="preserve">Hac autem detecta altitudine, detegimus etiam aliam a qua nempe corpus <lb />
<ptr xml:id="note-0394-05a" corresp="note-0394-05" type="noteAnchor" />
in fluido cadendo, ſepoſitâ reſiſtentiâ ex ſecunda cauſa, hanc eandem velo-<lb />citatem QA acquireret; </s>
          <s xml:space="preserve">eſt enim altitudo in vacuo ad altitudinem in fluido, <lb />ut retardatio ex pondere reſpectivo, dempta retardatione ex cohæſione par-<lb />tium, ad retardationem ex integro pondere <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Concipiamus hanc altitudinem re-
<ptr xml:id="note-0394-06a" corresp="note-0394-06" type="noteAnchor" />
præſentari lineâ BA, b O deſignabit velocitatem, eodem modo cadendo ab <lb />altitudine B b acquiſitam <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0394-05" corresp="note-0394-05a" place="margin">1032.</note>
              <note xml:space="preserve" xml:id="note-0394-06" corresp="note-0394-06a" n="*" anchored="true" place="margin">997</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">995</note>
        <p>
          <s xml:space="preserve">Præterea debemus determinare ſpatium, notâ quâdam portione rectæ AR, <lb />
<ptr xml:id="note-0394-08a" corresp="note-0394-08" type="noteAnchor" />
deſiguatum; </s>
          <s xml:space="preserve">quod fiet ſi ad hoc attendamus; </s>
          <s xml:space="preserve">in principio caſus corpus ac-<lb />celerari pondere reſpectivo demta retardatione ex prima cauſa, quia hæc ac-<lb />celeratio æquabilis eſt, non autem retardari ex ſecunda cauſa quia velocitas <lb />nulla eſt; </s>
          <s xml:space="preserve">ideoque velocitatem bO, in primo momento infinito exiguo, cadendo <lb />ab altitudine quæ Aa repræſentatur, acquiri ut in motu indicato, cadendo per <lb />Bb; </s>
          <s xml:space="preserve">repræſentantqueidcirco Bb &amp; </s>
          <s xml:space="preserve">Aa, in his lineis diverſis, ſpatia æqua-<lb />lia: </s>
          <s xml:space="preserve">ſed eſt Bb ad Aa, aut bN, ut BA ad AP, logarihtmicæ ſubtan-<lb />gentem; </s>
          <s xml:space="preserve">deſignant ergo etiam BA &amp; </s>
          <s xml:space="preserve">AP ſpatia æqualia; </s>
          <s xml:space="preserve">ſpatiumque ſub-<lb />tangente repræſentatum eſt altitudo à qua corpus in fluido cadendo, ſepoſita <lb />
<ptr xml:id="note-0394-09a" corresp="note-0394-09" type="noteAnchor" />
reſiſtentià ex inertia, velocitatem maximam acquirere poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0394-08" corresp="note-0394-08a" place="margin">1033.</note>
              <note xml:space="preserve" xml:id="note-0394-09" corresp="note-0394-09a" place="margin">1034</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ubi nunc tabulis utendum eſt, patet, altitudinem hanc ſe habere ad altitudinem <lb />quamcunque datam, AG, ut ſubtangens tabularum, 0, 43429, 54819. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> ad numerum in
<ptr xml:id="note-0394-10a" corresp="note-0394-10" type="noteAnchor" />
tabulis qui altitudinem datam exprimit. </s>
          <s xml:space="preserve">Numerus bicce eſt logaritbmus rationis <lb />
<ptr xml:id="note-0394-11a" corresp="note-0394-11" type="noteAnchor" />
BA &amp; </s>
          <s xml:space="preserve">GH, quæ ergo ratio datur; </s>
          <s xml:space="preserve">quare etiam datur ratio AB &amp; </s>
          <s xml:space="preserve">BI, qu æ <lb />eſt ratio quadratorum velocitatum AQ &amp; </s>
          <s xml:space="preserve">IK <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt velocitatis maximæ, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0394-12a" corresp="note-0394-12" type="noteAnchor" />
velocitatis, quam corpus in fluido revera acquirit, cadendo ab altitudine data AG <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0394-10" corresp="note-0394-10a" n="*" anchored="true" place="margin">987</note>
              <note xml:space="preserve" xml:id="note-0394-11" corresp="note-0394-11a" place="margin">1035</note>
              <note xml:space="preserve" xml:id="note-0394-12" corresp="note-0394-12a" n="*" anchored="true" place="margin">la Hire <lb />ſect. con. <lb />lib. 3. <lb />piop. 1.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 8. <lb />Illuſtratio quorundam quæ ad retardationem ſpectant.</head>
        <p>
          <s xml:space="preserve">VAria circa retardationes illuſtranda ſunt, quæ dum ex ante demonſtratis <lb />ſequuntur, non tamen bene inter ſe, aut cum ante demonſtratis, con-<lb />venire videntur, ſaltem primo intuitu; </s>
          <s xml:space="preserve">quos ut removeam ſcrupulos, <lb />&amp; </s>
          <s xml:space="preserve">ipſis ſublatis, magis, mutuâ omnium partium convenientiâ, confirmen-<lb />tur &amp; </s>
          <s xml:space="preserve">virium &amp; </s>
          <s xml:space="preserve">retardationum Theoriæ, ſcholium hoc reliquis addere ne-<lb />ceſſarium duxi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Scrupulus primus ſpectat quod diximus in n. </s>
          <s xml:space="preserve">989. </s>
          <s xml:space="preserve">Retardationem &amp; </s>
          <s xml:space="preserve">Ac-<lb />celerationem in ſingulis momentis infinite exiguis eſſe æquabiles; </s>
          <s xml:space="preserve">difficultas
</s>
          <pb facs="0395" n="293" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
autem datur reſpectu accelerationis, &amp; </s>
          <s xml:space="preserve">ſpectat convenientiam hujus propoſi-<lb />tionis cum demonſtratis de viribus inſitis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Concipiamus corpus quieſcens in fluido agitato; </s>
          <s xml:space="preserve">hoc illi in momento <lb />
<ptr xml:id="note-0395-01a" corresp="note-0395-01" type="noteAnchor" />
primo infinite exiguo velocitatem infinite exiguam communicat: </s>
          <s xml:space="preserve">Dividatur <lb />momentum in duas partes æquales, in ſingulis partibus æqualis communi-<lb />catur velocitas, propter accelerationem æquabilem; </s>
          <s xml:space="preserve">id eſt in prima parte u-<lb />nicus gradus infinite exiguus vis, &amp; </s>
          <s xml:space="preserve">in ſecunda tres ſimiles gradus com-<lb />municantur corpori <ptr type="noteAnchor" />, licet actio reſpectiva non aucta fuerit, quod im-
<ptr xml:id="note-0395-02a" corresp="note-0395-02" type="noteAnchor" />
poſſibile videtur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0395-01" corresp="note-0395-01a" place="margin">1036.</note>
              <note xml:space="preserve" xml:id="note-0395-02" corresp="note-0395-02a" n="*" anchored="true" place="margin">447.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut hunc tollamus ſcrupulum diſtinguendum dicimus inter actiones abſo-<lb />
<ptr xml:id="note-0395-03a" corresp="note-0395-03" type="noteAnchor" />
lutas &amp; </s>
          <s xml:space="preserve">actiones reſpectivas. </s>
          <s xml:space="preserve">Dum has conſideramus in caſu de quo agitur, <lb />æquales ſunt gradus velocitatis, qui in partibus æqualibus momenti infini-<lb />te exigui, communicantur, propter non ſenſibiliter mutatam actionem reſpecti-<lb />vam; </s>
          <s xml:space="preserve">etiam, ad motus reſpectivos attendendo, non major vis in ſecunda parte <lb />quàm in prima ipſius momenti, corpori imprimitur: </s>
          <s xml:space="preserve">corpus cui ſuperadditur <lb />gradus unus velocitatis, unicum gradum vis acquirit in nave, in qua corpus <lb />quieſcebat, quacunque velocitate hæc feratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0395-03" corresp="note-0395-03a" place="margin">1037.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In examine autem actionum abſolutarum non tantum actiones <lb />
<ptr xml:id="note-0395-04a" corresp="note-0395-04" type="noteAnchor" />
reſpectivæ, ſed &amp; </s>
          <s xml:space="preserve">abſolutæ conſiderandæ veniunt, &amp; </s>
          <s xml:space="preserve">ex ante demonſtra-<lb />tis de colliſionibus evidentiſſime ſequitur: </s>
          <s xml:space="preserve">corpus quodcunque A, veloci-<lb />tate a motum, in corpus B incurrens, majorem huic communicare vim, ſi B <lb />ad eandem partem cum A feratur, quàm ſi quieſceret; </s>
          <s xml:space="preserve">licet velocitas reſpecti-<lb />va in illo caſu minor ſit, ſi modo velocitas corporis B certum limitem non <lb />excedat. </s>
          <s xml:space="preserve">Diverſa enim eſt actio in corpus pro diverſa vi qua jam gaudet, &amp; </s>
          <s xml:space="preserve"><lb />impoſſibile ſi videatur, corpus idem, eodem modo motum, in idem corpus <lb />incurrens, majorem huic communicare vim in certo caſu in quo velocitas <lb />reſpectiva eſt minor, ad non bene intellectam virium theoriam illud refe-<lb />rendum eſt; </s>
          <s xml:space="preserve">quod enim experimentis immediatè probatur, ad impoſſibilia <lb />minime referri poſſe clarum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0395-04" corresp="note-0395-04a" place="margin">1038.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit corpus A, quod, velocitate 6.</s>
          <s xml:space="preserve">, in corpus æquale B, quieſcens, di-<lb />rectè incurrit, pono corpora non elaſtica, acquirit B velocitatem tria <ptr type="noteAnchor" />, id eſt
<ptr xml:id="note-0395-05a" corresp="note-0395-05" type="noteAnchor" />
vim quæ formando in argilla cavitates deſtrui poteſt; </s>
          <s xml:space="preserve">ponamus hanc con-<lb />ſumi formando cavitates novem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0395-05" corresp="note-0395-05a" n="*" anchored="true" place="margin">519.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Incurrat iterum corpus hoc idem A, velocitate 6. </s>
          <s xml:space="preserve">motum, in idem cor-<lb />pus B, ad eandem partem velocitate 2. </s>
          <s xml:space="preserve">translatum, habebit B poſt ictum ve-<lb />locitatem 4. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">513</note>
        <p>
          <s xml:space="preserve">Ante ictum corpus B habuit capacitatem formandi quatuor cavitates, qua-<lb />les memoravimus, poſt ictum habet vim qua ſedecim tales cavitates poteſt <lb />formare; </s>
          <s xml:space="preserve">ictu ergo, poſitâ velocitate reſpectivâ 4.</s>
          <s xml:space="preserve">, acquiſivit vim, qua po-<lb />teſt formare cavitates duodecim, dum in primo caſu, poſitâ velocitate re-<lb />ſpectivâ 6, tantum acquiſiverit facultatem formandi cavitates tales novem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hæc immediate conſtare experimentis in dubium nemo vocabit qui ad il-<lb />la, quæ de viribus &amp; </s>
          <s xml:space="preserve">colliſione in libro primo ſunt memorata, attendit, <lb />non neglecto experimento 4. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">22. </s>
          <s xml:space="preserve">quod in ipſo illo capite fuit præter-<lb />miſlum, ſed in fine Moniti de hac ſecunda editione memoratum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In primo caſu, ubi velocitas reſpectiva fuit 6, actio corporis A majoreſt <lb />
<ptr xml:id="note-0395-07a" corresp="note-0395-07" type="noteAnchor" />
quàm in ſecundo caſu, ubi tantum fuit 4.</s>
          <s xml:space="preserve">: ſunt autem actiones hæ ut 27. <lb /></s>
          <s xml:space="preserve">ad 20.</s>
          <s xml:space="preserve">; ſed vires commuicatæ corpori B non ſunt effectus integri harum a-<lb />ctionum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0395-07" corresp="note-0395-07a" place="margin">1039.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0396" n="294" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Corpus A ante actionem habet vim qua triginta ſex cavitates, memoratis <lb />æquales, formari poſſunt; </s>
          <s xml:space="preserve">ſi incurrat in B quod quieſcit, cavitates tales for-<lb />mabit octodecim, &amp; </s>
          <s xml:space="preserve">ipſi B communicabit vim, qua novem formari poſſunt, <lb />æqualemque vim ipſum ſuperſtitem habebit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In ſecundo caſu, in incurſu tantum formabit cavitates octo, communi-<lb />cabit vim qua duodecim formari poſſunt, habebitque ſuperſtitem facultatem <lb />formandi cavitates ſedecim. </s>
          <s xml:space="preserve">Effectus totales, non partiales, cauſis propor-<lb />tionales ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si agatur de corporibus quæ preſſione tantum agunt in alia, ſine partium <lb />
<ptr xml:id="note-0396-01a" corresp="note-0396-01" type="noteAnchor" />
introceſſione, ad hoc attendendum generaliter: </s>
          <s xml:space="preserve">motus corporis directionem <lb />non poſſe mutari, niſi deſtructo primo motu, generatoque novo, quantum <lb />nempe motus differunt; </s>
          <s xml:space="preserve">nam motus, per diverſas directiones, non proeo-<lb />dem motu haberi poſſunt, niſi quantum conſpirant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0396-01" corresp="note-0396-01a" place="margin">1040.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando corpus directionem ſuam mutat, ut in n. </s>
          <s xml:space="preserve">522. </s>
          <s xml:space="preserve">corpus premit <lb />in obſtaculum veramque in hoc exerit actionem, &amp; </s>
          <s xml:space="preserve">quidem vi inſitâ agit; <lb /></s>
          <s xml:space="preserve">quare hæc in ſingulis momentis infinite exiguis minuitur <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Sed obſtaculum
<ptr xml:id="note-0396-02a" corresp="note-0396-02" type="noteAnchor" />
reagit, &amp; </s>
          <s xml:space="preserve">cum hoc non cedat, neque vim accipiat, totâ ſuâ reſiſtentiâ novam <lb />
<ptr xml:id="note-0396-03a" corresp="note-0396-03" type="noteAnchor" />
corpori obſtaculum communicat vim, quæ ipſi amiſſæ æquatis eſt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">qua-
re ſingulis momentis vis deſtructa inſtauratur, ſervatque corpus velocitatem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0396-02" corresp="note-0396-02a" n="*" anchored="true" place="margin">458.</note>
              <note xml:space="preserve" xml:id="note-0396-03" corresp="note-0396-03a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In caſu n. </s>
          <s xml:space="preserve">521 corpora impingentia duos edunt effectus, corpori in quod <lb />incurrunt motum communicant &amp; </s>
          <s xml:space="preserve">viam flectunt, vimque quam in impa-<lb />ctu, intropremendo partes, conſumerent, nunc etiam in actione ſua con-<lb />ſumunt, licet aliam ipſi æqualem lateralem accipiant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ratiocinium ſimile ad fluida poſſe applicari, quæ etiam lateralem motum <lb />acquirunt, clarum eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſolam conſiderandam non eſſe actionem reſpecti-<lb />vam ubi de actione abſoluta agitur: </s>
          <s xml:space="preserve">integroſque effectus eſſe comparandos <lb />ut inter hos cauſarum proportionem detegamus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Scrupulus ſecundus, in hoc ſcholio removendus, ſpectat retardationem <lb />
<ptr xml:id="note-0396-04a" corresp="note-0396-04" type="noteAnchor" />
ex prima cauſa, quam æquabilem eſſedemonſtravimus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">unde ſequitur ex a-
<ptr xml:id="note-0396-05a" corresp="note-0396-05" type="noteAnchor" />
ctione, a cohæſione partium oriunda, quam ſuperius <ptr type="noteAnchor" /> explicavimus, æqua-
<ptr xml:id="note-0396-06a" corresp="note-0396-06" type="noteAnchor" />
li tempori, æqualem corpori quieſcenti communicari velocitatem, quacun-<lb />que velocitate fluidum in hoc incurrat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0396-04" corresp="note-0396-04a" place="margin">1041.</note>
              <note xml:space="preserve" xml:id="note-0396-05" corresp="note-0396-05a" n="*" anchored="true" place="margin">950.</note>
              <note xml:space="preserve" xml:id="note-0396-06" corresp="note-0396-06a" n="*" anchored="true" place="margin">901.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc autem convenire non videntur cum ante demonſtratis: </s>
          <s xml:space="preserve">vidimus e-<lb />nim corpus, ex actione a partium cohæſione oriunda, quando in loco re-<lb />tinetur, pati preſſionem, quæ ad inſtar velocitatis augetur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">circa preſſionem
<ptr xml:id="note-0396-07a" corresp="note-0396-07" type="noteAnchor" />
in genere demonſtravimus, hanc corpori quieſcenti, in momento determi-<lb />nato, infinite exiguo, communicare velocitatem, quæ ipſius preſſionis ra-<lb />tionem ſequitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0396-07" corresp="note-0396-07a" n="*" anchored="true" place="margin">894. 908.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">107. 243.</note>
        <p>
          <s xml:space="preserve">Fundamentum ratiocinii, quo hanc tolli credimus difficultatem ſupetius <lb />
<ptr xml:id="note-0396-09a" corresp="note-0396-09" type="noteAnchor" />
indicavimus <ptr type="noteAnchor" />, ipſum nunc ratiocinium clarius explicandum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0396-09" corresp="note-0396-09a" place="margin">1042.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">945.</note>
        <p>
          <s xml:space="preserve">Diximus diſtinguendum inter preſſionem quæ immediate corpus transfert <lb />&amp; </s>
          <s xml:space="preserve">preſſionem quæ non immediate corpus transfert De prima agitur in n. <lb /></s>
          <s xml:space="preserve">107. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ipſius demonſtratio non poteſt applicari ad caſum, in quo preſſio <lb />quæ ſeparat particulas, ita agit, ut &amp; </s>
          <s xml:space="preserve">eodem tempore obſtaculum transferre <lb />debeat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hæc actiones toto cœlo diſtinctas exerit, pro ut in obſtacula immobilia <lb />aut mobilia, majora, aut minora, agit. </s>
          <s xml:space="preserve">Ut autem quæ hoc genus preſ-<lb />fionum ſpectant determinemus, quæ ſequuntur conſideranda erunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Actio fluidi in corpus, ex cohæſione partium oriunda, analoga &amp; </s>
          <s xml:space="preserve">ſimilis
</s>
          <pb facs="0397" n="295" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XII.</fw>
eſt actioni, quam corpora ut A, B, filo juncta, in corpus C exerunt, dum <lb />
<ptr xml:id="note-0397-01a" corresp="note-0397-01" type="noteAnchor" />
ad latera hujus tranſeunt, filumque, actione ſua in C, frangunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0397-01" corresp="note-0397-01a" place="margin">TAB. XXXVII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">901.</note>
        <p>
          <s xml:space="preserve">Corpora A &amp; </s>
          <s xml:space="preserve">B, quamdiu partes fili cohærent, premunt in C, filo fracto ceſſat <lb />preſſio, ſed ſi ſtatim, eodem modo, alia duo ſimilia D &amp; </s>
          <s xml:space="preserve">F, premant, &amp; </s>
          <s xml:space="preserve">poſt hæc <lb />G &amp; </s>
          <s xml:space="preserve">H, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">dabitur preſſio, quæ a preſſione fluidi ex cohæſione oriun-<lb />da non differt, ſatis ergo erit demonſtrare, motis hiſce corporibus, æqua-<lb />li tempore, æqualem corpori C communicari velocitatem, quacunque ve-<lb />locitate ferantur corpora A, B, D, E, F, G, &amp;</s>
          <s xml:space="preserve">c, quæ æqualia ponimus, &amp; </s>
          <s xml:space="preserve">æ-<lb />quali velocitate mota. </s>
          <s xml:space="preserve">Ipſa autem in obſtaculum immobile exerere preſſio-<lb />nem quæ ſequitur rationem velocitatis qua feruntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpus omne quod quieſcit aut cujus velocitas datur, eo magis reſiſtit <lb />
<ptr xml:id="note-0397-03a" corresp="note-0397-03" type="noteAnchor" />
quo celerius acceleratur; </s>
          <s xml:space="preserve">dum enim determinatum gradum velocitatis ac-<lb />quirit determinatus gradus, vis ipſi communicatur propter primam datam <lb />velocitatem; </s>
          <s xml:space="preserve">dum autem gradum determinatum vis acquirit determinatam <lb />exerit reſiſtentiam <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">hæc idcirco eadem eſt ſive lentius ſive velocius gradus
<ptr xml:id="note-0397-04a" corresp="note-0397-04" type="noteAnchor" />
hicce vis communicetur, conſiderando nempe totalem reſiſtentiam. </s>
          <s xml:space="preserve">Eâdem <lb />de cauſa, reſiſtentia inſtantanea eo major eſt, quo celerius corpus accelera-<lb />tur, totalis enim reſiſtentia ſequitur proportionem reſiſtentiæ inſtantaneæ, <lb />&amp; </s>
          <s xml:space="preserve">temporis per quod duravit, ſi ergo hoc minuatur illa augenda erit, ut <lb />totalis reſiſtentia ſervetur: </s>
          <s xml:space="preserve">tempus vero minuitur in ratione in qua ipſa <lb />acceleratio augetur, creſcitque cum ipſa acceleratione inſtantanea reſiſten-<lb />tia, ſi totalis reſiſtentia determinata ſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0397-03" corresp="note-0397-03a" place="margin">1043.</note>
              <note xml:space="preserve" xml:id="note-0397-04" corresp="note-0397-04a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando acceleratio æquabilis eſt, reſiſtit corpus in ratione velocitatis <lb />quam habet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin"><unclear reason="illegible" /></note>
        <p>
          <s xml:space="preserve">Generaliter ergo corporis, quod acceleratur, inſtantanea reſiſtentia eſtin ratione <lb />
<ptr xml:id="note-0397-06a" corresp="note-0397-06" type="noteAnchor" />
compoſita velocitatis quam babet, &amp; </s>
          <s xml:space="preserve">ipſius accelerationis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0397-06" corresp="note-0397-06a" place="margin">1044.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si ergo detur reſiſtentia inſtantanea, velocitas corporis eſt inverſè, ut accelera-<lb />
<ptr xml:id="note-0397-07a" corresp="note-0397-07" type="noteAnchor" />
tio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0397-07" corresp="note-0397-07a" place="margin">1045.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propoſitio hæc ad caſum de quo agitur applicanda nunc eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpora A &amp; </s>
          <s xml:space="preserve">B in corpus C agunt, donec hujus inſtantanea reſiſtentia, <lb />
<ptr xml:id="note-0397-08a" corresp="note-0397-08" type="noteAnchor" />
quæ ſola cum preſſione contrariè agere poteſt, æqualis ſit ipſi preſſioni qua <lb />fili partes cohærent; </s>
          <s xml:space="preserve">acceleratio eo uſque durat; </s>
          <s xml:space="preserve">ſed ubi hæc datur æquali-<lb />tas, ceſſat actio, &amp; </s>
          <s xml:space="preserve">filum frangitur; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, ſive celerius ſive lentius moveantur <lb />corpora A &amp; </s>
          <s xml:space="preserve">B, conſtans in corpore C inſtantanea reſiſtentia deſideratur, <lb />ut filum frangatur. </s>
          <s xml:space="preserve">Sed quo velocius A &amp; </s>
          <s xml:space="preserve">B moventur, eo major eſt ac-<lb />celeratio, dum hæc protrahunt corpus C; </s>
          <s xml:space="preserve">eo ergo minor velocitas ipſi C <lb />communicata eſt, dum frangitur filum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">tripla ſit velocitas cor-
<ptr xml:id="note-0397-09a" corresp="note-0397-09" type="noteAnchor" />
porum A &amp; </s>
          <s xml:space="preserve">Bin uno caſu quàm in alio, dum in utroque C quieſcit, quia in <lb />caſu primo tripla eſt acceleratio, tertia pars velocitatis tantum corpori C com-<lb />municatur, dum durat actio corporum in C. </s>
          <s xml:space="preserve">Si hic gradus velocitatis fuerit exi-<lb />guus, ut actio reſpectiva ſequentium corporum D &amp; </s>
          <s xml:space="preserve">E non ſenſibiliter difterat, <lb />hæc æqualem gradum velocitatis communicabunt, &amp; </s>
          <s xml:space="preserve">niſi poſt tria fila con-<lb />fracta habebit C velocitatem, quam habet, dum unicum diſrumpitur filum in <lb />ſecundo caſu. </s>
          <s xml:space="preserve">Sed dum in ſecundo caſu ſola corpora A &amp; </s>
          <s xml:space="preserve">B juxta C tranſ-<lb />eunt, in primo tranſeunt, A, B, &amp; </s>
          <s xml:space="preserve">D, E, ut &amp; </s>
          <s xml:space="preserve">F, G; </s>
          <s xml:space="preserve">id eſt tria fila in <lb />primo caſu franguntur, dum unicum in ſecundo dilaceratur, &amp; </s>
          <s xml:space="preserve">æqualibus <lb />temporibus memoratæ æquales communicantur velocitates, Q.</s>
          <s xml:space="preserve">D.</s>
          <s xml:space="preserve">E.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0397-08" corresp="note-0397-08a" place="margin">1046.</note>
              <note xml:space="preserve" xml:id="note-0397-09" corresp="note-0397-09a" n="*" anchored="true" place="margin">1045.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Res vulgo nota eſt corpori, quod filo protrahitur, eo minorem communicari <lb />
<ptr xml:id="note-0397-10a" corresp="note-0397-10" type="noteAnchor" />
velocitatem, dum filum frangitur, quo celerius hoc trahitur; </s>
          <s xml:space="preserve">hac de cauſa
</s>
          <pb facs="0398" n="296" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſi lente corpus acceleretur, ipſi magna poterit communicari velocitas; </s>
          <s xml:space="preserve">licet <lb />tenui filo trahatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0397-10" corresp="note-0397-10a" place="margin">1047.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando corpora A &amp; </s>
          <s xml:space="preserve">B, frangendo filum, vim communicant corpori C, <lb />
<ptr xml:id="note-0398-01a" corresp="note-0398-01" type="noteAnchor" />
ex viribus amittunt, quantum communicant, &amp; </s>
          <s xml:space="preserve">quantum deſideratur, ad fi-<lb />lum dilacerandum; </s>
          <s xml:space="preserve">eo ergo minus ex vi amittunt quo celerius moven-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0398-01" corresp="note-0398-01a" place="margin">1048.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ex loco cedere nequeat obſtaculum C, unicus eſt eſtectus actionis cor-<lb />porum A &amp; </s>
          <s xml:space="preserve">B, &amp; </s>
          <s xml:space="preserve">ex vi tantum amittunt, quantum deſideratur ad filum fran-<lb />gendum, actioque, quam patitur illud quod retinet C in loco, eadem eſt pro <lb />ſingulis filis quæ franguntur. </s>
          <s xml:space="preserve">In præcedenti caſu, quo lentius moventur <lb />corpora A &amp; </s>
          <s xml:space="preserve">B, eo diutius agunt antequam C reſiſtat quantum requiritur, <lb />ut filum dilaceretur; </s>
          <s xml:space="preserve">in hoc autem caſu ubi filum accedit hæc datur reſi-<lb />ſtentia: </s>
          <s xml:space="preserve">Quare in hoc caſu actio quam patitur C ſequitur rationem filorum <lb />determinato tempore fractorum, id eſt velocitatis corporum. </s>
          <s xml:space="preserve">Quod etiam <lb />demonſtrandum crat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quid analogum cum iis quæ ſuperius <ptr type="noteAnchor" /> explicavimus, obſervamus in col-
<ptr xml:id="note-0398-02a" corresp="note-0398-02" type="noteAnchor" />
liſione corporum; </s>
          <s xml:space="preserve">corpora duo inæqualia corporibus duobus æqualibus qui-<lb />
<ptr xml:id="note-0398-03a" corresp="note-0398-03" type="noteAnchor" />
eſcentibus, in colliſione directa, communicant velocitates, quæ ſunt inverſè <lb />ut velocitates corporum impingentium, ſi introceſſiones partium fuerint æ-<lb />quales, ponendo partes æquè facile in utraque colliſione cedere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0398-02" corresp="note-0398-02a" place="margin">1049.</note>
              <note xml:space="preserve" xml:id="note-0398-03" corresp="note-0398-03a" n="*" anchored="true" place="margin">1046.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Introceſſiones autem partium ſunt ut ipſæ velocitates corporum impingen-<lb />tium, ſi hæc æquales communicent corporibus quieſcentibus velocitates.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut hæc ſequuntur ex ante demonſtratis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">directis experimentis poſ-
<ptr xml:id="note-0398-04a" corresp="note-0398-04" type="noteAnchor" />
ſunt evinci.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0398-04" corresp="note-0398-04a" n="*" anchored="true" place="margin">520. 462. <lb />519.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">LIBRI II. Pars III. <lb />De Aëre, &amp; aliis Fluidis Elaſticis.</head>
        <head xml:space="preserve">CAPUT XIII. <lb />Aërem Fluidorum proprietates habere.</head>
        <p>
          <s xml:space="preserve">DE Aëre ſæpius locuti ſumus, cum in hoc vivamus &amp; </s>
          <s xml:space="preserve"><lb />hoc ſemper circumdemur, in multis Experimentis, ut <lb />monuimus, ad illius effectum attendendum eſt; </s>
          <s xml:space="preserve">nunc autem <lb />ipſius proprietates ſingulatim examinandæ veniunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Aërem vocamus fluidum, quod Telluris ſuperficiem <lb />
<ptr xml:id="note-0398-05a" corresp="note-0398-05" type="noteAnchor" />
obtegit, ipſamque tellurem ab omni parte cingit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0398-05" corresp="note-0398-05a" place="margin">1050.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fluido autem Tellurem circumdari conſtat; </s>
          <s xml:space="preserve">obſervamus
</s>
          <pb facs="0399" />
          <s xml:space="preserve">
</s>
          <pb facs="0399a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0399a-01a" corresp="fig-0399a-01" type="figureAnchor" />
</s>
          <pb facs="0400" />
          <s xml:space="preserve">
</s>
          <pb facs="0401" n="297" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP XIII.</fw>
enim corpore hanc obtegi quod grave eſt, cujus partes im-<lb />preſſioni cuicunque cedunt, &amp; </s>
          <s xml:space="preserve">facillime moventur inter <lb />ſe, quod premit pro altitudine ſua, &amp; </s>
          <s xml:space="preserve">cujus preſſio omnes <lb />partes verſus eſt æqualis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0399a-01" corresp="fig-0399a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0399a-01" />
                <label>0399a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Omnis aër, quo Terra circumdatur, ſimul conſideratus, <lb />
<ptr xml:id="note-0401-01a" corresp="note-0401-01" type="noteAnchor" />
vocatur Telluris Atmoſphæra, aut ſimpliciter Atmoſphæra.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0401-01" corresp="note-0401-01a" place="margin">1051</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Aëris altitudo ſupra Terræ ſuperficiem vocatur Atmoſphæ-<lb />
<ptr xml:id="note-0401-02a" corresp="note-0401-02" type="noteAnchor" />
ræ altitudo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0401-02" corresp="note-0401-02a" place="margin">1052.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ubique in Telluris ſuperficie corpus dari, quamvis ipſius <lb />
<ptr xml:id="note-0401-03a" corresp="note-0401-03" type="noteAnchor" />
partes plerumque viſum fugiant, experimento con <lb />ſtat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0401-03" corresp="note-0401-03a" place="margin">1053.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">27</note>
        <p>
          <s xml:space="preserve">Hoc impreſſioni cuicunque cedere, &amp; </s>
          <s xml:space="preserve">ipſius partes facile <lb />
<ptr xml:id="note-0401-05a" corresp="note-0401-05" type="noteAnchor" />
moveri, a nemine in dubium vocari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0401-05" corresp="note-0401-05a" place="margin">1054.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Grave eſſe probatur, quia in ceterorum fluidorum ſu-<lb />
<ptr xml:id="note-0401-06a" corresp="note-0401-06" type="noteAnchor" />
perficies premit, hæcque in tubis ſuſtinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0401-06" corresp="note-0401-06a" place="margin">1055.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Detur tubus vitreus AB, longitudinis circiter trium <lb />
<ptr xml:id="note-0401-07a" corresp="note-0401-07" type="noteAnchor" />
pedum, &amp; </s>
          <s xml:space="preserve">cujus cavitatis diameter ſit quartæ partis unius <lb />
<ptr xml:id="note-0401-08a" corresp="note-0401-08" type="noteAnchor" />
pollicis; </s>
          <s xml:space="preserve">ſi extremitas A obturetur, &amp; </s>
          <s xml:space="preserve">tubus mercurio re-<lb />pleatur, alteraque extremitas vaſe V mercurium continenti <lb />immergatur, mercurius ſuſtinebitur ad altitudinem circi-<lb />ter viginti novem pollicum. </s>
          <s xml:space="preserve">Oritur hoc ex aëris preſſio-<lb />ne in ſuperficiem mercurii in vaſe, quæ ubique æqualiter <lb />premi non poteſt, niſi in tubo, cui aër nullus ineſt, mercu-<lb />rii columna detur, quæ æqualiter cum aëre exteriori pre-<lb />mat <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Tubus hic Torricellianus dicitur; </s>
          <s xml:space="preserve">a primo qui hoc
<ptr xml:id="note-0401-09a" corresp="note-0401-09" type="noteAnchor" />
exp. </s>
          <s xml:space="preserve">demonſtravit Torricelli.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0401-07" corresp="note-0401-07a" place="margin">1056.</note>
              <note xml:space="preserve" xml:id="note-0401-08" corresp="note-0401-08a" place="margin">TAB XXXVIII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0401-09" corresp="note-0401-09a" n="*" anchored="true" place="margin">709.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Ne mutetur hæc preſſio, quando tubus inclinatur, re-<lb />
<ptr xml:id="note-0401-10a" corresp="note-0401-10" type="noteAnchor" />
quiritur, ut eandem mercurius ſervet altitudinem vertica-<lb />
<ptr xml:id="note-0401-11a" corresp="note-0401-11" type="noteAnchor" />
lem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò ſi dentur duo vaſa, hydrargyrum continentia,
<ptr xml:id="note-0401-12a" corresp="note-0401-12" type="noteAnchor" />
in quibus tubi, ut dictum, immerguntur, quorum ED <lb />ad horizontem inclinatur, ſuſtinetur mercurius ad alti-
</s>
          <pb facs="0402" n="298" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tudines hf, &amp; </s>
          <s xml:space="preserve">ig, ita ut f &amp; </s>
          <s xml:space="preserve">g ſint in eadem linea ho-<lb />rizontali, poſitis ſuperficiebus mercurii in vaſis in eodem <lb />plano.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0401-10" corresp="note-0401-10a" place="margin">1057.</note>
              <note xml:space="preserve" xml:id="note-0401-11" corresp="note-0401-11a" place="margin">TAB. XXXVIII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0401-12" corresp="note-0401-12a" n="*" anchored="true" place="margin">715.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Hæc eadem aëris preſſio ſuſtinet aquam in vitro V, quod <lb />
<ptr xml:id="note-0402-01a" corresp="note-0402-01" type="noteAnchor" />
aquâ immergitur &amp; </s>
          <s xml:space="preserve">hac repletur, deinde extrahitur, orifi-<lb />
<ptr xml:id="note-0402-02a" corresp="note-0402-02" type="noteAnchor" />
cio manente immerſo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0402-01" corresp="note-0402-01a" place="margin">1058.</note>
              <note xml:space="preserve" xml:id="note-0402-02" corresp="note-0402-02a" place="margin">TAB. XXXVIII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem modo aqua ſuſtineretur, licet vitri altitudo tri-<lb />
<ptr xml:id="note-0402-03a" corresp="note-0402-03" type="noteAnchor" />
ginta &amp; </s>
          <s xml:space="preserve">duos pedes æquaret. </s>
          <s xml:space="preserve">Hydrargyrum enim gravita-<lb />te ſua ſpecifica fere decies &amp; </s>
          <s xml:space="preserve">quater ſuperat aquæ gravita-<lb />tem ſpecificam, &amp; </s>
          <s xml:space="preserve">columna aquea, triginta &amp; </s>
          <s xml:space="preserve">duos pedes <lb />excedens, æqualiter cum mercurii columna viginti novem <lb />pollicum premit, quæ preſſio Atmoſphæræ preſſioni æqui-<lb />pollet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0402-03" corresp="note-0402-03a" place="margin">1059.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Preſſionem aëris ab hujus altitudine pendere, ex dictis <lb />
<ptr xml:id="note-0402-04a" corresp="note-0402-04" type="noteAnchor" />
facillimè deduci poteſt; </s>
          <s xml:space="preserve">ſed immediatè probatur, transfe-<lb />rendo tubum cum mercurio memoratum in locum <lb />elevatum, nam circiter octavâ parte unius pollicis deſcen-<lb />dit mercurius pro altitudine centum pedum, ad quam Ma-<lb />china elevatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0402-04" corresp="note-0402-04a" place="margin">1060.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aërem omnes partes verſus æqualiter premere ex eo patet, <lb />
<ptr xml:id="note-0402-05a" corresp="note-0402-05" type="noteAnchor" />
quod a corporibus mollibus hujus preſſio ſine figuræ muta-<lb />tione, &amp; </s>
          <s xml:space="preserve">à fragilibus ſine diſruptione, ſuſtineatur; </s>
          <s xml:space="preserve">quamvis hæc <lb />valeat preſſionem mercurii ad altitudinem viginti novem pol-<lb />licum, aut aquæ ad altitudinem triginta duorum pedum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nil,
<ptr xml:id="note-0402-06a" corresp="note-0402-06" type="noteAnchor" />
præter preſſionem æqualem ab omni parte, memorata corpo-<lb />ra intacta ſervare poſſe, quis non videt; </s>
          <s xml:space="preserve">hanc autem preſſio-<lb />nem illud præſtare conſtat <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sublato aëre ab una parte,
<ptr xml:id="note-0402-07a" corresp="note-0402-07" type="noteAnchor" />
preſſio in partem oppoſitam ſenſibilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0402-05" corresp="note-0402-05a" place="margin">1061.</note>
              <note xml:space="preserve" xml:id="note-0402-06" corresp="note-0402-06a" n="*" anchored="true" place="margin">1059.</note>
              <note xml:space="preserve" xml:id="note-0402-07" corresp="note-0402-07a" n="*" anchored="true" place="margin">745. 746.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Suſpendatur lanci uni, bilancis AB, tubus vitreus, <lb />
<ptr xml:id="note-0402-08a" corresp="note-0402-08" type="noteAnchor" />
clauſus in D, longitudinis circiter trium pedum; </s>
          <s xml:space="preserve">impleatur <lb />
<ptr xml:id="note-0402-09a" corresp="note-0402-09" type="noteAnchor" />
hic mercurio, &amp; </s>
          <s xml:space="preserve">extremitas E mercurio vaſe V, contento, <lb />immergatur. </s>
          <s xml:space="preserve">Hydrargyrum ex aëris preſſione ſuſtinetur ad <lb />altitudinem f, &amp; </s>
          <s xml:space="preserve">pars ſuperior tubi f D aëre vacua relinqui-
</s>
          <pb facs="0403" n="299" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XIII.</fw>
tur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ut æquilibrium detur, lanci oppoſitæ imponitur pon-
<ptr xml:id="note-0403-01a" corresp="note-0403-01" type="noteAnchor" />
dus, æquale ponderi tubi, &amp; </s>
          <s xml:space="preserve">mercurii in hoc contenti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0402-08" corresp="note-0402-08a" place="margin">1062.</note>
              <note xml:space="preserve" xml:id="note-0402-09" corresp="note-0402-09a" place="margin">TAB. XXXVIII. <lb />fig 3.</note>
              <note xml:space="preserve" xml:id="note-0403-01" corresp="note-0403-01a" n="*" anchored="true" place="margin">1056.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Mercurius in tubo libram gravare nequit; </s>
          <s xml:space="preserve">illius enim a-<lb />ctio in latera tubi, horizontalis eſt: </s>
          <s xml:space="preserve">ſed aër agit in ſupe-<lb />riorem partem tubi, &amp; </s>
          <s xml:space="preserve">columna quæ a tubo ſuſtinetur æ-<lb />quiponderat cum columna mercurii in tubo contenta. </s>
          <s xml:space="preserve">Si <lb />ſublato mercurio aër intromittatur, ſolus tubus libram gra-<lb />vat; </s>
          <s xml:space="preserve">quod probat, actionem aëris, in ſuperficiem inferiorem <lb />partis ſuperioris tubi, deſtruere actionem in ſuperficiem ex-<lb />teriorem ejuſdem partis tubi, aëremque ſurſum &amp; </s>
          <s xml:space="preserve">deorſum <lb />æqualiter premere.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hoc etiam Experimento, quæ de aëris gravitate dicta <lb />funt, confirmantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIV. <lb />De Aëris Elaſticitate.</head>
        <p>
          <s xml:space="preserve">CEterorum fluidorum proprietates aërem habere vidi-<lb />
<ptr xml:id="note-0403-02a" corresp="note-0403-02" type="noteAnchor" />
mus; </s>
          <s xml:space="preserve">præter has peculiarem habet, poteſtque locum <lb />majorem aut minorem occupare, prout vi diverſa compri-<lb />mitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſtatim ac vis hæc minuitur, ſeſe expandit. </s>
          <s xml:space="preserve">Pro-<lb />pter analogiam hujus effectus cum corporum elaſticitate, <lb />hæc aëris proprietas hujus Elaſticitas dicitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0403-02" corresp="note-0403-02a" place="margin">1063.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aërem poſſe comprimi Experimento jam memorato con-<lb />
<ptr xml:id="note-0403-03a" corresp="note-0403-03" type="noteAnchor" />
ſtat <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Et illum poſſe dilatari ſequenti probatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0403-03" corresp="note-0403-03a" place="margin">1064.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">17.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum.</hi> 1.</head>
        <p>
          <s xml:space="preserve">Detur tubus AB clauſus in A, inſundatur mercurius <lb />
<ptr xml:id="note-0403-05a" corresp="note-0403-05" type="noteAnchor" />
ita, ut in tubo aër relinquatur, qui in ſtatu aëris exterioris <lb />
<ptr xml:id="note-0403-06a" corresp="note-0403-06" type="noteAnchor" />
occupet ſpatium Al; </s>
          <s xml:space="preserve">ſi tubi extremitas B mercurio im-<lb />mergatur, deſcendet mercurius ad g, ibique hærebit. </s>
          <s xml:space="preserve">Al-<lb />titudo ig multum diſſert ab altitudine mercurii in Expe-<lb />rimento 1. </s>
          <s xml:space="preserve">capitis præcedentis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0403-05" corresp="note-0403-05a" place="margin">1065.</note>
              <note xml:space="preserve" xml:id="note-0403-06" corresp="note-0403-06a" place="margin">TAB. XXXVIII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hoc ex pondere aëris in tubo non oritur; </s>
          <s xml:space="preserve">ni-<lb />mium exiguum eſt hocce pondus, ut ſenſibilem diffe-
</s>
          <pb facs="0404" n="300" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
rentiam in altitudine mercurii producat: </s>
          <s xml:space="preserve">aëris ergo expanſio <lb />hujus effectus cauſa eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Experimento detegimus, aërem ſeſe ita dilatare, ut <lb />
<ptr xml:id="note-0404-01a" corresp="note-0404-01" type="noteAnchor" />
ſpatium ab hoc occupatum ſit inverſè ut vis qua comprimi-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0404-01" corresp="note-0404-01a" place="margin">1069.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina,</hi> <lb />Qua Aëris Dilatationes, ut &amp; Vires comprimentes, <lb />conferuntur inter ſe.</head>
        <p>
          <s xml:space="preserve">Machina hæc ex variis conſtat partibus. </s>
          <s xml:space="preserve">Pars prima eſt tu-<lb />
<ptr xml:id="note-0404-02a" corresp="note-0404-02" type="noteAnchor" />
bus vitreus AB, cujus cavitatis diameter eſt ſemipoll.</s>
          <s xml:space="preserve">, lon-<lb />
<ptr xml:id="note-0404-03a" corresp="note-0404-03" type="noteAnchor" />
gitudo circiter trium pedum; </s>
          <s xml:space="preserve">hujus extremitas clau-<lb />ſa, inferior A, cylindro cupreo, ab inferiori parte laminâ <lb />ejusdem metalli clauſo, circumdatur, qui cylindrus intritâ cum <lb />tubo jungitur; </s>
          <s xml:space="preserve">cautela hæc obſervanda eſt, ne hæc tubi <lb />extremitas frangatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0404-02" corresp="note-0404-02a" place="margin">1067.</note>
              <note xml:space="preserve" xml:id="note-0404-03" corresp="note-0404-03a" place="margin">TAB. XXXVIII. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tubo huic jungitur pyxis buxea cylindrica F, cujus dia-<lb />meter eſt circiter quatuor poll.</s>
          <s xml:space="preserve">, eſtque altitudo diametro <lb />proxime æqualis; </s>
          <s xml:space="preserve">jungitur tubus pyxidi dum cylindro li-<lb />gneo G, cum fundo pyxidis cohærenti, intruditur; </s>
          <s xml:space="preserve">da-<lb />turque in fundo pyxidis foramen, quo hæc cum tubo com-<lb />municationem habet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pyxis cum tubo regulæ ligneæ CD, quæ ſulcata eſt, ap-<lb />plicantur, &amp; </s>
          <s xml:space="preserve">firmantur transmittendo regulam per foramen <lb />menſæ, quæ regulæ extremum latius D ſuſtinet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hoc ipſo regulæ extremo D, pyxis F fulcitur, dum tubi <lb />extremitas A prominentiæ ligneæ e inſiſtit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pars ſecunda Machinæ eſt tubus vitreus HI, qui facile <lb />in tubum AB intruditur; </s>
          <s xml:space="preserve">clauſus eſt in I habetque ibidem <lb />indicem transverſum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tandem pars tertia conſtat ex duabus regulis LM, <lb />NO, juxta ſe invicem mobilibus, &amp; </s>
          <s xml:space="preserve">longæ circiter duos <lb />pedes cum ſemiſſe ſingulæ; </s>
          <s xml:space="preserve">diviſæ ſunt ambæ, initiaque <lb />diviſionum ſunt in inferioribus extremitatibus regularum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Poſterior regula diviſa eſt in pollices &amp; </s>
          <s xml:space="preserve">minores partes æ-<lb />quales. </s>
          <s xml:space="preserve">Anterior ſulcata eſt, ut tubum HI recipiat, ſuntque
</s>
          <pb facs="0405" n="301" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XIV.</fw>
hujus diviſiones inæquales, indicantes æquales partes cavi-<lb />tatis tubi HI.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si tubus hic exacte cylindricus foret, æquales hæ forent <lb />diviſiones, cumque raro admodum hoc contingat, dicam <lb />quomodo diviſiones regulæ LM notentur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Invertitur tubus HI, ipſique regulæ applicatur ita, <lb />ut index in I extremitati regulæ reſpondeat. </s>
          <s xml:space="preserve">In-<lb />funditur mercurius exiguâ copià, cujus ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">altitu-<lb />do in tubo quartam aut tertiam partem poll. </s>
          <s xml:space="preserve">valeat, nota-<lb />turque in regula altitudo ad quam pertingit; </s>
          <s xml:space="preserve">æqualis quan-<lb />titas mercurii iterum ſuperinfunditur, ſecundaque diviſio <lb />notatur; </s>
          <s xml:space="preserve">ſicque continuando regula tota dividi poteſt. </s>
          <s xml:space="preserve">Æ-<lb />quales mercurii quantitates ipſas ponderando determinan-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sed longum &amp; </s>
          <s xml:space="preserve">difficile eſt, tot portiunculas mercurii ſepa-<lb />rare ita, ut exacte æqualiter ponderent; </s>
          <s xml:space="preserve">ideò, ſi tubus re-<lb />gularis ſit, id eſt, ſi ſit portio coni truncanti, ut contin-<lb />git plerumque, ſi etiam parum a cylindro differat, <lb />quod facile habetur, alia methodo uti poſſumus; </s>
          <s xml:space="preserve">quia in <lb />hoc caſu diviſiones a progreſſione arithmetica non ſenſibi-<lb />liter aberrant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Primæ quatuor aut quinque diviſiones, methodo indica-<lb />tâ, notandæ ſunt, quia dum hermeticè clauditur tubus <lb />non regularem ſervat figuram; </s>
          <s xml:space="preserve">deinde decupla aut duo-<lb />decupla mercurii quantitas infundenda tubo erit, &amp; </s>
          <s xml:space="preserve">diviſio <lb />notanda erit, quæ ab ultima notata diſtabit, partibus de-<lb />cem aut duodecim partibus minoribus, &amp; </s>
          <s xml:space="preserve">continuando re-<lb />liquum regulæ, eodem modo in partes tales majores, æ-<lb />quales portiones capacitatis tubi deſignantes, dividendum <lb />erit; </s>
          <s xml:space="preserve">quæ dein geometrice ſubdividi debent ita, ut omnes <lb />minores continuam forment arithmeticam progreſſionem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Examinandum autem an majores notatæ diviſiones in a-<lb />rithmetica ſint progreſſione, ſin minus geometrica divi-<lb />ſio, propter tubi irregularitatem, locum habere nequit.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0406" n="302" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Menſurandum ante omnia exactè, ad quam altitudinem <lb />
<ptr xml:id="note-0406-01a" corresp="note-0406-01" type="noteAnchor" />
mercurius ſuſtineatur in tubo Torricelliano <ptr type="noteAnchor" />, cujus ſupe-
<ptr xml:id="note-0406-02a" corresp="note-0406-02" type="noteAnchor" />
rior extremitas bene aëre vacua eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0406-01" corresp="note-0406-01a" place="margin">1068.</note>
              <note xml:space="preserve" xml:id="note-0406-02" corresp="note-0406-02a" n="*" anchored="true" place="margin">1056.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tubus AB mercurio repletur ita, ut hic in ipſa pyxide <lb />F detur ad altitudinem ſemi, aut ſi velis, integri pollicis. </s>
          <s xml:space="preserve">Tu-<lb />bus HI pro parte mercurio repletur; </s>
          <s xml:space="preserve">aërque in hoc ipſo <lb />occupat longitudinem duorum, trium, aut quatuor polli-<lb />cum, vel etiam majorem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Extremitas aperta digito clauditur &amp; </s>
          <s xml:space="preserve">mercurio, pyxide <lb />F contento, immergitur, tubusque in tubum BH intruditur, <lb />deprimiturque donec ſuperficies mercurii in tubo HI, &amp; </s>
          <s xml:space="preserve"><lb />in pyxide, ſint in eodem plano.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Regula LM tubo applicatur ita, ut extremitas L mer-<lb />curii ſuperficiem tangat, index tunc I, indicat diviſionem <lb />regulæ, quæ ſpatium, ab aëre in tubo occupatum, de-<lb />monſtrat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Aër hic cum externo aëre æqualiter comprimitur <ptr type="noteAnchor" />, viſ-
<ptr xml:id="note-0406-03a" corresp="note-0406-03" type="noteAnchor" />
que comprimens ipſa eſt quæ mercurium ſuſtinet in tubo <lb />Torricelliano.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0406-03" corresp="note-0406-03a" n="*" anchored="true" place="margin">709.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Regula LM juxta poſteriorem nunc movetur ita, ut parsre-<lb />gulæ NO, quæ infra alîus regulæ extremitatem deſcendit, æ-<lb />qualis ſit ſemi altitudini mercurii in tubo Torricelliano, ſi <lb />tunc regulæ retineantur verticaliter, extremitasque inferior <lb />regulæ NO ſuperficiem Mercurii in pyxide tangat, &amp; </s>
          <s xml:space="preserve">ele-<lb />vetur tubus HI, donec mercurius in tubo ad extremita-<lb />tem L regulæ LM pertingat, capacitas tubi vacua LI, quæ <lb />diviſionibus regulæ LM menſuratur, dupla erit illius, quam <lb />aër occupavit in ſtatu aëris externi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Atmoſphæra, (cujus preſſione Mercurius in tubo Tor-<lb />
<ptr xml:id="note-0406-04a" corresp="note-0406-04" type="noteAnchor" />
ricelliano ſuſtinetur) dum in ſuperficiem mercurii in pyxide <lb />premit, duos exerit effectus, ſuſtinet mercurium ad L uſque, <lb />&amp; </s>
          <s xml:space="preserve">aërem in LI comprimit. </s>
          <s xml:space="preserve">Dimidio totius actionis mer-<lb />curium ſuſtinet, &amp; </s>
          <s xml:space="preserve">idcirco dimidio actionis comprimit aë-<lb />rem; </s>
          <s xml:space="preserve">id eſt reducta preſſione ad ſemiſſem aër duplum oc-<lb />cupat ſpatium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0406-04" corresp="note-0406-04a" place="margin">1069.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0407" n="303" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XIV.</fw>
        <p>
          <s xml:space="preserve">Quando altitudo Mercurii FL valet duas tertias partes <lb />altitudinis Mercurii in tubo Torricelliano, preſſio, quæ aë-<lb />rem in LI comprimit, eſt pars tertia totius actionis, quæ <lb />in aërem tubo incluſum egit, ubi in ſtatu fuit aëris externi; <lb /></s>
          <s xml:space="preserve">occupabit tunc etiam aër ſpatium triplum illius quod in <lb />hoc ſtatu occupavit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Poteſtque innumeris modis hac Machina variari experi-<lb />mentum, &amp; </s>
          <s xml:space="preserve">ſemper, altitudo mercurii iu tubo Torricellia-<lb />no ad differentiam altitudinis hujus cum altitudine aut e-<lb />levatione ipſius in tubo HI ſupra mercurium in pyxide; </s>
          <s xml:space="preserve">id <lb />eſt vis quæ aërem premit, ubi in ſtatu eſt aëris externi, ad <lb />vim quæ illum comprimit in experimento quocunque, ita <lb />ſe habet capacitas tubi, in hoc caſu aëre repleta, ad ſpa-<lb />tium quod in illo caſu occupat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hæc eadem regula in aëre compreſſo obtinet.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Detur tubus curvus ABCD, apertus in A, clauſus in <lb />
<ptr xml:id="note-0407-01a" corresp="note-0407-01" type="noteAnchor" />
D, pars BC mercurio impleatur ita, ut pars CD aërem <lb />
<ptr xml:id="note-0407-02a" corresp="note-0407-02" type="noteAnchor" />
contineat in eodem ſtatu cum aëre exteriori; </s>
          <s xml:space="preserve">vis ergo <lb />comprimens eſt columna mercurii, cujus altitudo eſt hf <lb />(Fig. </s>
          <s xml:space="preserve">1.)</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">hæc altitudo vim illam deſignat; </s>
          <s xml:space="preserve">ſpatium au-<lb />tem ab aëre occupatum eſt CD. </s>
          <s xml:space="preserve">Tubo AB mercurius <lb />infundatur ut ad g pertingat, aër reducetur in ſpatium e D: <lb /></s>
          <s xml:space="preserve">vis comprimens nunc valet columnam mercurii altitudinis <lb />fg, ut &amp; </s>
          <s xml:space="preserve">preſſionem aëris exterioris in ſuperficiem g mercurii; </s>
          <s xml:space="preserve"><lb />vis hæc deſignatur per ſummam altitudinum fg in hac figu-<lb />ra &amp; </s>
          <s xml:space="preserve">hf in fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Hæc ſumma eſt ſemper ad hf (fig. </s>
          <s xml:space="preserve">1.) </s>
          <s xml:space="preserve">ut <lb />CD ad eD; </s>
          <s xml:space="preserve">iterumque vires ſunt inverſe ut ſpatia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0407-01" corresp="note-0407-01a" place="margin">1070.</note>
              <note xml:space="preserve" xml:id="note-0407-02" corresp="note-0407-02a" place="margin">TAB. XXXVIII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aëris elaſticitas eſt ut hujus denſitas; </s>
          <s xml:space="preserve">hæc enim eſt in-<lb />
<ptr xml:id="note-0407-03a" corresp="note-0407-03" type="noteAnchor" />
verſè ut ſpatium ab aëre occupatum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ideò ut vis aë-
<ptr xml:id="note-0407-04a" corresp="note-0407-04" type="noteAnchor" />
rem comprimens <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ æqualis illi qua aër conatur ſeſe
<ptr xml:id="note-0407-05a" corresp="note-0407-05" type="noteAnchor" />
expandere <ptr type="noteAnchor" />, hæc autem eſt hujus elaſticiras.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0407-03" corresp="note-0407-03a" place="margin">1071.</note>
              <note xml:space="preserve" xml:id="note-0407-04" corresp="note-0407-04a" n="*" anchored="true" place="margin">738</note>
              <note xml:space="preserve" xml:id="note-0407-05" corresp="note-0407-05a" n="*" anchored="true" place="margin">1066.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">247.</note>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur, aërem in quo vivimus, ad illam quam <lb />in terræ viciniis habet denſitatem reduci ex preſſione aëris <lb />ſuperincumbentis, illumque magis aut minus comprimi pro
</s>
          <pb facs="0408" n="304" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
majore aut minore Atmoſphæræ pondere; </s>
          <s xml:space="preserve">ex qua etiam <lb />ratione in apice montis minus denſus eſt aer quàm in valle; <lb /></s>
          <s xml:space="preserve">minori enim pondere comprimitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vis, qua particulæ aëreæ ſeſe mutuo repellunt, creſcit <lb />
<ptr xml:id="note-0408-01a" corresp="note-0408-01" type="noteAnchor" />
in ratione in qua diſtantia inter centra particularum mi-<lb />
<ptr xml:id="note-0408-02a" corresp="note-0408-02" type="noteAnchor" />
nuitur, id eſt, vis illa eſt inverſè ut hæc diſtantia. </s>
          <s xml:space="preserve">Quod <lb />ut demonſtretur, conſiderentur duo cubi æquales A &amp; </s>
          <s xml:space="preserve">B, <lb />inæquales aëris quantitates continentes; </s>
          <s xml:space="preserve">ſint diſtantiæ inter <lb />centra particularum ut duo ad unum; </s>
          <s xml:space="preserve">in eadem ratione, ſed <lb />inverſa, erunt numeri particularum in lineis de &amp; </s>
          <s xml:space="preserve">hi: </s>
          <s xml:space="preserve">nu-<lb />meri particularum agentium in ſuperſicies dg &amp; </s>
          <s xml:space="preserve">hm ſunt <lb />ut unum ad quatuor, nempe ut quadrata numerorum parti-<lb />cularum in lineis æqualibus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ut horum numerorum cubi, <lb />ſcilicet ut unum ad octo, ſunt aëris quantitates in cubis <lb />contentæ; </s>
          <s xml:space="preserve">in qua etiam ratione ſunt vires comprimentes <lb />aërem in cubis <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Vires agentes in ſuperficies æquales dg
<ptr xml:id="note-0408-03a" corresp="note-0408-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">bm ſunt ut vires, quibus aër comprimitur <ptr type="noteAnchor" />, ſunt etiam
<ptr xml:id="note-0408-04a" corresp="note-0408-04" type="noteAnchor" />
in ratione compoſita numerorum particularum agentium, &amp; </s>
          <s xml:space="preserve"><lb />actionum ſingularum particularum; </s>
          <s xml:space="preserve">hæc ergo ratio compo-<lb />ſita eſt ratio unius ad octo: </s>
          <s xml:space="preserve">rationum componentium prima, <lb />ut dictum, eſt unius ad quatuor, quare neceſſario ſecunda <lb />eſt unius ad duo, quæ eſt ratio inverſa diſtantiæ inter par-<lb />ticulas. </s>
          <s xml:space="preserve">Hæcque demonſtratio generalis eſt, nam unum &amp; </s>
          <s xml:space="preserve"><lb />octo cubos quo@cunque, unum &amp; </s>
          <s xml:space="preserve">quatuor quadrata radicum <lb />cuborum, &amp; </s>
          <s xml:space="preserve">tandem unum &amp; </s>
          <s xml:space="preserve">duo ipſas radices, in genere <lb />deſignare poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0408-01" corresp="note-0408-01a" place="margin">1072.</note>
              <note xml:space="preserve" xml:id="note-0408-02" corresp="note-0408-02a" place="margin">TAB. XXXVIII. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0408-03" corresp="note-0408-03a" n="*" anchored="true" place="margin">1071. 247.</note>
              <note xml:space="preserve" xml:id="note-0408-04" corresp="note-0408-04a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc demonſtratio probat actionem, quam particulæ con-<lb />tinuò ab omni parte patiuntur, augeri in ratione in qua <lb />diſtantia inter centra particularum minuitur, ſive hæc actio ad <lb />particulas tantum vicinas, ſive etiam ad magis diſtantes, <lb />referri debeat: </s>
          <s xml:space="preserve">videbimus enim in capite ſequenti particulas <lb />aëreas ſeſe mutuo repellere, quamvis ſeſe invicem non im-<lb />mediate tangant. </s>
          <s xml:space="preserve">In primo caſu vis ipſa repellens, qua ſingu-<lb />læ particulæ gaudent, eſt ut actio memorata, id eſt, in-<lb />verſè ut diſtantia inter particularum centra.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0409" n="305" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XIV.</fw>
        <p>
          <s xml:space="preserve">In ſecundo caſu vis repellens ad omnes diſtantias eſt æqua-<lb />lis; </s>
          <s xml:space="preserve">tunc enim pendet actio in ſingulas particulas ab harum <lb />numero in eadem linea, qui numerus eſt inverſè ut di-<lb />ſtantia inter particularum centra. </s>
          <s xml:space="preserve">Tunc etiam, poſitâ eâ-<lb />dem aëris denſitate, ibi major erit elaſticitas, ubi major <lb />aëris quantitas, quod cum experimentis non congruit, <lb />primum idcirco caſum locum habere videmus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Effectus elaſticitatis aëris ſimiles ſunt effectibus gravi-<lb />
<ptr xml:id="note-0409-01a" corresp="note-0409-01" type="noteAnchor" />
tatis; </s>
          <s xml:space="preserve">aerque incluſus elaſticitate eodem modo quàm non <lb />incluſus pondere ſuo agit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0409-01" corresp="note-0409-01a" place="margin">1073.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aër, a totius Atmoſphæræ pondere gravatus, omnes <lb />partes verſus premit ex ipſa natura fluiditatis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">vim
<ptr xml:id="note-0409-02a" corresp="note-0409-02" type="noteAnchor" />
quam exerit ab elaſticitate nullo modo pendere liquet; </s>
          <s xml:space="preserve">quia, <lb />hac poſitâ aut ſublatâ, vis illa, quæ a pondere Atmoſphæ-<lb />ræ oritur, &amp; </s>
          <s xml:space="preserve">huic æqualis eſt, minime mutari poteſt. </s>
          <s xml:space="preserve">Cum <lb />vero aër ſit elaſticus, pondere Atmoſphæræ in tale ſpatium <lb />redigitur, ut elaſticitas, qua renititur in pondus compri-<lb />mens, hocce pondus æquet <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Elaſticitas autem creſcit
<ptr xml:id="note-0409-03a" corresp="note-0409-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">minuitur cum diminuta aut aucta diſtantia particularum <ptr type="noteAnchor" />,
<ptr xml:id="note-0409-04a" corresp="note-0409-04" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">non intereſt an pondere Atmoſphæræ an quocunque alio <lb />modo aër in certo ſpatio retineatur, in utroque caſu ea-<lb />dem cum vi ſeſe expandere conatur, &amp; </s>
          <s xml:space="preserve">omnes partes ver-<lb />ſus premit. </s>
          <s xml:space="preserve">Idcirco ſi in terræ viciniis aër, ſervata hujus <lb />denſitate, includatur, incluſi preſſio valebit totius Atmoſphæ-<lb />ræ pondus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0409-02" corresp="note-0409-02a" n="*" anchored="true" place="margin">711.</note>
              <note xml:space="preserve" xml:id="note-0409-03" corresp="note-0409-03a" n="*" anchored="true" place="margin">247.</note>
              <note xml:space="preserve" xml:id="note-0409-04" corresp="note-0409-04a" n="*" anchored="true" place="margin">1071.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Tubus, Torricellianus vitro DC includitur, ita <lb />
<ptr xml:id="note-0409-05a" corresp="note-0409-05" type="noteAnchor" />
ut aër, in ſuperſiciem mercurii vaſe V contenti pre-<lb />
<ptr xml:id="note-0409-06a" corresp="note-0409-06" type="noteAnchor" />
mens, nullam cum aëre exteriori communicationem ha-<lb />beat; </s>
          <s xml:space="preserve">aëris elaſticitate ad eandem, ac in aëre aperto, ſu-<lb />ſtinetur altitudinem mercurius in tubo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0409-05" corresp="note-0409-05a" place="margin">1074.</note>
              <note xml:space="preserve" xml:id="note-0409-06" corresp="note-0409-06a" place="margin">TAB. XXXIX. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Manente eadem aëris conſtitutione, prædicta ſemper lo-<lb />
<ptr xml:id="note-0409-07a" corresp="note-0409-07" type="noteAnchor" />
cum habent; </s>
          <s xml:space="preserve">ſed non immutabilis eſt hæc conſtitutio; </s>
          <s xml:space="preserve">au-<lb />getur ſæpe aut minuitur vis repellens particularum, licet
</s>
          <pb facs="0410" n="306" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
diſtantia inter harum centranon mutetur; </s>
          <s xml:space="preserve">de hac mutatione <lb />quædam in capite ſequenti dicam, in libro ſequenti etiam <lb />videbimus calore augeri elaſticitatem, frigore minui.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0409-07" corresp="note-0409-07a" place="margin">1075.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Alia quædam, circa aëris elaſticitatem, memorabo expe-<lb />rimenta in cap. </s>
          <s xml:space="preserve">XVII.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XV.</head>
        <head rend="italics" xml:space="preserve">De quibuſdam aliis Fluidis Elaſticis.</head>
        <p>
          <s xml:space="preserve">VAria dantur Fluida, in quibus circa aërem memoratam <lb />
<ptr xml:id="note-0410-01a" corresp="note-0410-01" type="noteAnchor" />
detegimus proprietatem, Elaſticitatem. <lb /></s>
          <s xml:space="preserve">Inter hæc vapor notabilem occupat locum, de hoc agi-<lb />mus in libro 3. </s>
          <s xml:space="preserve">capite 4.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0410-01" corresp="note-0410-01a" place="margin">1076.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fermentationibus, &amp; </s>
          <s xml:space="preserve">efferveſcentiis, ex corporibus flui-<lb />
<ptr xml:id="note-0410-02a" corresp="note-0410-02" type="noteAnchor" />
da exeunt elaſtica, diverſa pro corporum differentia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0410-02" corresp="note-0410-02a" place="margin">1077.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ex innumeris corporibus tale exit fluidum ubi preſſio <lb />
<ptr xml:id="note-0410-03a" corresp="note-0410-03" type="noteAnchor" />
aëris externi minuitur aut tollitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0410-03" corresp="note-0410-03a" place="margin">1078.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quod etiam in quibuſdam obſervatur, ubi tantum made-<lb />
<ptr xml:id="note-0410-04a" corresp="note-0410-04" type="noteAnchor" />
facta ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0410-04" corresp="note-0410-04a" place="margin">1079.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fluida hæc omnia quantumvis diverſa inter ſe, eodem <lb />nomine aëris, ſi forte vaporem excipiamus, deſignantur <lb />plerumque. </s>
          <s xml:space="preserve">Cum vero aër ſit fluidum hoc, quo Telluris <lb />
<ptr xml:id="note-0410-05a" corresp="note-0410-05" type="noteAnchor" />
tota ſuperficies obtegitur, hic proprie loquendo eſt mixtum <lb />ex variis fluidis elaſticis, in quo natant corpuſcula inumera <lb />varii generis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0410-05" corresp="note-0410-05a" place="margin">1080.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpuſcula hæc pro diverſa gravitate ſpeciſica ad varias <lb />adſcendunt altitudines <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">etiam diverſorum corporum
<ptr xml:id="note-0410-06a" corresp="note-0410-06" type="noteAnchor" />
exhalationes quæ fluida ſunt elaſtica ad diverſas elevantur <lb />altitudines: </s>
          <s xml:space="preserve">Unde deducimus, aërem in loco elevato non <lb />
<ptr xml:id="note-0410-07a" corresp="note-0410-07" type="noteAnchor" />
tantum denſitate differre cum aëre inferiori.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0410-06" corresp="note-0410-06a" n="*" anchored="true" place="margin">749. 750</note>
              <note xml:space="preserve" xml:id="note-0410-07" corresp="note-0410-07a" place="margin">1081.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Fluida elaſtica diverſa diverſas proprietates habere, in <lb />
<ptr xml:id="note-0410-08a" corresp="note-0410-08" type="noteAnchor" />
dubium non facile vocari poteſt, quod etiam experimen-<lb />tis conſtat; </s>
          <s xml:space="preserve">effectus enim diverſarum exhalationum diffe-<lb />runt inter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0410-08" corresp="note-0410-08a" place="margin">1082.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0411" n="307" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XV.</fw>
        <p>
          <s xml:space="preserve">Dum ſluida elaſtica in corporibus hærent, ad fluida ela-<lb />
<ptr xml:id="note-0411-01a" corresp="note-0411-01" type="noteAnchor" />
ſtica non magis referri poſſunt, quàm aqua, antequam in <lb />vaporem convertatur, pro vapore haberi poteſt,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0411-01" corresp="note-0411-01a" place="margin">1083.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Spatium autem occupatum, a materia elaſtica, dum in <lb />ipſis corporibus hæret, exiguum admodum eſt collatum <lb />cum ſpatio quod occupat, dum elaſticitatem exerit, præ-<lb />cipue ſi parum comprimatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Aqua, dum ſe in vaporem convertit, licet hic a ponde-<lb />
<ptr xml:id="note-0411-02a" corresp="note-0411-02" type="noteAnchor" />
re totius atmoſphæræ comprimatur, ad mi imum decies &amp; </s>
          <s xml:space="preserve"><lb />quater millies ſeſe expandit, inipſis illis locis ex quibus aë-<lb />rem excludit; </s>
          <s xml:space="preserve">hanc autem expanſionem in immenſum poſ-<lb />ſe augeri, ſublata atmoſphæræ preſſione, quis non vi-<lb />det?</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0411-02" corresp="note-0411-02a" place="margin">1084.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aqua fluidum continet Elaſticum, quod calore, frigore, <lb />
<ptr xml:id="note-0411-03a" corresp="note-0411-03" type="noteAnchor" />
aut ſublata aëris preſſione ex hac ſeparatur, hancque ad-<lb />modum ſubitaneam obſervamus ſeparationem, ſi ſubito o-<lb />mnis preſſio tollatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0411-03" corresp="note-0411-03a" place="margin">1085.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> I.</head>
        <p>
          <s xml:space="preserve">Vas vitreum AB exactiſſimè aqua repletur; </s>
          <s xml:space="preserve">in extremi-<lb />
<ptr xml:id="note-0411-04a" corresp="note-0411-04" type="noteAnchor" />
tate B cum ipſo cohæret cylindrus æneus, ut, ope cochleæ, <lb />
<ptr xml:id="note-0411-05a" corresp="note-0411-05" type="noteAnchor" />
ipſi jungatur antlia, quæ in fig. </s>
          <s xml:space="preserve">6, Tab 42. </s>
          <s xml:space="preserve">exhibetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0411-04" corresp="note-0411-04a" place="margin">1086.</note>
              <note xml:space="preserve" xml:id="note-0411-05" corresp="note-0411-05a" place="margin">TAB XXXVIII <lb />fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum antliæ embolus extrahitur, aqua gravitate in an-<lb />tliam deſcendit, locuſque in ſuperiori vaſis parte aquâ &amp; </s>
          <s xml:space="preserve"><lb />aëre vacuus datur. </s>
          <s xml:space="preserve">Statim etiam ubique in aquâ innume-<lb />ræ bullæ fluidi elaſtici, eodem momento, ſeſe demonſtrant, <lb />totaque aqua hiſce bullis albeſcit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Fluidum hoc elaſticum ab aëre, quo Telluris ſuperficies <lb />
<ptr xml:id="note-0411-06a" corresp="note-0411-06" type="noteAnchor" />
obtegitur, differt, licet magnâ copiâ in aëre detur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0411-06" corresp="note-0411-06a" place="margin">1087.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Si phiala repleatur aquâ, ex qua igne, aut aliter, omne flui-<lb />
<ptr xml:id="note-0411-07a" corresp="note-0411-07" type="noteAnchor" />
dum elaſticum fuit expulſum, &amp;</s>
          <s xml:space="preserve">, relictâ exiguâ aëris bullâ, <lb />invertatur phiala, aperturaque immergatur aquâ, vaſe quo-<lb />cunque contentâ, bulla hæc aërea, in tempore aliquot die-<lb />rum, tota intrabit in aquam, &amp; </s>
          <s xml:space="preserve">ſucceſſive eodem modo va-<lb />riæ bullæ aquam intrant. </s>
          <s xml:space="preserve">Sed reſpectu ſingularum hoc
</s>
          <pb facs="0412" n="308" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
obſervandum, primo die partem multo majorem bullæ quam <lb />diebus ſequentibus intrare.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0411-07" corresp="note-0411-07a" place="margin">1088.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hoc Experimento ſequitur dari partem aëris, quæ <lb />
<ptr xml:id="note-0412-01a" corresp="note-0412-01" type="noteAnchor" />
facilius in aquam intrat, ibique hæret, quàm reliquum <lb />aëris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0412-01" corresp="note-0412-01a" place="margin">1089.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde ſequitur, dum aqua aëri aperto expoſita eſt, in ipſam <lb />majori copia penetrare illius materiæ, quæ facilius intrat, &amp; </s>
          <s xml:space="preserve"><lb />aërem, quiintravit, ab ipſo aëre externo differre, obſervamus <lb />etiam ſæpe magis hocce fluidum imminuta preſſione ſeſe <lb />dilatare quàm juxta regulam n. </s>
          <s xml:space="preserve">1066. </s>
          <s xml:space="preserve">Hujus autem fluidi ex-<lb />panſio immenſa eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Memorat Mariotte experimentum de dilatatione hujus <lb />
<ptr xml:id="note-0412-02a" corresp="note-0412-02" type="noteAnchor" />
materiæ elaſticæ, qua conſtat, materiam hanc, quæ alore ex <lb />aqua fuerat expulſa, ubi refrigerata erat, &amp; </s>
          <s xml:space="preserve">pon@ustoti us at-<lb />moſphæræ ſuſtinebat, occupaſſe ſpatium decuplum ſpatii ab <lb />ipſa aqua, qua contenta fuerat, occupati.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0412-02" corresp="note-0412-02a" place="margin">1090.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Conſtat etiam nunquam experimentis diminutionem vo-<lb />luminis aquæ, dum materia elaſtica ex hac exit obſervari <lb />potuiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tandem aliud memorat Mariotte experimentum, in quo <lb />materia elaſtica, quæ aqua fuerat contenta, quatuor millies, <lb />ſublata preſſione, magis expanſa fuit, quàm ubi preſſionem <lb />atmoſphæræ ſuſtinuit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Collatis hiſce quis non videt, ſpatium ab hac materia, in <lb />
<ptr xml:id="note-0412-03a" corresp="note-0412-03" type="noteAnchor" />
ultimùm memorato experimento, occupatum, ad minimum, <lb />variis vicibus, centum millies ſuperaſſe ſpatium, quod ipſa <lb />in aqua occupabat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0412-03" corresp="note-0412-03a" place="margin">1091.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex quibus deducimus, fluidorum elaſticorum particulas <lb />
<ptr xml:id="note-0412-04a" corresp="note-0412-04" type="noteAnchor" />
non eſſe ejuſdem naturæ cum cæteris corporibus elaſticis, <lb />nam non poſſunt particulæ ſingulæ centum millies, &amp; </s>
          <s xml:space="preserve">quod <lb />excedit, ſeſe expandere ſervata ſuperficie, omni inæquali-<lb />tate, aut angulo, experta; </s>
          <s xml:space="preserve">in omni enim expanſione partes <lb />facile moventur inter ſe: </s>
          <s xml:space="preserve">unde ſequitur particulas ſeſe mu-<lb />tuo non tangere, quamvis ſeſe invicem repellant, qualem par-<lb />ticularum proprietatem ſuperius jam memoravimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0412-04" corresp="note-0412-04a" place="margin">1092.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">61.</note>
        <pb facs="0413" />
        <pb facs="0413a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0413a-01" />
          <label>0413a-01</label>
        </figure>
        <pb facs="0414" />
        <pb facs="0415" n="309" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XVI.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVI.</head>
        <head rend="italics" xml:space="preserve">De Antlia Pneumatica.</head>
        <p>
          <s xml:space="preserve">AEris elaſticitas fundamentum eſt conſtructionis Machi-<lb />
<ptr xml:id="note-0415-01a" corresp="note-0415-01" type="noteAnchor" />
næ, qua aër ex vaſe exhauritur. </s>
          <s xml:space="preserve">Antlia Pneumati-<lb />ca vocatur, quæ variis modis conſtruitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0415-01" corresp="note-0415-01a" place="margin">1093.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In omnibus pars præcipua eſt cylindrus metallicus cavus, ab <lb />interiori parte politus; </s>
          <s xml:space="preserve">in hoc movetur embolus, exactiſſime <lb />cum cylindri ſuperficie interiori congruens; </s>
          <s xml:space="preserve">ne aëri tranſitus <lb />ad latera detur. </s>
          <s xml:space="preserve">Fundo cylindri embolus applicatur, deinde <lb />elevatur, quo ex cylindri cavitate aër omnis excluditur. </s>
          <s xml:space="preserve">Si <lb />cum vaſe quocunque, per tubum in fundo cylindri, cavi-<lb />tas hæc communicationem habeat, aër in vaſe ſeſe expan-<lb />det, &amp; </s>
          <s xml:space="preserve">pro parte cylindrum intrabit, donec in cylindro &amp; </s>
          <s xml:space="preserve"><lb />vaſe eandem habeat denſitatem. </s>
          <s xml:space="preserve">Claudatur communicatio <lb />inter vas &amp; </s>
          <s xml:space="preserve">cylindrum, aërque ex cylindro ejiciatur, &amp; </s>
          <s xml:space="preserve"><lb />embolus fundo applicetur. </s>
          <s xml:space="preserve">Si ſecunda vice embolus ele-<lb />vetur, reſeratâ communicatione inter cylindrum &amp; </s>
          <s xml:space="preserve">vas me-<lb />moratum, iterum aëris denſitas in vaſe minuetur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">repe-<lb />tito emboli motu tandem aër in vaſe ad denſitatem mini-<lb />mam reducetur. </s>
          <s xml:space="preserve">aër tamen omnis hac methodo nunquam <lb />exhauriri poteſt; </s>
          <s xml:space="preserve">ſingulis enim vicibus aër ſeſe ita expandit, <lb />ut eandem in cylindro denſitatem habeat ac in vaſe, in quo <lb />ideò ſemper aër quidam ſupereſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Antliæ omnes prædicta communia habent, in multis ta-<lb />
<ptr xml:id="note-0415-02a" corresp="note-0415-02" type="noteAnchor" />
men differunt. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Variis modis clauditur &amp; </s>
          <s xml:space="preserve">reſeratur com-<lb />municatio inter vas exhauriendum &amp; </s>
          <s xml:space="preserve">cylindrum. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Variæ <lb />dantur methodi, quibus aër ex cylindro expellitur, quan-<lb />do embolus fundo admovetur. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Emboli in variis antliis <lb />differunt. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Situs cylindri non in omnibus eſt idem. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">Di-<lb />verſæ adhibentur machinæ, quibus embolus agitatur. <lb /></s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">Tandem duo ſæpe junguntur cylindri, in quorum uno <lb />embolus elevatur, dum in alio deprimitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0415-02" corresp="note-0415-02a" place="margin">1094.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Antlia noſtra hic delineatur; </s>
          <s xml:space="preserve">pars oppoſita thecæ, non <lb />
<ptr xml:id="note-0415-03a" corresp="note-0415-03" type="noteAnchor" />
</s>
          <pb facs="0416" n="310" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
apertâ januâ, quæ ad illam partem datur, videtur in fig. </s>
          <s xml:space="preserve">2. <lb /></s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">43. </s>
          <s xml:space="preserve">Antliæ hujus deſcriptionem non dabo, ge-<lb />neralia tantum quædam notabo, peculiarem omnium par-<lb />tium explicationem alia occaſione daturus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0415-03" corresp="note-0415-03a" place="margin">TAB. XXXIX. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi> <hi rend="small caps">Pneumatica</hi>.</head>
        <p>
          <s xml:space="preserve">In fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">39. </s>
          <s xml:space="preserve">antlia repræſentatur a parte antica, <lb />
<ptr xml:id="note-0416-01a" corresp="note-0416-01" type="noteAnchor" />
ſublatis nempe thecæ, cui includitur, januis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0416-01" corresp="note-0416-01a" place="margin">1095.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Antlia eadem, ex theca extracta, a parte poſtica, deli-<lb />neatur in fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">40. </s>
          <s xml:space="preserve">liſdem litteris eædem partes in <lb />utraque figura notantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Conſtat antlia duobus cylindris, A, B; </s>
          <s xml:space="preserve">in utroque mo-<lb />vetur embolus, cujus partes ſeparatæ exhibentur in C, D, E, F, <lb />(fig. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">40.)</s>
          <s xml:space="preserve">.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Partes E, F, cochleâ junguntur, &amp; </s>
          <s xml:space="preserve">inter ipſas firmatur <lb />
<ptr xml:id="note-0416-02a" corresp="note-0416-02" type="noteAnchor" />
annulus coriaceus, qui ab omni parte prominet, &amp; </s>
          <s xml:space="preserve">qui, <lb />dum embolus cylindro intruditur, ſeſe ſuperficiei e e ap-<lb />plicat. </s>
          <s xml:space="preserve">Methodus hæc in Anglia in uſu eſt. </s>
          <s xml:space="preserve">Corium hoc-<lb />ce in oleo &amp; </s>
          <s xml:space="preserve">aqua macerari debet, ut monuimus in n. </s>
          <s xml:space="preserve">722.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0416-02" corresp="note-0416-02a" place="margin">TAB. XL. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Embolis, quando antliis intruduntur, aqua ſuperinfunditur, <lb />cujus aliquando, exſiccatis paululum coriis, pars quædam in <lb />antlias deſcendit, quod tamen experimenta turbare non po-<lb />teſt; </s>
          <s xml:space="preserve">in quo caſu emboli extrahendi ſunt &amp; </s>
          <s xml:space="preserve">per aliquotho-<lb />ras in aqua relinquendi, oleoque probe eliniri debent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cauda C emboli, ut fere in omnibus antliis, dentata eſt; <lb /></s>
          <s xml:space="preserve">hujus extremitas inferior cc cylindrica eſt, &amp; </s>
          <s xml:space="preserve">cochleâ ter-<lb />minatur. </s>
          <s xml:space="preserve">Transmittitur cylindrica pars hæc per cavitatem <lb />cylindricam in prominentia f emboli; </s>
          <s xml:space="preserve">cujus cavitatis dia-<lb />meter parum tantum ſuperat cylindri c c diametrum. </s>
          <s xml:space="preserve">Cum <lb />hoc conjungitur nunc conus truncatus D, qui cochleam <lb />fæminam continet, &amp; </s>
          <s xml:space="preserve">firmatur hic transverſâ cochleâ g: </s>
          <s xml:space="preserve"><lb />poteſtque cauda C elevari &amp; </s>
          <s xml:space="preserve">deprimi per ſpatium trium <lb />partium quartarum pollicis, ipſo embolo immoto manente.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Emboli ambo moventur agitatione rotæ R, cujus motus, <lb />
<ptr xml:id="note-0416-03a" corresp="note-0416-03" type="noteAnchor" />
dum it &amp; </s>
          <s xml:space="preserve">redit, parum deficit à tertiâ circuli parte.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0416-03" corresp="note-0416-03a" place="margin">TAB. XXXIX. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XL. <lb />fig. 1.</note>
        <p>
          <s xml:space="preserve">Vaſa exhaurienda laminæ L L imponuntur, &amp; </s>
          <s xml:space="preserve">hæc per
</s>
          <pb facs="0417" n="311" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XVI.</fw>
tubum D communicationem habent cum antliis. </s>
          <s xml:space="preserve">Da-<lb />tur enim infra laminam L L, cavitas quæ tubo E E reſpon-<lb />det, in quo duo dantur epiſtomia, inter quæ cum tubo <lb />hoc conjungitur tubus OO, qui infra laminam, cui antliæ <lb />imponuntur, cum his communicatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Antliæ ſingulæ epiſtomium infra fundum ſuum habent, <lb />horum caudæ videntur in G, G, quæ regulis æneis ad ſe <lb />invicem applicatis junguntur ita, ut motu harum regularum <lb />epiſtomia ambo eodem tempore moveantur. </s>
          <s xml:space="preserve">Inter regulas, <lb />in medio longitudinis, rotula ænea datur T. </s>
          <s xml:space="preserve">Cum a-<lb />xe rotæ R a poſtica parte jungitur crux ferrea HKNM, <lb />qua epiſtomia hæc agitantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In ſitu in quo partes machinæ in his figuris repræſentan-<lb />tur, antlia B cum vaſe exhauriendo communicationem ha-<lb />bet, antlia A cum aëre externo; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">deprimendo hujus an-<lb />tliæ embolum omnis aër ex hac ejicitur, &amp; </s>
          <s xml:space="preserve">interea magis <lb />elevatur embolus alter.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ubi verò embolus fundo antliæ A applicatur, extremi-<lb />tas N crucis ad n pertingit, in quo motu ſuper rotulâ <lb />T tranſit, hancque in motu radit; </s>
          <s xml:space="preserve">Eo autem momento <lb />quo N tranſit ſuper T, clavus, aut cylindrus, ferreus K, <lb />ad vectem CF, ferreum, incurvatum, circa P mobilem, <lb />in b accedit; </s>
          <s xml:space="preserve">huncque premit in motu puncti N à T ad n.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Rotatur interea vectis circa centrum P, &amp; </s>
          <s xml:space="preserve">extremitas F <lb />in rotulam T premit, hancque elevat; </s>
          <s xml:space="preserve">quo ſitus epiſto-<lb />miorum paululum quidem mutatur, non tamen me-<lb />moratæ communicationes antliæ B cum vaſe exhauriendo, <lb />&amp; </s>
          <s xml:space="preserve">A cum aëre externo, obturantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Motus rotæ nunc in contrariam partem dirigendus eſt. <lb /></s>
          <s xml:space="preserve">Ubi in reditu punctum N ab n ad T pervenit, quia rotula <lb />elevata fuit, in hanc incurrit crucis extremum, trochleam-<lb />que propellit, donec converſione epiſtomiorum G, G, ita <lb />deprimatur, ut ſuper hac tranſeat N.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hac epiſtomiorum converſione, G, G, arcus deſcri-<lb />bunt, qui paululum tantum excedunt gradus nonaginta;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0418" n="312" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
clauditurque communicatio antliæ B cum vaſe, &amp; </s>
          <s xml:space="preserve">nova <lb />cum aëre externo reſeratur; </s>
          <s xml:space="preserve">contrarium reſpectu antliæ A <lb />locum habet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Durante hac epiſtomiorum agitatione, elevatur quidem <lb />Q, ſed embolusipſe fundo antliæ A applicatus manet; </s>
          <s xml:space="preserve">quod <lb />deſideratur ne aër externus iterum in antliam intret, &amp; </s>
          <s xml:space="preserve"><lb />quod quomodo fiat in deſcriptione embolorum dixi-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si nunc motus rotæ continuetur, elevatur embolus an-<lb />tliæ A, quæ cum vaſe exhauriendo communicationem ha-<lb />bet, &amp; </s>
          <s xml:space="preserve">ex antlia B aër ejicitur, extremitasque M crucis ſu-<lb />per rotula T tranſit, clavuſque K in vectem Spremit, &amp; </s>
          <s xml:space="preserve"><lb />quæ in motu contrario fuere explicata, in hoc caſu eodem <lb />modo, obtinent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Rota agitatur manubrio MM, cujus longitudo eſt cir-<lb />
<ptr xml:id="note-0418-01a" corresp="note-0418-01" type="noteAnchor" />
citer duorum pedum, &amp; </s>
          <s xml:space="preserve">quod in ſitu datur horizontali, dum <lb />pars HK crucis eſt verticalis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0418-01" corresp="note-0418-01a" place="margin">TAB. XXXIX. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando in hac agitatione contingit, majorem dari reſi-<lb />ſtentiam, ubi epiſtomia moventur, quàm in reliquo motu, <lb />indicium hoc eſt, oleo &amp; </s>
          <s xml:space="preserve">cerâ eliniri debere epiſtomia; </s>
          <s xml:space="preserve">quod <lb />in tempeſtate calidiori repeti debet, ubi per tres aut qua-<lb />tuor horas machina in continuo fuit motu.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quod ſpectat epiſtomia E, E, ſuperius memorata, uno, <lb />communicatio, exhauſtio aëre, clauditur inter vas exhau-<lb />ſtum &amp; </s>
          <s xml:space="preserve">cylindros; </s>
          <s xml:space="preserve">altero, aër de novo vaſe intromittitur, <lb />&amp; </s>
          <s xml:space="preserve">cummunicatio impeditur cum indice mercuriali.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Index hicce mercurialis in hac figura commode repræ-<lb />ſentari non potuit; </s>
          <s xml:space="preserve">hujus uſus eſt determinatio quantitatis <lb />aëris ex vaſe exhauſti, ut &amp; </s>
          <s xml:space="preserve">quantitatis in hoc ſuperſtitis; <lb /></s>
          <s xml:space="preserve">eo etiam vaſorum exhauriendorum capacitates menſurantur; </s>
          <s xml:space="preserve"><lb />quæ ut exacte notæ ſint in variis Experimetis deſideratur; </s>
          <s xml:space="preserve"><lb />index noſter a vulgaribus differt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In D ſæpe ope cochleæ orbi jungitur cylindrus parvus, <lb />cochlea circumdatus, quo globus exhauriendus, aut vas ali-<lb />ud, machinæ applicari poteſt,</s>
        </p>
        <pb facs="0419" />
        <pb facs="0419a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0419a-01" />
          <label>0419a-01</label>
        </figure>
        <pb facs="0420" />
        <pb facs="0421" n="313" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XVI.</fw>
        <p>
          <s xml:space="preserve">In medio Orbis LL foramen datur, quod cochleâ clau-<lb />ditur, ſed quo machinæ variæ cum orbe jungi queunt,</s>
        </p>
        <p>
          <s xml:space="preserve">Sæpe hac methodo orbi adaptatur pyxis cylindrica, or-<lb />
<ptr xml:id="note-0421-01a" corresp="note-0421-01" type="noteAnchor" />
bibus coriaceis, cerâ imbutis, repleta, per quorum centra <lb />tranſmittitur filum æneum, quod ope manubrii agitari po-<lb />teſt, quæ agitatio communicatur in loco aëre vacuo; </s>
          <s xml:space="preserve">co-<lb />chleâ circumdatur, &amp; </s>
          <s xml:space="preserve">pyxidem intrat hujus operculum, quo <lb />coria comprimuntur, ut exactius tranſitum aëris impe-<lb />diant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0421-01" corresp="note-0421-01a" place="margin">1096.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pyxis ſimilis ſæpe jungitur operculo, quod vaſis exhau-<lb />riendis ſuperimponitur, ut videtur in fig. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Tab 41. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />in fig. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">47.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando vaſa orbi LL imponuntur; </s>
          <s xml:space="preserve">aut quando operculis <lb />
<ptr xml:id="note-0421-02a" corresp="note-0421-02" type="noteAnchor" />
vaſa obteguntur, aut quando cochleis machinæ junguntur, <lb />&amp; </s>
          <s xml:space="preserve">in genere quando aëris ingreſſus cohibendus eſt, utimur <lb />mixto ex quatuor partibus ceræ albæ, duabus reſinæ, &amp; </s>
          <s xml:space="preserve"><lb />una olei olivarum, æſtate minor, hieme major olei copia de-<lb />ſideratur. </s>
          <s xml:space="preserve">In multis experimentis ſatis eſt, ſi vaſa corio <lb />madido ſuperimponantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0421-02" corresp="note-0421-02a" place="margin">1097.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVII.</head>
        <head rend="italics" xml:space="preserve">Experimenta varia circa Aëris Gravitatem &amp; <lb />hujus Elaſticitatem.</head>
        <p>
          <s xml:space="preserve">AErem gravem eſſe vidimus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">poteſt ut cetera corpo-
<ptr xml:id="note-0421-03a" corresp="note-0421-03" type="noteAnchor" />
ra ponderari, &amp; </s>
          <s xml:space="preserve">hujus denſitas cum ceterorum cor-<lb />
<ptr xml:id="note-0421-04a" corresp="note-0421-04" type="noteAnchor" />
porum denſitate conferri <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si vas idem aërem continens,
<ptr xml:id="note-0421-05a" corresp="note-0421-05" type="noteAnchor" />
ut &amp; </s>
          <s xml:space="preserve">exhauſto aëre, ponderetur, ponderum differentia e-<lb />rit aëris pondus; </s>
          <s xml:space="preserve">quæ methodus hoc incommodi habet, <lb />quod ſæpe bilance, etiam exactiſſimâ, pondere magno gra-<lb />vatâ, ponderum differentiæ minores exactè non detegan-<lb />tur; </s>
          <s xml:space="preserve">ſequenti in hoc caſu methodo utendum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0421-03" corresp="note-0421-03a" place="margin">1098.</note>
              <note xml:space="preserve" xml:id="note-0421-04" corresp="note-0421-04a" n="*" anchored="true" place="margin">1055.</note>
              <note xml:space="preserve" xml:id="note-0421-05" corresp="note-0421-05a" n="*" anchored="true" place="margin">737.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <note xml:space="preserve" place="margin">1099.</note>
        <p>
          <s xml:space="preserve">Exhauſto aëre ex globo vitreo, cujus capacitas eſt 283. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0421-07a" corresp="note-0421-07" type="noteAnchor" />
</s>
          <pb facs="0422" n="314" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
pollicum cubicorum, &amp; </s>
          <s xml:space="preserve">pondere tali huic adjuncto, ut gra-<lb />vitate ſpecifica aquæ gravitatem ſpecificam fere æquet, <lb />aquâ vaſe DE contentâ globus immergatur, filo jungatur <lb />unco adhærenti lanci libræ AB, de qua ſuperius <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ele-
<ptr xml:id="note-0422-01a" corresp="note-0422-01" type="noteAnchor" />
vetur bilanx, donec pondere minimo æquilibrium detur; <lb /></s>
          <s xml:space="preserve">ſi, aperto epiſtomio, aër globum intret, in lance oppoſita, <lb />ut æquilibrium inſtauretur, requiritur pondus P circiter <lb />centum granorum, aliquando majus, ſæpe minus, pro di-<lb />verſa aëris conftitutione, quæ pondere Atmoſphæræ muta-<lb />to, &amp; </s>
          <s xml:space="preserve">aliis de cauſis, variationem ſubit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0421-07" corresp="note-0421-07a" place="margin">TAB XLII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0422-01" corresp="note-0422-01a" n="*" anchored="true" place="margin">705.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cùm autem nactus ſim bilancem, quæ, quamvis ponde-<lb />re aliquot librarum gravata, minimam differentiam indicat, <lb />immerſionem in aquam negligo, ubi aëris pondus deter-<lb />minare ſuſcipio.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpora fluidis immerſa ab iis ſuſtinentur, magiſque aut <lb />minus pro volumine corporis majori aut minori <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">pon-
<ptr xml:id="note-0422-02a" corresp="note-0422-02" type="noteAnchor" />
dus amiſſum ex nota fluidi denſitate determinatur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Præ-
<ptr xml:id="note-0422-03a" corresp="note-0422-03" type="noteAnchor" />
cedenti Experimento cognoſcitur ergo, quantum corpora in <lb />aëre minus quam in vacuo gravitent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0422-02" corresp="note-0422-02a" n="*" anchored="true" place="margin">756.</note>
              <note xml:space="preserve" xml:id="note-0422-03" corresp="note-0422-03a" n="*" anchored="true" place="margin">751.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ex his etiam deducimus, corpora in æquilibrio in aëre, <lb />
<ptr xml:id="note-0422-04a" corresp="note-0422-04" type="noteAnchor" />
ſi horum volumina fuerint inæqualia, in loco aëre vacuo <lb />non æque ponder are, quod confirmatur ſequenti Experi-<lb />mento.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0422-04" corresp="note-0422-04a" place="margin">1100.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Lancibus bilancis a b imponuntur fruſtum ceræ c &amp; </s>
          <s xml:space="preserve">pon-<lb />
<ptr xml:id="note-0422-05a" corresp="note-0422-05" type="noteAnchor" />
dus metallicum p, &amp; </s>
          <s xml:space="preserve">datur æquilibrium. </s>
          <s xml:space="preserve">Bilanx in reci-<lb />piente vitreo ſuſpenditur, &amp; </s>
          <s xml:space="preserve">aere exhauſto præponderat ce-<lb />ra, cujus volumen ſuperat volumen corporis p, &amp; </s>
          <s xml:space="preserve">magis ab <lb />aëre ſuſtinetur, quando hic in recipiente admittitur, quo <lb />æquilibrium inſtauratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0422-05" corresp="note-0422-05a" place="margin">TAB. XLI. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aëris elaſticitas, in capite 14. </s>
          <s xml:space="preserve">probata, magis fit ſenſi-<lb />bilis Experimento ſequenti.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Veſica exacte clauſa parvam admodum aëris quantitatem-<lb />
<ptr xml:id="note-0422-06a" corresp="note-0422-06" type="noteAnchor" />
contineat, vitro tegatur, &amp; </s>
          <s xml:space="preserve">exhauriatur aër, quo preſſio
</s>
          <pb facs="0423" />
          <s xml:space="preserve">
<pb facs="0423a" />
<ptr xml:id="fig-0423a-01a" corresp="fig-0423a-01" type="figureAnchor" />
<pb facs="0424" />
<pb facs="0425" n="315" /><fw type="head">MATHEMATICA. LIB. II. CAP. XVII.</fw>
in veſicæ ſuperficiem exteriorem minuitur; </s>
          <s xml:space="preserve">eodem <lb />tempore aë veſicæ incluſus ſeſe expandet, &amp; </s>
          <s xml:space="preserve">hæc inflabi-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0422-06" corresp="note-0422-06a" place="margin">1101.</note>
              <figure xml:id="fig-0423a-01" corresp="fig-0423a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0423a-01" />
                <label>0423a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Elaſticitatis vim totius Atmoſphæræ ponderi æquari vi-<lb />dimus; </s>
          <s xml:space="preserve">effectus hujus vis ſub oculos ſequenti Experimento <lb />ponitur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Veſica exacte clauſa, &amp; </s>
          <s xml:space="preserve">aëre pro parte tantum repleta, <lb />
<ptr xml:id="note-0425-01a" corresp="note-0425-01" type="noteAnchor" />
pyxidi æneæ A, cujus diameter eſt trium pollicum cum ſe-<lb />
<ptr xml:id="note-0425-02a" corresp="note-0425-02" type="noteAnchor" />
miſſe, includitur, obtegiturque hæc operculo ligneo, aut <lb />plumbeo, quod in ipſam pyxidem penetrat ita, ut quamvis e-<lb />levetur non decidat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0425-01" corresp="note-0425-01a" place="margin">1102.</note>
              <note xml:space="preserve" xml:id="note-0425-02" corresp="note-0425-02a" place="margin">TAB. XLI. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Operculo pondera plumbea P, P, imponuntur, habent hæc <lb />foramen in medio, &amp; </s>
          <s xml:space="preserve">trajiciuntur cylindro E, cum oper-<lb />culo cohærenti. </s>
          <s xml:space="preserve">Exhauſto aëre veſica, ut in præcedenti Ex-<lb />perimento, inflatur, quo pondera elevantur. </s>
          <s xml:space="preserve">Plura pro vitri <lb />magnitudine adhibentur pondera, &amp; </s>
          <s xml:space="preserve">licet borum ſumma ſe-<lb />xaginta aut ſeptuaginta libras ſuperet, facillime elevantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Aëris gravitas, hujus preſſio quæ ex gravitate oritur, ut <lb />&amp; </s>
          <s xml:space="preserve">elaſticitas, effectus varios notabiles edunt; </s>
          <s xml:space="preserve">quoſdam ſe-<lb />ligam, &amp; </s>
          <s xml:space="preserve">Experimentis confirmabo.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Foramini in medio orbis LL antliæ pneumaticæ, in in-<lb />
<ptr xml:id="note-0425-03a" corresp="note-0425-03" type="noteAnchor" />
feriori parte, ope cochleæ, jungitur cylindrus æneus per-<lb />
<ptr xml:id="note-0425-04a" corresp="note-0425-04" type="noteAnchor" />
foratus, cohærens cum tubo vitreo AB, ab utraque parte <lb />aperto, cujus extremitas B mercurio immergitur. </s>
          <s xml:space="preserve">In tu-<lb />bo e g, clauſo in e, &amp; </s>
          <s xml:space="preserve">aëre vacuo, mercurius ſuſtinetur, ut <lb />antea dictum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Vas V cum tubo orbi L L imponitur &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0425-05a" corresp="note-0425-05" type="noteAnchor" />
vitro D C obtegitur, quo omnis communicatio tollitur in-<lb />ter aërem exteriorem &amp; </s>
          <s xml:space="preserve">vas V, quod cum cavitate tubi AB <lb />communicatur. </s>
          <s xml:space="preserve">Aër in hoc tubo elaſticitate ſua impedit, <lb />ne mercurius preſſione aëris externi, in tubum adſcendat; <lb /></s>
          <s xml:space="preserve">aër etiam recipienti DC incluſus elaſticitate ſuſtinet mer-<lb />curium in tubo g e <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ex vaſe DC aër exhauriatur; </s>
          <s xml:space="preserve">dum
<ptr xml:id="note-0425-06a" corresp="note-0425-06" type="noteAnchor" />
denſitas minuitur, elaſticitas etiam decreſcit <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">minor
<ptr xml:id="note-0425-07a" corresp="note-0425-07" type="noteAnchor" />
</s>
          <pb facs="0426" n="316" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
eſt vis cum qua mercurius in tubo g e ſuſtinetur, deſcendit <lb />ergo hydrargyrum. </s>
          <s xml:space="preserve">Eodem tempore reſiſtentiam in tubo <lb />AB vincit preſſio aëris externi, &amp; </s>
          <s xml:space="preserve">in tubum mercurius ad-<lb />ſcendit. </s>
          <s xml:space="preserve">Diminutio elaſticitatis in tubo AB, &amp; </s>
          <s xml:space="preserve">in vaſe <lb />BC, eadem eſt, &amp; </s>
          <s xml:space="preserve">effectus diminutionis in utroque caſu <lb />idem: </s>
          <s xml:space="preserve">idcirco tantum in tubo e g deſcendit mercurius, <lb />quantum adſcendit in tubum AB, quod cum Experimen-<lb />to congruit. </s>
          <s xml:space="preserve">Elevatur hac methodo mercurius ad f, dum <lb />tubus g e fere omnino vacuus remanet; </s>
          <s xml:space="preserve">admiſſo iterum <lb />aëre, mercurius in tubum g e adſcendit, dum in tubo AB <lb />deprimitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0425-03" corresp="note-0425-03a" place="margin">1103.</note>
              <note xml:space="preserve" xml:id="note-0425-04" corresp="note-0425-04a" place="margin">TAB. XXXIX. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0425-05" corresp="note-0425-05a" place="margin">* 1056.</note>
              <note xml:space="preserve" xml:id="note-0425-06" corresp="note-0425-06a" place="margin">* 1073.</note>
              <note xml:space="preserve" xml:id="note-0425-07" corresp="note-0425-07a" place="margin">* 1071.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Detur antlia A, cujus embolus fundo applicetur, tubus <lb />
<ptr xml:id="note-0426-01a" corresp="note-0426-01" type="noteAnchor" />
cum antlia cohærens aquâ immergatur; </s>
          <s xml:space="preserve">elevetur embolus, <lb />
<ptr xml:id="note-0426-02a" corresp="note-0426-02" type="noteAnchor" />
inſequetur illum aqua; </s>
          <s xml:space="preserve">hæcque cavum inter antliæ fundum <lb />&amp; </s>
          <s xml:space="preserve">embolum implebit, quod ex preſſione aëris exterioris o-<lb />ritur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0426-01" corresp="note-0426-01a" place="margin">1104.</note>
              <note xml:space="preserve" xml:id="note-0426-02" corresp="note-0426-02a" place="margin">TAB. XLII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In loco aëre vacuo non adſcendit aqua in antliam, cum <lb />hæc deficiat preſſio.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Cum antlia A, quæ cum operculo, quo vitrum exhau-<lb />
<ptr xml:id="note-0426-03a" corresp="note-0426-03" type="noteAnchor" />
riendum obtegitur, cohæret, conjungatur tubus vitreus b c, <lb />
<ptr xml:id="note-0426-04a" corresp="note-0426-04" type="noteAnchor" />
cujus extremitas c infra aquæ, vaſe V contentæ, ſuperfici-<lb />em deſcendit; </s>
          <s xml:space="preserve">fundo antliæ embolus applicetur, &amp; </s>
          <s xml:space="preserve">ex re-<lb />cipiente aër exhauriatur. </s>
          <s xml:space="preserve">Si embolus elevetur, non adſcen-<lb />det aqua.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0426-03" corresp="note-0426-03a" place="margin">1105.</note>
              <note xml:space="preserve" xml:id="note-0426-04" corresp="note-0426-04a" place="margin">TAB. XLII. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Vis, qua aër in corpora premit, hæc ſæpe diſrumpit, <lb />
<ptr xml:id="note-0426-05a" corresp="note-0426-05" type="noteAnchor" />
quando preſſio ab omni parte non eſt æqualis. </s>
          <s xml:space="preserve">Cylindrus <lb />
<ptr xml:id="note-0426-06a" corresp="note-0426-06" type="noteAnchor" />
æneus, aut conus truncatus, A laminâ vitreâ planâ obtegitur, <lb />ſi ex cylindro aër extrahatur, preſſione aëris externi con-<lb />fringitur lamina vitrea, &amp; </s>
          <s xml:space="preserve">in fruſta exigua quaſi in pulverem <lb />redigitur, ſi non nimium tenuis ſit; </s>
          <s xml:space="preserve">nimis craſſa preſſionem <lb />ſuſtinet, &amp; </s>
          <s xml:space="preserve">non disrumpitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0426-05" corresp="note-0426-05a" place="margin">1106.</note>
              <note xml:space="preserve" xml:id="note-0426-06" corresp="note-0426-06a" place="margin">TAB. XLI. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0427" n="317" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XVII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Detur antlia A diametri trium partium quartarum unius <lb />
<ptr xml:id="note-0427-01a" corresp="note-0427-01" type="noteAnchor" />
pollicis; </s>
          <s xml:space="preserve">applicetur embolus fundo antliæ, &amp; </s>
          <s xml:space="preserve">apertura in <lb />
<ptr xml:id="note-0427-02a" corresp="note-0427-02" type="noteAnchor" />
fundo antliæ claudatur; </s>
          <s xml:space="preserve">ſi pondus ſex librarum P cum an-<lb />tlia conjungatur, &amp; </s>
          <s xml:space="preserve">manubrium B emboli ſuſtineatur, non <lb />deſcendit antlia; </s>
          <s xml:space="preserve">deſcendere enim non poteſt, niſi pondus <lb />ſuperet aëris preſſionem, &amp; </s>
          <s xml:space="preserve">emboli attritum; </s>
          <s xml:space="preserve">illa vero <lb />preſſio ſola ſex libras excedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0427-01" corresp="note-0427-01a" place="margin">1107.</note>
              <note xml:space="preserve" xml:id="note-0427-02" corresp="note-0427-02a" place="margin">TAB. XLII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum.</hi> 10.</head>
        <p>
          <s xml:space="preserve">In loco aëre vacuo ſolo pondere p, quo attritus emboli <lb />
<ptr xml:id="note-0427-03a" corresp="note-0427-03" type="noteAnchor" />
ſuperatur, deſcendit antlia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0427-03" corresp="note-0427-03a" place="margin">1108.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XLII. <lb />fig 1.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 11.</head>
        <p>
          <s xml:space="preserve">Magis ſenſibilem videmus effectum compreſſionis aëris, <lb />
<ptr xml:id="note-0427-05a" corresp="note-0427-05" type="noteAnchor" />
quando duo ſphæræ ſegmenta H &amp; </s>
          <s xml:space="preserve">I junguntur. </s>
          <s xml:space="preserve">Sit utri-<lb />
<ptr xml:id="note-0427-06a" corresp="note-0427-06" type="noteAnchor" />
uſque ora polita, &amp; </s>
          <s xml:space="preserve">congruant hæ inter ſe, cerâque cir-<lb />cumpoſitâ aër excludatur. </s>
          <s xml:space="preserve">In ſegmento H epiſtomium da-<lb />tur, quo ſegmenta conjuncta antliæ pneumaticæ applican-<lb />tur, &amp; </s>
          <s xml:space="preserve">quod exhauſto aëre clauditur. </s>
          <s xml:space="preserve">Annulo A ſegmen-<lb />ta ſuſpenduntur, &amp; </s>
          <s xml:space="preserve">ope annuli Q his pondera appendun-<lb />tur, quæ tabulæ T imponuntur. </s>
          <s xml:space="preserve">Poſito ſegmentorum dia-<lb />metro trium pollicum cum ſemiſſe, pondus centum &amp; </s>
          <s xml:space="preserve">cir-<lb />citer quadraginta librarum requiritur ut ſegmenta ſeparentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0427-05" corresp="note-0427-05a" place="margin">1109.</note>
              <note xml:space="preserve" xml:id="note-0427-06" corresp="note-0427-06a" place="margin">TAB. XLII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 12.</head>
        <p>
          <s xml:space="preserve">Ut in Experimento præcedenti ſegmenta ſphæræ jungan-<lb />tur, &amp; </s>
          <s xml:space="preserve">aër exhauriatur; </s>
          <s xml:space="preserve">ſi in loco aëre vacuo ſuſpenſa fue-<lb />
<ptr xml:id="note-0427-07a" corresp="note-0427-07" type="noteAnchor" />
rint pondere exiguo P, quo ceræ cohæſio ſuperatur, ſe-<lb />
<ptr xml:id="note-0427-08a" corresp="note-0427-08" type="noteAnchor" />
parantur. </s>
          <s xml:space="preserve">In hoc Experimento cum orbe L L conjungitur <lb />pyxis cum coriis <ptr type="noteAnchor" />, quam filum æneum EF, cui pondus ap-
penditur, trajicit. </s>
          <s xml:space="preserve">Ne, caſu ſegmenti inferioris, vitrum, <lb />
<ptr xml:id="note-0427-09a" corresp="note-0427-09" type="noteAnchor" />
in quo Experimentum fit, frangatur, cylindro ligneo cavo <lb />M hoc ſegmentum recipitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0427-07" corresp="note-0427-07a" place="margin">1110.</note>
              <note xml:space="preserve" xml:id="note-0427-08" corresp="note-0427-08a" place="margin">TAB. XLIII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0427-09" corresp="note-0427-09a" place="margin">* 1096.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vi eâdem, quæ in Experimento 11. </s>
          <s xml:space="preserve">deſideratur, ad ſe-<lb />gmenta memorata ſeparanda, hæc a ſe mutuo divellun-<lb />tur, quando, vaſe incluſa, relicto inter ſegmenta aëre <lb />in ſtatu aëris externi, &amp; </s>
          <s xml:space="preserve">clauſo epiſtomio, in vaſe aër ad
</s>
          <pb facs="0428" n="318" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
denſitatem duplam redigitur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Machina</hi>,</head>
        <head rend="italics" xml:space="preserve">Qua in Aëre compreſſo Experimenta inſtituuntur.</head>
        <p>
          <s xml:space="preserve">Tabulæ ligneæ a a, longitudinis circiter quindecim &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0428-01a" corresp="note-0428-01" type="noteAnchor" />
latitudinis decem pollicum, imponitur orbis æneus N, dia-<lb />
<ptr xml:id="note-0428-02a" corresp="note-0428-02" type="noteAnchor" />
metri quinque aut ſex pollicum, cujus figura ſeparata da-<lb />tur in N Tab. </s>
          <s xml:space="preserve">42. </s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve">; cum hoc, ab inferiori parte, co-<lb />hæret cauda, aut prominentia, cylindrica P, quæ non <lb />perforatur, &amp; </s>
          <s xml:space="preserve">tabulam a a trajicit. </s>
          <s xml:space="preserve">Huic orbi imponitur, &amp; </s>
          <s xml:space="preserve"><lb />cum ipſo cochleis jungitur vas æneum VV, altitudinis cir-<lb />citer decem pollicum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0428-01" corresp="note-0428-01a" place="margin">1111.</note>
              <note xml:space="preserve" xml:id="note-0428-02" corresp="note-0428-02a" place="margin">TAB. XLIV. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Obtegitur vas operculo D. </s>
          <s xml:space="preserve">Columnæ CS, CS, cum ta-<lb />bula a a cohærent, trajiciuntque lignum d e, quo opercu-<lb />lum D arcte cum vaſe conjungitur, ope cochlearum f f. </s>
          <s xml:space="preserve">Ta-<lb />lis arcta compreſſio maxime eſt neceſſaria, ingreſſuſque aë-<lb />ris interpoſitis coriis, oleo imbutis, cohibetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Operculi ſeparata Figura datur in D, Tab. </s>
          <s xml:space="preserve">42. </s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve">; <lb />cum hoc cohæret pyxis cum coriis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ne ſuperficiei ni-
<ptr xml:id="note-0428-03a" corresp="note-0428-03" type="noteAnchor" />
mis parvæ applicetur lignum d e, circumdatur pyxis annulo, <lb />qui cum operculo cohæret &amp; </s>
          <s xml:space="preserve">diametrum habet diametro <lb />operculi fere æqualem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0428-03" corresp="note-0428-03a" place="margin">* 1096.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Trajicit pyxidem cum coriis filum æneum perforatum C, <lb />cum quo cohæret epiſtomium B.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Comprimitur aër in vaſe, jungendo epiſtomio poſtremo <lb />
<ptr xml:id="note-0428-04a" corresp="note-0428-04" type="noteAnchor" />
memorato antliam AB: </s>
          <s xml:space="preserve">cum hac conjunctum datur epiſto-<lb />
<ptr xml:id="note-0428-05a" corresp="note-0428-05" type="noteAnchor" />
mium, in quo, præter foramen ſolitum, aliud obliquum <lb />datur, quod ad f pervenit, &amp; </s>
          <s xml:space="preserve">quo, clauſa communicatione <lb />inter vas &amp; </s>
          <s xml:space="preserve">antliam, hæc cum aëre exteriori communicatur, <lb />&amp; </s>
          <s xml:space="preserve">aëre impletur elevando embolum. </s>
          <s xml:space="preserve">Aperta communica-<lb />tione inter vas &amp; </s>
          <s xml:space="preserve">antliam, deſcenſu emboli aër in antlia con-<lb />tentus vaſe intruditur; </s>
          <s xml:space="preserve">hacque ſæpius repetita operatione <lb />tandem ad propoſitam denſitatem redigitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0428-04" corresp="note-0428-04a" place="margin">1112.</note>
              <note xml:space="preserve" xml:id="note-0428-05" corresp="note-0428-05a" place="margin">TAB. XLII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Indice mercuriali denſitas aëris determinatur. </s>
          <s xml:space="preserve">Eſt index hic <lb />tubus vitreus, admodum anguſtus, qui cohæret cum fruſto <lb />æneo, quod cochleis inter epiſtomia Machinæ &amp; </s>
          <s xml:space="preserve">Antliæ <lb />aptatur. </s>
          <s xml:space="preserve">Dum aër in Machina comprimitur, mercurius in
</s>
          <pb facs="0429" />
          <s xml:space="preserve">
</s>
          <pb facs="0429a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0429a-01a" corresp="fig-0429a-01" type="figureAnchor" />
</s>
          <pb facs="0430" />
          <s xml:space="preserve">
</s>
          <pb facs="0431" n="319" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XVII.</fw>
tubo comprimit aërem in poſtica tubi parte, &amp; </s>
          <s xml:space="preserve">hæc <lb />compreſſio, quæ æqualis eſt compreſſioni in vaſe, facile men-<lb />ſuratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0429a-01" corresp="fig-0429a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0429a-01" />
                <label>0429a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 13.</head>
        <p>
          <s xml:space="preserve">Ut nunc in aëre compreſſo ſegmenta ſphærica ſeparen-<lb />
<ptr xml:id="note-0431-01a" corresp="note-0431-01" type="noteAnchor" />
tur, ſuſtentaculo ML ſegmentum I cum orbe N conjun-<lb />
<ptr xml:id="note-0431-02a" corresp="note-0431-02" type="noteAnchor" />
gitur, ope cochlearum in M &amp; </s>
          <s xml:space="preserve">L. </s>
          <s xml:space="preserve">Eodem modo, co-<lb />chleis in F &amp; </s>
          <s xml:space="preserve">E, ſegmentum H cum filo C cohæret. </s>
          <s xml:space="preserve">Se-<lb />gmenta ſibi mutu o applicantur, &amp; </s>
          <s xml:space="preserve">cerâ circumdantur. </s>
          <s xml:space="preserve">De ce-<lb />tero, quæ in deſcriptione machinæ dicta ſunt, obſervantur, aër-<lb />que in vaſe comprimitur, ut habeat denſitatem duplam illius <lb />quâm ex Atmoſphæræ compreſſione acquirit. </s>
          <s xml:space="preserve">In Pannulus Q <lb />orbi N annectitur, ut &amp; </s>
          <s xml:space="preserve">annulus A epiſtomio B. </s>
          <s xml:space="preserve">Invertitur ma-<lb />
<ptr xml:id="note-0431-03a" corresp="note-0431-03" type="noteAnchor" />
china, &amp; </s>
          <s xml:space="preserve">annulo Q ſuſpenditur; </s>
          <s xml:space="preserve">tabula T, cui pondera im-<lb />ponuntur, annulo A appenditur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ni pondera centum &amp; </s>
          <s xml:space="preserve"><lb />quadraginta libras circiter valeant, non ſeparantur ſegmen-<lb />ta. </s>
          <s xml:space="preserve">Ne nimium, in ſegmentorum ſeparatione, deſcendat <lb />tabula T, cavetur, quia cochleâ elevatur, &amp; </s>
          <s xml:space="preserve">deprimitur un-<lb />cus, cui appenditur annulus Q, quod commode fit, ſi cylin-<lb />drus ferreus cochleâ circumdatus, &amp; </s>
          <s xml:space="preserve">circa quem cochlea <lb />exterior movetur, trajiciat lignum, quod tripode ſuſtinetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0431-01" corresp="note-0431-01a" place="margin">1113.</note>
              <note xml:space="preserve" xml:id="note-0431-02" corresp="note-0431-02a" place="margin">TAB. XLII. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0431-03" corresp="note-0431-03a" place="margin">TAB. XLII. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quæ hìc repræſentatur Machina, vitrea eſt, ſed cùm mi-<lb />hi bis contigerit, in experimentis confractum fuiſſe tale vi-<lb />trum, cupreâ machinâ nunc utor.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 14.</head>
        <p>
          <s xml:space="preserve">Orbi LL machinæ pneumaticæ adaptetur tubus AB, <lb />
<ptr xml:id="note-0431-04a" corresp="note-0431-04" type="noteAnchor" />
epiſtomium in ſuperiori parte connexum habens, &amp; </s>
          <s xml:space="preserve">jun-<lb />
<ptr xml:id="note-0431-05a" corresp="note-0431-05" type="noteAnchor" />
ctus cum tubo minori ſupra orbem prominenti. </s>
          <s xml:space="preserve">Huic im-<lb />ponitur recipiens vitreus R, quo tubus prominens obtegi-<lb />tur. </s>
          <s xml:space="preserve">Extremitas B tubi A B, aquâ vaſe V contentâ, immer-<lb />gitur, &amp; </s>
          <s xml:space="preserve">evacuato recipiente R, epiſtomium aperitur; </s>
          <s xml:space="preserve">ma-<lb />gna cum vi in recipientem proſilit aqua, eadem preſſione, <lb />qua, in tubo aëre vacuo, ad altitudinem triginta duorum <lb />
<ptr xml:id="note-0431-06a" corresp="note-0431-06" type="noteAnchor" />
pedum ſuſtineri poteſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0431-04" corresp="note-0431-04a" place="margin">1114.</note>
              <note xml:space="preserve" xml:id="note-0431-05" corresp="note-0431-05a" place="margin">TAB. XLIII. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0431-06" corresp="note-0431-06a" n="*" anchored="true" place="margin">1059.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <note xml:space="preserve" place="margin">1115.</note>
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 15. <lb />
</head>
        <p>
          <s xml:space="preserve">Aëris elaſticitas eundem edit effectum. </s>
          <s xml:space="preserve">Detur vas æ-<lb />
<ptr xml:id="note-0431-08a" corresp="note-0431-08" type="noteAnchor" />
</s>
          <pb facs="0432" n="320" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
neum cylindricum V, exactiſſime clauſum; </s>
          <s xml:space="preserve">in fundo aper-<lb />tura datur, per quam aqua infunditur, &amp; </s>
          <s xml:space="preserve">quæ cochleâ clau-<lb />ditur. </s>
          <s xml:space="preserve">Superiori vaſis parti adferruminatur tubus ad fun-<lb />dum vaſis fere pertingens, &amp; </s>
          <s xml:space="preserve">cui in extremitate extra vas <lb />prominenti epiſtomium jungitur (vide fig.</s>
          <s xml:space="preserve">4.)</s>
          <s xml:space="preserve">. </s>
          <s xml:space="preserve">Open co-<lb />chleæ adaptatur vas hocce inferiori parti orbis LL antliæ <lb />pueumaticæ, datur &amp; </s>
          <s xml:space="preserve">hic tubus prominens, qui recipienti <lb />R obtegitur. </s>
          <s xml:space="preserve">Si ex hoc aër exhauriatur, &amp; </s>
          <s xml:space="preserve">vas V circiter <lb />duabus partibus tertiis aquâ impletum ſit, aperto epiſtomio <lb />violenter in recipientem aqua proſiliet, exelaſticitate aëris, <lb />in ſuperiori parte vaſis V contenti. </s>
          <s xml:space="preserve">Aër hic in aquæ ſuper-<lb />ficiem premit, in tubo autem, aperto epiſtomio, preſſio mi-<lb />nor datur; </s>
          <s xml:space="preserve">tubum ideo aqua intrat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0431-08" corresp="note-0431-08a" place="margin">TAB. XLIII. <lb />. 3.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 16.</head>
        <p>
          <s xml:space="preserve">In ipſo aëre aperto violentiſſime proſiliet aqua ex vaſe V, <lb />
<ptr xml:id="note-0432-01a" corresp="note-0432-01" type="noteAnchor" />
ſi, hoc duabus partibus tertiis aqua repleto, aër in ſuperio-<lb />
<ptr xml:id="note-0432-02a" corresp="note-0432-02" type="noteAnchor" />
rem partem intrudatur, adhibitâ antliâ antea memora-<lb />tâ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0432-01" corresp="note-0432-01a" place="margin">1116.</note>
              <note xml:space="preserve" xml:id="note-0432-02" corresp="note-0432-02a" place="margin">TAB. XLIII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1112.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 17.</head>
        <p>
          <s xml:space="preserve">Vitrum R everſum aquâ vaſe V contentâ immergitur, <lb />
<ptr xml:id="note-0432-04a" corresp="note-0432-04" type="noteAnchor" />
aër aquam excludit, ad quamcunque profunditatem im-<lb />
<ptr xml:id="note-0432-05a" corresp="note-0432-05" type="noteAnchor" />
mergatur; </s>
          <s xml:space="preserve">quo tamen vitrum profundius deſcendit, eo <lb />etiam in minus ſpatium aër in hoc reducitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0432-04" corresp="note-0432-04a" place="margin">1117.</note>
              <note xml:space="preserve" xml:id="note-0432-05" corresp="note-0432-05a" place="margin">TAB. XLIV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hoc fundamento nituntur machinæ, quibus urinatores in <lb />
<ptr xml:id="note-0432-06a" corresp="note-0432-06" type="noteAnchor" />
mare deſcendunt. </s>
          <s xml:space="preserve">Campanæ ſpeciem referunt hæ, &amp; </s>
          <s xml:space="preserve">gravitate <lb />ſua deſcendunt; </s>
          <s xml:space="preserve">aqua ad ipſum urinatorem non pertingit; </s>
          <s xml:space="preserve">no-<lb />vus aër continuo huic mittitur, contentus in veſicis, funi al-<lb />ligatis, quas ad ſe trahit. </s>
          <s xml:space="preserve">Aër inſpiratione calefactus ad ſu-<lb />periorem partem machinæ adſcendit, &amp; </s>
          <s xml:space="preserve">per epiſtomium in <lb />eo loco expellitur, preſſione aquæ, quæ in inferiori par-<lb />te in aërem campana contentum premit, quæ preſſio <lb />vim ſuperat, qua aqua per epiſtomium deſcendere co-<lb />natur; </s>
          <s xml:space="preserve">preſſio enim fluidorum cum profunditate auge-<lb />tur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0432-06" corresp="note-0432-06a" place="margin">1118.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">* 743.</note>
        <pb facs="0433" />
        <pb facs="0433a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0433a-01" />
          <label>0433a-01</label>
        </figure>
        <pb facs="0434" />
        <pb facs="0435" n="321" />
        <fw type="head">MATHEMATICA. LIB. H. CAP. XVII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 18.</head>
        <p>
          <s xml:space="preserve">Ex vitro conflantur homuli altitudinis circiter unius pol-<lb />
<ptr xml:id="note-0435-01a" corresp="note-0435-01" type="noteAnchor" />
licis cum ſemiſſe; </s>
          <s xml:space="preserve">cavi hi ſunt, &amp; </s>
          <s xml:space="preserve">aëre replentur, foramen-<lb />
<ptr xml:id="note-0435-02a" corresp="note-0435-02" type="noteAnchor" />
que exiguum in pedum altero datur. </s>
          <s xml:space="preserve">Ut aquâ paululum le-<lb />viores ſint etiam requiritur. </s>
          <s xml:space="preserve">Aquâ vaſe <hi rend="small caps">A</hi>B contentâ im-<lb />merguntur. </s>
          <s xml:space="preserve">Vas hoc altitudinem habet unius pedis, aut <lb />quindecim pollicum, &amp; </s>
          <s xml:space="preserve">veſicâ obtegitur, quæ ſuperiori <lb />vaſis parti firmiter alligatur, relictâ aëris bullâ inter veſi-<lb />cam &amp; </s>
          <s xml:space="preserve">aquæ ſuperficiem. </s>
          <s xml:space="preserve">Si digito veſica comprimatur, <lb />in minus ſpatium aër memoratus redigitur, &amp; </s>
          <s xml:space="preserve">aquæ ſuper-<lb />ficies magis comprimitur; </s>
          <s xml:space="preserve">aqua magis compreſſa homun-<lb />culos intrat per foramina in illorum pedibus, &amp; </s>
          <s xml:space="preserve">aërem <lb />in ipſis magis comprimit. </s>
          <s xml:space="preserve">Graviores homuli facti fundum <lb />vafis petunt, citius aut lentius pro foraminis magnitudine, <lb />etiam pro gravitate ſpecifica homuncionum magis aut <lb />minus cum aquæ gravitate ſpecifica congruente. </s>
          <s xml:space="preserve">Subla-<lb />to digito minus in homulis compreſſus aër ſeſe expandit, <lb />&amp; </s>
          <s xml:space="preserve">aquam expellit, iterumque ad aquæ ſuperficiem adſcen-<lb />dunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0435-01" corresp="note-0435-01a" place="margin">1119.</note>
              <note xml:space="preserve" xml:id="note-0435-02" corresp="note-0435-02a" place="margin">TAB. XLIV. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 19.</head>
        <p>
          <s xml:space="preserve">Animalia ad vivendum aëre indigent. </s>
          <s xml:space="preserve">Si animal quod-<lb />
<ptr xml:id="note-0435-03a" corresp="note-0435-03" type="noteAnchor" />
cunque vitro V includudatur, &amp; </s>
          <s xml:space="preserve">aër exhauriatur, ſtatim vio-<lb />
<ptr xml:id="note-0435-04a" corresp="note-0435-04" type="noteAnchor" />
lento motu agitatur, &amp; </s>
          <s xml:space="preserve">ni ſubito aër iterum admittatur, <lb />vitæ expers cadit. </s>
          <s xml:space="preserve">Dantur quædam animalia quæ diutius <lb />in loco evacuato vivnt. </s>
          <s xml:space="preserve">Inflantur animalium corpora, <lb />dum, ſublatâ externâ preſſione, aër, aut fluidum quod-<lb />cunque elaſticum, in vaſis ſeſe expandit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0435-03" corresp="note-0435-03a" place="margin">1120.</note>
              <note xml:space="preserve" xml:id="note-0435-04" corresp="note-0435-04a" place="margin">TAB. XLIV. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 20.</head>
        <p>
          <s xml:space="preserve">Quidam etiam piſces ſine aëre vivere nequeunt; </s>
          <s xml:space="preserve">in aliis <lb />
<ptr xml:id="note-0435-05a" corresp="note-0435-05" type="noteAnchor" />
nulla fere obſervatur mutatio, niſi quod oculi inflentur. </s>
          <s xml:space="preserve">Ex-<lb />
<ptr xml:id="note-0435-06a" corresp="note-0435-06" type="noteAnchor" />
perimenta circa piſces inſtituenda ſunt in vitro V, quod <lb />orbi antliæ pneumaticæ imponitur, &amp; </s>
          <s xml:space="preserve">foramini, per quod <lb />aër exhauritur, jungitur tubus ad vitri partem ſuperiorem <lb />fere pertingens; </s>
          <s xml:space="preserve">aqua infunditur; </s>
          <s xml:space="preserve">piſces in hanc injiciun-<lb />tur; </s>
          <s xml:space="preserve">operculo vitrum clauditur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pars vitri ſuperior eva-
</s>
          <pb facs="0436" n="322" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cuatur. </s>
          <s xml:space="preserve">Sublata aëris preſſione in aquæ ſuperficiem ſeſe aër <lb />in piſcis corpore expandit, quo hic levior factus in aquam <lb />deſcendere nequit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0435-05" corresp="note-0435-05a" place="margin">1121.</note>
              <note xml:space="preserve" xml:id="note-0435-06" corresp="note-0435-06a" place="margin">TAB. XLIV <lb />fig. 44</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 21.</head>
        <p>
          <s xml:space="preserve">In aëre compreſſo Experimenta circa animalia inſtituun-<lb />
<ptr xml:id="note-0436-01a" corresp="note-0436-01" type="noteAnchor" />
tur, ope machinæ ſuperius deſcriptæ <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In hoc caſu non
<ptr xml:id="note-0436-02a" corresp="note-0436-02" type="noteAnchor" />
ſubito animalia moriuntur, quia compreſſione aëris va-<lb />
<ptr xml:id="note-0436-03a" corresp="note-0436-03" type="noteAnchor" />
ſa in corpore non franguntur, ſi tamen diutius in tali aëre <lb />degant, noxius illis eſt, &amp; </s>
          <s xml:space="preserve">etiam in compreſſione majori, <lb />brevi tempore pereunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0436-01" corresp="note-0436-01a" place="margin">1122.</note>
              <note xml:space="preserve" xml:id="note-0436-02" corresp="note-0436-02a" place="margin">TAB. XLIV. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0436-03" corresp="note-0436-03a" n="*" anchored="true" place="margin">1111.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 22.</head>
        <p>
          <s xml:space="preserve">Fluida pleraque aërem, aut aliud fluidum elaſticum con-<lb />
<ptr xml:id="note-0436-04a" corresp="note-0436-04" type="noteAnchor" />
tinent; </s>
          <s xml:space="preserve">quando vitro obteguntur, &amp; </s>
          <s xml:space="preserve">aër ex hoc extrahitur <lb />fluidum elaſticum ſeſe ſeparat, dilatat &amp; </s>
          <s xml:space="preserve">exit. </s>
          <s xml:space="preserve">In hoc caſu <lb />ſæpiſſime fluidi violentiſſimam obſervamus ebullitionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0436-04" corresp="note-0436-04a" place="margin">1123.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVIII.</head>
        <head xml:space="preserve">Variarum Machinarum, quarum Actio ab Aëre <lb />pendet, Deſcriptio, &amp; harum Effectuum <lb />Explicatio.</head>
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">TUbi incurvi a S b extremitas a aquâ immergitur, dum <lb />
<ptr xml:id="note-0436-05a" corresp="note-0436-05" type="noteAnchor" />
extremitas b infra aquæ ſuperficiem deſcendit. </s>
          <s xml:space="preserve">Siſu-<lb />
<ptr xml:id="note-0436-06a" corresp="note-0436-06" type="noteAnchor" />
gendo, aut quocunque alio modo, aëre evacuetur tubus, <lb />fluet aqua per b. </s>
          <s xml:space="preserve">Hæc machina ſipho vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0436-05" corresp="note-0436-05a" place="margin">1124.</note>
              <note xml:space="preserve" xml:id="note-0436-06" corresp="note-0436-06a" place="margin">TAB. XLV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hujus effectus a preſſione aëris pendet; </s>
          <s xml:space="preserve">qui aquam in <lb />
<ptr xml:id="note-0436-07a" corresp="note-0436-07" type="noteAnchor" />
ſiphonem pellit, premens in ſuperficiem aquæ vaſe contentæ; <lb /></s>
          <s xml:space="preserve">premit etiam aër in aquam ex orificio b exeuntem, illam-<lb />que ſuſtinet; </s>
          <s xml:space="preserve">preſſiones hæ ſunt æquales, &amp; </s>
          <s xml:space="preserve">in ſuperiori <lb />parte ſiphonis contrarie agunt, ibique valent Atmoſphæræ <lb />pondus, demto pondere columnarum aquearum, quæ a <lb />preſſionibus ſuſtinentur. </s>
          <s xml:space="preserve">Columna aquea in crure S b al-<lb />titudine oppoſitam columnam ſuperat; </s>
          <s xml:space="preserve">ergo a parte b S ma-
</s>
          <pb facs="0437" />
          <s xml:space="preserve">
</s>
          <pb facs="0437a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0437a-01a" corresp="fig-0437a-01" type="figureAnchor" />
</s>
          <pb facs="0438" />
          <s xml:space="preserve">
</s>
          <pb facs="0439" n="323" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XVIII.</fw>
gis aëris preſſio minuitur, &amp; </s>
          <s xml:space="preserve">preſſio oppoſita hanc vincit, <lb />fluitque aqua b verſus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0436-07" corresp="note-0436-07a" place="margin">1125.</note>
              <figure xml:id="fig-0437a-01" corresp="fig-0437a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0437a-01" />
                <label>0437a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Sipho memoratus hoc incommodi habet, quod, ab effe-<lb />
<ptr xml:id="note-0439-01a" corresp="note-0439-01" type="noteAnchor" />
ctu ſi ceſſaverit, non iterum aqua fluat, niſi aëre tubus de <lb />novo evacuetur. </s>
          <s xml:space="preserve">Corrigitur defectus hic, conſtruendo ſipho-<lb />
<ptr xml:id="note-0439-02a" corresp="note-0439-02" type="noteAnchor" />
nem figuræ a S b, cujus cruraſunt æqualia &amp; </s>
          <s xml:space="preserve">incurvata; </s>
          <s xml:space="preserve">ſi e-<lb />nim aquâ impleatur ſipho, &amp; </s>
          <s xml:space="preserve">crus unum aquâ immergatur, ut <lb />aqua orificium ſuperet, ex ratione, in explicatione præce-<lb />dentis Experimenti data, fluet aqua per crus alterum. <lb /></s>
          <s xml:space="preserve">Crura cùm incurvata ſint, non evacuatur ſipho, quando flu-<lb />xus aquæ ceſſat, &amp; </s>
          <s xml:space="preserve">ſemel impleto ſiphone, ſemper ad effe-<lb />ctum ſuum producendum paratus eſt. </s>
          <s xml:space="preserve">Aqua per illum <lb />fluit &amp; </s>
          <s xml:space="preserve">refluit pro majori altitudine ab una aut alia parte.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0439-01" corresp="note-0439-01a" place="margin">1126.</note>
              <note xml:space="preserve" xml:id="note-0439-02" corresp="note-0439-02a" place="margin">TAB. XLIV. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Sipho</hi>,</head>
        <head xml:space="preserve">Quo aqua elevatur.</head>
        <p>
          <s xml:space="preserve">Eodem, cum machinis præcedentibus, nititur fundamen-<lb />
<ptr xml:id="note-0439-03a" corresp="note-0439-03" type="noteAnchor" />
to ſipho ad aquam in receptaculum evehendam adaptatus. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0439-04a" corresp="note-0439-04" type="noteAnchor" />
Effectus hujus ſiphonis ſenſibilis redditur ope machinæ, con-<lb />ſtantis ex duobus globis vitreis H &amp; </s>
          <s xml:space="preserve">I, qui junguntur tubo <lb />CDE. </s>
          <s xml:space="preserve">Globus I cum aqua evehenda communicationem <lb />habet tubo AB, qui ad globi ſummitatem fere pertingit. <lb /></s>
          <s xml:space="preserve">In inferiori parte jungitur globo H tubus FG, longitudi-<lb />ne tubum integrum AB æquans.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0439-03" corresp="note-0439-03a" place="margin">1127.</note>
              <note xml:space="preserve" xml:id="note-0439-04" corresp="note-0439-04a" place="margin">TAB. XLV. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus H aquâ impletur ope infundibuli, &amp; </s>
          <s xml:space="preserve">hoc obtu-<lb />ratur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In machinis quæ ad uſum applicantur ex receptaculo, <lb />aquam evehendam continenti, quocunque modo, hæc in <lb />vas H deducitur, &amp; </s>
          <s xml:space="preserve">epiſtomio inter vas &amp; </s>
          <s xml:space="preserve">receptaculum <lb />clauditur communicatio.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Aperto epiſtomio G fluet aqua, &amp; </s>
          <s xml:space="preserve">per tubum AB in <lb />
<ptr xml:id="note-0439-05a" corresp="note-0439-05" type="noteAnchor" />
vas I adſcendet; </s>
          <s xml:space="preserve">quo repleto deducitur aqua in locum quem-<lb />cunque, &amp; </s>
          <s xml:space="preserve">repetita machinæ operatione continuatur aquæ <lb />elevatio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0439-05" corresp="note-0439-05a" place="margin">1128.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0440" n="324" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Aperto epiſtomio G, premit aër in aquam ex tubo FG <lb />
<ptr xml:id="note-0440-01a" corresp="note-0440-01" type="noteAnchor" />
exeuntem; </s>
          <s xml:space="preserve">premit etiam aër in ſuperficiem aquæ in rece-<lb />ptaculo, qua preſſione in tubo AB ſuſtinetur. </s>
          <s xml:space="preserve">Preſſio-<lb />nes hæ ſunt æquales, &amp; </s>
          <s xml:space="preserve">ab hiſce demtis aquæ columnis <lb />quas ſuſtinent, dantur vires quibus agunt in aërem, in <lb />yaſorum partibus ſuperioribus, &amp; </s>
          <s xml:space="preserve">tubo CDE, con-<lb />tentum. </s>
          <s xml:space="preserve">Columna FG, quia ei ſuperadditur aquæ <lb />altitudo in vaſe H, ſemper ſuperat columnam in tubo <lb />AB; </s>
          <s xml:space="preserve">preſſio ergo in G alia magis minuitur &amp; </s>
          <s xml:space="preserve">ab ipſa ſu-<lb />peratur, adſcenditque aqua per tubum AB, deſcendit ve-<lb />ro per FG.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0440-01" corresp="note-0440-01a" place="margin">1129.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Antliæ</hi> <hi rend="small caps">Vulgares</hi>.</head>
        <p>
          <s xml:space="preserve">Ut antliarum vulgarium actio &amp; </s>
          <s xml:space="preserve">effectus ante oculos po-<lb />
<ptr xml:id="note-0440-02a" corresp="note-0440-02" type="noteAnchor" />
natur, conſtruitur antlia parva ex vitro. </s>
          <s xml:space="preserve">Sit AB cylin-<lb />
<ptr xml:id="note-0440-03a" corresp="note-0440-03" type="noteAnchor" />
drus vitreus longitudinis ſex aut ſeptem pollicum, &amp; </s>
          <s xml:space="preserve">cujus <lb />diameter ſit unius pollicis cum ſemiſſe. </s>
          <s xml:space="preserve">In ſundo ei jungi-<lb />tur tubus cujuſcunque longitudinis CD. </s>
          <s xml:space="preserve">Hujus apertura <lb />ſuperior clauditur globo plumbeo ita, ut aqua ex cylindro <lb />AB defcendere nequeat, in hunc autem adſcendere facile poſ-<lb />ſit elevando globum, quo loco valvulæ utimur. </s>
          <s xml:space="preserve">Embolus in cy-<lb />lindro AB movetur, qui corio circumdatus hujus capacita-<lb />tem exactè implet: </s>
          <s xml:space="preserve">datur in embolo foramen, quod etiam, loco <lb />valvulæ, globo obturatur, ita ut per embolum aqua ad-<lb />ſcendere, deſcendere non verò poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0440-02" corresp="note-0440-02a" place="margin">1130.</note>
              <note xml:space="preserve" xml:id="note-0440-03" corresp="note-0440-03a" place="margin">TAB. XLV. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Fundo cylindri admoveatur embolus, huic ſuperinfun-<lb />
<ptr xml:id="note-0440-04a" corresp="note-0440-04" type="noteAnchor" />
datur aqua, ut aëris tranſitus cohibeatur, ſi aquâ immer-<lb />gatur extremitas D tubi CD, &amp; </s>
          <s xml:space="preserve">elevetur embolus, adſcen-<lb />det aqua in cylindrum AB <ptr type="noteAnchor" />, ex quo deſcendere nequit;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0440-05a" corresp="note-0440-05" type="noteAnchor" />
quare per embolum tranſit, quando hic deſcendit. </s>
          <s xml:space="preserve">Elevato <lb />iterum embolo novâ aquâ cylindrus repletur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">prima in <lb />vas ligneum F cum cylindro vitreo cohærens elevatur, ex <lb />quo per tubum G fluit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0440-04" corresp="note-0440-04a" place="margin">1131.</note>
              <note xml:space="preserve" xml:id="note-0440-05" corresp="note-0440-05a" n="*" anchored="true" place="margin">1104.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum omnium machinarum in hoc capite deſcriptarum <lb />
<ptr xml:id="note-0440-06a" corresp="note-0440-06" type="noteAnchor" />
effectus ab Atmoſphæræ preſſione pendeant, non multum
</s>
          <pb facs="0441" />
          <s xml:space="preserve">
<pb facs="0441a" />
<ptr xml:id="fig-0441a-01a" corresp="fig-0441a-01" type="figureAnchor" />
<pb facs="0442" />
<pb facs="0443" n="325" /><fw type="head">MATHEMATICA. LIB. H. CAP. XVIII.</fw>
ultra triginta duos pedes in hiſce machinis aqua adſcen-<lb />dit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0440-06" corresp="note-0440-06a" place="margin">1132.</note>
              <figure xml:id="fig-0441a-01" corresp="fig-0441a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0441a-01" />
                <label>0441a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1059.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Fonticulus</hi> <hi rend="small caps">Heronis</hi>.</head>
        <p>
          <s xml:space="preserve">Fonticuli varii dantur Heronis dicti; </s>
          <s xml:space="preserve">unius conſtructio-<lb />
<ptr xml:id="note-0443-02a" corresp="note-0443-02" type="noteAnchor" />
nem explicabo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0443-02" corresp="note-0443-02a" place="margin">1133.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XLV. <lb />fig. 4.</note>
        <p>
          <s xml:space="preserve">Vaſa elliptica duo æqualia AB &amp; </s>
          <s xml:space="preserve">CD, ab omni parte <lb />exacte clauſa, ex ære conſtruuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In utroque datur ſeparatio per centrum ellipſeos tranſiens <lb />&amp; </s>
          <s xml:space="preserve">vas integrum in duas partes æquales ſecans.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Separatio l m n i in vaſe DC ad ellipſis axim perpendi-<lb />cularis eſt, ſeparatio c f g h alterius vaſis ad hunc axim in-<lb />clinatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Orâ elevatâ lamina ſuperior vaſis AB circumdatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quatuor tubis vaſa junguntur. </s>
          <s xml:space="preserve">Primus o p cavitatem B <lb />vaſis AB trajicit, &amp; </s>
          <s xml:space="preserve">nullam cum hac communicationem <lb />habet, &amp; </s>
          <s xml:space="preserve">ad fundum uſque cavitatis D fere deſcendit. </s>
          <s xml:space="preserve">Se-<lb />cundus s t ſuperiori parti cavitatis D adferruminatur, &amp; </s>
          <s xml:space="preserve"><lb />ad ſupremam partem cavitatis B adſcendit, non vero lami-<lb />nam ſupremam tangit. </s>
          <s xml:space="preserve">Tertius q r ab inferiori parte ca-<lb />vitatis B fere ad fundum cavitatis C pervenit. </s>
          <s xml:space="preserve">Quartus <lb />x v ſuperiori parti cavitatis cohæret, &amp; </s>
          <s xml:space="preserve">ad ſuperiorem par-<lb />tem cavitatis A fere pertingit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Datur tandem tubus z y, qui dum laminam ſupremam <lb />vaſis AB trajicit, &amp; </s>
          <s xml:space="preserve">illi adferruminatur, in cavitatem A <lb />deſcendit, ita ut extremitas z a fundo non multum di-<lb />ſtet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cavitatibus ſingulis junguntur epiſtomia; </s>
          <s xml:space="preserve">aut in illis aliæ <lb />aperturæ dantur, quæ cochleis, &amp; </s>
          <s xml:space="preserve">interpoſito corio, ob-<lb />turantur; </s>
          <s xml:space="preserve">harum præcipuus uſus eſt, ut exactè cavitates <lb />evacuentur, ne ab interiori parte æruginem contrahant.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Tubo o p aqua infundatur, qua cavitas D impletur; </s>
          <s xml:space="preserve">ad-<lb />
<ptr xml:id="note-0443-04a" corresp="note-0443-04" type="noteAnchor" />
ſcenditque aqua, ſi infuſio continuetur, per tubum s t, &amp; </s>
          <s xml:space="preserve"><lb />per q r in cavitatem C deſcendit, quæ etiam impletur, aë-<lb />re adſcendente per x v &amp; </s>
          <s xml:space="preserve">exunte per z y. </s>
          <s xml:space="preserve">Evertatur ma-
</s>
          <pb facs="0444" n="326" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
china, apertis epiſtomiis cavitatum C &amp; </s>
          <s xml:space="preserve">D, deſcendet a-<lb />qua in cavitates B &amp; </s>
          <s xml:space="preserve">A. </s>
          <s xml:space="preserve">Clauſis iterum epiſtomiis, ut &amp; </s>
          <s xml:space="preserve">a-<lb />pertura y tubi z y erigatur machina, &amp; </s>
          <s xml:space="preserve">infundatur aqua <lb />de novo tubo o p, donec ſuperficies ſuprema machinæ aqua <lb />obtegatur. </s>
          <s xml:space="preserve">Si nunc apertura y reſeratur, aqua in altum <lb />proſiliet fere ad altitudinem duplam totius machinæ, &amp; </s>
          <s xml:space="preserve"><lb />durabit aquæ motus donec cavitas C evacuata fuerit. </s>
          <s xml:space="preserve">Mi-<lb />nuetur continuo aquæ proſilientis altitudo, &amp; </s>
          <s xml:space="preserve">in fine non <lb />erit dupla diſtantiæ inter vaſa.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0443-04" corresp="note-0443-04a" place="margin">1134.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hujus machinæ effectus tribuendus eſt compreſſioni aëris <lb />
<ptr xml:id="note-0444-01a" corresp="note-0444-01" type="noteAnchor" />
in vaſis. </s>
          <s xml:space="preserve">Preſſio Atmoſphæræ in o &amp; </s>
          <s xml:space="preserve">in y, ut &amp; </s>
          <s xml:space="preserve">preſſiones inde <lb />oriundæ in ipſis vaſis ſunt æquales, &amp; </s>
          <s xml:space="preserve">hæ preſſiones ſeſe mutuo <lb />deſtruunt, quare in examine machinæ non conſiderantur. <lb /></s>
          <s xml:space="preserve">Quando ultimo loco aqua tubo op infunditur, in hoc ſuſtinetur <lb />preſſione aëris in cavitate D contenti, &amp; </s>
          <s xml:space="preserve">in ſuperficiem aquæ, <lb />quæ ad parvam in hac cavitate altitudinem datur, agentis; </s>
          <s xml:space="preserve">qui <lb />ergo aër comprimitur pondere aquæ ad altitudinem po: </s>
          <s xml:space="preserve">a-<lb />gitur de preſſione qua preſſio Atmoſphæræ ſuperatur. </s>
          <s xml:space="preserve">Aër, <lb />in ſuperiori parte cavitatis B contentus, per tubum s t, cum <lb />aëre memorato communicationem habet, &amp; </s>
          <s xml:space="preserve">æqualiter com-<lb />primitur, eademque cum vi agit in ſuperficiem aquæ in hac <lb />cavitate. </s>
          <s xml:space="preserve">Hæc preſſio ſuperaddenda eſt preſſioni ex aquæ <lb />altitudine, ut habeamus vim qua aër, qui continetur in <lb />cavitate C, comprimitur, ut &amp; </s>
          <s xml:space="preserve">ille qui inſuperiori parte <lb />cavitatis A hæret, propter communicationem per tubum <lb />x v. </s>
          <s xml:space="preserve">Preſſio ergo quæ in ſuperficiem aquæ, in hac cavitate A, <lb />datur, valet columnam aqueam, cujus altitudo eſt fere du-<lb />plum altitudinis totius machinæ; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò proſilit, quaſi a <lb />tali columna premeretur; </s>
          <s xml:space="preserve">id eſt, ad altitudinem non <lb />multum ab altitudine hujus columnæ differentem adſcen-<lb />dit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0444-01" corresp="note-0444-01a" place="margin">1135.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">301.</note>
        <p>
          <s xml:space="preserve">Minuitur continuo altitudo hæc; </s>
          <s xml:space="preserve">columnæ enim aqueæ, <lb />quæ aërem comprimunt, continuo minuuntur; </s>
          <s xml:space="preserve">quia aqua <lb />in cavitatibus C &amp; </s>
          <s xml:space="preserve">D elevatur, &amp; </s>
          <s xml:space="preserve">hujus altitudo minuitur <lb />in cavitate B. </s>
          <s xml:space="preserve">Eodem tempore etiam continuò evacuatur
</s>
          <pb facs="0445" />
          <s xml:space="preserve">
</s>
          <pb facs="0445a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0445a-01a" corresp="fig-0445a-01" type="figureAnchor" />
</s>
          <pb facs="0446" />
          <s xml:space="preserve">
</s>
          <pb facs="0447" n="327" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP XIX.</fw>
cavitas A, &amp; </s>
          <s xml:space="preserve">per majus ſpatium adſcendit aqua antequam <lb />ad y perveniat; </s>
          <s xml:space="preserve">ideoque ad minorem ſupra y altitudinem <lb />propellitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0445a-01" corresp="fig-0445a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0445a-01" />
                <label>0445a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIX.</head>
        <head xml:space="preserve">De Aëris motu undulatorio, ubi de Sono.</head>
        <p>
          <s xml:space="preserve">S l aër quocunque modo agitetur, particulæ motæ e loco <lb />
<ptr xml:id="note-0447-01a" corresp="note-0447-01" type="noteAnchor" />
recedunt, vicinaſque in minus ſpatium reducunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />aër dum in uno loco dilatatur in vicino comprimitur Aër <lb />compreſſus, dum inſtauratur elater, ad priſtinum non mo-<lb />do ſtatum redit, ſed ipſe dilatatur a particulis, motu ac-<lb />quiſito, ultra priſtinum ſtatum, a ſe invicem receden-<lb />tibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0447-01" corresp="note-0447-01a" place="margin">1136.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hoc motu, aër primo dilatatus, ad primum ſtatum redit, <lb />aërque alias partes verſus comprimitur. </s>
          <s xml:space="preserve">Hoc iterum obti-<lb />net dum aër ultimo compreſſus ſeſe expandit, quo de no-<lb />vo aër comprimitur. </s>
          <s xml:space="preserve">Oritur ergo ex agitatione quacunque <lb />motus analogus cum motu undæ in aquæ ſuperficie <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eodem
<ptr xml:id="note-0447-02a" corresp="note-0447-02" type="noteAnchor" />
nomine datur, &amp; </s>
          <s xml:space="preserve">vocatur aëris unda aër compreſſus cum <lb />inſequenti dilatato <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0447-02" corresp="note-0447-02a" n="*" anchored="true" place="margin">872.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">873.</note>
        <p>
          <s xml:space="preserve">Aër compreſſus omnes partes verſus dilatatur, &amp; </s>
          <s xml:space="preserve">motus <lb />
<ptr xml:id="note-0447-04a" corresp="note-0447-04" type="noteAnchor" />
undarum eſt motus ſphæræ ſeſe expandentis, eodem <lb />modo ac in ſuperficie aquæ undæ per circulum moven-<lb />tur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0447-04" corresp="note-0447-04a" place="margin">1137.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">875.</note>
        <p rend="italics">
          <s xml:space="preserve">Dum unda in aëre movetur ubicunque tranſit, particulæ <lb />
<ptr xml:id="note-0447-06a" corresp="note-0447-06" type="noteAnchor" />
e loco removentur &amp; </s>
          <s xml:space="preserve">ad hunc redeunt, ſpatiumque breviſſi-<lb />mum itu &amp; </s>
          <s xml:space="preserve">reditu percurrunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0447-06" corresp="note-0447-06a" place="margin">1138.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut hujus motus leges pateant, concipiamus particulas aë-<lb />
<ptr xml:id="note-0447-07a" corresp="note-0447-07" type="noteAnchor" />
reas ad diſtantias æquales in linearecta eſſe diſpoſitas a, b, c, d, <lb />&amp; </s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">f; </s>
          <s xml:space="preserve">moveatur unda per hanc lineam; </s>
          <s xml:space="preserve">ponamus autem il-<lb />lam perveniſſe inter b &amp; </s>
          <s xml:space="preserve">p; </s>
          <s xml:space="preserve">aërem dilatari inter b &amp; </s>
          <s xml:space="preserve">h, <lb />comprimi vero inter h &amp; </s>
          <s xml:space="preserve">p; </s>
          <s xml:space="preserve">ut hæc omnia in linea 1. </s>
          <s xml:space="preserve">re-<lb />præſentantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0447-07" corresp="note-0447-07a" place="margin">TAB. XLVI. <lb />fig 1.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0448" n="328" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p rend="italics">
          <s xml:space="preserve">Denſitas maxima datur in m, loco medio inter h &amp; </s>
          <s xml:space="preserve">p, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0448-01a" corresp="note-0448-01" type="noteAnchor" />
maxima dilatatio inter b &amp; </s>
          <s xml:space="preserve">h in medio e.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0448-01" corresp="note-0448-01a" place="margin">1139.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vbicunque particulæ vicinæ non æquè diſtant, actio ex e-<lb />
<ptr xml:id="note-0448-02a" corresp="note-0448-02" type="noteAnchor" />
laſticitate datur, qua particulæ minus diſtantes magis di-<lb />ſtantes verſus premuntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hæcque preſſio, ſepoſito omni
<ptr xml:id="note-0448-03a" corresp="note-0448-03" type="noteAnchor" />
motu acquiſito, examinanda eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0448-02" corresp="note-0448-02a" place="margin">1140.</note>
              <note xml:space="preserve" xml:id="note-0448-03" corresp="note-0448-03a" n="*" anchored="true" place="margin">1072.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Inter b &amp; </s>
          <s xml:space="preserve">e datur preſſio a b verſus e, id eſt, cum motu <lb />
<ptr xml:id="note-0448-04a" corresp="note-0448-04" type="noteAnchor" />
undæ conſpirans; </s>
          <s xml:space="preserve">quæ etiam datur inter m &amp; </s>
          <s xml:space="preserve">p.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0448-04" corresp="note-0448-04a" place="margin">1141.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Preſſio autem contraria eſt inter e &amp; </s>
          <s xml:space="preserve">m, &amp; </s>
          <s xml:space="preserve">ab m verſus <lb />
<ptr xml:id="note-0448-05a" corresp="note-0448-05" type="noteAnchor" />
e dirigitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0448-05" corresp="note-0448-05a" place="margin">1142.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In m &amp; </s>
          <s xml:space="preserve">e, ubi motus directiones mutantur, nulla ex e-<lb />
<ptr xml:id="note-0448-06a" corresp="note-0448-06" type="noteAnchor" />
laſticitate datur actio, quia particulæ vicinæ ad diſtantias <lb />æquales inter ſe poſitæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0448-06" corresp="note-0448-06a" place="margin">1143.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In locis b, h, &amp; </s>
          <s xml:space="preserve">p omnium maxima eſt diſtantiarum parti-<lb />
<ptr xml:id="note-0448-07a" corresp="note-0448-07" type="noteAnchor" />
cularum vicinarum differentia; </s>
          <s xml:space="preserve">ideoque omnium maxima <lb />elaſticitatis actio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0448-07" corresp="note-0448-07a" place="margin">1144.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Deducimus ex his particulam, pro vario in unda ſitu, va-<lb />riam ab elaſticitate actionem pati, qua illius motus genera-<lb />tur, acceleratur, minuitur, aut deſtruitur; </s>
          <s xml:space="preserve">idcirco dire-<lb />ctio motus particulæ, ex ſola directione memoratæ actio-<lb />nis, determinari nequit, &amp; </s>
          <s xml:space="preserve">cum hac directione non ſemper <lb />congruit illa, ſingularumque particularum motus omnibus <lb />momentis mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Particulæ omnes inter b &amp; </s>
          <s xml:space="preserve">p tranſlatæ ſunt, juxta ordi-<lb />nem litterarum. </s>
          <s xml:space="preserve">Particulæ inter h &amp; </s>
          <s xml:space="preserve">p juxta hanc dire-<lb />ctionem motum continuant, ceteræ inter h &amp; </s>
          <s xml:space="preserve">b verſus b <lb />redeunt, ut in ſequentibus dicetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Perſeverant hæ in motu quo redeunt, donec ex actione <lb />elateris, cujus directio in puncto e mutatur, motus acqui-<lb />ſitus altera vice deſtruatur; </s>
          <s xml:space="preserve">in quo caſu particula ut b ad <lb />quietem &amp; </s>
          <s xml:space="preserve">priſtinum ſitum redit. </s>
          <s xml:space="preserve">In momento ſequenti <lb />particula c in ſitu priſtino quieſcit, p vero ad q accedit, ut <lb />in linea 2; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſucceſſive, in momentis æqualibus, adipiſci-<lb />tur unda omnes ſitus, qui hîc in lineis 1. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">13. </s>
          <s xml:space="preserve">viden-<lb />tur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">dum unda a ſitu in linea 1. </s>
          <s xml:space="preserve">ad ſitum in linea 13. </s>
          <s xml:space="preserve">per-<lb />
<ptr xml:id="note-0448-08a" corresp="note-0448-08" type="noteAnchor" />
</s>
          <pb facs="0449" n="329" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP XIX.</fw>
venit, totam percurrit latitudinem ſuam. </s>
          <s xml:space="preserve">Particula p in <lb />hoc motu it &amp; </s>
          <s xml:space="preserve">redit, hujuſque motus in hac figura ſenſi-<lb />bilis eſt, &amp;</s>
          <s xml:space="preserve">, ut clare patet, particula hæc ſucceſſivè per <lb />omnes ſitus particularum in unda tranſit. </s>
          <s xml:space="preserve">Singulæ particu-<lb />læ ſucceſſivè ſimili motu agitantur: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">diviſo tempore, in <lb />
<ptr xml:id="note-0449-01a" corresp="note-0449-01" type="noteAnchor" />
quo unda latitudinem percurrit, in tot partes quot <lb />particulæ dantur in ipſa latitudine, particula unaquæque <lb />in eo ſitu datur, in quo momento præcedenti fuit particula <lb />ſequens, quæ per unum momentum tale diutius fuit in mo-<lb />tu.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0448-08" corresp="note-0448-08a" place="margin">1145.</note>
              <note xml:space="preserve" xml:id="note-0449-01" corresp="note-0449-01a" place="margin">1146.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus cujuſcunque particulæ, ut p, in itu &amp; </s>
          <s xml:space="preserve">reditu ſuo, <lb />
<ptr xml:id="note-0449-02a" corresp="note-0449-02" type="noteAnchor" />
analogus eſt cum motu penduli vibratorio, dum duas peragit <lb />oſcillationes; </s>
          <s xml:space="preserve">id eſt, ſemel it &amp; </s>
          <s xml:space="preserve">redit. </s>
          <s xml:space="preserve">Pendulum in o-<lb />ſcillatione deſcendit, motuſque acquiſitus cum gravitatis a-<lb />ctione conſpirat &amp; </s>
          <s xml:space="preserve">hac acceleratur, donec ad punctum ar-<lb />cus deſcribendi infimum, id eſt medium viæ percurrendæ, <lb />pervenerit; </s>
          <s xml:space="preserve">pergit motu acquiſito, qui actione gravitatis, <lb />cujus directio in hoc puncto mutatur, deſtruitur, dum cor-<lb />pus per alteram arcus deſcribendi partem adſcendit: </s>
          <s xml:space="preserve">corpus <lb />hoc iisdem legibus redit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0449-02" corresp="note-0449-02a" place="margin">1147.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Particula p ex elaſticitate movetur, motuſque accelera-<lb />tur ex elaſticitatis actione, donec ipſa ad ſitum particulæ <lb />m in linea 1. </s>
          <s xml:space="preserve">pervenerit <ptr type="noteAnchor" />, qui ſitus in linea 4. </s>
          <s xml:space="preserve">vide-
<ptr xml:id="note-0449-03a" corresp="note-0449-03" type="noteAnchor" />
tur, in qua particula p occupat punctum medium <lb />ſpatii itu &amp; </s>
          <s xml:space="preserve">reditu percurrendi. </s>
          <s xml:space="preserve">Motu acquiſito, <lb />quamvis elaſticitas contrarie agat <ptr type="noteAnchor" />, in motu perſeverat,
<ptr xml:id="note-0449-04a" corresp="note-0449-04" type="noteAnchor" />
donec hac actione totus motus ſit deſtructus; </s>
          <s xml:space="preserve">quod fit per-<lb />currendo ſpatium æquale illi in quo fuit generatus; </s>
          <s xml:space="preserve">datur <lb />tunc particula p in ſitu, in quo videtur in linea 7.</s>
          <s xml:space="preserve">, qui re-<lb />ſpondet cum ſitu particulæ h in linea 1. </s>
          <s xml:space="preserve">Ex elaſticitate <lb />tunc particula redit &amp; </s>
          <s xml:space="preserve">acceleratur, donec ſitum particulæ <lb />e in linea 1. </s>
          <s xml:space="preserve">adepta ſit <ptr type="noteAnchor" />, ut in linea 10.</s>
          <s xml:space="preserve">; id eſt, donec ite-
<ptr xml:id="note-0449-05a" corresp="note-0449-05" type="noteAnchor" />
rum, ut in linea 4, verſetur in puncto medio viæ percurren-<lb />dæ. </s>
          <s xml:space="preserve">In reditu ſuo continuat particula donec ex actione e-<lb />lateris, cujus directio iterum mutatur <ptr type="noteAnchor" />, totus motus de-
<ptr xml:id="note-0449-06a" corresp="note-0449-06" type="noteAnchor" />
</s>
          <pb facs="0450" n="330" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſtruatur; </s>
          <s xml:space="preserve">tuncque particula ad priſtinum ſitum, ut in linea <lb />13.</s>
          <s xml:space="preserve">, redit, &amp; </s>
          <s xml:space="preserve">ibi, cùm nova actione non agitetur, quieſcit. <lb /></s>
          <s xml:space="preserve">Quæ omnia ex demonſtratis in ſcholio 1. </s>
          <s xml:space="preserve">ſequenti profluunt. </s>
          <s xml:space="preserve"><lb />Idcirco ceſſante motu corporis tremulo, quo aër agitatur, <lb />
<ptr xml:id="note-0450-01a" corresp="note-0450-01" type="noteAnchor" />
novæ undæ non generantur, numeruſque undarum a nume-<lb />ro agitationum ipſius corporis non differt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0449-03" corresp="note-0449-03a" n="*" anchored="true" place="margin">1141.</note>
              <note xml:space="preserve" xml:id="note-0449-04" corresp="note-0449-04a" n="*" anchored="true" place="margin">1142.</note>
              <note xml:space="preserve" xml:id="note-0449-05" corresp="note-0449-05a" n="*" anchored="true" place="margin">1142.</note>
              <note xml:space="preserve" xml:id="note-0449-06" corresp="note-0449-06a" n="*" anchored="true" place="margin">1143.</note>
              <note xml:space="preserve" xml:id="note-0450-01" corresp="note-0450-01a" place="margin">1148.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si in pendulo poſt duas vibrationes gravitatis actio ceſſa-<lb />
<ptr xml:id="note-0450-02a" corresp="note-0450-02" type="noteAnchor" />
ret, ut in aëre, poſt itum &amp; </s>
          <s xml:space="preserve">reditum particulæ, elaſticita-<lb />tis actio in hanc particulam ceſſat, in omnibus motus par-<lb />ticulæ aëreæ cum motu corporis penduli congrueret. </s>
          <s xml:space="preserve">In <lb />puncto medio arcus oſcillatione percurrendi nulla datur gra-<lb />vitatis actio, hujuſque directio mutatur; </s>
          <s xml:space="preserve">in puncto medio <lb />ſpatii a particula p, itu &amp; </s>
          <s xml:space="preserve">reditu, percurrendi, in quo datur <lb />in linea 4. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">10.</s>
          <s xml:space="preserve">, congruit hujus particulæ ſitus cum ſitu <lb />particularum m &amp; </s>
          <s xml:space="preserve">e in linea 1.</s>
          <s xml:space="preserve">, in quibus punctis nulla ela-<lb />ſticitatis actio datur, &amp; </s>
          <s xml:space="preserve">hujus directio mutatur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In pen-
<ptr xml:id="note-0450-03a" corresp="note-0450-03" type="noteAnchor" />
dulo quo magis corpus oſcillatum a puncto infimo, aut me-<lb />dio, arcus deſcribendi diſtat, eo magis vis gravitatis in il-<lb />lud agit; </s>
          <s xml:space="preserve">quo magis etiam particula p a puncto medio ſpatii <lb />percurrendi diſtat, eo major in illam eſt elaſticitatis actio, <lb />&amp; </s>
          <s xml:space="preserve">in lineis 1. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">13.</s>
          <s xml:space="preserve">, in quibus maximè à puncto memo-<lb />rato diſtat particula, ſitus hujus congruit cum punctis b, h, <lb />&amp; </s>
          <s xml:space="preserve">p, in linea 1.</s>
          <s xml:space="preserve">, in quibus elaſticitatis actio eſt omnium <lb />maxima <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0450-02" corresp="note-0450-02a" place="margin">1149.</note>
              <note xml:space="preserve" xml:id="note-0450-03" corresp="note-0450-03a" n="*" anchored="true" place="margin">1143</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1144.</note>
        <p>
          <s xml:space="preserve">Qua lege hæc elaſticitatis actio, cum aucta a ſæpius me-<lb />
<ptr xml:id="note-0450-05a" corresp="note-0450-05" type="noteAnchor" />
morato puncto medio diſtantia creſcat, determinatur ex le-<lb />ge ipſa elaſticitatis aëris, cujus particulæ ſeſe mutuo fugiunt <lb />cum vi quæ eſt inverſè ut diſtantia inter particularum cen-<lb />tra <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">demonſtramus in ſcholio 1. </s>
          <s xml:space="preserve">huic capiti ſubjuncto ela-
<ptr xml:id="note-0450-06a" corresp="note-0450-06" type="noteAnchor" />
ſticitatis actionem, in particulam up p, ad inſtar diſtantiæ a <lb />puncto ſpatii percurrendi medio augeri aut minui.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0450-05" corresp="note-0450-05a" place="margin">1150.</note>
              <note xml:space="preserve" xml:id="note-0450-06" corresp="note-0450-06a" n="*" anchored="true" place="margin">1072.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Qua de cauſa particulæ ſingulæ, in motu ſuo, eunt, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0450-07a" corresp="note-0450-07" type="noteAnchor" />
redeunt, juxta legem corporis in cycloïde oſcillati <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0450-07" corresp="note-0450-07a" place="margin">1151.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">287.</note>
        <p>
          <s xml:space="preserve">In eodem ſcholio demonſtramus, undæ velocitatem æqua-<lb />
<ptr xml:id="note-0450-09a" corresp="note-0450-09" type="noteAnchor" />
lem eſſe illi, quam corpus acquirit cadendo a ſemialtitudi-
</s>
          <pb facs="0451" n="331" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XIX.</fw>
ne, quam Atmoſphæra haberet, ſi manente aëris quantita-<lb />te, ubique illam haberet denſitatem, quam habet in loco, <lb />in quo unda movetur. </s>
          <s xml:space="preserve">Et demonſtratio locum habet <lb />quæcunque fuerit undæ latitudo, &amp; </s>
          <s xml:space="preserve">ſive per majus aut mi-<lb />nus ſpatium particulæ in itu &amp; </s>
          <s xml:space="preserve">reditu excurrant; </s>
          <s xml:space="preserve">unde con-<lb />ſtat, Vndas omnes æquali celeritate moveri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0450-09" corresp="note-0450-09a" place="margin">1152.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">1153.</note>
        <p>
          <s xml:space="preserve">Locum hoc habebit quamdiu altitudo Atmoſphæræ, po-<lb />ſitâ hac ubique ejuſdem denſitatis, non mutatur, mutata <lb />autem hac, celeritas undarum mutatur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſequuntur qua-<lb />
<ptr xml:id="note-0451-02a" corresp="note-0451-02" type="noteAnchor" />
drata celeritatum rationem altitudinum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Mutatur autem
<ptr xml:id="note-0451-03a" corresp="note-0451-03" type="noteAnchor" />
ſæpe altitudo hæc, nam manente elaſticitate aëris denſitas <lb />
<ptr xml:id="note-0451-04a" corresp="note-0451-04" type="noteAnchor" />
ſæpe variat: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">mutari poteſt elaſticitas denſitate manente: <lb /></s>
          <s xml:space="preserve">tandem ambæ ſimul mutationi ſæpiſſime obnoxiæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0451-02" corresp="note-0451-02a" place="margin">1154.</note>
              <note xml:space="preserve" xml:id="note-0451-03" corresp="note-0451-03a" n="*" anchored="true" place="margin">1152 255.</note>
              <note xml:space="preserve" xml:id="note-0451-04" corresp="note-0451-04a" place="margin">1155.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In primo caſu, manente nempe elaſticitate, dum denſitas <lb />variat, poſitâ Atmoſphærâ ubique ejuſdem denſitatis, alti-<lb />tudo mutatur, quantitas verò aëris comprimentis non vari-<lb />at: </s>
          <s xml:space="preserve">quia hujus pondus æquale eſt elaſticitati; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eſt altitu-<lb />do ut ſpatium ab aere occupatum; </s>
          <s xml:space="preserve">ideo inverſè ut denſitas <ptr type="noteAnchor" />,
<ptr xml:id="note-0451-05a" corresp="note-0451-05" type="noteAnchor" />
quare undarum celeritatum quadrata ſunt inverſè ut denſita-<lb />tes <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0451-05" corresp="note-0451-05a" n="*" anchored="true" place="margin">738.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1154.</note>
        <p>
          <s xml:space="preserve">Quando denſitas manet, ſed mutatur elaſticitas, altitu-<lb />
<ptr xml:id="note-0451-07a" corresp="note-0451-07" type="noteAnchor" />
do Atmoſphæræ mutatur, ut pondus comprimens, id eſt, <lb />ut elaſticitas <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ergo quadrata celeritatum undarum ſunt ut
<ptr xml:id="note-0451-08a" corresp="note-0451-08" type="noteAnchor" />
elaſticitatis gradus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0451-07" corresp="note-0451-07a" place="margin">1156.</note>
              <note xml:space="preserve" xml:id="note-0451-08" corresp="note-0451-08a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1154.</note>
        <p rend="italics">
          <s xml:space="preserve">Si &amp; </s>
          <s xml:space="preserve">elaſticitas &amp; </s>
          <s xml:space="preserve">denſitas differant, quadrata velocita-<lb />
<ptr xml:id="note-0451-10a" corresp="note-0451-10" type="noteAnchor" />
tum undarum erunt in ratione compoſita directæ elaſticita-<lb />tis <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">inverſæ denſitatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0451-10" corresp="note-0451-10a" place="margin">1157.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1156.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1155.</note>
        <p>
          <s xml:space="preserve">Si denſitas &amp; </s>
          <s xml:space="preserve">elaſticitas creſcant, aut minuantur, in eadem <lb />
<ptr xml:id="note-0451-13a" corresp="note-0451-13" type="noteAnchor" />
ratione, inverſa ratio denſitatis directam elaſticitatis deſtru-<lb />et, &amp; </s>
          <s xml:space="preserve">non mutabitur undarum celeritas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0451-13" corresp="note-0451-13a" place="margin">1158.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ultimus hic caſus exſtat in aëris compreſſione ex aëre ad-<lb />fluente <ptr type="noteAnchor" />, quo etiam, ſi de cetero maneat aëris conſtitutio,
<ptr xml:id="note-0451-14a" corresp="note-0451-14" type="noteAnchor" />
altitudo Atmoſphæræ, poſitâ hac ubique ejuſdem denſita-<lb />tis, non mutatur; </s>
          <s xml:space="preserve">nam pro ratione ponderis ſuperadditi in <lb />minus ſpatium redigitur. </s>
          <s xml:space="preserve">Idcirco ex mutata altitudine co-<lb />
<ptr xml:id="note-0451-15a" corresp="note-0451-15" type="noteAnchor" />
</s>
          <pb facs="0452" n="332" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
lumnæ mercurii, quæ ex Atmoſphæræ preſſione in tubo aëre <lb />vacuo ſuſtinetur <ptr type="noteAnchor" />, quod pondus, quo aër in terræ viciniis
<ptr xml:id="note-0452-01a" corresp="note-0452-01" type="noteAnchor" />
comprimitur, mutatum indicat, non debemus undarum ce-<lb />leritatem mutatam dijudicare. </s>
          <s xml:space="preserve">Eadem de cauſa undæ æqua-<lb />
<ptr xml:id="note-0452-02a" corresp="note-0452-02" type="noteAnchor" />
li celeritate in apice montis &amp; </s>
          <s xml:space="preserve">in valle moverentur; </s>
          <s xml:space="preserve">niſiaë-<lb />ris conſtitutio differret pro majori elevatione <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0451-14" corresp="note-0451-14a" n="*" anchored="true" place="margin">1071.</note>
              <note xml:space="preserve" xml:id="note-0451-15" corresp="note-0451-15a" place="margin">1159.</note>
              <note xml:space="preserve" xml:id="note-0452-01" corresp="note-0452-01a" n="*" anchored="true" place="margin">1056.</note>
              <note xml:space="preserve" xml:id="note-0452-02" corresp="note-0452-02a" place="margin">1160.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1081.</note>
        <p>
          <s xml:space="preserve">Vndas æſtate celerius quam hieme moveri ex aëris elaſti-<lb />
<ptr xml:id="note-0452-04a" corresp="note-0452-04" type="noteAnchor" />
citate calore aucta <ptr type="noteAnchor" /> deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0452-04" corresp="note-0452-04a" place="margin">1161.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1075.</note>
        <p>
          <s xml:space="preserve">Altitudo Atmoſphæræ, poſitâ hac ubique ejuſdem den-<lb />
<ptr xml:id="note-0452-06a" corresp="note-0452-06" type="noteAnchor" />
ſitatis, detegitur, ſi menſuretur altitudo columnæ Mercurii, <lb />quæ in tubo Torricelliano cum preſſione Atmoſphæræ æ-<lb />quiponderat <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">comparando aëris denſitatem cum den-
<ptr xml:id="note-0452-07a" corresp="note-0452-07" type="noteAnchor" />
ſitate mercurii; </s>
          <s xml:space="preserve">quod ponderando aërem <ptr type="noteAnchor" /> fieri poteſt. </s>
          <s xml:space="preserve">De-
<ptr xml:id="note-0452-08a" corresp="note-0452-08" type="noteAnchor" />
tectâ verò Atmoſphæræ altitudine, celeritas, quam corpus <lb />a dimidia hac altitudine cadendo acquirit, per experimen-<lb />ta pendulorum determinatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0452-06" corresp="note-0452-06a" place="margin">1162.</note>
              <note xml:space="preserve" xml:id="note-0452-07" corresp="note-0452-07a" n="*" anchored="true" place="margin">1055.</note>
              <note xml:space="preserve" xml:id="note-0452-08" corresp="note-0452-08a" n="*" anchored="true" place="margin">1099.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">288. 290.</note>
        <p>
          <s xml:space="preserve">Aëris motus, de quo in hac computatione agitur, <lb />a ſola elaſticitate pendet, &amp; </s>
          <s xml:space="preserve">exacta eſſet computatio, <lb />ſi particulæ ipſæ ad interſtitia inter has ſenſibilem ra-<lb />tionem non haberent; </s>
          <s xml:space="preserve">ſi verò ponamus dari hìc ratio-<lb />nem ſenſibilem, velocior erit undarum motus; </s>
          <s xml:space="preserve">propa-<lb />gatur enim per corpora ſolida in inſtanti, quod etiam <lb />referri debet ad corpuſcula heterogenea in aëre natan-<lb />tia.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Conſideravimus autem particulas aëreas, quaſi eſſent <lb />
<ptr xml:id="note-0452-10a" corresp="note-0452-10" type="noteAnchor" />
puncta, &amp; </s>
          <s xml:space="preserve">celeritates, quæ in hac bypotheſi deteguntur, au-<lb />gendæ ſunt pro ratione quam habet materia ad interſtitia, <lb />ut veræ detegantur velocitates.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0452-10" corresp="note-0452-10a" place="margin">1163.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quare quamdiu idem aër ſuam ſervat denſitatem, ean-<lb />
<ptr xml:id="note-0452-11a" corresp="note-0452-11" type="noteAnchor" />
dem cum ipſa velocitate rationem ſequitur hujus angmentum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0452-11" corresp="note-0452-11a" place="margin">1164.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si vero denſitas mutetur, augmentum non modo ſequitur <lb />
<ptr xml:id="note-0452-12a" corresp="note-0452-12" type="noteAnchor" />
rationem velocitatis, ſed &amp; </s>
          <s xml:space="preserve">rationem, materiæ ad materi-<lb />am in eadem linea, quæ eſt ratio radicis cubicæ denſita-<lb />tis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0452-12" corresp="note-0452-12a" place="margin">1165.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si de diverſo aëre agatur, hæc regula non procedit, nam <lb />
<ptr xml:id="note-0452-13a" corresp="note-0452-13" type="noteAnchor" />
</s>
          <pb facs="0453" n="333" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XIX.</fw>
ipſæ particulæ, ſervata aëris denſitate, diverſam denſita-<lb />tatem habere poſſunt, &amp; </s>
          <s xml:space="preserve">mutabitur ratio diametrorum par-<lb />ticularum ad interſtitia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0452-13" corresp="note-0452-13a" place="margin">1166.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vndarum in aëre motus ſonum producit; </s>
          <s xml:space="preserve">de quo ante-<lb />
<ptr xml:id="note-0453-01a" corresp="note-0453-01" type="noteAnchor" />
quam agamus, pauca de ſenſationibus in genere præmitten-<lb />da ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0453-01" corresp="note-0453-01a" place="margin">1167.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Adeo arctum eſt mentis &amp; </s>
          <s xml:space="preserve">corporis vinculum, ut qui-<lb />
<ptr xml:id="note-0453-02a" corresp="note-0453-02" type="noteAnchor" />
dam motus in hoc cum certis in illa ideis quaſi cohæreant, <lb />&amp; </s>
          <s xml:space="preserve">ſeparari nequeant. </s>
          <s xml:space="preserve">Ex corporis motu omnibus momen-<lb />tis ideæ novæ in mente excitantur, taleſque ſunt rerum <lb />omnium ſenſibilium ideæ; </s>
          <s xml:space="preserve">nihil tamen commune in-<lb />ter motum in corpore &amp; </s>
          <s xml:space="preserve">ideam in mente percipimus. <lb /></s>
          <s xml:space="preserve">Nexus qui hic datur perſpicientiam noſtram fugit, ne-<lb />que ullum poſſibilem eſſe concipimus. </s>
          <s xml:space="preserve">Innumera in <lb />rerum univerſitate latent, quæ ne quidem ideis attingi-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0453-02" corresp="note-0453-02a" place="margin">1168.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aëris motus undulatorius agitat tympanum auris, quo <lb />
<ptr xml:id="note-0453-03a" corresp="note-0453-03" type="noteAnchor" />
aëri, hoc organo contento, motus communicatur, qui ubi <lb />in nervum auditorium eſt tranſlatus, ſoni idea in mente <lb />excitatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0453-03" corresp="note-0453-03a" place="margin">1169.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Auris ſtructura mirabilis eſt, &amp; </s>
          <s xml:space="preserve">interna, &amp; </s>
          <s xml:space="preserve">externa; </s>
          <s xml:space="preserve">ſed <lb />de motu aëris agimus; </s>
          <s xml:space="preserve">hunc eſſe vehiculum ſoni Experi-<lb />
<ptr xml:id="note-0453-04a" corresp="note-0453-04" type="noteAnchor" />
mento probatur,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0453-04" corresp="note-0453-04a" place="margin">1170.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum i</hi>.</head>
        <p>
          <s xml:space="preserve">Orbi plumbeo O adhærent cylindri ex eodem metallo <lb />
<ptr xml:id="note-0453-05a" corresp="note-0453-05" type="noteAnchor" />
C, C, campana minor A filo æneo b d jungitur; </s>
          <s xml:space="preserve">ligulis alli-<lb />
<ptr xml:id="note-0453-06a" corresp="note-0453-06" type="noteAnchor" />
gatur illa cylindris C, C. </s>
          <s xml:space="preserve">Orbis O laminæ æneæ Machinæ <lb />Pneumaticæ, interpoſito pulvillo ex bombyce xyli, impo-<lb />nitur; </s>
          <s xml:space="preserve">campana A, cum orbe &amp; </s>
          <s xml:space="preserve">cylindris, vitro obtegun-<lb />tur. </s>
          <s xml:space="preserve">Clauditur hoc operculo cum pyxide, quam filum æ-<lb />neum mobile DE trajicit <ptr type="noteAnchor" />, cohærente, filo jungitur lami-
<ptr xml:id="note-0453-07a" corresp="note-0453-07" type="noteAnchor" />
na e f, ita. </s>
          <s xml:space="preserve">ut circumvolutione fili campana A agitetur: </s>
          <s xml:space="preserve">Aër <lb />ſi exhauriatur ex vitro memorato, &amp;</s>
          <s xml:space="preserve">, ut dictum, agitetur cam-<lb />pana, ſonus non auditur. </s>
          <s xml:space="preserve">Unica circumvolutione fili DE <lb />campana variis vicibus in motuſuo it &amp; </s>
          <s xml:space="preserve">redit, &amp; </s>
          <s xml:space="preserve">de hoc
</s>
          <pb facs="0454" n="334" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
motu agitur, in quo lamina ef non tangit filum bd. </s>
          <s xml:space="preserve">Ad-<lb />miſſo aëre ſonus ut ante auditur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0453-05" corresp="note-0453-05a" place="margin">1171.</note>
              <note xml:space="preserve" xml:id="note-0453-06" corresp="note-0453-06a" place="margin">TAB. XLVI. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0453-07" corresp="note-0453-07a" n="*" anchored="true" place="margin">1096.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex eo ſolo quod aër ſit vehiculum ſoni, &amp; </s>
          <s xml:space="preserve">quod ſine <lb />aëris tranilatione ſonus per illum moveatur, clare ſequitur <lb />in ſono motum aëris undulatorium dari, &amp; </s>
          <s xml:space="preserve">ſonum ex motu <lb />
<ptr xml:id="note-0454-01a" corresp="note-0454-01" type="noteAnchor" />
corporum tremulo oriri. </s>
          <s xml:space="preserve">Hoc etiam extra omne dubium <lb />eſt, in chordis aut nervis tenſis, ex quibus agitatione tre-<lb />mula ſonus elicitur. </s>
          <s xml:space="preserve">In campanis majoribus &amp; </s>
          <s xml:space="preserve">in multis <lb />aliis corporibus motus hicce tremulus admodum ſenſibilis <lb />eſt; </s>
          <s xml:space="preserve">in campana vitrea ſonum edente, Experimento ſequen-<lb />ti, viſibilis fit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0454-01" corresp="note-0454-01a" place="margin">1172.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Campana vitrea CC gypſo, aut arenato, coagmentatur <lb />
<ptr xml:id="note-0454-02a" corresp="note-0454-02" type="noteAnchor" />
cochleæ ligneæ, cujus ope campana firmiter cum ligno AB <lb />
<ptr xml:id="note-0454-03a" corresp="note-0454-03" type="noteAnchor" />
conjungitur; </s>
          <s xml:space="preserve">ſuſtinetur hoc duabus columnis S, S, &amp; </s>
          <s xml:space="preserve">co-<lb />chleis firmatur. </s>
          <s xml:space="preserve">Harum columnarum alteram, ad altitudi-<lb />nem oræ campanæ, trajicit clavus cochlea circumdatus, <lb />ita ut hunc circumvolvendo extremitas ad quamcumque di-<lb />ſtantiam a campanæ ora firmetur. </s>
          <s xml:space="preserve">Poſitâ diſtantiâ hac exi-<lb />guâ, ſi pulſetur campana, motu ſuo tremulo in clavi extre-<lb />mitatem variis vicibus impinget.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0454-02" corresp="note-0454-02a" place="margin">1173.</note>
              <note xml:space="preserve" xml:id="note-0454-03" corresp="note-0454-03a" place="margin">TAB. XLVI. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Non tamen immediate ab hoc motu viſibili pendet ſonus, <lb />
<ptr xml:id="note-0454-04a" corresp="note-0454-04" type="noteAnchor" />
ſed ab alio motu tremulo, quo, in motu memorato, particu-<lb />læ minores afficiuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0454-04" corresp="note-0454-04a" place="margin">1174.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Lamina ferrea elaſtica ACB, motu tremulo viſibili affi-<lb />
<ptr xml:id="note-0454-05a" corresp="note-0454-05" type="noteAnchor" />
citur, ſi ad ſe invicem applicatis extremitatibus <hi rend="small caps">A</hi> &amp; </s>
          <s xml:space="preserve">B, <lb />
<ptr xml:id="note-0454-06a" corresp="note-0454-06" type="noteAnchor" />
hæ ſubito relaxentur, non tamen ſonus auditur; </s>
          <s xml:space="preserve">ſi autem <lb />alio ferro lateraliter percutiatur, quo non motu viſibili tre-<lb />mulo agitatur, ex ipſa ſonus elicitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0454-05" corresp="note-0454-05a" place="margin">1175.</note>
              <note xml:space="preserve" xml:id="note-0454-06" corresp="note-0454-06a" place="margin">TAB. XLVII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpus percuſſum per aliquod tempus poſt ictum ſonum e-<lb />
<ptr xml:id="note-0454-07a" corresp="note-0454-07" type="noteAnchor" />
dit; </s>
          <s xml:space="preserve">nam fibra agitata per aliquod tempus ex elaſticitate vi-<lb />brationes continuat <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sonus etiam, ſubſiſtente motu tre-
<ptr xml:id="note-0454-08a" corresp="note-0454-08" type="noteAnchor" />
mulo, ceſſat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0454-07" corresp="note-0454-07a" place="margin">1176.</note>
              <note xml:space="preserve" xml:id="note-0454-08" corresp="note-0454-08a" n="*" anchored="true" place="margin">686.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sæpiſſime videmus, ut in Experimento 1.</s>
          <s xml:space="preserve">, corpus ſo-
</s>
          <pb facs="0455" n="335" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XIX.</fw>
num edere, licet aër ab eo agitatus nullam cum aëre ex-<lb />teriori communicationem habeat; </s>
          <s xml:space="preserve">ex quo ſequitur aëris a-<lb />
<ptr xml:id="note-0455-01a" corresp="note-0455-01" type="noteAnchor" />
gitatione fibras, ex quibus corpora conſtant, moveri; </s>
          <s xml:space="preserve">qui <lb />motus in aërem exteriorem transfertur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0455-01" corresp="note-0455-01a" place="margin">1177.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc ſoni tranſſatio ex fibrarum motu tremulo maxime <lb />notabilis eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quouſque hujus motus communicatio ſeſe <lb />extendat, unico Experimento patebit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Differt hoc cum Experimento 1. </s>
          <s xml:space="preserve">in hoc ſolo, loco <lb />
<ptr xml:id="note-0455-02a" corresp="note-0455-02" type="noteAnchor" />
machinæ plumbeæ COC campana funibus alligatur extre-<lb />
<ptr xml:id="note-0455-03a" corresp="note-0455-03" type="noteAnchor" />
mitatibus laminæ æneæ ad inſtar gnomonis duplicis inflexæ, <lb />quæ cum orbe Antliæ Pneumaticæ ope cochleæ cohæret. <lb /></s>
          <s xml:space="preserve">De cetero, evacuato aëre, campana eodem modo ac in 1. </s>
          <s xml:space="preserve"><lb />Experimento agitatur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">parva tantum inter ſonos, admiſſo <lb />aut exhauſto aëre, percipitur differentia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0455-02" corresp="note-0455-02a" place="margin">1178.</note>
              <note xml:space="preserve" xml:id="note-0455-03" corresp="note-0455-03a" place="margin">TAB. XLVI. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus tremulus partium campanæ communicatur filo <lb />
<ptr xml:id="note-0455-04a" corresp="note-0455-04" type="noteAnchor" />
æneo bd, quo funes, quibus campana ſuſpenditur, moven-<lb />tur, motuſque transfertur in laminam æneam inflexam; <lb /></s>
          <s xml:space="preserve">cochlea, qua hæc cum orbe æneo Machinæ Pneumaticæ <lb />conjungitur, orbem hunc tangit, &amp; </s>
          <s xml:space="preserve">huic motum tremu-<lb />lum communicat, quo aër agitatur, &amp; </s>
          <s xml:space="preserve">ſonus campanæ au-<lb />ditur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0455-04" corresp="note-0455-04a" place="margin">1179.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut per ſolida corpora, ſic &amp; </s>
          <s xml:space="preserve">per fluida propagatur ſonus, <lb />
<ptr xml:id="note-0455-05a" corresp="note-0455-05" type="noteAnchor" />
in quo tamen caſu admodum debilitatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0455-05" corresp="note-0455-05a" place="margin">1180.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Vitro A includitur companula C quæ malleis m, m, motu ro-<lb />
<ptr xml:id="note-0455-06a" corresp="note-0455-06" type="noteAnchor" />
tulæ agitatis, percutitur; </s>
          <s xml:space="preserve">rotæque motus elafterio, illis ſimili, <lb />
<ptr xml:id="note-0455-07a" corresp="note-0455-07" type="noteAnchor" />
quæ in horologiis portatilibus uſu veniunt, per duo aut tria <lb />minuta prima continuatur, vitrum operculo ligneo O obtegi-<lb />tur, &amp; </s>
          <s xml:space="preserve">cerâ molli ingreſſus aquæ cohibetur. </s>
          <s xml:space="preserve">Vitrum hoc-<lb />ce vitro majori B, cujus fundus, ad altitudinem unius aut <lb />duorum pollicum, mercurio obtegitur, immittitur, &amp; </s>
          <s xml:space="preserve"><lb />vitrum B aquâ repletur. </s>
          <s xml:space="preserve">Sonus auditur debilitatus tamen.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0455-06" corresp="note-0455-06a" place="margin">1181.</note>
              <note xml:space="preserve" xml:id="note-0455-07" corresp="note-0455-07a" place="margin">TAB. XLVII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nulla autem inter campanam &amp; </s>
          <s xml:space="preserve">aërem externum, niſi <lb />per fluida, aquam aut mercurium, communicatio datur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0456" n="336" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Celeritas ſoni eadem eſt cum celeritate undarum, quæ au-<lb />
<ptr xml:id="note-0456-01a" corresp="note-0456-01" type="noteAnchor" />
rem percutiunt, &amp; </s>
          <s xml:space="preserve">quæ de harum celeritate dicta ſunt <ptr type="noteAnchor" />
<ptr xml:id="note-0456-02a" corresp="note-0456-02" type="noteAnchor" />
huc referri debent. </s>
          <s xml:space="preserve">Circa n. </s>
          <s xml:space="preserve">1152. </s>
          <s xml:space="preserve">notandum ſoni celeri-<lb />tatem computatione minime poſſe determinari <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ignota
<ptr xml:id="note-0456-03a" corresp="note-0456-03" type="noteAnchor" />
enim eſt proportio inter diametros particularum &amp; </s>
          <s xml:space="preserve">interſtitia <lb />inter has; </s>
          <s xml:space="preserve">ut &amp;</s>
          <s xml:space="preserve">, quantum ſpatium particulæ hetorogeneæ <lb />in aëre occupant, non conſtat. </s>
          <s xml:space="preserve">Immediatè Experimento <lb />detegitur ſoni celeritas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0456-01" corresp="note-0456-01a" place="margin">1182.</note>
              <note xml:space="preserve" xml:id="note-0456-02" corresp="note-0456-02a" n="*" anchored="true" place="margin">1152. 1153. <lb />1155. 1156. <lb />1157. 1158. <lb />1159. 1160. <lb />1161. 1163. <lb />1164. 1165. <lb />1166.</note>
              <note xml:space="preserve" xml:id="note-0456-03" corresp="note-0456-03a" n="*" anchored="true" place="margin">1162.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nocte accendatur ignis cum ſtrepitu conjunctus, ad <lb />
<ptr xml:id="note-0456-04a" corresp="note-0456-04" type="noteAnchor" />
quamcunque ab hoc igne antea menſuratam diſtantiam de-<lb />tur ſpectator, qui breviori pendulo menſuret tempus inter <lb />lumen viſum &amp; </s>
          <s xml:space="preserve">ſonum auditum, quo datur ſoni celeritas; <lb /></s>
          <s xml:space="preserve">luminis enim motus, ſaltem in ſpatio in quo hoc Experi-<lb />mentum inſtitui poteſt, eſt momentaneus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0456-04" corresp="note-0456-04a" place="margin">1183.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tali Experimento in Gallia enotuit ſonum percurrere pe-<lb />
<ptr xml:id="note-0456-05a" corresp="note-0456-05" type="noteAnchor" />
des Gallicos mille &amp; </s>
          <s xml:space="preserve">octoginta, id eſt, Rhenolandicos mille-<lb />centum &amp; </s>
          <s xml:space="preserve">ſeptemdecim, in ſpatio temporis unius minuti <lb />ſecundi: </s>
          <s xml:space="preserve">ſed non conſtans eſt hæc celeritas <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0456-05" corresp="note-0456-05a" place="margin">1184.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1161.</note>
        <p>
          <s xml:space="preserve">Si eodem tempore, in quo hac methodo determinatur <lb />
<ptr xml:id="note-0456-07a" corresp="note-0456-07" type="noteAnchor" />
ſoni velocitas, detegatur ſpatium percurſum ex elaſticitate <ptr type="noteAnchor" />,
<ptr xml:id="note-0456-08a" corresp="note-0456-08" type="noteAnchor" />
dabitur ſoni acceleratio ex craſſitie particularum &amp; </s>
          <s xml:space="preserve">mate-<lb />ria heterogenea.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0456-07" corresp="note-0456-07a" place="margin">1185.</note>
              <note xml:space="preserve" xml:id="note-0456-08" corresp="note-0456-08a" n="*" anchored="true" place="margin">1152. 1162.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Soni celeritas eſt æquabilis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in majori nihilominus ſpa-
<ptr xml:id="note-0456-09a" corresp="note-0456-09" type="noteAnchor" />
tio aliquando acceler atur aut retardatur <ptr type="noteAnchor" />, ex diverſo ela-
<ptr xml:id="note-0456-10a" corresp="note-0456-10" type="noteAnchor" />
<ptr xml:id="note-0456-11a" corresp="note-0456-11" type="noteAnchor" />
ſticitatis gradu, qui in variis locis, ſæpe datur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0456-09" corresp="note-0456-09a" place="margin">1186.</note>
              <note xml:space="preserve" xml:id="note-0456-10" corresp="note-0456-10a" n="*" anchored="true" place="margin">1153.</note>
              <note xml:space="preserve" xml:id="note-0456-11" corresp="note-0456-11a" n="*" anchored="true" place="margin">1156.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1075.</note>
        <p>
          <s xml:space="preserve">Soni celeritas parum variat ex vento cum illius motu con-<lb />
<ptr xml:id="note-0456-13a" corresp="note-0456-13" type="noteAnchor" />
ſpirante, aut in contrarium flante. </s>
          <s xml:space="preserve">Vento certa aëris quanti-<lb />tas de loco in locum transfertur; </s>
          <s xml:space="preserve">acceleratur ſonus, quam-<lb />diu per illam aëris partem movetur, ſi ſoni directio cum <lb />venti directione eadem fuerit; </s>
          <s xml:space="preserve">cum autem ſonus celerrime <lb />moveatur, in tempore breviſſimo percurrit aërem a vento <lb />agitatum, &amp; </s>
          <s xml:space="preserve">non diu acceleratio durat; </s>
          <s xml:space="preserve">quæ de cetero <lb />non admodum eſt magna: </s>
          <s xml:space="preserve">venti enim violentiſſimi, quo <lb />arbores eradicantur, &amp; </s>
          <s xml:space="preserve">ædificia ſubvertuntur, celeritas ſe <lb />habet ad ſoni velocitatem, circiter ut unum ad triginta tria.</s>
          <s xml:space="preserve">
</s>
          <pb facs="0457" n="337" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XIX.</fw>
Eodem argumento exiguam ex vento dari in ſoni motu re-<lb />tardationem probatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0456-13" corresp="note-0456-13a" place="margin">1187.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Spatium a particulis itu &amp; </s>
          <s xml:space="preserve">reditu percurſum a vento au-<lb />geri aut minui poteſt; </s>
          <s xml:space="preserve">idcirco ad majorem aut minorem di-<lb />
<ptr xml:id="note-0457-01a" corresp="note-0457-01" type="noteAnchor" />
ſtantiam ſonus auditur pro venti directione.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0457-01" corresp="note-0457-01a" place="margin">1188.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Intenſitas ſoni pendet ab ictibus aëris in nervum audito-<lb />
<ptr xml:id="note-0457-02a" corresp="note-0457-02" type="noteAnchor" />
rium; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſunt hi ut vires particulis percutientibus inſi-<lb />tæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0457-02" corresp="note-0457-02a" place="margin">1189.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires hæ ſunt ut numeri particularum eodem tempore in <lb />tympanum incurrentium, &amp; </s>
          <s xml:space="preserve">ut quadrata celeritatum qui-<lb />bus incurrunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">476.</note>
        <p rend="italics">
          <s xml:space="preserve">In determinanda ſoni intenſitate, conſideranda ergo ſunt, <lb />
<ptr xml:id="note-0457-04a" corresp="note-0457-04" type="noteAnchor" />
aëris denſitas, ſoni velocitas, ſpatium itu &amp; </s>
          <s xml:space="preserve">reditu a par-<lb />ticulis percur ſum, &amp; </s>
          <s xml:space="preserve">numerus undarum certo tempore in au-<lb />rem incurrentium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0457-04" corresp="note-0457-04a" place="margin">1190.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cæteris manentibus ſi mutetur tantum pondus quo aër com-<lb />
<ptr xml:id="note-0457-05a" corresp="note-0457-05" type="noteAnchor" />
primitur, non eo mutabitur ſpatium itu &amp; </s>
          <s xml:space="preserve">reditu a par-<lb />ticulis percurſum, quod tantum aucta, aut imminuta, agi-<lb />tatione tremula partium corporis variat; </s>
          <s xml:space="preserve">neque numerus <lb />undarum, hæ etiam a corpore tremulo pendent; </s>
          <s xml:space="preserve">non etiam <lb />mutatur ſoni velocitas <ptr type="noteAnchor" />, ſepoſita acceleratione de qua in
<ptr xml:id="note-0457-06a" corresp="note-0457-06" type="noteAnchor" />
n. </s>
          <s xml:space="preserve">1163. </s>
          <s xml:space="preserve">locuti ſumus, quæ hîc non conſideranda eſt, quia <lb />agitur de velocitatè qua ſingulæ particulæ feruntur; </s>
          <s xml:space="preserve">ſola <lb />ergo variat denſitas, id eſt, ſolus mutatur numerus par-<lb />
<ptr xml:id="note-0457-07a" corresp="note-0457-07" type="noteAnchor" />
ticularum certo tempore incurrentium, &amp; </s>
          <s xml:space="preserve">in hac ratio-<lb />ne mutatur ſoni intenſitas <ptr type="noteAnchor" />, id eſt, in ratione ipſius
<ptr xml:id="note-0457-08a" corresp="note-0457-08" type="noteAnchor" />
denſitatis, quæ ponderis comprimentis rationem ſequi-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0457-05" corresp="note-0457-05a" place="margin">1191.</note>
              <note xml:space="preserve" xml:id="note-0457-06" corresp="note-0457-06a" n="*" anchored="true" place="margin">1153.</note>
              <note xml:space="preserve" xml:id="note-0457-07" corresp="note-0457-07a" n="*" anchored="true" place="margin">1189.</note>
              <note xml:space="preserve" xml:id="note-0457-08" corresp="note-0457-08a" n="*" anchored="true" place="margin">1066.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Augeri intenſitatem experimento conſtat.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Agitetur campana A, in aëre compreſſo <ptr type="noteAnchor" />, eodem modo
<ptr xml:id="note-0457-09a" corresp="note-0457-09" type="noteAnchor" />
<ptr xml:id="note-0457-10a" corresp="note-0457-10" type="noteAnchor" />
ac in vacuo agitatur in Experimento 1.</s>
          <s xml:space="preserve">, augebitur ſonus; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0457-11a" corresp="note-0457-11" type="noteAnchor" />
qui iterum minuetur, ſi aperto epiſtomio aër in ſtatum pri-<lb />ſtinum inſtauretur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0457-09" corresp="note-0457-09a" place="margin">1192.</note>
              <note xml:space="preserve" xml:id="note-0457-10" corresp="note-0457-10a" n="*" anchored="true" place="margin">1111.</note>
              <note xml:space="preserve" xml:id="note-0457-11" corresp="note-0457-11a" place="margin">TAB. XLVI. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum in aëre compreſſo incluſo ſoni intenſitas major ſit,
</s>
          <pb facs="0458" n="338" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
etiam magis fibræ ex quibus vas VV conſtat agitantur, ma-<lb />jorque agitatio aëri exteriori communicatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si cetera maneant, elaſticitas autem augeatur, in ea-<lb />
<ptr xml:id="note-0458-01a" corresp="note-0458-01" type="noteAnchor" />
dem ratione cum aucta elaſticitate minuitur quidem den-<lb />ſitas <ptr type="noteAnchor" />, ſed demonſtramus in ſcholio, huic capiti ſubjun-
<ptr xml:id="note-0458-02a" corresp="note-0458-02" type="noteAnchor" />
cto, ſoni intenſitatem augeri in ratione quam ſequitur <lb />radix quadrata elaſticitatis. </s>
          <s xml:space="preserve">Unde ſequitur Æſtate, <lb />
<ptr xml:id="note-0458-03a" corresp="note-0458-03" type="noteAnchor" />
cæteris paribus, ſoni intenſitatem majorem eſſe quàm Hie-<lb />me.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-01" corresp="note-0458-01a" place="margin">1193.</note>
              <note xml:space="preserve" xml:id="note-0458-02" corresp="note-0458-02a" n="*" anchored="true" place="margin">1071</note>
              <note xml:space="preserve" xml:id="note-0458-03" corresp="note-0458-03a" place="margin">1194.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Campana A in vitro ſuſpendatur, habeatque, aperto e-<lb />
<ptr xml:id="note-0458-04a" corresp="note-0458-04" type="noteAnchor" />
piſtomio, aër in vitro communicationem cum aëre exterio-<lb />
<ptr xml:id="note-0458-05a" corresp="note-0458-05" type="noteAnchor" />
ri. </s>
          <s xml:space="preserve">Agitetur vitrum, &amp; </s>
          <s xml:space="preserve">determinetur diſtantia ad quam ſo-<lb />nus audiri poteſt, Calefacto vitro cum aëre interno, &amp; </s>
          <s xml:space="preserve"><lb />Experimento repetito, ad majorem diſtantiam audietur ſo-<lb />nus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-04" corresp="note-0458-04a" place="margin">1195.</note>
              <note xml:space="preserve" xml:id="note-0458-05" corresp="note-0458-05a" place="margin">TAB. XLVI. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datur etiam differentia in ſono ex numero vibrationum <lb />
<ptr xml:id="note-0458-06a" corresp="note-0458-06" type="noteAnchor" />
fibrarum corporis ſonum edentis, id eſt, ex numero unda-<lb />rum certo tempore in aëre productarum; </s>
          <s xml:space="preserve">pro diverſo enim <lb />numero percuſſionum in aurem, ſenſatio diverſa in mente <lb />datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-06" corresp="note-0458-06a" place="margin">1196.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ab hoc vibrationum numero pendet tonus muſicus, qui <lb />
<ptr xml:id="note-0458-07a" corresp="note-0458-07" type="noteAnchor" />
eo magis acutus dicitur, quo magis crebri ſunt recurſus <lb />in aëre; </s>
          <s xml:space="preserve">eo vero gravior, quo minor eſt undarum nume-<lb />rus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-07" corresp="note-0458-07a" place="margin">1197.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Gradusque acuminis diver ſorum ſonorum ſunt inter ſe ut <lb />
<ptr xml:id="note-0458-08a" corresp="note-0458-08" type="noteAnchor" />
undarum numeri, quæ eodem tempore in aëre dantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-08" corresp="note-0458-08a" place="margin">1198.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Tonus ab intenſitate ſoni non pendet, &amp; </s>
          <s xml:space="preserve">chorda agitata <lb />
<ptr xml:id="note-0458-09a" corresp="note-0458-09" type="noteAnchor" />
eundem edit ſonum, ſive per majus ſive per minus ſpatium <lb />eat, &amp; </s>
          <s xml:space="preserve">redeat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-09" corresp="note-0458-09a" place="margin">1199.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">686. 1197.</note>
        <p rend="italics">
          <s xml:space="preserve">Conſonantiæ oriuntur ex convenientia inter varios mo-<lb />
<ptr xml:id="note-0458-11a" corresp="note-0458-11" type="noteAnchor" />
tus in aëre, qui eodem tempore nervum auditorium affi-<lb />ciunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-11" corresp="note-0458-11a" place="margin">1200.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si duo corpora tremula, temporibus æqualibus, vibratio-<lb />
<ptr xml:id="note-0458-12a" corresp="note-0458-12" type="noteAnchor" />
nes peragant, nulla inter tonos datur differentia, &amp; </s>
          <s xml:space="preserve">con-
</s>
          <pb facs="0459" />
          <s xml:space="preserve">
<pb facs="0459a" />
<ptr xml:id="fig-0459a-01a" corresp="fig-0459a-01" type="figureAnchor" />
<pb facs="0460" />
<pb facs="0461" n="339" /><fw type="head">MATHEMATICA. LIB. II. CAP. XIX.</fw>
ſonantia hæc omnium perfectiſſima Vniſonus dicitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0458-12" corresp="note-0458-12a" place="margin">1201.</note>
              <figure xml:id="fig-0459a-01" corresp="fig-0459a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0459a-01" />
                <label>0459a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si vibrationes fuerint ut unum ad duo, conſonantia vo-<lb />
<ptr xml:id="note-0461-01a" corresp="note-0461-01" type="noteAnchor" />
catur Octava, aut Diapaſon.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-01" corresp="note-0461-01a" place="margin">1202.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitis vibrationibus ut duo ad tria, id eſt, ſi unius cor-<lb />
<ptr xml:id="note-0461-02a" corresp="note-0461-02" type="noteAnchor" />
poris vibratio ſecunda cum tertia alterius ſemper concur-<lb />rat, conſonantia dicitur Quinta, aut Diapente.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-02" corresp="note-0461-02a" place="margin">1203.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Vibrationes, quæ ſunt ut tria ad quatuor, dant conſo-<lb />
<ptr xml:id="note-0461-03a" corresp="note-0461-03" type="noteAnchor" />
nantiam, quæ vocatur Quarta, aut Diate{ſS}aron.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-03" corresp="note-0461-03a" place="margin">1204.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ditonus nominatur, ſi aëris recurſus fuerint ut quatuor <lb />
<ptr xml:id="note-0461-04a" corresp="note-0461-04" type="noteAnchor" />
ad quinque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-04" corresp="note-0461-04a" place="margin">1205.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Et Seſquiditonus dicitur conſonantia ex concur ſu quintæ <lb />
<ptr xml:id="note-0461-05a" corresp="note-0461-05" type="noteAnchor" />
vibrationis unius corporis cum ſexta alterius.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-05" corresp="note-0461-05a" place="margin">1206.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Conſonantiæ ex agitatione chordarum, ſi hæ fuerint e-<lb />juſdem generis, ex notis harum dimenſionibus ut &amp; </s>
          <s xml:space="preserve">tenſio-<lb />ne, facile determinantur; </s>
          <s xml:space="preserve">minimarum enim partium agita-<lb />tiones ab in integrarum chordarum agitationibus pen-<lb />dent.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ceteris paribus, ſi duarum chordarum longitudines fue-<lb />
<ptr xml:id="note-0461-06a" corresp="note-0461-06" type="noteAnchor" />
rint ut numeri recur ſuum in conſonantia, datur hæc inter <lb />ſonos quos chordæ edunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-06" corresp="note-0461-06a" place="margin">1207.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">689.</note>
        <p rend="italics">
          <s xml:space="preserve">Idem obtinet, ſi ceteris paribus diametri prædictam pro-<lb />
<ptr xml:id="note-0461-08a" corresp="note-0461-08" type="noteAnchor" />
portionem habent <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-08" corresp="note-0461-08a" place="margin">1208.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">690.</note>
        <p rend="italics">
          <s xml:space="preserve">Etiam ſi ceteris paribus proportio vibrationum in conſo-<lb />
<ptr xml:id="note-0461-10a" corresp="note-0461-10" type="noteAnchor" />
nantia detur inter radices quadratas tenſionum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-10" corresp="note-0461-10a" place="margin">1209.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">688.</note>
        <p rend="italics">
          <s xml:space="preserve">Et generaliter, poſitis chordis ejuſdem generis quibus-<lb />
<ptr xml:id="note-0461-12a" corresp="note-0461-12" type="noteAnchor" />
cunque, ſi ratio compoſita ex directa longitudinum, &amp; </s>
          <s xml:space="preserve">dia-<lb />metrorum, &amp; </s>
          <s xml:space="preserve">inverſa radicum quadratarum tenſionum, ſit <lb />ratio inter numeros vibrationum eodem tempore peractarum <lb />in conſonantia quacunque, datur hæc ex agitatione chor-<lb />darum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-12" corresp="note-0461-12a" place="margin">1210.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">691.</note>
        <p>
          <s xml:space="preserve">Hæc omnia a Muſicis fuere Experimentis confir-<lb />mata.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Notarunt hi circa haſce chordas Phænomenon admodum <lb />notabile, cujus caſus varii digni ſunt qui explicentur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dentur chordæ quæcunquæ tenſæ, vibrationes ſuas æqua-<lb />
<ptr xml:id="note-0461-14a" corresp="note-0461-14" type="noteAnchor" />
</s>
          <pb facs="0462" n="340" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
libus temporibus peragentes; </s>
          <s xml:space="preserve">agitetur una, movebitur &amp; </s>
          <s xml:space="preserve"><lb />altera. </s>
          <s xml:space="preserve">Singulæ aëris undæ ex illius chordæ motu tremu-<lb />lo impingunt in hanc, motumque minimum huic communi-<lb />cant; </s>
          <s xml:space="preserve">ex motu quantumvis exiguo variis vicibus it &amp; </s>
          <s xml:space="preserve">re-<lb />dit chorda <ptr type="noteAnchor" />, moveturque ex prioris undæ ictu, dum ſe-
<ptr xml:id="note-0462-01a" corresp="note-0462-01" type="noteAnchor" />
cunda accedit, cujus motus cum chordæ motu conſpirat <ptr type="noteAnchor" />,
<ptr xml:id="note-0462-02a" corresp="note-0462-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">hunc accelerat. </s>
          <s xml:space="preserve">Quæ de ſecunda unda dicuntur, etiam <lb />ad ſequentes referri debent, &amp; </s>
          <s xml:space="preserve">acceleratio dabitur donec <lb />ambarum chordarum motus fuerint fere æquales.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0461-14" corresp="note-0461-14a" place="margin">1211.</note>
              <note xml:space="preserve" xml:id="note-0462-01" corresp="note-0462-01a" n="*" anchored="true" place="margin">686.</note>
              <note xml:space="preserve" xml:id="note-0462-02" corresp="note-0462-02a" n="*" anchored="true" place="margin">686.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ex eadem demonſtratione ſequitur chordam agitatam mo-<lb />
<ptr xml:id="note-0462-03a" corresp="note-0462-03" type="noteAnchor" />
tum communicare alteri, quæ duas aut tres peragit vibra-<lb />tiones dum prior ſemel vibratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0462-03" corresp="note-0462-03a" place="margin">1212.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si autem chorda agitata varias peragit vibrationes dum <lb />
<ptr xml:id="note-0462-04a" corresp="note-0462-04" type="noteAnchor" />
chorda ex aëre movenda unicam peragere poteſt, ex præ-<lb />cedenti demonſtratione ſequetur motum peculiarem huic <lb />communicatum iri. </s>
          <s xml:space="preserve">Qui ut detegatur, notandum, dura-<lb />tionem vibrationis &amp; </s>
          <s xml:space="preserve">chordæ longitudinem reciprocari ita, <lb />ut, ceteris manentibus, determinata longitudo ab immi-<lb />nuta duratione vibrationis ſeparari neutiquam poſſit. <lb /></s>
          <s xml:space="preserve">Si ergo chorda quæcumque variis ictibus percutiatur, quibus <lb />huic motus communicatur, &amp; </s>
          <s xml:space="preserve">ictus magis crebri ſint, quam <lb />qui longitudini chordæ conveniunt, hujus pars, cujus longitu-<lb />do cum duratione communicatarum vibrationum reſpondet, <lb />tantum agitabitur, &amp; </s>
          <s xml:space="preserve">motus quaſi undulatorius chordæ com-<lb />municabitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">longitudo undarum in chorda pendebit a du-<lb />ratione vibrationis communicatæ, id eſt, a tempore inter ictus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0462-04" corresp="note-0462-04a" place="margin">1213.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dentur duæ chordæ, quarum una bis vibratur dum al-<lb />
<ptr xml:id="note-0462-05a" corresp="note-0462-05" type="noteAnchor" />
tera ſemel, &amp; </s>
          <s xml:space="preserve">illa agitetur, duratio vibrationum, quæ ex <lb />aëris motu huic chordæ communicantur, competit chordæ <lb />ſemilongitudinis hujus <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">talis eſt longitudo undarum in
<ptr xml:id="note-0462-06a" corresp="note-0462-06" type="noteAnchor" />
hac ipſa. </s>
          <s xml:space="preserve">Idcirco ex motu communicato dividitur chorda in <lb />duas partes æquales, punctumque medium quieſcit. </s>
          <s xml:space="preserve">Expe-<lb />rimento hoc confirmatur jungendo chartæ fruſtum chordæ, <lb />cui motus communicatur, quod ſi in puncto medio pona-<lb />tur quieſcit, in omni alio loco motu tremulo afficitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0462-05" corresp="note-0462-05a" place="margin">1214.</note>
              <note xml:space="preserve" xml:id="note-0462-06" corresp="note-0462-06a" n="*" anchored="true" place="margin">689.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0463" n="341" />
        <fw type="head">MATHEMATICA. LIB. II. CAP. XIX.</fw>
        <p>
          <s xml:space="preserve">Si chorda agitata, ut ex hujus motu altera moveatur, <lb />
<ptr xml:id="note-0463-01a" corresp="note-0463-01" type="noteAnchor" />
tres peragat vibrationes dum chorda movenda ſemel vibratur, <lb />ex motu communicato dividetur hæc in tres partes, &amp; </s>
          <s xml:space="preserve">duo <lb />dabuntur puncta quietis, quod eodem modo Experimento <lb />confirmatur. </s>
          <s xml:space="preserve">Alii caſus motus communicati, qui a Muſicis <lb />obſervantur, facile ex prædictis deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0463-01" corresp="note-0463-01a" place="margin">1215.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quæ de reflexione &amp; </s>
          <s xml:space="preserve">inflexione undarum in aqua dicta <lb />
<ptr xml:id="note-0463-02a" corresp="note-0463-02" type="noteAnchor" />
ſunt <ptr type="noteAnchor" />, ad harum reflexionem in aëre referri poſſunt, ela-
<ptr xml:id="note-0463-03a" corresp="note-0463-03" type="noteAnchor" />
ſticitate in hoc caſu eundem effectum cum preſſione aquæ <lb />elevatæ in illo exerente.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0463-02" corresp="note-0463-02a" place="margin">1216.</note>
              <note xml:space="preserve" xml:id="note-0463-03" corresp="note-0463-03a" n="*" anchored="true" place="margin">877. 879. <lb />880. 883.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex ſoni reflexione ſæpiſſime oritur ſoni repetitio, quæ <lb />
<ptr xml:id="note-0463-04a" corresp="note-0463-04" type="noteAnchor" />
Echo vocatur. </s>
          <s xml:space="preserve">Si ejuſdem undæ, per ſphæram ſeſe expan-<lb />dentis <ptr type="noteAnchor" />, partes variæ in varias ſuperficies impingant ita,
<ptr xml:id="note-0463-05a" corresp="note-0463-05" type="noteAnchor" />
ut reflexæ concurrant, fortior ibi eſt aëris motus, &amp; </s>
          <s xml:space="preserve">ſonus <lb />auditur. </s>
          <s xml:space="preserve">Variis vicibus ſæpe idem ſonus repetitur, ex va-<lb />
<ptr xml:id="note-0463-06a" corresp="note-0463-06" type="noteAnchor" />
riis ejuſdem undæ partibus ad varias diſtantias reflexis, &amp; </s>
          <s xml:space="preserve"><lb />quarum quædam ſucceſſive in eodem loco concurrunt. </s>
          <s xml:space="preserve">Ta-<lb />lis repetitio etiam aliquando datur ex repetita reflexione.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0463-04" corresp="note-0463-04a" place="margin">1217.</note>
              <note xml:space="preserve" xml:id="note-0463-05" corresp="note-0463-05a" n="*" anchored="true" place="margin">1137.</note>
              <note xml:space="preserve" xml:id="note-0463-06" corresp="note-0463-06a" place="margin">1218.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In tubo per reflexionem augetur ſonus; </s>
          <s xml:space="preserve">ut in tubis ften-<lb />
<ptr xml:id="note-0463-07a" corresp="note-0463-07" type="noteAnchor" />
toreis obſervatur. </s>
          <s xml:space="preserve">Figura omnium perfectiſſima, quæ ta-<lb />li tubæ dari poteſt, eſt parabolæ, circa lineam axi ad di-<lb />ſtantiam quartæ partis pollicis parallelam, rotantis. </s>
          <s xml:space="preserve">Si e-<lb />nim quis in tali tuba loquatur, ponendo os in axe machinæ <lb />&amp; </s>
          <s xml:space="preserve">in foco parabolæ, undæ ita reflectuntur, ut ſingulæ harum <lb />partes motum, axi machinæ parallelum, acquirant; </s>
          <s xml:space="preserve">quo un-<lb />dæ vis &amp; </s>
          <s xml:space="preserve">etiam ſonus multum augetur. </s>
          <s xml:space="preserve">Tubi extremitas, <lb />major ex qua ſonus exit, ad formam labiorum inflectitur, <lb />ut facilius unda quaquaverſum ſeſe diſpergat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0463-07" corresp="note-0463-07a" place="margin">1219.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Loquatur quis ſubmiſſa voce, dum os aperturæ minori <lb />
<ptr xml:id="note-0463-08a" corresp="note-0463-08" type="noteAnchor" />
Tubæ memoratæ applicat, ſi hæc longitudinem habeat qua-<lb />
<ptr xml:id="note-0463-09a" corresp="note-0463-09" type="noteAnchor" />
tuor pedum, ſonus ad magnam diſtantiam, &amp; </s>
          <s xml:space="preserve">in vicimis ad-<lb />modum auctum, audietur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0463-08" corresp="note-0463-08a" place="margin">1220.</note>
              <note xml:space="preserve" xml:id="note-0463-09" corresp="note-0463-09a" place="margin">TAB. XLVII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0464" n="342" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM. 1.</head>
        <head xml:space="preserve">Demonſtrationes n. 1150. 1152.</head>
        <p>
          <s xml:space="preserve">UT, quæ de lege, cui particulæ, in motu undulatorio, in itu &amp; </s>
          <s xml:space="preserve">reditu, ſub-<lb />
<ptr xml:id="note-0464-01a" corresp="note-0464-01" type="noteAnchor" />
jiciuntur, dicta ſunt, pateant, conſiderandum; </s>
          <s xml:space="preserve">legem elaſticitatis deter-<lb />minare aëris motum, &amp; </s>
          <s xml:space="preserve">vice verſa, ex motu dato, poſſe determinari legem <lb />elaſticitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0464-01" corresp="note-0464-01a" place="margin">1221.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hac utar ſecundâ methodo, &amp; </s>
          <s xml:space="preserve">ponendo, ſingulas particulas, in itu &amp; </s>
          <s xml:space="preserve">re-<lb />ditu, agitari, ut corpus quod in cycloïde vibratur, id eſt, ipſas premi vi <lb />quæ cum diſtantia a puncto medio ſpatii, itu &amp; </s>
          <s xml:space="preserve">reditu percurſi, augetur &amp; </s>
          <s xml:space="preserve"><lb />minuitur <ptr type="noteAnchor" />, demonſtrabo ad hoc requiri illam ipſam legem elaſticitatis, quam
<ptr xml:id="note-0464-02a" corresp="note-0464-02" type="noteAnchor" />
in aëre locum habere ante vidimus <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">unde conſtabit, particulas aëreas re-
<ptr xml:id="note-0464-03a" corresp="note-0464-03" type="noteAnchor" />
vera moveri juxta legem corporis penduli in cycloïde oſcillati.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0464-02" corresp="note-0464-02a" n="*" anchored="true" place="margin">287.</note>
              <note xml:space="preserve" xml:id="note-0464-03" corresp="note-0464-03a" n="*" anchored="true" place="margin">1072.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur circulus AFB, cujus circumferentia æqualis ſit latitudini undæ <lb />
<ptr xml:id="note-0464-04a" corresp="note-0464-04" type="noteAnchor" />
ſit circulus minor, priori concentricus, GIOL, cujus diameter æqualis <lb />
<ptr xml:id="note-0464-05a" corresp="note-0464-05" type="noteAnchor" />
ſit ſpatio itu &amp; </s>
          <s xml:space="preserve">reditu percurſo a particulis, quod cum exiguum ſit, circulus <lb />hic reſpectu alterius ſenſibilem non habet magnitudinem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0464-04" corresp="note-0464-04a" place="margin">1222.</note>
              <note xml:space="preserve" xml:id="note-0464-05" corresp="note-0464-05a" place="margin">T. XLVII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus circumferentiam circuli minoris repræſentare tempus, in quo <lb />unda latitudinem ſuam percurrit, id eſt tempus, in quo particula it &amp; </s>
          <s xml:space="preserve">re-<lb />dit <ptr type="noteAnchor" />, ideoque bis lineam GO percurrit, juxta legem corporis gravitate in
<ptr xml:id="note-0464-06a" corresp="note-0464-06" type="noteAnchor" />
cycloïde moti: </s>
          <s xml:space="preserve">ſemicirculus ergo repræſentat tempus, in quo ſemel linea <lb />hæc percurritur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0464-06" corresp="note-0464-06a" n="*" anchored="true" place="margin">1145.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit, in majori circulo, EF diſtantia inter centra duarum particularum vi-<lb />cinarum quieſcentium; </s>
          <s xml:space="preserve">ductis ex E &amp; </s>
          <s xml:space="preserve">F lineis ad centrum, arcus I i, in <lb />minori circulo, repræſentabit momentum ex his, de quibus n. </s>
          <s xml:space="preserve">1146. </s>
          <s xml:space="preserve">majo-<lb />rem enim circumferentiam latitudini undæ æqualem poſuimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Idcirco, ſi particula translata ſit per GH, ſequens particula, quæ per mo-<lb />mentum unum diutius fuit agitata, translata erit per G b <ptr type="noteAnchor" />, ductis
<ptr xml:id="note-0464-07a" corresp="note-0464-07" type="noteAnchor" />
IH, ih, perpendicularibus ad GO; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">differentia translationum erit Hb; <lb /></s>
          <s xml:space="preserve">differentia autem translationum particularum vicinarum, eſt augmentum, aut <lb />diminutio, diſtantiæ inter has: </s>
          <s xml:space="preserve">in hoc caſu, in quo antecedens particula <lb />per minus ſpatium fuit translata, H b, aut I m, quam huic parallelam po-<lb />nimus, eſt diminutio diſtantiæ, quæ ergo eſt EF minus I m.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0464-07" corresp="note-0464-07a" n="*" anchored="true" place="margin">304.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ratio quæ datur inter I m &amp; </s>
          <s xml:space="preserve">EF eſt compoſita, ex ratione I m ad I i, <lb />&amp; </s>
          <s xml:space="preserve">I i ad EF. </s>
          <s xml:space="preserve">Prima ratio eſt quæ datur inter IH &amp; </s>
          <s xml:space="preserve">IC; </s>
          <s xml:space="preserve">propter ſimilia <lb />rectangula triangula I m i, IHC. </s>
          <s xml:space="preserve">Secunda ratio eſt eadem quæ datur in-<lb />ter IC &amp; </s>
          <s xml:space="preserve">CE, ut patet. </s>
          <s xml:space="preserve">Ratio ex his compoſita eſt IH ad EC, aut <lb />AC.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Idcirco ſi ſemidiametro majoris circuli diſtantiam inter particulas, antea-<lb />gitationem, deſignemus, HI repræſentabit diminutionem diſtantiæ, dum <lb />arcus GI tempus agitationis repræſentat <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ſimili demonſtratione conſtat, in
<ptr xml:id="note-0464-08a" corresp="note-0464-08" type="noteAnchor" />
reditu particularum, HL repræſentare augmentum diſtantiæ, ſi arcus OL <lb />tempus reditus repræſentat, id eſt, arcus GIOL tempus agitationis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0464-08" corresp="note-0464-08a" n="*" anchored="true" place="margin">304.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc concipiamus lineam PQ, parallelam GO, &amp; </s>
          <s xml:space="preserve">quæ in P circulum <lb />majorem tangat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">continuetur HI in R; </s>
          <s xml:space="preserve">erit HR æqualis AC, ſubtractâ <lb />HI reſtat IR, quæ diſtantiam particulæ cum vicina deſignat, poſito tem-<lb />pore agitationis GI; </s>
          <s xml:space="preserve">ſi foret hoc GIOL diſtantia inter particulas eſlet
</s>
          <pb facs="0465" n="343" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. II. CAP. XIX.</fw>
RL, &amp; </s>
          <s xml:space="preserve">diſtantiæ in momentis quibuſcunque deſignantur lineis parallelis <lb />lineæ PC, ab una parte lineâ QP &amp; </s>
          <s xml:space="preserve">ad aliam ſemicirculo GIO in itu, &amp; </s>
          <s xml:space="preserve"><lb />OLG in reditu, terminatis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Differentia inter duas diſtantias vicinas eſt im aut nl, ſi Ii, aut L l, ut <lb />ante deſignat momentum, de quo in n. </s>
          <s xml:space="preserve">1146. </s>
          <s xml:space="preserve">in quo caſu hæ lineolæ conſtan-<lb />tes ſunt: </s>
          <s xml:space="preserve">ſed cum ponamus particulas agitari, in itu &amp; </s>
          <s xml:space="preserve">reditu, juxta legem <lb />corporis penduli, gravitate in cycloïde oſcillati, lineolæ ut im aut nl, ſi <lb />I i aut L l fuerint conſtantes, deſignant vim accelerantem motum, dum <lb />tempus agitationis deſignatur per GI, aut GIOL <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Ergo vis accelerans,
<ptr xml:id="note-0465-01a" corresp="note-0465-01" type="noteAnchor" />
quæ in particulas ſingulas, in motu quem finximus, omnibus momentis agit, pro. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0465-02a" corresp="note-0465-02" type="noteAnchor" />
portionalis eſt differentiæ inter diſtantias vicinas particularum; </s>
          <s xml:space="preserve">ſi nempe vis hæc <lb />accelerans in eo cum gravitate conveniat, ut agat in particulam motam, ut <lb />in quieſcentem ageret <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod obtinebit, ſi vis accelerans ab aëris elaſtici-
<ptr xml:id="note-0465-03a" corresp="note-0465-03" type="noteAnchor" />
tate pendeat, tunc enim cauſa movens cum ipſis particulis transfertur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0465-01" corresp="note-0465-01a" place="margin">1223.</note>
              <note xml:space="preserve" xml:id="note-0465-02" corresp="note-0465-02a" n="*" anchored="true" place="margin">305.</note>
              <note xml:space="preserve" xml:id="note-0465-03" corresp="note-0465-03a" n="*" anchored="true" place="margin">252.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ipſam autem hanc vim accelerantem revera in aëre locum habere demon-<lb />
<ptr xml:id="note-0465-04a" corresp="note-0465-04" type="noteAnchor" />
ſtramus. </s>
          <s xml:space="preserve">Vis, qua particulæ, quarum diſtantia deſignatur per IR, ſeſemu-<lb />tuo repellunt, eſt ad vim qua a ſe invicem repelluntur particulæ, quarum <lb />diſtantia exprimitur per ir, ut {I/RI} ad {I/ri} <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">harum virium differentia eſt
<ptr xml:id="note-0465-05a" corresp="note-0465-05" type="noteAnchor" />
vls, qua particula media agitatur, quæ vis exprimitur per <lb />{I/ri} - {I/RI} <unclear reason="illegible" /> {RI - ri/RI x ri <unclear reason="illegible" /> {mi/RI x ri}; </s>
          <s xml:space="preserve">dum vis, qua particulæ quieſcentes ſeſe mu-<lb />tuo fugiunt, quarum diſtantiam deſignat GQ, eſt {I/GQ}.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0465-04" corresp="note-0465-04a" place="margin">1224.</note>
              <note xml:space="preserve" xml:id="note-0465-05" corresp="note-0465-05a" n="*" anchored="true" place="margin">1272.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sunt ergo vires hæ ut {mi/RI x ri} ad {I/GQ}, ſive ut mi x GQ ad RI x ri; </s>
          <s xml:space="preserve">aut <lb />ad GQ<hi rend="superscript">q</hi>; </s>
          <s xml:space="preserve">quia cùm circulus minor, reſpectu majoris, ſenſibilem magnitu-<lb />dinem non habeat, QG, RI, ri, pro æqualibus ſine errore ſenſibili ha-<lb />beri poſſunt. </s>
          <s xml:space="preserve">Ultima ergo memorata ratio eſt, quæ datur inter mi &amp; </s>
          <s xml:space="preserve">GQ; <lb /></s>
          <s xml:space="preserve">dividendo nempe utramque quantitatem per GQ, quo ratio inter has non mu-<lb />tatur. </s>
          <s xml:space="preserve">Si ergo per GQ deſignemus vim, qua particulæ quieſcentes ſeſe <lb />mutuo fugiunt, im, id eſt differentia diſtantiarum vicinarum, vimacceleran-<lb />tem exprimet, quæ eſt ipſa quæ requiritur, ut ſingulæ particulæ juxta legem <lb />
<ptr xml:id="note-0465-06a" corresp="note-0465-06" type="noteAnchor" />
corporis in cycloide oſcillati agitentur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quod demonſtrandum erat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0465-06" corresp="note-0465-06a" n="*" anchored="true" place="margin">1223.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis accelerans, quæ in aëris particulas agit, cum gravitate poteſt conferri, <lb />
<ptr xml:id="note-0465-07a" corresp="note-0465-07" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">celeritas undæ cum celeritate corporis cadentis, ut diximus in n. </s>
          <s xml:space="preserve">1152.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0465-07" corresp="note-0465-07a" place="margin">1225.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando corpus in cycloïde oſcillatum, hanc integram percurrit curvam, <lb />in punctis, a puncto medio viæ percurrendæ maximè remotis, toto ſuo pre-<lb />mitur pondere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Idcirco, ut cum gravitate conferamus vim accelerantem
<ptr xml:id="note-0465-08a" corresp="note-0465-08" type="noteAnchor" />
motum particulæ, dum per GO it &amp; </s>
          <s xml:space="preserve">redit, debemus cum pondere particu-<lb />læ conferre vim, quæ in hanc agit in G, aut O, &amp; </s>
          <s xml:space="preserve">hanc C verſus, premit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0465-08" corresp="note-0465-08a" n="*" anchored="true" place="margin">285. 316.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lineæ ut I i &amp; </s>
          <s xml:space="preserve">im in puncto G confunduntur; </s>
          <s xml:space="preserve">ideo poſitis AD &amp; </s>
          <s xml:space="preserve">EF <lb />æqualibus, id eſt, poſitâ AD æquali diſtantiæ inter centra particularum <lb />quieſcentium, &amp; </s>
          <s xml:space="preserve">ductâ DC ad centrum, G g, quæ æqualis eſt I i, expri-
</s>
          <pb facs="0466" n="344" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
met vim quæ in G particulam C verſus premit, dum GQ vim exprimit, <lb />qua particulæ quieſcentes ſeſe mutuo repellunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ponamus Atmoſphæram, non mutatâ aëris quantitate, ubique ſupra lo-<lb />cum, in quo unda movetur, eſſe ejuſdem denſitatis cum aëre in hoc loco, <lb />&amp; </s>
          <s xml:space="preserve">ſit in hoc caſu altitudo Atmoſphæræ SV; </s>
          <s xml:space="preserve">ſit S s; </s>
          <s xml:space="preserve">æqualis AD, diſtan-<lb />tiæ inter centra duarum particularum vicinarum; </s>
          <s xml:space="preserve">Ss eſt ad SV, ut unitas <lb />ad numerum particularum in s V; </s>
          <s xml:space="preserve">id eſt Ss ad SV, ut pondus unius par-<lb />ticulæ ad pondus quo particulæ S, s, ad ſe mutuo pelluntur, quodpondus va-<lb />let vim qua elaſticitate particulæ hæ a ſe mutuo recedere conantur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">247.</note>
        <p>
          <s xml:space="preserve">Pondus autem unius particulæ eſt ad vim in G, de qua ſtatim locuti ſu-<lb />mus, in ratione compoſita ponderis unius particulæ ad vim elaſticam aë-<lb />ris quieſcentis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hujus vis elaſticæ ad vim in G, id eſt in ratione compo-<lb />ſita Ss ad SV, &amp; </s>
          <s xml:space="preserve">QG ad Gg. </s>
          <s xml:space="preserve">Ultima hæc ratio componitur <lb />ex ratione QG, aut AC, ad GC, &amp; </s>
          <s xml:space="preserve">GC ad Gg, quæ eadem eſt cum ra-<lb />tione AC ad AD aut Ss. </s>
          <s xml:space="preserve">Idcirco ratio compoſita ex rationibus Ss ad SV, <lb />&amp; </s>
          <s xml:space="preserve">QG ad Gg, etiam componitur ex rationibus, Ss ad SV, AC ad <lb />GC, &amp; </s>
          <s xml:space="preserve">AC ad Ss; </s>
          <s xml:space="preserve">quæ eſt ratio Ss X AC X AC ad SV X GC X Ss, <lb />aut AC<hi rend="superscript">q</hi>, ad SV X GC; </s>
          <s xml:space="preserve">ſunt ergo in hac ratione, vis gravitatis cum vi <lb />qua particulæ in motu undulatorio agitantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">qua vi, ſi pendulum longi-<lb />tudinis CG loco gravitatis agitaretur, aduas perageret vibrationes, in tem-<lb />pore in quo unda latitudinem ſuam percurrit; </s>
          <s xml:space="preserve">in hoc enim tempore parti-<lb />cula it &amp; </s>
          <s xml:space="preserve">redit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1145.</note>
        <p>
          <s xml:space="preserve">Ergo ſi aliud detur pendulum vi gravitatis agitatum &amp; </s>
          <s xml:space="preserve">longitudinis SV, <lb />quadratum temporis in quo hoc duas peragit vibrationes, eſt ad quadratum <lb />temporis in quo unda latitudinem ſuam percurrit, in ratione compoſita di-<lb />rectæ SV ad GC, &amp; </s>
          <s xml:space="preserve">inverſæ AC<hi rend="superscript">q</hi> ad SV X GC <ptr type="noteAnchor" />, ex quibus componitur
<ptr xml:id="note-0466-03a" corresp="note-0466-03" type="noteAnchor" />
ratio SV<hi rend="superscript">q</hi> ad AC<hi rend="superscript">q</hi>. </s>
          <s xml:space="preserve">Idcirco ipſa tempora ſunt ut SV ad AC. </s>
          <s xml:space="preserve">Tempus <lb />autem, in quo pendulum, cujus longitudo eſt SV, duas peragit vibratio-<lb />nes, eſt æquale tempori, in quo corpus, celeritate, cadendo a ſemialtitu-<lb />ne SV acquiſitâ, poteſt percurrere circumferentiam circuli, cujus ſemidia-<lb />meter eſt SV <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod tempus cum ſit ad tempus, in quo unda latitudinem
<ptr xml:id="note-0466-04a" corresp="note-0466-04" type="noteAnchor" />
ſuam, id eſt, circumferentiam circuli, cujus ſemidiameter AC percurrit, <lb />ut SV eſt ad AC, in qua ratione ſunt ipſæ circumferentiæ, ſpatia percur-<lb />ſa ſunt tempora; </s>
          <s xml:space="preserve">ideo velocitates æquales <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">conſtat propoſitio in n.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0466-05a" corresp="note-0466-05" type="noteAnchor" />
1152. </s>
          <s xml:space="preserve">tradita.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0466-03" corresp="note-0466-03a" n="*" anchored="true" place="margin">302.</note>
              <note xml:space="preserve" xml:id="note-0466-04" corresp="note-0466-04a" n="*" anchored="true" place="margin">257. 288. 307.</note>
              <note xml:space="preserve" xml:id="note-0466-05" corresp="note-0466-05a" n="*" anchored="true" place="margin">95.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">SCHOLIUM 2.</head>
        <head rend="italics" xml:space="preserve">De Soni intenſitate.</head>
        <p>
          <s xml:space="preserve">VIdimus ſoni intenſitatem ſequi rationem compoſitam, ex ratione nume-<lb />
<ptr xml:id="note-0466-06a" corresp="note-0466-06" type="noteAnchor" />
ri particularum, certo tempore, in aurem incurrentium &amp; </s>
          <s xml:space="preserve">ratione qua-<lb />
<ptr xml:id="note-0466-07a" corresp="note-0466-07" type="noteAnchor" />
drati velocitatis qua incurrunt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Rationes hæ nunc determinandæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0466-06" corresp="note-0466-06a" place="margin">1226.</note>
              <note xml:space="preserve" xml:id="note-0466-07" corresp="note-0466-07a" n="*" anchored="true" place="margin">1198.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Numerus particularum ſequitur rationem denſitatis aëris. </s>
          <s xml:space="preserve">Ut &amp; </s>
          <s xml:space="preserve">ratio-<lb />nem velocitatis undæ; </s>
          <s xml:space="preserve">quo enim hæc velocior eſt, eo idem numerus particu-<lb />larum breviori tempore in aurem agit, &amp; </s>
          <s xml:space="preserve">eo major eſt numerus particula-
</s>
          <pb facs="0467" />
          <s xml:space="preserve">
<pb facs="0467a" />
<ptr xml:id="fig-0467a-01a" corresp="fig-0467a-01" type="figureAnchor" />
<pb facs="0468" />
<pb facs="0469" n="345" /><fw type="head">MATHEMATICA. LIB. II. CAP XIX.</fw>
rum eodem tempore agentium. </s>
          <s xml:space="preserve">Etiam rationem ſpatii itu &amp; </s>
          <s xml:space="preserve">reditu a par-<lb />ticulis percurſi; </s>
          <s xml:space="preserve">quo enim hoc ſpatium majus eſt, eo particulæ à tym-<lb />pano magis remotæ in hoc incurrunt. </s>
          <s xml:space="preserve">Tandem rationem inverſam latitu-<lb />dinis undæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0467a-01" corresp="fig-0467a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0467a-01" />
                <label>0467a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quadratum velocitatis quo ſingulæ particulæ agunt, ſequitur rationem <lb />quadrati velocitatis undæ. </s>
          <s xml:space="preserve">Quadrati ſpatii itu &amp; </s>
          <s xml:space="preserve">reditu percurſi. </s>
          <s xml:space="preserve">Tandem <lb />rationem inverſam quadrati latitudinis undæ,</s>
        </p>
        <p>
          <s xml:space="preserve">Quando velocitas undæ non mutatur ratio inverſa latitudinis undæ eſt ratio di-<lb />
<ptr xml:id="note-0469-01a" corresp="note-0469-01" type="noteAnchor" />
recta numeri undarum determinato tempore in aurem incurrentium; </s>
          <s xml:space="preserve">poſitis un-<lb />dis æqualibus ſeſe mutuo inſequentibus, quales ſunt undæ, quæ ex continua-<lb />ta fibræ agitatione generantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0469-01" corresp="note-0469-01a" place="margin">1227.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ratio compoſita ex memoratis omnibus eſt ratio compoſita ex ratione <lb />denſitatis, ratione cubi velocitatis, ratione cubi ſpatii itu &amp; </s>
          <s xml:space="preserve">reditu percurſi, <lb />&amp; </s>
          <s xml:space="preserve">ratione inverſa cubi latitudinis undæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si ſeponamus accelerationem in n. </s>
          <s xml:space="preserve">1163. </s>
          <s xml:space="preserve">memoratam, (quæ non mutat <lb />velocitatem qua ſingulæ particulæ moventur, de qua in hiſce tantum agitur;) <lb /></s>
          <s xml:space="preserve">cubus velocitatis ſequitur rationem ſeſquiplicatam directam Elaſticitatis <lb />&amp; </s>
          <s xml:space="preserve">ſeſquiplicatam inverſam denſitatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1157.</note>
        <p>
          <s xml:space="preserve">Duæ ergo primæ rationes memoratæ reducuntur ad rationem ſeſquiplica-<lb />tam elaſticitatis &amp; </s>
          <s xml:space="preserve">rationem inverſam ſubduplicatam denſitatis. </s>
          <s xml:space="preserve">Elaſticitas <lb />autem eſt ut pondus comprimens <ptr type="noteAnchor" />, quod ſequitur rationem altitudinis Mer-
<ptr xml:id="note-0469-03a" corresp="note-0469-03" type="noteAnchor" />
curii in Tubo Torricelliano.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0469-03" corresp="note-0469-03a" n="*" anchored="true" place="margin">247.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Generaliter ergo, eſt ſoni intenſitas directe ut radix quadrata cubi altitudinis <lb />
<ptr xml:id="note-0469-04a" corresp="note-0469-04" type="noteAnchor" />
Mercurii in tubo Torricelliano, ut cubus ſpatii itu &amp; </s>
          <s xml:space="preserve">reditupercurſi, &amp; </s>
          <s xml:space="preserve">inverſè ut <lb />subus latitudinis undæ, &amp; </s>
          <s xml:space="preserve">ut radix quadrata denſitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0469-04" corresp="note-0469-04a" place="margin">1228.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">FINIS.</head>
        <head xml:space="preserve">CORRIGENDA.</head>
        <note xml:space="preserve" place="margin"> <lb />Pag. # lin. # dele # lege <lb />10. # 5. # augulos # angulos <lb />10. # 18. # logarhthmicas # logarithmicas <lb />69. # 18. # pendulorum # penduli <lb />72. # 4. # Abl # Hbl <lb />72. # 36. # OQ # BQ <lb />72. # 37. # A # P <lb />77. # 5. # BEl # BEL <lb />80. # 23. # AMB # ALB <lb />98. # penult. # continentur # continetur <lb />100. # 35. # quorum # quarum <lb />101. # 4. a fine # ALb # AbL <lb />101. # 3. a fine # A eſt L # eſt AL <lb />102. # 4. # LI, # LI <lb /></note>
        <pb facs="0470" />
        <note xml:space="preserve" place="margin"> <lb />pag. # lin. # dele # lege <lb />102. # 17. # ad # ut <lb />110. # 21. # generatur. # generatur, aut deſtrui- \\ tur. <lb />117. # 5. # &amp; #  <lb />120. # 1. # primi # primis <lb />128. # 1. # formantur # terminantur <lb />140. # 13. # antequam corpora \\ P, P, puncta # ubi corpora P, P, ad \\ puncta <lb />140. # 14. # veniant # veniant <lb />143. # 22. # e # d <lb />144. # 1. # m # n <lb />144. # 15. # Aaa X Ccc # Aaa + Ccc <lb />161. # 34. # actionem # actionum <lb />167. # 5. # Ab # Ab <lb />175. # 16. # n. 610. # n. 623. <lb />178. # 13. # LE # ad LE <lb />179. # 19. # EKG # EKD <lb />186. # 3. a fine # ſuma # ſumma <lb />187. # 28. # C X D # C X HD <lb />189. # 3. a fine. # determinatur # determinamus <lb />199. # 4. a fine # n. 691. # n. 692. <lb />207. # 7. # &amp; in hac figura non # ut in hac figura <lb />222. # 15. # cylindro # cubo <lb />259. # 15. # qui # quæ <lb />262. # 20. # aperto # apertis <lb />263. # 6. a fine # non <lb />282. # 25. # AB # AC <lb />308. # 13. # qua # quo <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">IN MARGINE</head>
        <note xml:space="preserve" place="margin"> <lb />61. # 4. # TAB. VIII. # 19. El. VI. <lb />64. # ult. # fig 1. <lb />70. # 25. # TAB. VIII. # TAB XL. <lb />109. # 4. # 397. # 379. <lb />116. # 5. a fine # 353. # 453. <lb />127. # 29. # TAB. XXIII. # TAB. XVIII. <lb />163. # 15. # 585. # 584. <lb />163. # 20. # 584. # 567. <lb />166. # 25. # 59. # 598. <lb />177. # 10. # # * 472. <lb />245. # 9. &amp; 21. # TAB. XXXV. # TAB. XXXVI. <lb />343. # 18. # 1272. # 1172. <lb />444. # 5. # 1198. # 1189. <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">FINIS.</head>
        <pb facs="0471" />
        <fw type="head">CATALOGUE</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">De quelques Livres nouveaux &amp; autres, que PIERRE VANDER Aa a LEIDE a <lb />imprimé oureçu de divers endroits, &amp; quiſe trouvent dans ſa Boutique.</head>
        <note xml:space="preserve" place="margin"> <lb />Academie univerſelle des Feux, 12°. 2 voll. <lb />Atlas des plus celebres Itineraires, fol. 2 voll. <lb /># de 103. Nouv. Cartes Geographiques. fol. <lb /># Item de 203. Cartes Geogr. fol. 2 voll. <lb /># Item avec les Villes Capitales, fol. 3 voll. <lb />Boerhaave de comparando certo in Phyſicis, 4°. <lb /># de Chemia ſuos errores expurgante. 4°. <lb /># de Vita &amp; Obitu Prof. Bernardi Albini, 4°. <lb /># Index Plantarum Horti Academici L. Bat. 8°. <lb /># Alter Index Plant. ejuſd. Horti, 4°. 2 voll. <lb /># &amp; Ruyſch de Glandulis, 4°. <lb />Bartholini Anatomie, 4°. <lb />Livre de Gueux, par Blommert, 4°. <lb />Beſchryving van Morea, fol. # China, door Nieuhof, fol. <lb />Brief over de Oudheid van’t Hof van Holland, 8°. &amp; fol. <lb />Cabinet de 42. grandes Villes d’ Europe, chacun de 4. ſeuilles, fol <lb />Les cing Sens, fol. magno. <lb />Comedies de Plaute, par Gedeville, 12°. 10 voll. <lb />Colloques d’ Eraſine, par Gedeville, 12°. 6 voll. <lb />Côtes de France &amp; d’ Eſpagne, fol. 2 voll. <lb />Catalogus Bibliothecæ publicæ Acad. Lug. Bat. fol. <lb /># publ. Acad. Franekeranæ, fol. <lb /># J. G. Grævii, 12°. <lb />Creenii Muſæum Philologicum, 8°. 2 voll. <lb /># Helvici Elenchus Judaicus, 8°. <lb /># Faſciculus Exerc. Phil. tom. Primus 8°. <lb /># Analecta Critico-Sacra, 8°. 2 voll. <lb /># Faſcis Exercitat. tomi aliquot. 8°. <lb />Conſultatien en Advyſen van Holland. 4°. 6 deelen. <lb />Delices d’ Eſpagne &amp; Portugal, 12°. 6 voll. <lb /># d’ Italie, 12°. 6 voll. <lb /># de Rome ancienne &amp; moderne, 12°. 10 voll, <lb />Delices de Suiſſe, 12°. 4 voll. --- de France, 12°. 2 voll. <lb /># &amp; Galanteries del’ Ile de France, 12°. <lb /># de la Ville de Leide, 8°. <lb />Devoirs des Maitres par Fleury, 12°. <lb />Divers Ouvrages de belles figures par Caratz, G. Reni &amp; c. ſol. <lb />Habits des Paiſans &amp; c. d’ Hollande, fol. <lb />Effigies Veter. Illuſtr. Virorum ac Fœminar. fol. 4 voll. <lb /># Profeſſorum Leydenſium, fol. 2 voll. <lb />Eraſmi Epiſtolæ omnes fol. 2. voll. <lb /># Nov. Teſt. Gr. Lat. fol. <lb /># Paraphraſis N. Teſtam. fol. <lb /># Opera Omnia, fol. XI. voll. <lb />Lettres d’ Oſſat, 12°. 5 voll. <lb />Forces del’ Europe, nouv. edition augmentée, fol 20. voll. <lb />Livre des toutes ſortes des Oyſeaux, fol. <lb />Grand Theatre Hiſtorique, par Imhof, fol. 5 voll. gr. pap. <lb /># Supplement, fol. <lb /></note>
        <note xml:space="preserve" place="margin"> <lb />Graveſande Phyſices Elementa Mathem. 4°. 2. voll. Auctior. <lb /># Supplementum ad 1. part. prim. editionis, 4°. <lb /># Inſtitutiones Philoſophiæ Newtonianæ, 12°. <lb />Gronovii marmorea baſis Coloſſi Tiberio Cæſ. erectæ, 8°. <lb />Gereformeerd Gezangboek, door Halma, 8°. &amp; 12°. <lb />Gottfried Ooſt en Weſt-Indiſe Voyagien, fol. 8. deelen. <lb />La Haye, avec ſes Edifues, Vues, &amp; c. fol. <lb />Habillemens de pluſieurs Nations 4°. <lb />Hiſtoria del Teſtam. Vecchio, di Raſael Urb. fol. <lb />Hermanni Paradiſus Batavus, 4°. <lb />Honslaardyk avec ſes Vues, &amp; c. fol. <lb />Icones Arborum, Fruticum &amp; Herb, exoticarum. 4°. <lb />Voyagien van Robert Harcourt, 8°. <lb />Imagines Principum &amp; Eruditorum Virorum, fol. <lb /># XIX. Clar. Theolog. &amp; Philolog. fol. <lb /># XX. Celeb. Medicorum. &amp; c. fol. <lb /># XLI. Viror. Celeb. in Politicis &amp;c. fol. <lb />Kippingii Antiquitates Romanæ, 8°. <lb />Nouvelle Carte d’ Allemagne, avec les Poſtes, 9. feuilles. <lb /># d’ Eſpagne &amp; du Portugal, 9. feuilles. <lb /># de la France, 6. ſeuilles. # d’ Italie, 6. ſeuilles. <lb />Nouvelle Carte des XVII. Provinces, 9. feuilles. <lb /># des Provinces Unies, 5 {1/2}. ſeuilles. <lb />La Maiſon d’ Autriche, Portraits des Empereurs, fol. <lb /># Majeſté de Veniſe, fol. 2. voll. <lb />Le Monde, en tailles douces, per Allard, fol. <lb /># Nouveau grand Theatre du Monde. fol. Atlanti. <lb />La Ville de Leide, avec ſes Ediſices, &amp; c. <lb />Les Indes Orientales &amp; Occid. par Romein de Hooge, fol. <lb />Les principales Fortereſſes de France, d’ Eſpagne &amp;c, fol. <lb /># Villes de l’ Europe, grand folio &amp; petit. <lb />Portraits des premiers Evêques du Pais bas, fol. <lb />Livre de toutes ſortes des Fleurs, par Viſſcher, ſol. <lb />Theatre des Martyrs Mennonites, par Luyke 4°. <lb />Magniſicence d’ Amſterdam, avec ſes Ediſices &amp; c. fol. <lb />Morale de Tacite, par Amelot, 12°. <lb />Magnol Hortus Regius Botanic. Monſpelienſis, 8°. <lb />Maimonides de Siclis, Hebr. &amp; Lat. cum notis 4°. <lb />Marckii Diſſertationes Phil. V. Teſtamenti, 4°. <lb />Nouveau Atlas portatif du Voyageur en general, 8°. <lb /># d’ Allemagne, 8°. <lb /># d’ Eſpagne &amp; du Portugal, 8°. <lb /># de la France &amp; Suiſſe, 8°. <lb /># de la Grand Bretagne &amp; Irlande, 8°. <lb /># d’ Italie, Naples Sicile &amp; c 8°. <lb /># des XVII. Provinces, 8°. Deux differens Sortes. <lb /># de Suede &amp; Danemarc, 8°. <lb /># d’ Aſie, Afrique &amp; Amerique, 8°. <lb />Noodt Opera Varia. 4°. <lb /></note>
        <pb facs="0472" />
        <fw type="head">CATALOGUE</fw>
        <note xml:space="preserve" place="margin"> <lb />Loo, avec ſes Vues, &amp;c. fol. <lb />Oeuvres de Coquillage, Corail, &amp;c. par Rumphius, fol. <lb /># de Mariotte, 4°. 2 voll. <lb /># de Perrault en Phyſique &amp; Mathem. 4°. 2 voll. <lb /># d’ Architecture, par Poſt fol. <lb /># par Scamozzi, fol. <lb /># par Vingboons, fol. <lb />XXV. Differens Plans des Villes, par Mortier, fol. <lb />Portraits des Dieux Payens, Heros, Rois, Reines, anciens <lb />Philoſaphes, Medicins, Poetes, Hiſtoriens, &amp; c. fol. 8 voll. <lb /># XLVIII. de quelques Papes, Empereurs, &amp; c. fol. <lb /># des Hommes Illuſtres en forme de medailles, fol. <lb /># XLI. des Grands Ducs &amp; c. fol. <lb /># des Princes &amp; Princeſſes de ce tems, fol. <lb /># XLVIII. des Comtes, Barons &amp;c. fol. <lb /># XXV. des Hommes’ Celebres, fol. <lb /># des premiers Reformateurs, fol. <lb />Paris, avec ſes principaux Edifices &amp;c. fol. <lb />Les Tuilleries, en grand. # Fontame bleau, en grand. <lb />Verſailles avec ſes Battimens. Vues, &amp; c. fol. <lb />Perizonii Stemmata Illuſtrium Familiar. fol. <lb /># Tabulæ Chronologicæ, fol. plano. <lb />Recueil de belles tailles douces en maniere noire, fol. <lb /># de pluſieurs nouv. Machines, par Perrault, 4°. <lb />Reftexions, Penſées &amp; bons mots anecdotes, 12°. <lb />Vignole regles d’ Architecture, 8°. <lb />Ruſes &amp; ſtratagemes de la Guerre, 12°. <lb />Rumphii Theſaurus Conchyliorum, &amp;c. ſol. <lb />Rotterdam avec ſes Edifices, Vues, &amp;c. fol. <lb />Sardaigne paranymphe de la Paix. <lb />Scheuchzeri Herbarium Diluvianum, duplo auctior. fol. <lb /># Itinera Alpina, novem, 4°. 4 voll. <lb />Ughellii Italia Sacra, fol. 10. voll. <lb />Spanhemii Hiſtoria Jobi, 8°. <lb />Villes &amp; Habits du Monde, par Allard, fol. <lb />Portraits de cinquante Saints &amp; Saintes, fol. <lb />Theatre de la Fontaine, 12°. <lb /># des Villes du Monde, par de Wit, grand fol. 4 voll. <lb />Portraits des Comtes d’ Hollande, par Soutman, fol. <lb />Vaillant de ſtructura Florum, 4°. <lb /># Botanicon Pariſienſe, 8°. <lb />Vie de Charles V. en tres belles figures, fol. <lb />Les Villes de Friſe, par Allard, fol. <lb />Voyages aux Indes Orientales, par Bontekoe, 12°. <lb />Voyages en Moſcovie, Tartarie &amp;c. par Olearius &amp; Mandelslo, fol. <lb />4 voll beaucoup augmenté &amp; avec tresbelles figures. <lb />Vuës des Villes, Edifices &amp;c. d’ Ejpagne &amp; Portugal, 4°. <lb /># de France, fol. 2 voll. <lb /># de la Grande Bretagne &amp; Irlande, 4°. 6. voll. <lb />Vuës des Villes, Edifices &amp; e. d’ Eſeoſſe &amp; d’ Irlande 4°. 2 voll. <lb /># de l’ Italie, de Naples &amp; c. 4°. <lb /># de la Ville de Cambridge, fol. <lb /># de Londres, Canterbury, &amp;c. ſol. 2. voll. <lb /></note>
        <note xml:space="preserve" place="margin"> <lb /># d’ Oxford. fol. <lb /># de Yorck, Lancaſter, &amp; c. fol. <lb />Verſameling van Ooſt en Weſt-Indiſe Voyagien, 8°. 29. deelen. <lb />Vignole van de 5 orders der Architecture, 8°. <lb />Vingboons Architectuur Werken, fol. 3. voll. <lb />Wilſon principia Trigonometriæ 8°. <lb />Ambaſſade des Hollandois au Fapon, 12°. 2 voll. <lb />Arrianus Gr. Lat Gronovii, fol. <lb />Catalogus Libror. Theſauri Italiæ, &amp;c. 12°. <lb />Arriani ars Tactica, Gr. Lat. cum notis, 8°. <lb />Authores de Cruce, 12°. 4 voll. <lb />Begeri Bellum Trojanum, 4°. <lb />Beughem la France Savante, 12°. <lb />Boſſe ordres del’ Archicecture, fol. <lb />Chambrai Paralelle de l’ Architecture, fol. <lb />Pautre Oeuvres d’ Architecture, fol. <lb />Broekhuyſen Oeconomia Animalis. 4°. <lb /># Rationes Philoſophico-Medicæ, 4°. <lb />Commelini Flora Malebarica, 8°. <lb />Deſcription de France, par Fig. de la Force, 12°. 6 voll. <lb />Harpocrationis Lexicon, Gronovii, 4°. <lb />Dictionaire Geographique de Baudrand, fol. <lb />Emmii Reſpublica Græciæ, 24°. 2 voll. <lb />Epiſtolæ Præſtantium Virorum, fol. <lb />Ferratii Selectæ Queſtiones, 8°. <lb />Fleetwood Inſcriptiones, 8°. <lb />Gronovii variæ Lectiones in Srephanum de Urbibus, fol. <lb /># Emendationes Pandectarum, 8°. <lb /># Indices in Theſaur. Antiq. Græcar. fol. <lb />Guericke Experimenta de vacuo ſpatio, fol. <lb />Heidani Corpus Theologiæ, 4°. 2 voll. <lb />Diſputationes Theol. Philol. Profeſſor. Leidens. 4°. <lb />Hiſtoriæ rei Nummariæ Scriptores, 4°. 2 voll. <lb />Jocoſeriæ Diſſertationes, 12°. <lb />Lipſii Opera Omnia, 8°. 4 voll. <lb /># Opuſcula, 4°. z voll. <lb />Hifloria del Gianſeniſino, per l’ Abb. Tozzi, 12°. 3 voll. <lb />Loix Civiles dans leur ordre Naturel, fol. 2. voll. <lb />Lubinietzkii Theatrum Cometicum, fol. 2 voll. <lb />Cavacii Hiſtoria Cœnobii D. Juſtinæ, 4°. <lb />Marmi Eruditi di Sert. Orſato, 4 <lb />Lydius de re Militari 4. <lb />Vita &amp; res geſtæ Franciſci Mauroceni, 4°. <lb />Mobachius de triumpho Romano, 8°. <lb />Muntingii vera Herba Brittannica, 4°. <lb />Newton Optica, 4°. <lb />{ictet Morale Chrêtienne, 12. 8 voll. <lb />Plumier Art de Tourner, fol. <lb />Przipcovii Opera, fol. <lb />Rozzi Memorie Breſciane, 4°. <lb />Iſtoria Fiorentina di B. Varchi, fol. <lb />Stockmans Opera J uridica, 4°. <lb />Teyler Architectura militaris, 4°. <lb /></note>
        <pb facs="0473" />
        <fw type="head">DES LIVRES.</fw>
        <note xml:space="preserve" place="margin"> <lb />Theſaurus Theologiælocupletiſſimus, fol. <lb />Biblia Græca LXX. Interpretum, per Bos; 4°. <lb />Bocharti Opera Omnia, fol. 2 voll. <lb />Ennii Fragmenta Columnæ, 4°. <lb />Rocchi Pirri Sicilia Sacra, fol. 2 voll. <lb />Hildeberti &amp; Marbodæi Opera, fol. <lb />Lydii Agoniſtica Sacra, 12°. <lb />Smidt Miſcellanea Sacra, 8°. 2 voll. <lb /># de VII. Aſiæ Eccleſiis, 8°. 2 voll. <lb />Tentamen de Variolis, 12°. <lb />Chauvini Lexicon Philoſophicum, fol. <lb />Bible de Martin, fol. &amp; 4°. <lb /># par Sacy, 4°. 2 voll. <lb /># Idem avec figures 4°. 2 voll. <lb />Entretiens de Charles V. &amp; Francois. I. 12°. <lb />Hiſtoire des Martyrs du tems de la Reſormation, 12°. <lb />Vies des Electeurs de Brandenbourg, fol. <lb /># des Saints, par Ribadeneira, fol. 2 voll. <lb />Beſchryving van Arabien, Archipel, Japan, fol. <lb />Galilæi Opera Mathematica 4°. <lb />Grævii &amp; Burmanni Theſaurus Antiq. &amp; Hiſtor. Italiæ, <lb />Magnæ Græciæ, Neapolis &amp;c. fol 30 voll. <lb /># Theſaur. Antiq. &amp; Hiſtor. Siciliæ, fol. 15. voll. <lb />Hauteroche Oeuvres, 12°. <lb />Ruſes de la Guerre, 12°. <lb />Semaine de Montalban, 12°. <lb />Boccalini Raguagli di Parnaſſo, 12°. 2 voll. <lb />Bois Hiſtoria Eccleſ. Pariſienſis, fol. 2 voll. <lb />Fontenelle Oeuvres, 8°. <lb />Herbelot Bibliotheque Orientale, fol. <lb />Herodote, pardu Ryer, 12°. 3 voll. <lb />Hiſtoire du Wiclefianiſme, 12. <lb /># de Floride, par la Vega, 12°. 2 voll. <lb />Leydecker de Republica Hebræorum, fol. <lb />Hiſtoire de Bretagne, par Lobineau, ſol 2 voll. <lb />Plaidoyez de le Maitre, 4°. # de Patru. 4°, <lb />Geometrie de Mallet 8°. 4 voll. <lb />Opere di Moliere, 12°. 4 voll. <lb />Cabinet de S. Genevieve, par Molinet, fol. <lb />Morale du Janſeniſme, 8°. <lb />Dictionaire Mathematique par Ozanam, 4°. <lb />Hiſtoire Univerſelle, par Petau, 12°. 5. voll. <lb /># des Drogues, par Pomet, fol. <lb />Renaudot Hiſtoria Patriarcharum, 4°. <lb />Sanſon l’ Univers, 4°. <lb />Seguini Numiſmata, 4°. 2 voll. <lb />Vaillant de Coloniis, fol. 2 voll. <lb />Virgile Oeuvres par Martignac, 12°. 3 voll. <lb />Ocuvres de le Noble, 12°. 19 voll. <lb />Barrelierius de Plantis, fol. <lb />Veteris Orbis Tabulæ Geographicæ ad Melam, 4°. <lb /></note>
        <note xml:space="preserve" place="margin"> <lb />Architecture Francoiſe, par Savot, 8°. <lb />Authores in uſum Delphini, 4°. <lb /># Apulejus, A. Gellius, Catullus, Tib. Prop. Ciceroni <lb />Epiſt. C. Nepos, Horatius, Juvenalis &amp; Perſius, Plau-<lb />tus, &amp; Ovidius. <lb />Hilarii Opera, fol. <lb />Ediſices antiques de Rome, par Desgodets, fol. <lb />Themiſti Orationes, Gr. Lat. fol. <lb />Hiſtoriæ Byzantinæ poſt Theophanem, Gr. Lat. fol. <lb />Nicephorus Gregoras, Gr. Lat. fol. 2 voll. <lb />Chronicon Orientale, Gr. Lat. fol. <lb /># Paſchale, Gr. Lat. fol. <lb />Cinnamus, Gr. Lat. fol. <lb />Zonaras, Gr. Lat fol. 2 voll. <lb />Notitia Dignitatum Imperii, 12°. <lb />Hommes Illuſtres, par Colombiere, fol. <lb />Hippocrates &amp; Galenus, Gr. Lat. fol. 13 voll. <lb />Montfaucon Palæographia, fol. <lb />Reyneau Analyſe demontrée, 4°. 2 voll. <lb /># Science du Calcul, 4°. <lb />Defenſe des Ss. Peres accuſez de Platoniſme, par Baltus, 4°. <lb />Cabaſſutii Notitia Eccl. Conciliorum, fol. <lb />Chryſogoni Mundus Marianus, fol. <lb />Auguſtini Operum Appendix, Clerici, fol. <lb />Proſperi Aquitanici Opera, fol. <lb />Bnrnet Theſaurus Medicinæ Practicæ, 4°. <lb />Jacob Bril-Werken, 4°. <lb />Collegium Argentoratenſe, per Biceium, 4°. <lb />Begeri Numiſmata Imperatorum Romanorum, fol. <lb />Geometrie Francoiſe par Beaulieu, 8°. <lb />Hiſtoire du V. &amp; N. Teſtament, par Baſnage, 12° 4 voll. <lb />Bayeri Oryctographia Norica, 4°. <lb />Aſtorius in antiquum Alcmanis Monumentum, fol. <lb />Admiranda rerum memorabilium encomia, 12°. <lb />Admonitio de morte corporali, 4° <lb />Fables d’ Eſope, en quatrains 12°. <lb />Animadverſiones in Salmaſii Specimen, 8°. <lb />Antonini Iter Brittannicum, Gale, 4°. <lb />Antoninus Liberalis, Gr Lat Berkeli, 12. <lb />Secrets concernant les Arts &amp; Metiers, 12°. <lb />Cant Impetus primi Anatomici, fol. <lb />Petri Cunaei, Eloquentiae &amp; Juris Romani quondam in <lb />Academia Batava Profeſſoris, &amp; Doctorum Virorum ad <lb />eumdem Epiſtolae. Quibus accedit Oratio in obitum Bo-<lb />naventurae Vulcanii. Nunc primum editae. Cura Petri Bur-<lb />manni. 8°. <lb />Catalogus Rariſſimorum &amp; Praeſtantiſſimorum Libro-<lb />rum qui in Theſauris Romano Graeco Italico &amp; Siculo <lb />continentur. Secundum Nomina Auctorem per Alpha-<lb />beti Ordinem Digeſtus, cum Praefatione Petri Burman-<lb />ni. 8°. <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">ET AUTRES</head>
        <pb facs="0474" />
        <pb facs="0475" />
      </div>
      <div type="section">
        <head xml:space="preserve">PHYSICES ELEMENTA</head>
      </div>
      <div type="section">
        <head xml:space="preserve">MATHEMATICA,
EXPERIMENTIS CONFIRMATA.
Sive
Introductio ad Philoſophiam</head>
      </div>
      <div type="section">
        <head xml:space="preserve">NEWTONIANAM.</head>
        <head rend="italics" xml:space="preserve">Auctore</head>
        <head xml:space="preserve">GULIELMO JACOB ’s GRAVESANDE,</head>
        <head xml:space="preserve">A. L. M. Jur. Vtr. &amp; Phil. Doctore, Regiæ Societ. Lond. Socio, <lb />Aſtron. &amp; Math. in Acad. Lugd. Bat. Profeſſore ordinario.</head>
        <head xml:space="preserve"><hi rend="small caps">Tomus</hi> <hi rend="small caps">Secundus</hi>.</head>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0475-01" />
          <label>0475-01</label>
        </figure>
      </div>
      <div type="section">
        <head xml:space="preserve">LUGDUNI BATAVORUM, <lb />Apud{<hi rend="red">PETRUM VANDER Aa,</hi>\\ Typographum Academiæ atque Civitatis,\\-&amp;\\<hi rend="red">B.</hi> &amp; <hi rend="red">P. JANSSONIOS VANDER Aa.</hi>}Bibliop.</head>
        <head xml:space="preserve">MDCC XXI. <lb />Cum Privilegio Præpotent. Ordd. Hollandiæ &amp; Weſt-Friſiæ.</head>
        <pb facs="0476" />
        <pb facs="0477" />
      </div>
      <div type="section">
        <head xml:space="preserve">PRIVILEGIE.</head>
        <p rend="italics">
          <s xml:space="preserve">DE Staaten van Holland ende Weſt-Vrieſland, doen <lb />te weeten, alſoo ons vertoont is by Pieter vander <lb />Aa, Boekverkooper tot Leyden, hoe dat by Supplt<unclear reason="illegible" />, nu al-<lb />dereerſt nizuw hadde gedrukt Gulielmi Jacobi’s Gra-<lb />veſande Phyſices Elementa Mathematica, experimen-<lb />tis confirmata. </s>
          <s xml:space="preserve">Sive Introductio ad Philoſophiam New-<lb />tonianam, in Quarto, cum figuris, het eerſte deel, ſyn-<lb />de het vervolgh van het voorſz. </s>
          <s xml:space="preserve">werk by den ſupplt. <lb /></s>
          <s xml:space="preserve">meede tegenwoordigh onder de Pars, dogh alſoo den <lb />Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">beducht was, dat eenige nydige, off baetſoeken-<lb />de Menſchen, ’t ſy binnen off buytens Lands, hem’t <lb />voorn. </s>
          <s xml:space="preserve">werk ſouden mogen koomen naate drucken, waar <lb />door by van alle ſyne groote koſten en arbeyd tot nu toe <lb />gedaan en nog te doen, ſoude verſteken ſyn, ſoo keerde <lb />den Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">ſig tot Ons verſoekende Ons Octroy, om <lb />het voorn. </s>
          <s xml:space="preserve">werk en vervolg voor den tyd van vyftien <lb />cerſt achter een volgende Jaren, alleen met ſecluſie van <lb />allen anderen hier te Lande te mogen drucken, uyt te ge-<lb />ven, en te verkopen in ſodanige taalen en formaten, als <lb />den Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">voor ſyn intereſt beſt oirbaar joude vinden, <lb />met expres verbod, waar by aan allen en eenen ygelyc-<lb />ken buyten hem Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">off die ſyn actie off recht naer-<lb />maels mochten verkrygen, door Ons verboden wiert, <lb />het voorn. </s>
          <s xml:space="preserve">werck off vervolg van dien in enigerhande <lb />taalen te drucken, naate drucken, te doen naadrucken, <lb />uyt te geven, te verkopen, ofte verhandelen, in’t groot <lb />noch klein, in’t geheel noch ten deelen, noch met, noch <lb />ſonder Platen, noch onder pretext van vermeerdering, <lb />verbeteringh, veranderingh van naem, valſche tekens, <lb />ofte hoedanigh het ook genoemt ſoude mogen werden, <lb />ofte in eenigerhande taal off taalen buyten deſen Lande <lb />gedrukt werdende, deſelve niet te mogen inbrengen, te <lb />verhandelen, off te verkopen, alles telckens op verbeurte <lb />van alle de naagedruckte, ingebrachte, verhandelde off <lb />verkogte Exemplaren, ſoo dikwils en menigmaal als <lb />deſelve ſouden werden achterhaelt, mitsgaders daar <lb />en boven een boete van drie duyſent guldens by Ons te-<lb />gens de Contraventeurs te ſiellen. </s>
          <s xml:space="preserve">SOO IS’T, dat Wy <lb />de ſaake, en’t vorſoek voorſz. </s>
          <s xml:space="preserve">overgemerkt hebbende, <lb />ende genegen weſende ter beede van den Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">uyt Onſe <lb />rechte wetenſchap, Souveraine magt, en authoriteyt <lb />den ſelven Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">geconſenteert, geaccordeert, ende geo-<lb />ctroyeert hebben, conſenteeren, accordeeren, en octro-<lb />yeeren hem mitsdeſen, dat by geduyrende den tyd van <lb />vyftien eerſt achter een volgende Jaren het voorſz werk <lb />genaemt Gulielmi Jacobi’s Graveſande Phyſices Ele-<lb />menta Mathematica, experimentis confirmata, ſive In-<lb />troductio ad Philoſophiam Newtonianam, in Quarto <lb />cum figuris met het vervolg van dien, binnen den <lb />voorſz. </s>
          <s xml:space="preserve">Onſen Lande alleen ſal mogen drucken, doen <lb />drucken, uytgeven, en verkoopen, in ſodanige taa-<lb />len en formaten, als den Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">voor ſynintereſt beſt <lb />oirbaar ſal vinden, verbiedende daerom allen, ende een <lb />ygelycken het ſelve Werk en Vervolg in eenigerhan-<lb />de taalen in ’t geheel, ofte ten deelen naa te druc-<lb />ken, te doen naa drucken, te verhandelen, ofte te ver-<lb />kopen, ofte elders naergedruckt, binnen den ſelven <lb />Onſen Lande te brengen, uvt te geven, te verhan-<lb />delen ofte te verkoopen, op verbeurte van alle de <lb />naagedruckte, ingebragte, verhandelde ofte verkog-<lb />te Exemplaren, ende een boete van drie duyſent guldens <lb />daer en boven te verbeuren, te appliceren een derde part <lb />voor den Officier, die de Calangie doen ſal, een derde <lb />part voor den Armen der plaatſe daer het caſus voor-<lb />vallen ſal, en het reſterende derde part voor den Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve"><lb />ende dit telkens ſoo menigmael als deſelve ſullen wer-<lb />den achterhaelt, alles in dien verſtande, dat W, den <lb />Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">met deſen Onſen Octroye alleen willlende gratifi-<lb />ceren totver hoedinge van ſyne ſchade door het naadruc-<lb />ken van het voorſz Werk of Vervolg, daar door in geni-<lb />gen deele verſtaen den inhoude van den te authoriſee-<lb />ren ofte te advoueren, ende veel min het ſelve onder <lb />Onſe protectie ende beſcherminge enigh meerder credit, <lb />aanſien ofte reputatie te geven, nemaar den Suppliant in <lb />cas daer in iets onbehoorlykx ſoude influeeren, alle het ſel-<lb />ve tot ſynen laſte ſal gehouden weſen te verantwoorden, <lb />tot dien eynde wel expreſſelyck begeerende, dat by aldien <lb />hy deſen Onſen Octroye voor het ſelveWerk ſalwillen ſtel-<lb />len, daar van geen geabrevieer de ofte gecontrabeerde <lb />mentie ſal mogen maecken, nemaer gehouden ſal weſen, <lb />het ſelve Octroy in ’t geheel ende ſonder eenige Omiſſie <lb />daer voor te drucken, ofte te doen drucken, ende dat by <lb />gehouden ſal ſyn een Exemplaer van het voorſz werk <lb />gebonden ende wel geconditioneert te brengen in de Bi-<lb />bliotbeeck van Onſe Univerſiteyt tot Leyden, en daer <lb />van behoorlyck te doen blycken, a les op pæne van het <lb />effect van dien te verlieſen; </s>
          <s xml:space="preserve">ende ten eynde den Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">de-<lb />ſen Onſen Conſente en Octroye moge genieten als naer be-<lb />horen, laſtenWy allen ende een ygelycken die ’t aangaen <lb />mag, dat ſy den Supplt<unclear reason="illegible" />. </s>
          <s xml:space="preserve">van den inhoude van deſen <lb />doen laten ende gedogen, ruſtelyck, vredelyck ende <lb />volkomentlyk genieten ende gebruycken, ceſſeerende alle <lb />beleth ter contrarie. </s>
          <s xml:space="preserve">Gedaen in den Hage onder Onſen <lb />Grooten Zegele bier aen doen hangen op den aghtſten <lb />November in’t Jaer onſes Heeren en Zaligmdakers ſe-<lb />venthien hondert en negentien.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Was getekent,</s>
        </p>
        <p>
          <s xml:space="preserve">A: </s>
          <s xml:space="preserve">HEINSIUS, vt</s>
        </p>
        <p rend="italics">
          <s xml:space="preserve">Ter Ordonnantie van de Staten,</s>
        </p>
        <p>
          <s xml:space="preserve">SIMON <hi rend="small caps">VAN</hi> BEAUMONT.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0478" />
        <pb facs="0479" />
        <fw type="head">LECTORI S.</fw>
        <p>
          <s xml:space="preserve">DE Methodo Philoſophandi, in Capite primo <lb /><hi rend="small caps">Tomi</hi> <hi rend="small caps">Primi</hi>, egi. </s>
          <s xml:space="preserve">Quam ſecutus ſum, eam <lb />conatus ſum in Præfatione vindicare. </s>
          <s xml:space="preserve">Præ-<lb />ſtantiæ hujus Methodi exempla præclara hoc <lb /><hi rend="small caps">Tomo</hi> continentur; </s>
          <s xml:space="preserve">quibus patet, quantum <lb />ingenio cæteros anteceſſit Philoſophos <lb />Newtonus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ante illum innumera, quæ lumen &amp; </s>
          <s xml:space="preserve">præcipuè colores <lb />ſpectant, Phyſicos latuere. </s>
          <s xml:space="preserve">Quis, ut unicum memorem, <lb />unquam ſuſpicatus eſt, corporis opacitatem ab interſtitiis <lb />pendere; </s>
          <s xml:space="preserve">ita ut, his repletis medio ejuſdem denſitatis cum <lb />particulis ipſius corporis, tranſlucidum fiat hoc.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Non minus digna eſt quæ in perpetuum celebretur <lb />totius Syſtematis Planetarii, &amp; </s>
          <s xml:space="preserve">præcipuè motus Lunæ, ex-<lb />plicatio Phyſica. </s>
          <s xml:space="preserve">Hac poterit Aſtronomia proferriultra limi-<lb />tes, quibus attentus Obſervator artem ſuam circumſcribi <lb />imaginatur. </s>
          <s xml:space="preserve">Quem enim non latent, quibus Syſtema re-<lb />gitur, leges, exactiùs, ex præviis obſervationibus, motus <lb />cœleſtes computatione determinabit, quàm ſi obſervatio-<lb />nes unicum computationis fundamentum forent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propoſitum noſtrum, in libris duobus, hoc <hi rend="small caps">Tomo</hi> conten-<lb />tis, fuit, ideam generalem tradere præcipuorum inven-<lb />torum Newtoni in Phyſicis; </s>
          <s xml:space="preserve">ut lectorem, qui primis tantum <lb />principiis Geometriæ præmunitus ad hæc Elementa legenda <lb />aptus erit, excitemus ad ſubtiliora Matheſeos ſtudia; </s>
          <s xml:space="preserve">quibus <lb />in fonte ipſo, id eſt in noſtri Philoſophi ſcriptis, poterit ea <lb />haurirè, ad quæ ne quidem præſtantiſſmi Philoſophi po-<lb />tuere attingere, &amp; </s>
          <s xml:space="preserve">quæ, niſi cum Mathematicis diligen-<lb />tioribus, non communicavit Newtonus.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0480" />
        <fw type="head">LECTORI.</fw>
        <p>
          <s xml:space="preserve">Supereſt ut lectorem Anglicum de verſionibus hujus ope-<lb />ris Anglicis ſequentia moneam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Auctorum querelas lectori faſtidii multum adferre ple-<lb />niſſimè perſuaſum habeo; </s>
          <s xml:space="preserve">has tamen vetitas quis aſſeret, <lb />ubi, à lectoris intereſſe, injuria, quam ſibi illatam con-<lb />tendit auctor, ſeparari nequit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Anglicum ſermonem tranſlatus <hi rend="small caps">Tomus</hi> primus ho-<lb />rum Elementorum, brevi poſtquam publici juris factus eſt, <lb />editus fuit Londini, cum inſcriptione nominis Celeberrimi <lb />Profeſſoris; </s>
          <s xml:space="preserve">quaſi Mathematicus Doctiff. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſcriptis ſuis Cla-<lb />rus interpretationem emendaſſet: </s>
          <s xml:space="preserve">de abuſu autem Cl. </s>
          <s xml:space="preserve">No-<lb />minis nemo dubitabit, qui vel unicam paginam, ferè ad li-<lb />bitum electam, ad examen revocabit; </s>
          <s xml:space="preserve">ubique enim, Ma-<lb />theſeos aut Phyſices principia interpreti non ſatis <lb />fuiſſe nota clarè patet. </s>
          <s xml:space="preserve">Silentio prætereo negligentiam <lb />reſpectu corrigendorum, ad calcem Libri adjectorum, <lb />ad quæ non attendit; </s>
          <s xml:space="preserve">reſpectu numerorum in margine; <lb /></s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">reſpectu diſtinctionum Propoſitionum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ante ſuſceptam illam, &amp; </s>
          <s xml:space="preserve">aliam ejuſdem libri interpre-<lb />tationem Anglicam inchoaverat Philoſophus ingenioſus <lb />Job. </s>
          <s xml:space="preserve">Theoph. </s>
          <s xml:space="preserve">Deſaguliers, cujus peritia in inſtituendis Ex-<lb />perimentis nota eſt. </s>
          <s xml:space="preserve">Hic tamen, occaſione præcedentis <lb />verſionis, nimis opus maturans, non omnes potuit feſti-<lb />nationis ſcopulos effugere. </s>
          <s xml:space="preserve">Mihi etiam inopinatum ac-<lb />cidit, hanc publicari quaſi me rogante ſuſceptam, quod me <lb />inſcio factum, interpretis ad me datæ litteræ teſtantur. </s>
          <s xml:space="preserve">Hic <lb />querelis meis reſpondit, ſe inſcio &amp; </s>
          <s xml:space="preserve">abſente, hoc à Biblio-<lb />polâ Monito interpretis fuiſſe inſertum. </s>
          <s xml:space="preserve">Ut errores Typo-<lb />graphicos condonet Lector, &amp; </s>
          <s xml:space="preserve">ad corrigenda, in fine utrius-<lb />que Tomi adjecta, velit attendere, rogatur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0481" />
      </div>
      <div type="section">
        <head xml:space="preserve">INDEX <lb />CAPITUM.</head>
        <head xml:space="preserve">LIBER TERTIUS.</head>
        <head xml:space="preserve"><hi rend="small caps">Pars</hi> <hi rend="small caps">Prima</hi>. De Igne.</head>
        <note xml:space="preserve" rend="italics" place="margin"> <lb /><hi rend="small caps">Cap</hi>. I. De Ignis proprietatibus in genere. # Pag. 1 <lb /># II. Ignem corporibus adhærere, &amp; hiſce contineri. Ubi de Electricitate. # 2 <lb /># III. De motu Ignis. Ubi de Calore &amp; Lumine. # 10 <lb /># IV. De Dilatatione ex Calore. # 13 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Pars</hi> <hi rend="small caps">Secunda</hi>. De Inflectione, Refractione, <lb />&amp; Reflectione Luminis.</head>
        <note xml:space="preserve" rend="italics" place="margin"> <lb /><hi rend="small caps">Cap</hi>. V. De Inflectione Radiorum Luminis. # 17 <lb /># VI. De Luminis Refractione, &amp; bujus legibus. # 19 <lb /># VII. De Luminis Refractione quando Media ſuperficie planâ ſeparantur. # 28 <lb /># VIII. De Refractione Luminis, poſitis Mediis ſuperficie ſphæricâ ſepara-<lb /># tis. # 31 <lb /># IX. De motu Luminis trans Medium denſius. Ubi de Lentium affectioni-<lb /># bus. # 38 <lb /># X. De Viſu. Ubi de Oculi conſtructione. # 42 <lb /># XI. De viſione trans Vitra, &amp; corrigendis quibuſdam Oculorum vitiis. # 49 <lb /># XII. De Microſcopiis &amp; Teleſcopiis. # 54 <lb /># XIII. De Reflectione Luminis. # 59 <lb /># XIV. De Speculis planis. # 64 <lb /># XV. De Speculis ſphæricis. # ibid. <lb /># XVI. De Lucernâ Magicâ. # 72 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Pars</hi> <hi rend="small caps">Tertia</hi>. De Opaco &amp; Coloribus.</head>
        <head xml:space="preserve"><hi rend="small caps">Cap</hi>. XVII. De corporum opacitate. # 75</head>
        <note xml:space="preserve" rend="italics" place="margin"> <lb /># XVIII. De diverſâ Radiorum Solarium refrangibilitate. # 78 <lb /># XIX. De Radiorum Coloribus &amp; horum immutabilitate. # 84 <lb /># XX. De Colorum permixtione. Ubi de Albore. # 89 <lb /># XXI. De Iride. # 92 <lb /># XXII. De tenuium Laminarum Coloribus. # 98 <lb /># XXIII. De corporum naturalium Coloribus. # 103 <lb /></note>
        <pb facs="0482" />
      </div>
      <div type="section">
        <head xml:space="preserve">INDEX CAPITUM. <lb />LIBER QUARTUS. <lb /><hi rend="small caps">Pars</hi> <hi rend="small caps">Prima</hi>. De Mundi Syſtemate.</head>
        <note xml:space="preserve" rend="italics" place="margin"> <lb /><hi rend="small caps">Cap</hi>. I. Idea generalis Syſtematis Planetarii. # Pag.107 <lb /># II.De Motu Apparenti. # 114 <lb /># III.De Phænomenis Solis ex motu Telluris in Orbitâ. # 117 <lb /># IV.De Phænomenis Planetarum Inferiorum, ex horum &amp; Telluris moti-<lb /># bus in Orbitis ſuis. # 119 <lb /># V.De Phænomenis Planetarum Superiorum ex horum &amp; Telluris motibus in <lb /># Orbitis ſuis. # 122 <lb /># VI.De Phænomenis Satellitum ex motu horum in Orbitis. Ubi de Eclipſibus <lb /># Solis &amp; Lunæ. # 123 <lb /># VII.De Phænomenis ex motu Solis, Planetarum &amp; Lunæ circa Axes. # 128 <lb /># VIII.De Phænomenis Telluris ſuperficiem &amp; peculiares bujus partes ſpectan-<lb /># tibus. # 132 <lb /># IX.De Phænomenis ex motu Axeos Telluris. # 143 <lb /># X.De Stellis fixis. # 144 <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Pars</hi> <hi rend="small caps">Secunda</hi>. Motuum Cœleſtium caulæ <lb />Phyſicæ.</head>
        <note xml:space="preserve" rend="italics" place="margin"> <lb /><hi rend="small caps">Cap</hi>. XI.De Univerſali Gravitate. # 146 <lb /># XII.De Materiâ Cœleſti. # Ubi vacuum dari probatur. # 153 <lb /># XIII.De Motu Telluris. # 157 <lb /># XIV.De Denſitate Planetarum. # 160 <lb /># XV.Totius Syſtematis Planetarii Explicatio Phyſica. # 165 <lb /># XVI.Motus Lunæ Explicatio Phyſica. # 170 <lb /># XVII.De Planetarum Figuris. # 185 <lb /># XVIII.Motus Axeos Telluris Explicatio Phyſica. # 189 <lb /># XIX.De Æſtu Maris. # 191 <lb /># XX.De Lunæ Denſitate &amp; Figurâ. # 197 <lb /></note>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0482-01" />
          <label>0482-01</label>
        </figure>
        <pb facs="0483" n="(1)" />
      </div>
      <div type="section">
        <head xml:space="preserve">PHYSICES <lb />ELEMENTA MATHEMATICA, <lb />EXPERIMENTIS CONFIRMATA.</head>
        <head xml:space="preserve">LIBER III. <lb />Pars I. De Igne. <lb />CAPUT I. <lb />De Ignis proprietatibus in genere.</head>
        <p>
          <s xml:space="preserve">VArias Ignis proprietates novimus, multa tamen <lb />circa hunc nos latent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hypotheſes non fingam, ex Experimentis ratio-<lb />cinaturus ſum &amp; </s>
          <s xml:space="preserve">quod nondum pleniſſime no-<lb />tum eſt intactum relinquam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ignis omnia corpora quantumvis denſa &amp; </s>
          <s xml:space="preserve">dura facillime <lb />
<ptr xml:id="note-0483-01a" corresp="note-0483-01" type="noteAnchor" />
penetrat. </s>
          <s xml:space="preserve">Nullum enim novimus corpus quod admoto <lb />igne non in omnibus punctis calefiat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0483-01" corresp="note-0483-01a" place="margin">544.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ignis celerrime movetur; </s>
          <s xml:space="preserve">conſtat hoc ex obſervationibus <lb />
<ptr xml:id="note-0483-02a" corresp="note-0483-02" type="noteAnchor" />
Aſtronomicis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0483-02" corresp="note-0483-02a" place="margin">545.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ignis ſeſe corporibus jungit; </s>
          <s xml:space="preserve">nam quando igni admoven-<lb />
<ptr xml:id="note-0483-03a" corresp="note-0483-03" type="noteAnchor" />
tur, ut jam dictum, incaleſcunt; </s>
          <s xml:space="preserve">in hoc etiam caſu expan-<lb />
<ptr xml:id="note-0483-04a" corresp="note-0483-04" type="noteAnchor" />
duntur: </s>
          <s xml:space="preserve">Quæ expanſio etiam obſervatur in corporibus cu-<lb />jus partes non cohærent, in quo caſu elaſticitatem, ſæ-<lb />
<ptr xml:id="note-0483-05a" corresp="note-0483-05" type="noteAnchor" />
pe perquam magnam, acquirunt, ut illud obſervatur in aëre <lb />&amp; </s>
          <s xml:space="preserve">vaporibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0483-03" corresp="note-0483-03a" place="margin">546.</note>
              <note xml:space="preserve" xml:id="note-0483-04" corresp="note-0483-04a" place="margin">547.</note>
              <note xml:space="preserve" xml:id="note-0483-05" corresp="note-0483-05a" place="margin">548.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ignem a corporibus ad certam ab his diſtantiam attrahi, <lb />
<ptr xml:id="note-0483-06a" corresp="note-0483-06" type="noteAnchor" />
in parte ſequenti patebit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0483-06" corresp="note-0483-06a" place="margin">549.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">611.</note>
        <p>
          <s xml:space="preserve">Si corpora quæcunque juxta ſe mutuo violento motu agi-<lb />tentur ex attritu incaleſcunt, &amp; </s>
          <s xml:space="preserve">quidem magnopere, quod <lb />ignis præſentiam indicat, id eſt, omnia corpora ignem conti-<lb />
<ptr xml:id="note-0483-08a" corresp="note-0483-08" type="noteAnchor" />
nere: </s>
          <s xml:space="preserve">ex attritu enim ignis quidem moveri, a corpore ſepa-<lb />rari, minime vero generari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0483-08" corresp="note-0483-08a" place="margin">550.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0484" n="(2)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Quibus in genere expoſitis pleraque peculiarius ſunt exa-<lb />minanda.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT II.</head>
        <p>
          <s xml:space="preserve">Ignem corporibus adbærere &amp; </s>
          <s xml:space="preserve">in hiſce contineri, <lb /># ubi de electricitate.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">IGnem omnibus corporibus contineri ex eo probari <lb />
<ptr xml:id="note-0484-01a" corresp="note-0484-01" type="noteAnchor" />
diximus, quod nulla dentur corpora quæ ex attritu non ca-<lb />lefiant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">illumque arcte cum corporum partibus cohærere in
fumo &amp; </s>
          <s xml:space="preserve">vaporibus patet: </s>
          <s xml:space="preserve">conſtant enim fumus &amp; </s>
          <s xml:space="preserve">vapor ex <lb />partibus a corporibus ſeparatis &amp; </s>
          <s xml:space="preserve">ab igne cum illis conjuncto <lb />agitatis, ſæpe violentiſſime.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0484-01" corresp="note-0484-01a" n="*" anchored="true" place="margin">550.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Varia de cætero dantur notabilia phœnomena ex igne <lb />corporibus contento oriunda, quorum quædam hic ſunt <lb />memoranda: </s>
          <s xml:space="preserve">inter hæc dantur, quæ cum electricitate con-<lb />nexionem notabilem habent, qua de cauſa de his ipſis ele-<lb />ctricitatis phœnomenis agendum etiam erit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p rend="italics">
          <s xml:space="preserve">Electricitas eſt hæc corporum proprietas qua, ſi attritu ca-<lb />
<ptr xml:id="note-0484-02a" corresp="note-0484-02" type="noteAnchor" />
lefiant, trahunt, &amp; </s>
          <s xml:space="preserve">repellunt, corpora leviora ad diſtantiam <lb />ſenſibilem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0484-02" corresp="note-0484-02a" place="margin">551.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Dentur duo fruſta cryſtalli montanæ, agitentur juxta ſe mu-<lb />
<ptr xml:id="note-0484-03a" corresp="note-0484-03" type="noteAnchor" />
tuo, ſtatim lucida in totum fiunt, licet ex attritu calorem <lb />ſenſibilem non acquirant. </s>
          <s xml:space="preserve">Lumen æque ac calor ignem da-<lb />ri indicat; </s>
          <s xml:space="preserve">lumen autem major datur in punctis in quibus <lb />ambo fruſta ſeſe mutuo tangunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0484-03" corresp="note-0484-03a" place="margin">552.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Tubus vitreus longitudinis circiter quindecim aut octode-<lb />
<ptr xml:id="note-0484-04a" corresp="note-0484-04" type="noteAnchor" />
cim pollicum &amp; </s>
          <s xml:space="preserve">diametri unius pollicis, ſi linteo aut panno <lb />quocunque in loco obſcuro atteratur, lumen emittit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0484-04" corresp="note-0484-04a" place="margin">553.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Idem hicce tubus attritu calefactus electricitatem ſenſibi-<lb />
<ptr xml:id="note-0484-05a" corresp="note-0484-05" type="noteAnchor" />
lem admodum habet; </s>
          <s xml:space="preserve">ſi enim corpora levia, ut fruſta folii <lb />
<ptr xml:id="note-0484-06a" corresp="note-0484-06" type="noteAnchor" />
aurei tenuiſſimi &amp; </s>
          <s xml:space="preserve">fuligo, plano imponantur, &amp; </s>
          <s xml:space="preserve">admovea-<lb />tur tubus, agitantur hæc corpora; </s>
          <s xml:space="preserve">a tubo attrahuntur &amp; </s>
          <s xml:space="preserve">re-
</s>
          <pb facs="0485" n="(3)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. II.</fw>
pelluntur variiſque motibus afficiuntur. </s>
          <s xml:space="preserve">Et exerit tubus <lb />hunc ſuum effectum ad varias diſtantias pro varia aëris con-<lb />ſtitutione, aliquando ad diſtantiam unius pedis; </s>
          <s xml:space="preserve">vapores in <lb />aëre effectum minuunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0484-05" corresp="note-0484-05a" place="margin">554.</note>
              <note xml:space="preserve" xml:id="note-0484-06" corresp="note-0484-06a" place="margin">TAB. I. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa hoc experimentum notatu dignum, &amp; </s>
          <s xml:space="preserve">explicatu dif-<lb />
<ptr xml:id="note-0485-01a" corresp="note-0485-01" type="noteAnchor" />
ficillimum, eſt quod ſpectat directionem attritus; </s>
          <s xml:space="preserve">manu ex-<lb />tremitas tubi tenetur dum manu altera atteritur, quod ſi fiat <lb />recedendo a manu tenente, effectus ſenſibilis non eſt; </s>
          <s xml:space="preserve">con-<lb />trarium obſervatur ſi attritus ab extremitate tubi libera diri-<lb />gatur verſus illam quæ manu tenetur. </s>
          <s xml:space="preserve">Hæcque indeſcrimi-<lb />natim obtinent, quando cum tubo ab una parte clauſo ab al-<lb />tera aperto experimentum inſtituitur, ſive tubi extremitas <lb />clauſa, ſive altera extremitas manu teneatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0485-01" corresp="note-0485-01a" place="margin">555.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Experimentis ſequentibus globi vitrei celerrime circum-<lb />
<ptr xml:id="note-0485-02a" corresp="note-0485-02" type="noteAnchor" />
rotantur; </s>
          <s xml:space="preserve">quod ut fiat requiritur ut in duobus locis oppoſi-<lb />
<ptr xml:id="note-0485-03a" corresp="note-0485-03" type="noteAnchor" />
tis cylindrice terminentur globi, unus tantum ex hiſce <lb />cylindris apertus eſt, ambo cylindris cupreis circumdantur; <lb /></s>
          <s xml:space="preserve">talis globus videtur in G : </s>
          <s xml:space="preserve">ad partem globi apertam cum cy-<lb />lindro aeneo jungitur epiſtomium E, &amp; </s>
          <s xml:space="preserve">cum cylindro aeneo <lb />oppoſito jungitur rota minor r diametri circiter unius pol-<lb />licis cum ſemiſſe; </s>
          <s xml:space="preserve">cum rota hac in centro cohæret &amp; </s>
          <s xml:space="preserve">pro-<lb />minet cylindrus aeneus exiguus; </s>
          <s xml:space="preserve">ſimilis ad partem oppoſitam <lb />datur qui jungitur cum epiſtomio E, ope cochleæ, ut <lb />quando neceſſe eſt tolli poſſit. </s>
          <s xml:space="preserve">Cylindri hi ad profundita-<lb />tem quartæ partis unius pollicis intrant foramina in ſuſten-<lb />taculis S, S, quibus globus ſuſtinetur, &amp; </s>
          <s xml:space="preserve">ſuper his cylindris <lb />movetur globus &amp; </s>
          <s xml:space="preserve">circa axem revolvitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0485-02" corresp="note-0485-02a" place="margin">556.</note>
              <note xml:space="preserve" xml:id="note-0485-03" corresp="note-0485-03a" place="margin">TAB. I. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Imponuntur ſuſtentacula S, S, tabulæ ligneæ firmiſſimæ <lb />craſſitiei ad minimum ſeſqui pollicis quæ tribus aliis tabulis <lb />ut in figura videtur ſuſtinetur: </s>
          <s xml:space="preserve">in harum anteriori datur fo-<lb />ramen f ut ſuſtentaculum S ope cochleæ firmari poſſit, eo-<lb />dem modo ope cochleæ in inferiori parte tabulæ ſuperioris <lb />firmatur ſuſtentaculum alterum S, quod in ſciſſura movetur: <lb /></s>
          <s xml:space="preserve">neceſſe eſt enim hicce motus ad globos in hoc ſitu firmandos <lb />aut tollendos, &amp; </s>
          <s xml:space="preserve">ut ſeiſſura longitudinem quatuor aut quin-<lb />que pollicum habeat deſideratur, quia globis majoribus &amp; </s>
          <s xml:space="preserve">mi-<lb />noribus pro variis experimentis utendum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0486" n="(4)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Rota major R manubrio M agitatur, &amp; </s>
          <s xml:space="preserve">illius ope globus <lb />G celerrime circumvolvitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ad latus tabulæ ſuperioris hujus machinæ datur ſciſſu-<lb />ra, per quam movetur trochlea t; </s>
          <s xml:space="preserve">cohæret hæc cum co-<lb />chlea c, cujus ope per ſciſſuram movetur, quo tenditur fu-<lb />nis rotas R &amp; </s>
          <s xml:space="preserve">r circumdans.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4. &amp; 5.</head>
        <p>
          <s xml:space="preserve">Globus vitreus diametri circiter octo aut novem pollicum, <lb />
<ptr xml:id="note-0486-01a" corresp="note-0486-01" type="noteAnchor" />
machinæ memoratæ conjungatur, &amp; </s>
          <s xml:space="preserve">celerrime in loco ob-<lb />
<ptr xml:id="note-0486-02a" corresp="note-0486-02" type="noteAnchor" />
ſcuro agitetur, dum manu globo applicata attritus datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0486-01" corresp="note-0486-01a" place="margin">557.</note>
              <note xml:space="preserve" xml:id="note-0486-02" corresp="note-0486-02a" place="margin">TAB. II. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si globus aëre ſit vacuus, totus quaſi lucidus fit ab inte-<lb />riori parte, lumenque majus eſt in locis in quibus manus vi-<lb />trum tangit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si autem glòbus aërem contineat, &amp; </s>
          <s xml:space="preserve">eodem modo agite-<lb />
<ptr xml:id="note-0486-03a" corresp="note-0486-03" type="noteAnchor" />
tur, &amp; </s>
          <s xml:space="preserve">manus applicetur, nullum in interiori aut exteriori <lb />globi ſuperficie lumen apparet; </s>
          <s xml:space="preserve">corpora vero ad exiguam a <lb />globo diſtantiam ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">quartæ partis unius pollicis aut mi-<lb />norem lucida fiunt, ſicque ſolæ partes manus applicatæ, <lb />quæ terminant aut potius circumdant partes immediate tan-<lb />gentes globum, lucidæ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0486-03" corresp="note-0486-03a" place="margin">558.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Eodem globo quo uſi ſumus in experimentis præcedenti-<lb />
<ptr xml:id="note-0486-04a" corresp="note-0486-04" type="noteAnchor" />
bus &amp; </s>
          <s xml:space="preserve">hic utimur, eodem modo machinæ ut circumvolvi <lb />
<ptr xml:id="note-0486-05a" corresp="note-0486-05" type="noteAnchor" />
poſſit applicatur; </s>
          <s xml:space="preserve">circumdatur globi pars ſuperior, ad diſtan-<lb />tiam a globo circiter quatuor pollicum, filo æneo a b c, in <lb />ſuperiori parte circulariter inflexo, cui fila tenuia annectun-<lb />turquæ verſus centrum globi protenſa ad diſtantiam quartæ <lb />partis unius pollicis a globo pertingunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0486-04" corresp="note-0486-04a" place="margin">559.</note>
              <note xml:space="preserve" xml:id="note-0486-05" corresp="note-0486-05a" place="margin">TAB. I. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Agitetur globus &amp; </s>
          <s xml:space="preserve">manus applicetur, ſtatim ex aëris agi-<lb />tatione fila irregulariter agitantur; </s>
          <s xml:space="preserve">calefacto vero ex attritu <lb />vitro, fila omnia, ut in fig. </s>
          <s xml:space="preserve">videtur, verſus globi centrum di-<lb />riguntur, ſi manus globo paululum ad latus applicetur verſus <lb />punctum in axe ad latus etiam diriguntur fila.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si globo aër extrahatur effectus totus hicce ceſſat.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">560.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 7.</head>
        <p>
          <s xml:space="preserve">Detur globus in eo ſolo cum eo quo præcedentia experi-<lb />
<ptr xml:id="note-0486-07a" corresp="note-0486-07" type="noteAnchor" />
menta inſtituuntur differens, quod in hoc experimento a-<lb />
<ptr xml:id="note-0486-08a" corresp="note-0486-08" type="noteAnchor" />
</s>
          <pb facs="0487" n="(5)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. II.</fw>
pertura globi G major requiratur, ut in hoc circellus ligneus <lb />o cum filo aut cylindro æneo conjunctus, intrudatur. </s>
          <s xml:space="preserve">Co-<lb />hæret cylindrus hic, ut in medio globi firmetur circellus, <lb />cum operculo quod in h. </s>
          <s xml:space="preserve">aperturæ globi, ad hanc obturan-<lb />dam, applicatur &amp; </s>
          <s xml:space="preserve">cochleis firmatur; </s>
          <s xml:space="preserve">epiſtomium E in cen-<lb />tro operculi huic conjungitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0486-07" corresp="note-0486-07a" place="margin">561.</note>
              <note xml:space="preserve" xml:id="note-0486-08" corresp="note-0486-08a" place="margin">TAB. I. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circumferentiæ circelli o junguntur fila tenuia quæ pro-<lb />tenſa ad globi ſuperficiem fere pertingunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Machinæ antea memoratæ globus applicatur &amp; </s>
          <s xml:space="preserve">agitatur, <lb />attrituſque ut in experimentis præcedentibus datur, calefacto <lb />attritu globo, ſi ceſſet agitatio manuſque tollatur, ſtatim fi-<lb />la eriguntur &amp; </s>
          <s xml:space="preserve">ut radii circuli verſus globi ſuperficiem diri-<lb />guntur, vix tamen per momentum temporis quieſcunt, &amp; </s>
          <s xml:space="preserve"><lb />agitatione aëris exterioris, licet globus ab omni parte exacte <lb />ſit clauſus, agitantur fila hæc, ut patet flando verſus globum <lb />licet os ab hoc duos pedes &amp; </s>
          <s xml:space="preserve">ultra diſtet. </s>
          <s xml:space="preserve">Si digitus glo-<lb />bo admoveatur, licet ille hunc non tangat, fila vicina a di-<lb />gito attrahuntur &amp; </s>
          <s xml:space="preserve">verſus digitum diriguntur, aliquando <lb />etiam hunc fugiunt. </s>
          <s xml:space="preserve">Si manus globo applicetur, violenter <lb />&amp; </s>
          <s xml:space="preserve">irregulariter fila agitantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Extracto aëre etiam ut in experimento præcedenti totus <lb />
<ptr xml:id="note-0487-01a" corresp="note-0487-01" type="noteAnchor" />
effectus ceſſat &amp; </s>
          <s xml:space="preserve">filorum ſitus, poſt æque ac ante attritum, <lb />a gravitate pendet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0487-01" corresp="note-0487-01a" place="margin">562.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ad omnia præcedentia attendamus experimenta, ſe-<lb />quentes concluſiones ex illis deduci poſſe videntur, quas <lb />non ut certas tradimus, ſed ut valde probabiles; </s>
          <s xml:space="preserve">certum <lb />a probabile rite ſemper diſtinguendum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vitrum in ſe continere, hujuſque ſuperficiem circumdari at-<lb />
<ptr xml:id="note-0487-02a" corresp="note-0487-02" type="noteAnchor" />
moſphærâ quadam quæ attritu excitatur <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">motu vibratorio
<ptr xml:id="note-0487-03a" corresp="note-0487-03" type="noteAnchor" />
agitatur, trahit enim &amp; </s>
          <s xml:space="preserve">repellit corpora levia <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">partes mi-
<ptr xml:id="note-0487-04a" corresp="note-0487-04" type="noteAnchor" />
nimæ vitri ex atritu agitantur &amp; </s>
          <s xml:space="preserve">propter harum elaſticitatem <lb />motus hicce eſt vibratorius, qui at moſphæræ memoratæ com-<lb />municatur, ideoque atmoſphæra eo ad majorem diſtantiam <lb />actionem exerit quo ex majori attritu partes vitri magis agi-<lb />tantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0487-02" corresp="note-0487-02a" place="margin">563.</note>
              <note xml:space="preserve" xml:id="note-0487-03" corresp="note-0487-03a" n="*" anchored="true" place="margin">554. 559. 561.</note>
              <note xml:space="preserve" xml:id="note-0487-04" corresp="note-0487-04a" n="*" anchored="true" place="margin">554.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ignis vitro contentus ex actione hujus atmoſphæræ expel-<lb />
<ptr xml:id="note-0487-05a" corresp="note-0487-05" type="noteAnchor" />
litur, ſaltem cum hac atmoſphæra movetur; </s>
          <s xml:space="preserve">dum enim cor-
</s>
          <pb facs="0488" n="(6)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
pora levia ad diſtantiam a vitro agitantur, corpora etiam <lb />ad diſtantiam lucida fiunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0487-05" corresp="note-0487-05a" place="margin">564.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">559. 558.</note>
        <p>
          <s xml:space="preserve">Atmoſphæram &amp; </s>
          <s xml:space="preserve">ignem facilius moveri in vacuo etiam pa-<lb />
<ptr xml:id="note-0488-02a" corresp="note-0488-02" type="noteAnchor" />
tet: </s>
          <s xml:space="preserve">ſi enim globo aër extrahatur nullum lumen, neque ele-<lb />ctricitatis actio ab exteriori parte obſervari poſſunt <ptr type="noteAnchor" />, pars
<ptr xml:id="note-0488-03a" corresp="note-0488-03" type="noteAnchor" />
vero globi interior maxime lucida apparet, igniſque majori <lb />copia in hoc experimento quam in ſtatim memorato <ptr type="noteAnchor" /> ſenſi-
<ptr xml:id="note-0488-04a" corresp="note-0488-04" type="noteAnchor" />
bilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0488-02" corresp="note-0488-02a" place="margin">565.</note>
              <note xml:space="preserve" xml:id="note-0488-03" corresp="note-0488-03a" n="*" anchored="true" place="margin">557. 560.</note>
              <note xml:space="preserve" xml:id="note-0488-04" corresp="note-0488-04a" n="*" anchored="true" place="margin">558.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Electricitatis autem actio extracto aëre etiam ab interiori <lb />parte ceſſat <ptr type="noteAnchor" />, quo everti videtur quod de faciliori motu
<ptr xml:id="note-0488-05a" corresp="note-0488-05" type="noteAnchor" />
atmoſphæræ in vacuo dictum. </s>
          <s xml:space="preserve">Minime tamen probabile <lb />eſt atmoſphæram ſæpius memoratam in hoc caſu nullibi mo-<lb />veri. </s>
          <s xml:space="preserve">Videtur e contra illam eandem cum igne viam ſequi <lb />&amp; </s>
          <s xml:space="preserve">verſus illam partem moveri ad quam minor datur reſiſten-<lb />tia; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ceſſationem actionis electricitatis tribuendam eſſe <lb />ipſi privationi aëris, quo mediante ab atmoſphæra fila mo-<lb />
<ptr xml:id="note-0488-06a" corresp="note-0488-06" type="noteAnchor" />
ventur; </s>
          <s xml:space="preserve">eodem modo ut in ſequentibus videbimus <ptr type="noteAnchor" />, ac
<ptr xml:id="note-0488-07a" corresp="note-0488-07" type="noteAnchor" />
ignis, qui liberrime omnia corpora penetrat, mediante aëre <lb />aut vapore violenter in illa agit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0488-05" corresp="note-0488-05a" n="*" anchored="true" place="margin">561.</note>
              <note xml:space="preserve" xml:id="note-0488-06" corresp="note-0488-06a" place="margin">566.</note>
              <note xml:space="preserve" xml:id="note-0488-07" corresp="note-0488-07a" n="*" anchored="true" place="margin">605. 607.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Miſſis conjecturis, nixis licet multis experimentis, ad cæte-<lb />ra quæ ignem ſpectant redeamus. </s>
          <s xml:space="preserve">Varia autem experimen-<lb />ta in vacuo peragenda ſunt, in quibus attritus requiritur, <lb />quæ ſequenti Machinâ inſtituenda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit M Machina Pneumatica de qua antea actum <ptr type="noteAnchor" />, LL lami-
<ptr xml:id="note-0488-08a" corresp="note-0488-08" type="noteAnchor" />
na ænea cui vitrea vaſa ſuper imponuntur; </s>
          <s xml:space="preserve">ad latera lami-<lb />
<ptr xml:id="note-0488-09a" corresp="note-0488-09" type="noteAnchor" />
næ dantur columnæ ligneæ duæ AD, AD, harum baſes <lb />
<ptr xml:id="note-0488-10a" corresp="note-0488-10" type="noteAnchor" />
imponuntur tabulæ ſupremæ Machinæ Pneumaticæ, pro <lb />parte tamen infra hanc tabulam per foramina penetrant ut <lb />columnæ, lignis transverſis, facile firmentur &amp; </s>
          <s xml:space="preserve">finitis expe-<lb />rimentis tollantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0488-08" corresp="note-0488-08a" place="margin">567.</note>
              <note xml:space="preserve" xml:id="note-0488-09" corresp="note-0488-09a" place="margin">TAB. II. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0488-10" corresp="note-0488-10a" n="*" anchored="true" place="margin">437.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vas vitreum in quo experimenta inſtituuntur, cujus al-<lb />titudo eſt circiter novem poll. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">diameter ſex poll.</s>
          <s xml:space="preserve">. o-<lb />perculo obtegitur, cum quo cohæret pixis cum coriis <ptr type="noteAnchor" />,
<ptr xml:id="note-0488-11a" corresp="note-0488-11" type="noteAnchor" />
hanc pertranſit axis æneus, &amp; </s>
          <s xml:space="preserve">ne, dum axis circumrotatur <lb />operculum moveri poſſit datur pars pixidis quadrata, quæ <lb />exacte congruit cum foramine quadrato in tabella lignea EE, <lb />quæ ab operculo ſuſtinetur, &amp; </s>
          <s xml:space="preserve">quæ firmatur hanc cochleis
</s>
          <pb facs="0489" n="(7)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. II.</fw>
B, Bad latera deprimendo, non autem ab ipſis columnis ſu-<lb />ſtinetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0488-11" corresp="note-0488-11a" n="*" anchored="true" place="margin">440.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Verſus ſuperioreḿ columnarum partem ab his ſuſtinetur <lb />tabella minor FF, quæ ope cochlearum etiam firmatur, <lb />cum hac lamella in inferiori parte in medio cohæret fruſtum <lb />æneum g, in quo cavitas datur, in qua movetur extremitas ſu-<lb />perior axis memorati, cujus maxima pars vitro contenta, in <lb />formam helicis ſulco circumdata cochleam format, circa <lb />quam cochleæ exteriores duæ d, d, moventur ad varia cor-<lb />pora cum axe firmanda inſervientes.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Inferior axis extremitas in cavitate c movetur. </s>
          <s xml:space="preserve">Lami-<lb />na ænea inflexa elaſtica ff cum fruſto æneo c cohæret, &amp; </s>
          <s xml:space="preserve"><lb />ope cochleæ cum lamina LL connectitur in foramine, per <lb />quod aër extrahitur, ſervato tamen in c minori foramine ut <lb />aëri tranſitus detur &amp; </s>
          <s xml:space="preserve">vas exhauriri poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Evacuato vaſe vitreo, axis memoratus, propter coria in <lb />pixide P, circumrotatur nullo admiſſo aëre, ſed ut celeri-<lb />ter circumvolvatur datur rota ænea minor r diametri circi-<lb />ter duorum pollicum, pinnulis armata in fundo ſulci in quo <lb />funis applicatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Rota major R diametri circiter trium pedum in ſitu ver-<lb />ticali, cum ſuſtentaculo, ad latus Machinæ Pneumaticæ diſ-<lb />ponitur, &amp; </s>
          <s xml:space="preserve">cum hujus pede rotæ ſuſtentaculum ope cochle-<lb />arum jungitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Funis, minorem rotam r circumdans, ſuper trochleis <lb />oblique poſitis in ſuperiori parte columnarum C, C, dedu-<lb />citur, &amp; </s>
          <s xml:space="preserve">ibi inflexus ad majorem rotam pervenit quam cir-<lb />cumdat, ita ut agitatione rotæ verticalis R, axis ſæpius me-<lb />moratus celerrime circumrotetur, quo in vacuo datur motus <lb />ad varia experimenta inſtituenda.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Detur globus vitreus diametri trium pollicum, aut duo-<lb />
<ptr xml:id="note-0489-01a" corresp="note-0489-01" type="noteAnchor" />
rum pollicum cum ſemiſſe, perforatus ab utraque parte, etiam <lb />poteſt ad foramina cylindrice terminari. </s>
          <s xml:space="preserve">Per hæc forami-<lb />na, ut globus circumagatur, tranſmittitur axis ſtatim me-<lb />moratus; </s>
          <s xml:space="preserve">ſubere ab utraque parte globi ora obteguntur &amp; </s>
          <s xml:space="preserve">fir-<lb />mantur hic ope cochlearum d, d, eodem modo ac in figura,
</s>
          <pb facs="0490" n="(8)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
harum ope firmantur orbiculi per quos axis tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0489-01" corresp="note-0489-01a" place="margin">568.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus, ſic firmatus, cum axe in vacuo motu rotæ R celer-<lb />rime movetur: </s>
          <s xml:space="preserve">ut attritus detur, pannus applicatur ab utra-<lb />que parte laminæ f, f, quæ elaſticitate ab utraque parte <lb />globum premit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si in loco obſcuro experimentum inſtituatur globus luci-<lb />dus apparebit, continuato motu ut globus attritu incaleſcat, <lb />lumen quidem augetur, ſed fixum tunc datur in locis ubi at-<lb />tritus datur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sequitur ex hoc experimento Ignem vitro contentum ut <lb />
<ptr xml:id="note-0490-01a" corresp="note-0490-01" type="noteAnchor" />
appareat aëre non indigere, incaleſcit enim &amp; </s>
          <s xml:space="preserve">lucet ſublato <lb />aëre &amp; </s>
          <s xml:space="preserve">interno &amp; </s>
          <s xml:space="preserve">externo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0490-01" corresp="note-0490-01a" place="margin">569.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Detur orbis ligneus diametri circiter duorum pollicum <lb />
<ptr xml:id="note-0490-02a" corresp="note-0490-02" type="noteAnchor" />
aut duorum pollicum cum ſemiſſe, &amp; </s>
          <s xml:space="preserve">cujus craſſities ſit ſemi-<lb />pollicis, ad latus circumdetur orbis cavitatibus ut globulis <lb />gypſeis circumdari poſſit, qui ſi in cavitatibus applicentur, <lb />firmiter orbi alligari poterunt ope fili ſingulos globos per <lb />medium trajicientis. </s>
          <s xml:space="preserve">Si per centrum hujus orbis tranſeat <lb />axis in experimento præcedenti, memoratus &amp; </s>
          <s xml:space="preserve">orbis firme-<lb />tur ut de globo ibi dictum, &amp; </s>
          <s xml:space="preserve">detur attritus ut in illo experi-<lb />mento, evacuato vaſe, in loco obſcuro lumen apparebit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0490-02" corresp="note-0490-02a" place="margin">570.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 10.</head>
        <p>
          <s xml:space="preserve">Mercurium ignem continere experimentis in vacuo inſti-<lb />
<ptr xml:id="note-0490-03a" corresp="note-0490-03" type="noteAnchor" />
tutis patet. </s>
          <s xml:space="preserve">Si enim mercurius probe depurgatus in vitro <lb />aëre vacuo agitetur lucidus apparet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0490-03" corresp="note-0490-03a" place="margin">571.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si Globo vitreo contineatur Mercurius, poterit ille cir-<lb />
<ptr xml:id="note-0490-04a" corresp="note-0490-04" type="noteAnchor" />
cumrotari ut in aliis experimentis dictum, &amp; </s>
          <s xml:space="preserve">amœnum da-<lb />bitur ſpectaculum ſi lente moveatur globus. </s>
          <s xml:space="preserve">Ope aceti fer-<lb />vidiſſimi &amp; </s>
          <s xml:space="preserve">calidi depurgatur mercurius niſi ſtannum con-<lb />tineat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0490-04" corresp="note-0490-04a" place="margin">572.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Evacuatur aëre globus mercurium continens, jungendo <lb />
<ptr xml:id="note-0490-05a" corresp="note-0490-05" type="noteAnchor" />
cum globo tubum longitudinis circiter duorum pedum, &amp; </s>
          <s xml:space="preserve"><lb />jungendo aliam tubi extremitatem ab inferiori parte cum <lb />foramine in medio laminæ Machinæ Pneumaticæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0490-05" corresp="note-0490-05a" place="margin">573.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si tunc foramen hoc, ut &amp; </s>
          <s xml:space="preserve">illud per quod aër extrahitur, <lb />tegantur vaſe laminæ memoratæ ſuper impoſito, aër facile ex <lb />globo deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0491" n="(9)" />
        <fw type="head">MATHEMATICA. LIB. III. CAP. II.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 10.</head>
        <p>
          <s xml:space="preserve">Sit orbis O; </s>
          <s xml:space="preserve">jungatur hic, adhibito tubo EE, ope co-<lb />
<ptr xml:id="note-0491-01a" corresp="note-0491-01" type="noteAnchor" />
chleæ cum foramine in lamina Machinæ pneumaticæ ita ut <lb />
<ptr xml:id="note-0491-02a" corresp="note-0491-02" type="noteAnchor" />
aër ex vaſe R, orbi O ſuperimpoſito, extrahi poſſit. </s>
          <s xml:space="preserve">Tubus <lb />autem per quod aër extrahitur prominet in vaſe ad altitudi-<lb />nem quatuor aut quinque pollicum, inflectitur &amp; </s>
          <s xml:space="preserve">parvam <lb />habet aperturam; </s>
          <s xml:space="preserve">quæ omnia obſervanda ſunt, ne quam mi-<lb />nime Mercurius ad Machinam pneumaticam pervenire poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0491-01" corresp="note-0491-01a" place="margin">574.</note>
              <note xml:space="preserve" xml:id="note-0491-02" corresp="note-0491-02a" place="margin">TAB. I. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum orbe in medio jungitur tubus æneus B; </s>
          <s xml:space="preserve">inferior pars <lb />clauſa pertingit fere ad fundum vaſis V, Mercurium depur-<lb />gatum continentis; </s>
          <s xml:space="preserve">ad latus foramen datur, quod clavo A <lb />exacte obturatur, ſuperior tubi B extremitas in vaſe R datur <lb />&amp; </s>
          <s xml:space="preserve">aperturam habet exiguam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Altitudo vaſis R eſt circiter ſedecim pollicum, diameter <lb />quatuor pollicum; </s>
          <s xml:space="preserve">ſi ex hoc aër evacuetur &amp; </s>
          <s xml:space="preserve">foramen ad <lb />latus tubi B aperiatur, preſſione aëris exterioris violentiſſi-<lb />me Mercurius tubum intrabit, &amp; </s>
          <s xml:space="preserve">proſiliet magno impetu in <lb />ſuperiorem partem vaſis R impingens.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In loco obſcuro inſtituendum Experimentum eſt, &amp; </s>
          <s xml:space="preserve">Mer-<lb />curius lucidus apparebit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 11.</head>
        <p>
          <s xml:space="preserve">Notiſſima datur chemica præparatio ex urina, Phoſphorus <lb />
<ptr xml:id="note-0491-03a" corresp="note-0491-03" type="noteAnchor" />
Vrinæ dicta, in aqua ſervatur; </s>
          <s xml:space="preserve">ſi ex illo ſtilus formetur &amp; </s>
          <s xml:space="preserve"><lb />litteræ ſuper charta ſcribantur, in loco obſcuro, igneæ appa-<lb />rebunt. </s>
          <s xml:space="preserve">Phoſphorus ipſe aqua extractus ſtatim incaleſcit &amp; </s>
          <s xml:space="preserve"><lb />fumum emittit; </s>
          <s xml:space="preserve">quæ omnia ignem magnâ copiâ Phoſphoro <lb />contineri probant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0491-03" corresp="note-0491-03a" place="margin">575.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc Experimento ſenſibilem obſervamus aquæ actionem <lb />
<ptr xml:id="note-0491-04a" corresp="note-0491-04" type="noteAnchor" />
in ignem Phoſphoro contentum; </s>
          <s xml:space="preserve">illa enim hunc retinet ita, ut <lb />minimè ex Phoſphoro, quamdiu aquâ circumdatur, exire <lb />poſſit; </s>
          <s xml:space="preserve">ſublatâ autem aquâ calor &amp; </s>
          <s xml:space="preserve">fumus ſtatim indicant <lb />ignem a Phoſphoro recedentem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0491-04" corresp="note-0491-04a" place="margin">576.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aër etiam ignem aquâ calidâ contentum quodammodo in <lb />
<ptr xml:id="note-0491-05a" corresp="note-0491-05" type="noteAnchor" />
hac retinet, id eſt cohibet ne eadem celeritate ac in vacuo <lb />exeat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0491-05" corresp="note-0491-05a" place="margin">577.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 12.</head>
        <p>
          <s xml:space="preserve">Dentur duo vaſa quæcunque æqualia &amp; </s>
          <s xml:space="preserve">ſimilia, infunda-
</s>
          <pb facs="0492" n="(10)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tur aqua ebulliens, æquali quantitate in utroque; </s>
          <s xml:space="preserve">impona-<lb />tur unum laminæ Machinæ Pneumaticæ &amp; </s>
          <s xml:space="preserve">ſuperimpoſito <lb />vaſe aër ex hoc extrahatur; </s>
          <s xml:space="preserve">dum aër extrahitur ebullit aqua <lb />violenter ex actione ignis exeuntis; </s>
          <s xml:space="preserve">ſtatim enim hæc tepida <lb />fit, dum aqua, quæ in vaſe alio aëri remanſit expoſita, vix <lb />ex calore quid amiſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quid ſimile obſervamus reſpectu ligni lucidi; </s>
          <s xml:space="preserve">lignum enim <lb />
<ptr xml:id="note-0492-01a" corresp="note-0492-01" type="noteAnchor" />
datur, quod in terra putrefactum, ſi terrâ extrahatur, lucet; <lb /></s>
          <s xml:space="preserve">terra quæ lignum circundat retinet ignem, ſublatâ hac i-<lb />gnis exit &amp; </s>
          <s xml:space="preserve">per aliquot dies lucidum manet. </s>
          <s xml:space="preserve">In vacuo cito <lb />perit lumen &amp; </s>
          <s xml:space="preserve">admiſſo aëre non reſtituitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0492-01" corresp="note-0492-01a" place="margin">578.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quomodo autem ignis in corpore retineatur a corporibus <lb />circundantibus &amp; </s>
          <s xml:space="preserve">cuinam actioni effectus hic tribuendus ſit, <lb />non facile determinari poterit; </s>
          <s xml:space="preserve">minimè probabile eſt preſ-<lb />fionem hìc eſſe conſiderandam, cùm ignis omnia corpora <lb />ſubtilitate ſua facile penetret.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT III.</head>
        <head rend="italics" xml:space="preserve">De motu Ignis, ubi de Calore &amp; Lumine.</head>
        <p>
          <s xml:space="preserve">IGnem celerrime moveri diximus <ptr type="noteAnchor" />, motus hicce pro variis
<ptr xml:id="note-0492-02a" corresp="note-0492-02" type="noteAnchor" />
circumſtantiis diverſos edit effectus. </s>
          <s xml:space="preserve">Calor &amp; </s>
          <s xml:space="preserve">lumen di-<lb />verſitati motus ignis adſcribenda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0492-02" corresp="note-0492-02a" n="*" anchored="true" place="margin">545.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Calor in corpore calido eſt agitatio partium corporis &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0492-03a" corresp="note-0492-03" type="noteAnchor" />
ignis in hoc contenti, qua agitatione motus in corpore no-<lb />ſtro datur, qui ideam caloris in mente noſtra excitat;</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0492-03" corresp="note-0492-03a" place="margin">579.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Calor noſtri reſpectu nibil eſt præter illam ideam, &amp; </s>
          <s xml:space="preserve">in <lb />
<ptr xml:id="note-0492-04a" corresp="note-0492-04" type="noteAnchor" />
corpore calido nil datur præter motum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0492-04" corresp="note-0492-04a" place="margin">580.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hic in memoriam revocare debemus, quæ no. </s>
          <s xml:space="preserve">502. </s>
          <s xml:space="preserve">de <lb />ſenſationibus in genere dicta ſunt, quæ etiam ad lumen re-<lb />ſerri debent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando ignis per lineas rectas oculos noſtros intrat, ex <lb />
<ptr xml:id="note-0492-05a" corresp="note-0492-05" type="noteAnchor" />
motu quem fibris in fundo oculi communicat, ideam luminis <lb />excitat; </s>
          <s xml:space="preserve">de quo fibrarum motu in ſequentibus peculiarius <lb />erit agendum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Motum per lineas rectas in lumine dari ex
<ptr xml:id="note-0492-06a" corresp="note-0492-06" type="noteAnchor" />
obſtaculo quo lumen intercipitur facile probatur. </s>
          <s xml:space="preserve">Contra <lb />
<ptr xml:id="note-0492-07a" corresp="note-0492-07" type="noteAnchor" />
autem talem motum in calore non requiri, motumque irre-
</s>
          <pb facs="0493" />
          <s xml:space="preserve">
</s>
          <pb facs="0493a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0493a-01a" corresp="fig-0493a-01" type="figureAnchor" />
</s>
          <pb facs="0494" />
          <s xml:space="preserve">
</s>
          <pb facs="0495" n="11" />
          <s xml:space="preserve"><fw type="head">MATHEMATIC A LIB. III. CAP. III.</fw>
gularem magis aptum eſſe ex eo probatur, quòd radii ſola-<lb />res directe a Sole ad apicem montis pervenientes, ſenſibilem <lb />quantum ad calorem non edant effectum; </s>
          <s xml:space="preserve">dum in valle in <lb />quo motu irregulari variis reflexionibus agitantur radii, ca-<lb />lor ſæpe detur maxime intenſus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0492-05" corresp="note-0492-05a" place="margin">581.</note>
              <note xml:space="preserve" xml:id="note-0492-06" corresp="note-0492-06a" place="margin">582.</note>
              <note xml:space="preserve" xml:id="note-0492-07" corresp="note-0492-07a" n="*" anchored="true" place="margin">716.</note>
              <figure xml:id="fig-0493a-01" corresp="fig-0493a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0493a-01" />
                <label>0493a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p>
          <s xml:space="preserve">Corpus vocatur lucidum, quod lumen emittit, id eſt, i-<lb />gnem per lineas rectas agitat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lumen non ubique dari ubi datur ignis, extra omne du-<lb />
<ptr xml:id="note-0495-01a" corresp="note-0495-01" type="noteAnchor" />
bium eſt; </s>
          <s xml:space="preserve">corpora calida non ſemper lucere quotidie vide-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0495-01" corresp="note-0495-01a" place="margin">583.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">An autem corpus detur lucidum ſine calore determinari <lb />
<ptr xml:id="note-0495-02a" corresp="note-0495-02" type="noteAnchor" />
non poteſt. </s>
          <s xml:space="preserve">Calor in corporibus eſt motus qui in infinitum <lb />minui poteſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">motus ille dari poteſt licet nobis non ſit <lb />ſenſibilis, de quo calore ſæpe nihil inveſtigare poſſumus; <lb /></s>
          <s xml:space="preserve">Verùm enim verò certiſſime conſtat multa dari corpora lu-<lb />cida ſine calore nobis ſenſibili <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Circa quod notandum,
<ptr xml:id="note-0495-03a" corresp="note-0495-03" type="noteAnchor" />
nullum dari calorem nobis ſenſibilem, niſi corpus quod in <lb />organa noſtra agit habeat calorem ſuperantem calorem ipſo-<lb />rum organorum. </s>
          <s xml:space="preserve">Unde videmus judicium circa calorem, <lb />quod ſenſibus fertur, omnino eſſe incertum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0495-02" corresp="note-0495-02a" place="margin">584.</note>
              <note xml:space="preserve" xml:id="note-0495-03" corresp="note-0495-03a" n="*" anchored="true" place="margin">571.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando partes minimæ ex quibus corpus quodcunque con-<lb />ſtat, attritu, aut actione ignis extranei, aut alio quocunque mo-<lb />do agitantur, ignis ab his ſeparatur &amp; </s>
          <s xml:space="preserve">in corpore agitatur, tunc-<lb />que ignis &amp; </s>
          <s xml:space="preserve">particulæ corporis attractione in ſe mutuo agunt, <lb />ut illud, experimentis in ſequentibus memorandis <ptr type="noteAnchor" />, probatur.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0495-04a" corresp="note-0495-04" type="noteAnchor" />
Qua actione particulæ quædam a corpore ſeparantur &amp; </s>
          <s xml:space="preserve">mo-<lb />tu ignis a corpore auferuntur. </s>
          <s xml:space="preserve">Hæc autem eſt cauſa quare <lb />corpora duriora violento attritu ſæpe combur antur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0495-04" corresp="note-0495-04a" n="*" anchored="true" place="margin">611.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">585.</note>
        <p rend="italics">
          <s xml:space="preserve">Deducimus ex hiſce combuſtionem corporum eſſe partium <lb />
<ptr xml:id="note-0495-06a" corresp="note-0495-06" type="noteAnchor" />
ſeparationem ex actione mutua in ſe invicem partium cor-<lb />poris &amp; </s>
          <s xml:space="preserve">ignis; </s>
          <s xml:space="preserve">harum partium quædam motu ignis ablatæ <lb />
<ptr xml:id="note-0495-07a" corresp="note-0495-07" type="noteAnchor" />
flammam &amp; </s>
          <s xml:space="preserve">fumum formant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0495-06" corresp="note-0495-06a" place="margin">586.</note>
              <note xml:space="preserve" xml:id="note-0495-07" corresp="note-0495-07a" place="margin">587.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Videmus ulterius, corpus, quod admoto igne comburi-<lb />tur, non modo diſſolvi ex actione ignis extranei, ſed etiam <lb />ex actione ignis in ipſo corpore contenti; </s>
          <s xml:space="preserve">caloremque auge-<lb />ri &amp; </s>
          <s xml:space="preserve">ex novo igne accedente, &amp; </s>
          <s xml:space="preserve">ex aucta agitatione ignis
</s>
          <pb facs="0496" n="12" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
quem corpus ipſum continet, &amp; </s>
          <s xml:space="preserve">ita calorem non ſequi pro-<lb />
<ptr xml:id="note-0496-01a" corresp="note-0496-01" type="noteAnchor" />
portionem quantitatis ignis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0496-01" corresp="note-0496-01a" place="margin">588.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa motum luminis conſtat, ut diximus <ptr type="noteAnchor" />, hoc moveri
<ptr xml:id="note-0496-02a" corresp="note-0496-02" type="noteAnchor" />
per lineas rectas; </s>
          <s xml:space="preserve">ſed utrum ſit ſucceſſivus, an momenta-<lb />neus luminis motus, diſputatur, id eſt, utrum eodem quo <lb />corpus lucere inchoat momento, lumen ad diſtantiam quam-<lb />cunque ſenſibile ſit, an vero ſucceſſive lumen ad loca magis <lb />ac magis diſtantia perveniat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0496-02" corresp="note-0496-02a" n="*" anchored="true" place="margin">581.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex obſervationibus variis aſtronomicis clare ſequi videtur, <lb />
<ptr xml:id="note-0496-03a" corresp="note-0496-03" type="noteAnchor" />
motum hunc eſſe ſucceſſivum &amp; </s>
          <s xml:space="preserve">diu de eo non dubitarunt <lb />Philoſophi; </s>
          <s xml:space="preserve">quibuſdam tamen recentioribus obſervationibus <lb />concluſiones ex primis deductæ labefactantur, &amp; </s>
          <s xml:space="preserve">quid igno-<lb />tum circa motum luminis dari fateri cogimur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0496-03" corresp="note-0496-03a" place="margin">589.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus de loco in locum non ſucceſſivus contradictionem <lb />involvit, &amp; </s>
          <s xml:space="preserve">lumini motum de loco in locum eſſe tribuendum <lb />
<ptr xml:id="note-0496-04a" corresp="note-0496-04" type="noteAnchor" />
vix in dubium vocari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0496-04" corresp="note-0496-04a" place="margin">590.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Obſervamus enim tranſlationem ignis in vaporibus &amp; </s>
          <s xml:space="preserve">in <lb />fumo; </s>
          <s xml:space="preserve">in quibus caſibus ignis ſecum fert corpora quibus ad-<lb />hæret &amp; </s>
          <s xml:space="preserve">ſæpe tamen celeriter movetur: </s>
          <s xml:space="preserve">ſi ignis ſubtilitas <lb />confideretur, facile patebit illum in immenſum retardari a <lb />corporibus quibus adhæret, &amp; </s>
          <s xml:space="preserve">liberatum velocitate maxima <lb />debere transferri.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Circa calorem &amp; </s>
          <s xml:space="preserve">lumen varia præterea obſervanda ſunt, <lb />maxime digna quæ notentur, ſed quorum multa explicatu <lb />ſunt difficillima. </s>
          <s xml:space="preserve">In Phyſicis ubi cauſæ latent, effectus ſal-<lb />tem ſunt memorandi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpora calefacta videmus multa, quorum ſi calor augea-<lb />
<ptr xml:id="note-0496-05a" corresp="note-0496-05" type="noteAnchor" />
tur lucida fiunt; </s>
          <s xml:space="preserve">talia ſunt metalla: </s>
          <s xml:space="preserve">Partium agitatione ignem <lb />emittunt, ſed non per lineas rectas; </s>
          <s xml:space="preserve">aucto verò partium <lb />motu, per lineas rectas pro parte movetur ignis &amp; </s>
          <s xml:space="preserve">cor-<lb />pus lucet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0496-05" corresp="note-0496-05a" place="margin">591.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem plane modo fumus, ſi admotâ flammâ magis in-<lb />
<ptr xml:id="note-0496-06a" corresp="note-0496-06" type="noteAnchor" />
caleſcat, ipſe in flammam convertitur; </s>
          <s xml:space="preserve">id eſt in corpus lu-<lb />cidum mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0496-06" corresp="note-0496-06a" place="margin">592.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Sit candela C, flatu extincta, quæ fumum emittit F; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0496-07a" corresp="note-0496-07" type="noteAnchor" />
admoveatur candela alia A; </s>
          <s xml:space="preserve">fumus ſeſe convertet in flam-
</s>
          <pb facs="0497" n="13" />
          <s xml:space="preserve"><fw type="head">MATHEMATIC A. LIB. III. CAP. IV.</fw>
mam, &amp; </s>
          <s xml:space="preserve">quidem ſucceſſive ad candelam C uſque, quæ ta-<lb />li modo accenditur ope candelæ A, quæ a prima diſtat <lb />pollices ſex aut octo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0496-07" corresp="note-0496-07a" place="margin">TAB II. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Aërem in ignem agere diximus <ptr type="noteAnchor" />, illius actio in hunc in
<ptr xml:id="note-0497-01a" corresp="note-0497-01" type="noteAnchor" />
multis occaſionibus minime contemnenda datur reſpectu lu-<lb />minis. </s>
          <s xml:space="preserve">Sæpe ut lumen detur, aut ut ignis ſervetur, aëris <lb />
<ptr xml:id="note-0497-02a" corresp="note-0497-02" type="noteAnchor" />
præſentia neceſſaria eſt, quod in combuſtione omnium cor-<lb />porum obſervatur, quæ abſente aëre extinguuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0497-01" corresp="note-0497-01a" n="*" anchored="true" place="margin">577.</note>
              <note xml:space="preserve" xml:id="note-0497-02" corresp="note-0497-02a" place="margin">593.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Si candela lucens, laminæ Machinæ Pneumaticæ impoſi-<lb />ta, vitro obtegatur, &amp; </s>
          <s xml:space="preserve">aër extrahatur, ſtatim extinguitur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Detur orbis chalibeus diametri circiter trium pollicum, <lb />
<ptr xml:id="note-0497-03a" corresp="note-0497-03" type="noteAnchor" />
perforetur in medio, ut per orbem tranſeat axis in vacuo <lb />mobilis <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">firmetur ille inter duos orbes ligneos ope co-
<ptr xml:id="note-0497-04a" corresp="note-0497-04" type="noteAnchor" />
chlearum d, d; </s>
          <s xml:space="preserve">laminæ elaſticæ f f annectantur fruſta Pyritæ, <lb />ita ut motu axeos attritus detur inter peripheriam orbis cha-<lb />libei &amp; </s>
          <s xml:space="preserve">Pyritas. </s>
          <s xml:space="preserve">Quamdiu aër datur in vitro, lumen ex attri-<lb />tu dari obſervatur; </s>
          <s xml:space="preserve">extracto vero aëre, licet attritus conti-<lb />nuetur, lumen non apparet; </s>
          <s xml:space="preserve">admiſſo aëre iterum ſenſibile <lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0497-03" corresp="note-0497-03a" place="margin">TAB. II. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0497-04" corresp="note-0497-04a" n="*" anchored="true" place="margin">567.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Contra etiam obſervamus aëris abſentiam ſæpiſſime requi-<lb />
<ptr xml:id="note-0497-05a" corresp="note-0497-05" type="noteAnchor" />
ri in lumine, ut illud in experimentis ante memoratis obſer-<lb />
<ptr xml:id="note-0497-06a" corresp="note-0497-06" type="noteAnchor" />
vari potuit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Tandem ſublato aëre augetur aliquando lu-
<ptr xml:id="note-0497-07a" corresp="note-0497-07" type="noteAnchor" />
men, quod &amp; </s>
          <s xml:space="preserve">in aëre videri poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0497-05" corresp="note-0497-05a" place="margin">594.</note>
              <note xml:space="preserve" xml:id="note-0497-06" corresp="note-0497-06a" n="*" anchored="true" place="margin">557. 571.</note>
              <note xml:space="preserve" xml:id="note-0497-07" corresp="note-0497-07a" place="margin">595.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Phoſphoro urinæ, de quo antea <ptr type="noteAnchor" />, litteræ inſcribantur
<ptr xml:id="note-0497-08a" corresp="note-0497-08" type="noteAnchor" />
aut figuræ delineentur in charta; </s>
          <s xml:space="preserve">in loco obſcuro ut dictum <lb />lucidæ erunt; </s>
          <s xml:space="preserve">detur hæc charta in loco vacuo, magis lit-<lb />teræ eluceſcent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0497-08" corresp="note-0497-08a" n="*" anchored="true" place="margin">575.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IV.</head>
        <head rend="italics" xml:space="preserve">De dilatatione ex calore.</head>
        <p>
          <s xml:space="preserve">OMnia corpora ex ignis actione dilatantur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hanc autem
<ptr xml:id="note-0497-09a" corresp="note-0497-09" type="noteAnchor" />
dilat at ionem, cum mutato calore immutari obſervamus; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0497-10a" corresp="note-0497-10" type="noteAnchor" />
ita ut a motu ignis non verò ab hujus quantitate pendere vi-
</s>
          <pb facs="0498" n="14" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
deatur; </s>
          <s xml:space="preserve">corpora enim ſive attritu ſive admoto igne extraneo <lb />calefiant ſeſe expandunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0497-09" corresp="note-0497-09a" place="margin">596.</note>
              <note xml:space="preserve" xml:id="note-0497-10" corresp="note-0497-10a" n="*" anchored="true" place="margin">547.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Detur lamina ferrea L, longa circiter tres pedes, ſit hæc <lb />
<ptr xml:id="note-0498-01a" corresp="note-0498-01" type="noteAnchor" />
quadrata &amp; </s>
          <s xml:space="preserve">craſſitiei quartæ partis unius pollicis; </s>
          <s xml:space="preserve">ſuper ta-<lb />bula ponitur inter duo obſtacula firma O, O; </s>
          <s xml:space="preserve">inter obſtacu-<lb />lum unum &amp; </s>
          <s xml:space="preserve">laminæ extremitatem datur regula ferrea R r, <lb />longitudinis circiter quatuor aut quinque pollicum; </s>
          <s xml:space="preserve">latior eſt <lb />hæc regula in R quam in r quantitate quartæ partis unius <lb />pollicis, &amp; </s>
          <s xml:space="preserve">paululum eſt obliqua extremitas laminæ L ut cum <lb />regulæ latere congruat, quæ in partes æquales exiguas divi-<lb />ditur, &amp; </s>
          <s xml:space="preserve">quantum poteſt intruditur inter obſtaculum &amp; </s>
          <s xml:space="preserve">re-<lb />gulæ extremitatem, &amp; </s>
          <s xml:space="preserve">notatur diviſio quæ cum latere la-<lb />minæ congruit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0498-01" corresp="note-0498-01a" place="margin">TAB. III. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Calefiat deinde lamina ſive attritu, ſive admoto igne, ite-<lb />rumque inter obſtacula ponatur &amp; </s>
          <s xml:space="preserve">intrudatur regula R r, <lb />non ad eandem diviſionem quam antea poterit intrudi quod <lb />dilatatam laminam clariſſimè indicat.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Liquida eodem modo ac ſolida ex calore dilatari hac me-<lb />
<ptr xml:id="note-0498-02a" corresp="note-0498-02" type="noteAnchor" />
thodo probatur. </s>
          <s xml:space="preserve">Sit Globus vitreus G, cui annectitur tu-<lb />
<ptr xml:id="note-0498-03a" corresp="note-0498-03" type="noteAnchor" />
bus exiguus E D, ſi globus liquido quocunque impleatur ita, ut <lb />ad altitudinem quamcunque in tubo pertingat, calefacto <lb />globo aſcendet liquidum in tubo; </s>
          <s xml:space="preserve">ad quod calor exiguus <lb />ſufficit, etiamſi de Mercurio liquidorum denſiſſimo agatur. <lb /></s>
          <s xml:space="preserve">Experimentum eodem modo, ſed melius, procedit ſi loco glo-<lb />bi detur cylindrus cavus C cum annexo tubo B A; </s>
          <s xml:space="preserve">citius e-<lb />nim calor toto liquido communicatur in cylindro quam in <lb />globo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0498-02" corresp="note-0498-02a" place="margin">597.</note>
              <note xml:space="preserve" xml:id="note-0498-03" corresp="note-0498-03a" place="margin">TAB. II. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si tubus, E D aut B A in partes aquales dividatur; </s>
          <s xml:space="preserve">aut <lb />
<ptr xml:id="note-0498-04a" corresp="note-0498-04" type="noteAnchor" />
tubus, cum globo aut cylindro, tabulæ applicetur ita, ut di-<lb />viſiones æquales in tabula cum tubo congruant, poterit tali <lb />Machinâ calor quodammodo menſurari: </s>
          <s xml:space="preserve">aſcendit enim &amp; </s>
          <s xml:space="preserve"><lb />deſcendit liquidum in tubo dum creſcit aut minuitur calor <lb />corporum circumdantium. </s>
          <s xml:space="preserve">Thermometra vocantur hæ Ma-<lb />
<ptr xml:id="note-0498-05a" corresp="note-0498-05" type="noteAnchor" />
chinæ &amp; </s>
          <s xml:space="preserve">vulgares admodum ſunt. </s>
          <s xml:space="preserve">Indicant quidem hæ <lb />mutationem in calore, ſed an caloris gradum monſtrent in-
</s>
          <pb facs="0499" n="15" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. IV.</fw>
certum eſt, id eſt ignotum eſt quænam relatio detur inter <lb />mutationem in expanſione &amp; </s>
          <s xml:space="preserve">mutationem in calore; </s>
          <s xml:space="preserve">ut ex <lb />comparatis dilatationibus gradus caloris poſſint conferri in-<lb />ter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0498-04" corresp="note-0498-04a" place="margin">598.</note>
              <note xml:space="preserve" xml:id="note-0498-05" corresp="note-0498-05a" place="margin">599.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſubito incaleſcat globus G aut cylindrus C, ſtatim li-<lb />
<ptr xml:id="note-0499-01a" corresp="note-0499-01" type="noteAnchor" />
quidum in tubo deſcendit, ſed immediate poſt aſcendit. <lb /></s>
          <s xml:space="preserve">Ex calore ſubito citius vitrum ipſum incaleſcit quam liqui-<lb />dum in vitro contentum; </s>
          <s xml:space="preserve">ideo dilatato ex calore vitro, &amp; </s>
          <s xml:space="preserve"><lb />eo auctâ hujus capacitate, deſcendit liquidum, ſed imme-<lb />diate poſt calor liquido communicatur, quod ideo aſcendit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0499-01" corresp="note-0499-01a" place="margin">600.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex corporum expanſione patet particulas, ex quibus cor-<lb />
<ptr xml:id="note-0499-02a" corresp="note-0499-02" type="noteAnchor" />
pora conſtant, ex actione ignis acquirere vim repellentem <lb />qua a ſe mutuo recedere conantur, &amp; </s>
          <s xml:space="preserve">quæ cum vi qua par-<lb />ticulæ ſe ſe mutuo petunt <ptr type="noteAnchor" /> contrarie agit. </s>
          <s xml:space="preserve">Quamdiu hæc vis
<ptr xml:id="note-0499-03a" corresp="note-0499-03" type="noteAnchor" />
illam ſuperat particulæ cohœrent minus aut magis pro di-<lb />verſo caloris gradu. </s>
          <s xml:space="preserve">Quando vis repellens fere adæquat vim <lb />attrahentem, particulæ antea intimè junctæ vix cohœrent, &amp; </s>
          <s xml:space="preserve"><lb />inpreſſioni cuicunque cedunt &amp; </s>
          <s xml:space="preserve">facile moventur inter ſe; <lb /></s>
          <s xml:space="preserve">unde videmus corpus ſolidum calore in liquidum mutari, <lb />
<ptr xml:id="note-0499-04a" corresp="note-0499-04" type="noteAnchor" />
quod in omnibus corporibus quæ calore liquefiunt obſerva-<lb />tur, imminuto vero calore ad priſtinum ſtatum redeunt. <lb /></s>
          <s xml:space="preserve">Quæritur an non fluiditas omnis a calore pendeat? </s>
          <s xml:space="preserve">quod de-<lb />
<ptr xml:id="note-0499-05a" corresp="note-0499-05" type="noteAnchor" />
terminari non poteſt, quia corpus omnino igne deſtitutum <lb />nullum novimus; </s>
          <s xml:space="preserve">illud certum eſt calorem non modo cauſam <lb />eſſe fluiditatis in metallis, cerâ &amp; </s>
          <s xml:space="preserve">ſimilibus corporibus lique-<lb />factis, ſed multa corpora, quæ vulgo inter fluida referuntur, a <lb />calore ſolo fluere; </s>
          <s xml:space="preserve">ſic aqua eſt glacies liquefacta, ſublato <lb />
<ptr xml:id="note-0499-06a" corresp="note-0499-06" type="noteAnchor" />
enim proparte aquæ calore coaleſcit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0499-02" corresp="note-0499-02a" place="margin">601.</note>
              <note xml:space="preserve" xml:id="note-0499-03" corresp="note-0499-03a" n="*" anchored="true" place="margin">31.</note>
              <note xml:space="preserve" xml:id="note-0499-04" corresp="note-0499-04a" place="margin">602.</note>
              <note xml:space="preserve" xml:id="note-0499-05" corresp="note-0499-05a" place="margin">603.</note>
              <note xml:space="preserve" xml:id="note-0499-06" corresp="note-0499-06a" place="margin">604.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Calor ita poteſt adaugeri, ut in quibuſdam corporibus tota <lb />
<ptr xml:id="note-0499-07a" corresp="note-0499-07" type="noteAnchor" />
vis attrahens ſuperetur a vi repellente, in quo caſu particu-<lb />læ ſeſe mutuo fugiunt; </s>
          <s xml:space="preserve">id eſt vim elaſticam acquirunt, quæ <lb />ſimilis eſt illi qua particulæ aëris gaudent <ptr type="noteAnchor" />, quæ etiam in
<ptr xml:id="note-0499-08a" corresp="note-0499-08" type="noteAnchor" />
aëre calore augetur; </s>
          <s xml:space="preserve">effectum hunc obſervamus in fumo &amp; </s>
          <s xml:space="preserve"><lb />vaporibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0499-07" corresp="note-0499-07a" place="margin">605.</note>
              <note xml:space="preserve" xml:id="note-0499-08" corresp="note-0499-08a" n="*" anchored="true" place="margin">431.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Detur globus cavus æneus E, diametri circiter quatuor <lb />
<ptr xml:id="note-0499-09a" corresp="note-0499-09" type="noteAnchor" />
pollicum, cum manubrio M; </s>
          <s xml:space="preserve">cum globo jungitur tubus T
</s>
          <pb facs="0500" n="16" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cujus apertura vigeſimam pollicis partem vix æquat. </s>
          <s xml:space="preserve">Cale-<lb />fiat globus, aër in globo ſeſe expandet <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">per tubum exi-
<ptr xml:id="note-0500-01a" corresp="note-0500-01" type="noteAnchor" />
bit; </s>
          <s xml:space="preserve">aquâ frigidâ immergatur globus, frigore aër iterum con-<lb />denſabitur &amp;</s>
          <s xml:space="preserve">, preſſione atmoſphæræ in aquæ ſuperficiem, <lb />aqua intrabit globum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0499-09" corresp="note-0499-09a" place="margin">TAB. III. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0500-01" corresp="note-0500-01a" n="*" anchored="true" place="margin">597.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globo tali modo pro parte aquâ impleto ſuper igne pona-<lb />tur, eo momento quo aqua in vapores mutabitur exibunt va-<lb />pores per T; </s>
          <s xml:space="preserve">ſi autem calor augeatur ita ut violenter ebul-<lb />liat aqua, vapores compreſſi in ſuperiore parte globi ab omni <lb />parte elaſticitate ſua recedere conantur &amp; </s>
          <s xml:space="preserve">violento motu per <lb />tubum exeunt. </s>
          <s xml:space="preserve">Æoli Pila vocatur hæc Machina.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">606.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Magis ſenſibilem effectum vis elaſticæ vaporum in Expe-<lb />
<ptr xml:id="note-0500-03a" corresp="note-0500-03" type="noteAnchor" />
rimento ſequenti habemus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0500-03" corresp="note-0500-03a" place="margin">607.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus E cujus diameter eſt etiam quatuor pollicum, ſed <lb />
<ptr xml:id="note-0500-04a" corresp="note-0500-04" type="noteAnchor" />
qui ex craſſiori metallo conſtruitur quam globus quo in præ-<lb />cedenti experimento uſi ſumus, rhedæ exiguæ &amp; </s>
          <s xml:space="preserve">levi impo-<lb />nitur ut in figura videtur. </s>
          <s xml:space="preserve">In ſuperiori parte tubus T qua-<lb />dratus cum globo jungitur. </s>
          <s xml:space="preserve">In medio tubi ſeparatio datur &amp; </s>
          <s xml:space="preserve"><lb />cavitas poſterior communicationem cum globo habet; </s>
          <s xml:space="preserve">fora-<lb />men, cujus diameter eſt circiter pars octava pollicis, datur <lb />in medio ſeparationis in tubo, qui ab anteriori parte apertus <lb />eſt. </s>
          <s xml:space="preserve">Clauditur foramen laminâ quæ per duo tranſit forami-<lb />na in lateribus tubi &amp; </s>
          <s xml:space="preserve">ſeparationi in tubo applicatur; </s>
          <s xml:space="preserve">cùm la-<lb />mina paululum ſit obliqua, ſi ictu mallei intrudatur exacte <lb />claudet foramen.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0500-04" corresp="note-0500-04a" place="margin">TAB. III. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Globus a rheda ſeparatur &amp; </s>
          <s xml:space="preserve">foramen reſeratur, calefacto <lb />globo ſi hic aquâ immergatur, pro parte impletur aqua ut <lb />in experimento præcedenti. </s>
          <s xml:space="preserve">Clauſo foramine iterum glo-<lb />bus igni inponatur donec aqua violenter ebulliat; </s>
          <s xml:space="preserve">ſi tunc <lb />globus cum rheda jungatur &amp; </s>
          <s xml:space="preserve">foramen aperiatur, exibit <lb />vapor violenter verſus unam partem dum rheda verſus par-<lb />tem oppoſitam feretur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vapor violenter compreſſus conatur verſus omnes partes <lb />
<ptr xml:id="note-0500-05a" corresp="note-0500-05" type="noteAnchor" />
recedere &amp; </s>
          <s xml:space="preserve">quidem æqualiter, ideoque preſſiones oppoſitæ <lb />ſeſe mutuo deſtruunt, aperto vero foramine vapor qui exit <lb />non premit; </s>
          <s xml:space="preserve">tollitur ergo preſſio quædam ab una parte &amp; </s>
          <s xml:space="preserve"><lb />contraria prævalet, rheda movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0500-05" corresp="note-0500-05a" place="margin">608.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0501" />
        <pb facs="0501a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0501a-01" />
          <label>0501a-01</label>
        </figure>
        <pb facs="0502" />
        <pb facs="0503" n="17" />
        <fw type="head">MATHEMATIC A. LIB. III. CAP. V.</fw>
        <p>
          <s xml:space="preserve">Tubuli pulvere nitrato farti accenſi in altum feruntur, quia <lb />
<ptr xml:id="note-0503-01a" corresp="note-0503-01" type="noteAnchor" />
pulvis accenſus elaſticitatem acquirit, &amp; </s>
          <s xml:space="preserve">hujus partes quaqua-<lb />verſum conantur recedere: </s>
          <s xml:space="preserve">cùm ab una parte tubus ſit aper-<lb />tus, preſſio in tubum minor datur verſus illam partem &amp; </s>
          <s xml:space="preserve">con-<lb />traria ideo prævalet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0503-01" corresp="note-0503-01a" place="margin">609.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">LIBRI III. Pars II.</head>
        <p>
          <s xml:space="preserve">De Inflexione, Refractione, &amp; </s>
          <s xml:space="preserve">Reflexione luminis.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT V.</head>
        <head rend="italics" xml:space="preserve">De Inflexione radiorum luminis.</head>
        <p>
          <s xml:space="preserve">PRæmiſſis, in parte præcedenti, quæ ignem in genere ſpe-<lb />ctant, luminis proprietates &amp; </s>
          <s xml:space="preserve">phœnomena ex iis oriunda <lb />ad examen revocanda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Mira admodum ſunt quæ circa lumen obſervantur, pau-<lb />cis tamen naturæ legibus pleraque explicantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lumen movetur per lineas rectas <ptr type="noteAnchor" />, obſtaculo poteſt in-
<ptr xml:id="note-0503-02a" corresp="note-0503-02" type="noteAnchor" />
tercipi, quod totum illud &amp; </s>
          <s xml:space="preserve">quidem ſolum intercipit quod <lb />ad obſtaculum accedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0503-02" corresp="note-0503-02a" n="*" anchored="true" place="margin">581.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p>
          <s xml:space="preserve">Lumen quodcunque conſideratum juxta directionem mo-<lb />
<ptr xml:id="note-0503-03a" corresp="note-0503-03" type="noteAnchor" />
tus ſui, ſi totum juxta eandem directionem feratur, vocatur <lb />Radius luminis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0503-03" corresp="note-0503-03a" place="margin">610.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tale eſt lumen quod a Sole procedens per foramen tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ignis, ut antea dictum, a corporibus attrahitur <ptr type="noteAnchor" />, cujus
<ptr xml:id="note-0503-04a" corresp="note-0503-04" type="noteAnchor" />
attractionis effectus notabiles in combuſtione corporum ob-<lb />ſervamus; </s>
          <s xml:space="preserve">in lumine etiam ſenſibiles ſunt; </s>
          <s xml:space="preserve">deflectitur enim <lb />a via recta lumen quando juxta corpora tranſit; </s>
          <s xml:space="preserve">quod ut di-<lb />
<ptr xml:id="note-0503-05a" corresp="note-0503-05" type="noteAnchor" />
ſtinctè obſervetur ſequens inſtituendum experimentum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0503-04" corresp="note-0503-04a" n="*" anchored="true" place="margin">549.</note>
              <note xml:space="preserve" xml:id="note-0503-05" corresp="note-0503-05a" place="margin">611.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Detur tabella T longitudinis &amp; </s>
          <s xml:space="preserve">altitudinis circiter ſex pol-<lb />
<ptr xml:id="note-0503-06a" corresp="note-0503-06" type="noteAnchor" />
licum; </s>
          <s xml:space="preserve">in ſuperficie tabellæ datur cavitas c c, in qua moven-<lb />tur fruſta duo chalibea; </s>
          <s xml:space="preserve">utriuſque acies ſimilis eſt aciei cul-<lb />tri; </s>
          <s xml:space="preserve">concurrunt amborum acies in medio tabellæ, &amp; </s>
          <s xml:space="preserve">exactè
</s>
          <pb facs="0504" n="(18)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
junguntur. </s>
          <s xml:space="preserve">Datur ubi concurrunt foramen quadratum in ta-<lb />bella, cujus latus fere pollicem æquat, ut ad memoratas acies <lb />radius luminis in cubiculum tenebroſum per foramen, cujus <lb />diameter æquat quartam pollicis partem, penetrans perveni-<lb />re poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0503-06" corresp="note-0503-06a" place="margin">TAB. III. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si inter acies memoratas detur diſtantia circiter decimæ <lb />partis unius pollicis, &amp; </s>
          <s xml:space="preserve">lumen inter has tranſeat, poſita tabel-<lb />la T ad diſtantiam trium pedum a feneſtra, ſi lumen cadat <lb />ſuper charta A, ad diſtantiam quinque pedum a tabella, ad <lb />latera luminis apparebit, ab utraque parte, lumen ſimile caudæ <lb />cometæ, quod probat lumen inftecti dum juxta acies tranſit, <lb />ut ex figura ſatis patet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si magis ad ſe mutuo accedant acies, ut ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">diſtantia in-<lb />ter has ſit centeſimæ partis unius pollicis, loco luminis memo-<lb />rati ab utraque parte apparent fimbriæ coloratæ tres, in ſitu pa-<lb />rallelo ad acies, quæ &amp; </s>
          <s xml:space="preserve">magis diſtinctæ apparent, ſi foramen in <lb />feneſtra minuitur. </s>
          <s xml:space="preserve">Unde autem colores hi oriantur in ſequen-<lb />tibus dicam. </s>
          <s xml:space="preserve">Nunc ſatis erit ex hoc experimento deducere, <lb />lumen attrabi a corporibus a quibus radii inflectuntur; </s>
          <s xml:space="preserve">niſi e-<lb />nim daretur motus verſus corpus, per rectam radius motum <lb />continuaret.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Actio vero corporum, quâ in lumen agunt ad hoc attraben-<lb />
<ptr xml:id="note-0504-01a" corresp="note-0504-01" type="noteAnchor" />
dum, ſeſe exerit ad diſtantiam ſenſibilem; </s>
          <s xml:space="preserve">ut experimento <lb />conſtat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0504-01" corresp="note-0504-01a" place="margin">612.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Poſitis quæ in experimento præcedenti, ſi diſtantia inter <lb />
<ptr xml:id="note-0504-02a" corresp="note-0504-02" type="noteAnchor" />
acies detur circiter quadringenteſimæ partis pollicis, nullum <lb />lumen inter ſimbrias memoratas ſuper charta apparebit, ita <lb />ut, in hoc caſu, totum lumen quod inter acies tranſit verſus <lb />utramque partem inflectatur &amp; </s>
          <s xml:space="preserve">formet fimbrias memoratas. <lb /></s>
          <s xml:space="preserve">Quod clarè indicat chalibem ad minimum ad diſtantiam o-<lb />ctingenteſimæ partis pollicis in lumen agere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0504-02" corresp="note-0504-02a" place="margin">TAB. III. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Actionem illam cum imminutâ diſtantiâ augeri, etiam pro-<lb />
<ptr xml:id="note-0504-03a" corresp="note-0504-03" type="noteAnchor" />
batur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0504-03" corresp="note-0504-03a" place="margin">613.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Poſitis quæin præcedenti experimento, minuatur diſtantia <lb />
<ptr xml:id="note-0504-04a" corresp="note-0504-04" type="noteAnchor" />
inter acies; </s>
          <s xml:space="preserve">fimbriæ ſucceſſivè evaneſcunt, donec junctis a-
</s>
          <pb facs="0505" n="(19)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. VI.</fw>
ciebus lumen nullum inter has tranſeat. </s>
          <s xml:space="preserve">Primæ autem fim-<lb />briæ quæ evaneſcunt, ſunt quæ radiis minimè inflexis for-<lb />mantur, ultimæ quæ a radiis maximè inflexis; </s>
          <s xml:space="preserve">id eſt, dum <lb />accedunt ad ſe mutuo acies, umbra inter fimbrias ab utra-<lb />que acie formatas continuò augetur, donec tandem totum <lb />lumen ab utraque parte evaneſcat. </s>
          <s xml:space="preserve">Unde clarè ſequitur, eo <lb />magis inflecti radios, quo ad minorem diſtantiam ab aeiebus <lb />tranſeunt, id eſt attractionem cum imminutâ diſtantiâ au-<lb />geri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0504-04" corresp="note-0504-04a" place="margin">TAB. III. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc autem attractio, quid peculiare habet, nam attractio <lb />
<ptr xml:id="note-0505-01a" corresp="note-0505-01" type="noteAnchor" />
unius aciei admotâ aliâ augetur. </s>
          <s xml:space="preserve">Quod in hoc ultimo expe-<lb />rimento clare patet, nam in acceſſu acierum ad ſe mutuo <lb />inflexio radiorum continuò major eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0505-01" corresp="note-0505-01a" place="margin">614.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VI.</head>
        <head rend="italics" xml:space="preserve">De Luminis Refractione &amp; hujus legibus.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">OMne quod lumini tranſitum dat, vocatur Medium.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">615.</note>
        <p>
          <s xml:space="preserve">Vitrum, Aqua, ipſum Vacuum ſunt media.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dum radius ex uno medio in aliud penetrat, ſæpe a <lb />linea recta deflectitur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Inflectio hæc Refractio dicitur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">616.</note>
        <p rend="italics">
          <s xml:space="preserve">Vt detur refractio requiritur, ut media denſitate differant, <lb />
<ptr xml:id="note-0505-04a" corresp="note-0505-04" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">ut radius cum ſuperficie media dirimente angulum obli-<lb />quum formet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0505-04" corresp="note-0505-04a" place="margin">617.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Oritur refractio ex eo, quòd radii a denſiori medio magis <lb />
<ptr xml:id="note-0505-05a" corresp="note-0505-05" type="noteAnchor" />
quam a rariori attrahantur, a qua attractione, quæ in capi-<lb />te præcedenti probatur, omnia quæ refractionem ſpectant <lb />deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0505-05" corresp="note-0505-05a" place="margin">618.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit EF mediorum ſeparatio, ſit verſus X medium den-<lb />
<ptr xml:id="note-0505-06a" corresp="note-0505-06" type="noteAnchor" />
ſius, verſus Z medium rarius. </s>
          <s xml:space="preserve">Singulæ materiæ particulæ <lb />
<ptr xml:id="note-0505-07a" corresp="note-0505-07" type="noteAnchor" />
vi attractivâ gaudent <ptr type="noteAnchor" />, hæcque vis reſpectu luminis locum
<ptr xml:id="note-0505-08a" corresp="note-0505-08" type="noteAnchor" />
habet <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sit diſtantia, ad quam actionem ſuam particulæ exe-
<ptr xml:id="note-0505-09a" corresp="note-0505-09" type="noteAnchor" />
runt, illa, quæ datur inter lineas EF &amp; </s>
          <s xml:space="preserve">GH. </s>
          <s xml:space="preserve">Lumen er-<lb />go quod inter has lineas datur a medio X attrahitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0505-06" corresp="note-0505-06a" place="margin">619.</note>
              <note xml:space="preserve" xml:id="note-0505-07" corresp="note-0505-07a" place="margin">TAB. IV. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0505-08" corresp="note-0505-08a" n="*" anchored="true" place="margin">31.</note>
              <note xml:space="preserve" xml:id="note-0505-09" corresp="note-0505-09a" n="*" anchored="true" place="margin">611.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0506" n="(20)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Ad diſtantiam ad quam datur linea GH, ſolæ particulæ <lb />extremæ medii X in lumen agunt; </s>
          <s xml:space="preserve">in diſtantia minore cum <lb />his &amp; </s>
          <s xml:space="preserve">aliæ agunt ita, ut vis attrahens creſcat, quando diſtantia <lb />minuitur, ut ante jam obſervatum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Detur in medio den-
<ptr xml:id="note-0506-01a" corresp="note-0506-01" type="noteAnchor" />
ſiori X, linea IL ad eandem ab EF diſtantiam, ad quam in me-<lb />dio Z datur GH. </s>
          <s xml:space="preserve">Intret lumen medium X, ab omni par-<lb />te attrahetur a particulis medii, quarum diſtantiæ a lumine <lb />minores ſunt diſtantiâ inter EF &amp; </s>
          <s xml:space="preserve">GH; </s>
          <s xml:space="preserve">ad hanc enim <lb />diſtantiam lumen a particulis medii X attrahi ponitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0506-01" corresp="note-0506-01a" n="*" anchored="true" place="margin">613.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quamdiu lumen verſatur inter lineas EF &amp; </s>
          <s xml:space="preserve">IL, vis <lb />attrahens verſus JL prævalet, quia majori numero par-<lb />ticulæ verſus hanc partem trahunt; </s>
          <s xml:space="preserve">creſſente autem numero <lb />particularum in contrariam partem agentium, id eſt, creſ-<lb />ſente diſtantia ab EF minuitur vis verſus IL, donec in <lb />ipſa linea IL verſus omnes partes æqualiter attrahatur lu-<lb />men, quod ubique in Medio X ultra IL etiam obtinet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Accedat radius luminis A a &amp; </s>
          <s xml:space="preserve">obliquè incidat in ſuperficiem <lb />dirimentem media, aut potius in ſuperficiem GH, ubi da-<lb />tur initium actionis, qua lumen verſus Medium X pellitur; <lb /></s>
          <s xml:space="preserve">Quando radius pervenit ad a detorquetur a linea recta per <lb />vim, qua a medio X attrahitur; </s>
          <s xml:space="preserve">id eſt, qua juxta directio-<lb />nem ad hujus medii ſuperficiem perpendicularem verſus hoc <lb />pellitur. </s>
          <s xml:space="preserve">Et quidem in omnibus punctis deflectitur radius a <lb />linea recta, quamdiu datur inter lineas GH &amp; </s>
          <s xml:space="preserve">IL, inter <lb />quas memorata attractio agit; </s>
          <s xml:space="preserve">ideoque inter has lineas Ra-<lb />dius curvam a b deſcribit, eodem modo ac de gravibus pro-<lb />jectis dictum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ultra lineam IL ceſſat actio Radium de-
<ptr xml:id="note-0506-02a" corresp="note-0506-02" type="noteAnchor" />
flectens; </s>
          <s xml:space="preserve">rectâ ergo pergit per b B, juxta directionem curvæ <lb />in puncto b.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0506-02" corresp="note-0506-02a" n="*" anchored="true" place="margin">208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diſtantia inter lineas GH &amp; </s>
          <s xml:space="preserve">IL admodum eſt exigua, <lb />quare in conſideratione refractionis ad partem incurvatam <lb />radii non attendimus, radiuſque conſideratur quaſi con-<lb />ſtans ex duabus lineis rectis AC, CB concurrentibus in G, <lb />nempe in ſuperficie media dirimente.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Per C ad ſuperficiem EF detur perpendicularis NCM.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Pars A C Radii memorati vocatur Radius incidens.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">620.</note>
        <pb facs="0507" />
        <pb facs="0507a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0507a-01" />
          <label>0507a-01</label>
        </figure>
        <pb facs="0508" />
        <pb facs="0509" n="(21)" />
        <fw type="head">MATHEMATICA LIB. III. CAP. VI.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p>
          <s xml:space="preserve">Angulus A C N vocatur Angulus incidentiæ.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">621.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p>
          <s xml:space="preserve">Pars CB radii dicitur Radius refractus.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">622.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p>
          <s xml:space="preserve">Angulus BCM vocatur Angulus refractionis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">623.</note>
        <p>
          <s xml:space="preserve">In hoc caſu, ubi lumen e medio rariori in denſius penetrat, <lb />
<ptr xml:id="note-0509-04a" corresp="note-0509-04" type="noteAnchor" />
Angulus refractionis minor eſt Angulo incidentiæ, ex infle-<lb />xione radii; </s>
          <s xml:space="preserve">æquales enim forent hi anguli, ſi radius AC <lb />per CD rectâ viâ motum continuaret. </s>
          <s xml:space="preserve">Accedit autem Ra-<lb />dius CB magis ad perpendicularem CM; </s>
          <s xml:space="preserve">quare refractio <lb />dicitur fieri verſus perpendicularem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0509-04" corresp="note-0509-04a" place="margin">624.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Contra, ſi radius e medio denſiori in rarius tranſeat, rece-<lb />
<ptr xml:id="note-0509-05a" corresp="note-0509-05" type="noteAnchor" />
det a perpendiculari, quia attractio medii denſioris in ra-<lb />dium eadem eſt, ſive radius ex rariori in denſius, ſive e den-<lb />ſiori in rarius penetret. </s>
          <s xml:space="preserve">Idcirco ſi BC ſit radius inciden-<lb />tiæ, CA erit radius refractus, id eſt, per eaſdem lineas <lb />
<ptr xml:id="note-0509-06a" corresp="note-0509-06" type="noteAnchor" />
movetur radius a quacunque parte procedat. </s>
          <s xml:space="preserve">Ideoque, ſi duo <lb />
<ptr xml:id="note-0509-07a" corresp="note-0509-07" type="noteAnchor" />
radii, unus e medio denſiori in rarius, alter e rariori in denſius, <lb />penetrent, anguluſque refractionis bujus æqualis ſit angulo in-<lb />cidentiæ illius, reliqui duo anguli incidentiæ &amp; </s>
          <s xml:space="preserve">refractionis <lb />erunt æquales inter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0509-05" corresp="note-0509-05a" place="margin">625.</note>
              <note xml:space="preserve" xml:id="note-0509-06" corresp="note-0509-06a" place="margin">626.</note>
              <note xml:space="preserve" xml:id="note-0509-07" corresp="note-0509-07a" place="margin">627.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Exquibus ſequitur, directionemradii non mutari, ſi movea-<lb />
<ptr xml:id="note-0509-08a" corresp="note-0509-08" type="noteAnchor" />
tur trans medium terminatum duabus ſuperficiebus parallelis <lb />inter ſe, quantum enim in ingreſſu verſus aliquam partem <lb />deflectitur, in tantum exactiſſime dum exit verſus partem <lb />oppoſitam inflectitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0509-08" corresp="note-0509-08a" place="margin">628.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si radius perpendiculariter cadat in ſuperficiem qua duo <lb />
<ptr xml:id="note-0509-09a" corresp="note-0509-09" type="noteAnchor" />
media ſeparantur, a recta via non deflectetur attractione me-<lb />dii denſioris; </s>
          <s xml:space="preserve">actione hac cum radii motu in eadem dire-<lb />ctione in hoc caſu agente.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0509-09" corresp="note-0509-09a" place="margin">629.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut dicta Experimentis confirmentur, datur pixis P, lon-<lb />
<ptr xml:id="note-0509-10a" corresp="note-0509-10" type="noteAnchor" />
gitudinis circiter unius pedis, latitudinis &amp; </s>
          <s xml:space="preserve">altitudinis qua-<lb />
<ptr xml:id="note-0509-11a" corresp="note-0509-11" type="noteAnchor" />
tuor pollicum. </s>
          <s xml:space="preserve">Latera duo majora a b c d, a b c d, ſunt <lb />plana vitrea parallela inter ſe, pixis hæc aquam continet ad <lb />altitudinem circiter duorum pollicum cum ſemiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0509-10" corresp="note-0509-10a" place="margin">630.</note>
              <note xml:space="preserve" xml:id="note-0509-11" corresp="note-0509-11a" place="margin">TAB. IV. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In loco obſcuro inſtituuntur experimenta; </s>
          <s xml:space="preserve">lumen intromit-
</s>
          <pb facs="0510" n="(22)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
titur per ſciſſuram in orbe mobili O, qui in feneſtra datur, <lb />&amp; </s>
          <s xml:space="preserve">rotatur ut ſciſſura ad libitum poſſit inclinari; </s>
          <s xml:space="preserve">ſciſſuræ lon-<lb />gitudo eſt quatuor pollicum, latitudo octavæ pollicis partis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lumen intromiſſum in ſpeculum Simpingit; </s>
          <s xml:space="preserve">ita ſciſſura in-<lb />clinatur &amp; </s>
          <s xml:space="preserve">ſpeculum diſponitur, ut radius per ſciſſuram in-<lb />tromiſſus a ſpeculo horizontaliter reflectatur, manente ra-<lb />dio in ſitu verticali, ut tranſeat per ſciſſuram verticalem in <lb />tabella T, ſimilem illi quæ datur in orbe O. </s>
          <s xml:space="preserve">Tabella hæc <lb />cum fciſſura adhibetur ad minuendam radii intromſſi latitu-<lb />dinem, quæ continuo creſcit propter lumen a lateribus Solis <lb />proveniens.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Poſitis, quæ in explicatione Machinæ dicta, incidat ra-<lb />dius perpendiculariter in ſuperficiem a b c d; </s>
          <s xml:space="preserve">rectâ tranſi-<lb />bit per aquam ut per ſuperiorem pixidis partem, &amp; </s>
          <s xml:space="preserve">neque <lb />in ingreſſu, neque in exitu deflectetur a via: </s>
          <s xml:space="preserve">quo confirma-<lb />tur n. </s>
          <s xml:space="preserve">629.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Iiſdem poſitis, incidat oblique radius in ſuperficiem a b <lb />c d in f g; </s>
          <s xml:space="preserve">pars radii ſuperior motum ſuum per h rectâ viâ <lb />continuabit; </s>
          <s xml:space="preserve">pars verò inferior in aqua, inflectetur ver-<lb />ſus i, accedendo ad perpendicularem: </s>
          <s xml:space="preserve">quod confirmat <lb />n. </s>
          <s xml:space="preserve">624.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Manentibus quæ in Experimentis præcedentibus, radius <lb />qui in i, ex aqua in aërem tranſit, deflectitur a via ſua rece-<lb />dendo a perpendiculari, &amp; </s>
          <s xml:space="preserve">quidem ita, ut ſequatur eandem <lb />directionem cum radio in aquam incidente in g; </s>
          <s xml:space="preserve">ille enim <lb />motu parallelo fertur cum radio f h continuato: </s>
          <s xml:space="preserve">quod con-<lb />firmat n. </s>
          <s xml:space="preserve">625. </s>
          <s xml:space="preserve">626. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">628.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In dictis huc uſque, tantum conſideravimus attractionem <lb />medii denſioris quia hæc prævalet, non tamen contemnen-<lb />da eſt actio medii rarioris, quia hæc minuit actionem medii <lb />denſioris, quæ eo minor erit in lumen, quo media inter ſe <lb />minus denſitate differunt. </s>
          <s xml:space="preserve">Idcirco nulla datur refractio <lb />
<ptr xml:id="note-0510-01a" corresp="note-0510-01" type="noteAnchor" />
ubi denſitates mediorum ſunt æquales, &amp; </s>
          <s xml:space="preserve">eomajor eſt, quo hæ <lb />denſitates magis inter ſe differunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0510-01" corresp="note-0510-01a" place="margin">631.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0511" n="(23)" />
        <fw type="head">MATHEMATICA LIB. III. CAP. VI.</fw>
        <p>
          <s xml:space="preserve">Refractionis leges ex acceleratione quam generat attractio <lb />deducuntur; </s>
          <s xml:space="preserve">examinanda ideo eſt hæc acceleratio.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p>
          <s xml:space="preserve">Spatium planis GH &amp; </s>
          <s xml:space="preserve">IL terminatum, vocatur ſpatium <lb />
<ptr xml:id="note-0511-01a" corresp="note-0511-01" type="noteAnchor" />
attractionis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0511-01" corresp="note-0511-01a" place="margin">632.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. IV. <lb />fig. 1.</note>
        <p>
          <s xml:space="preserve">Inter plana quæ his lineis repreſentantur attractio obtinet, <lb />non ultra <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">619.</note>
        <p rend="italics">
          <s xml:space="preserve">Directio hujus actionis eſt perpendicularis ad ſuperficiem <lb />
<ptr xml:id="note-0511-04a" corresp="note-0511-04" type="noteAnchor" />
media dirimentem, ideoque ad ſuperficiem IL; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">inæqualis <lb />eſt ad varias diſtantias ab hac ſuperficie <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ad æquales ve-
<ptr xml:id="note-0511-05a" corresp="note-0511-05" type="noteAnchor" />
rò diſtantias æqualis eſt, quia media ambo homogenea &amp; </s>
          <s xml:space="preserve">u-<lb />bique ſibi ſimilia ponuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0511-04" corresp="note-0511-04a" place="margin">633.</note>
              <note xml:space="preserve" xml:id="note-0511-05" corresp="note-0511-05a" n="*" anchored="true" place="margin">619.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus radii AC poteſt reſolvi in duos alios motus juxta <lb />directiones AO &amp; </s>
          <s xml:space="preserve">OC <ptr type="noteAnchor" />, quarum prima ſuperficiei <ptr type="noteAnchor" /><unclear reason="illegible" /> F
<ptr xml:id="note-0511-06a" corresp="note-0511-06" type="noteAnchor" />
<ptr xml:id="note-0511-07a" corresp="note-0511-07" type="noteAnchor" />
parallela eſt, ſecunda huic eidem ſuperficiei perpendicula-<lb />ris; </s>
          <s xml:space="preserve">quorum motuum celeritates reſpectivè proportionales <lb />erunt hiſce lineis AO &amp; </s>
          <s xml:space="preserve">OC dum AC ipſius radii ce-<lb />leritatem denotat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0511-06" corresp="note-0511-06a" n="*" anchored="true" place="margin">192.</note>
              <note xml:space="preserve" xml:id="note-0511-07" corresp="note-0511-07a" n="*" anchored="true" place="margin">E</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">192.</note>
        <p rend="italics">
          <s xml:space="preserve">Motus juxta directionem AO ex attractione perpendicu-<lb />
<ptr xml:id="note-0511-09a" corresp="note-0511-09" type="noteAnchor" />
lari ad ſuperficiem IL non mutatur, ſolus motus juxta OC <lb />acceleratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0511-09" corresp="note-0511-09a" place="margin">634.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poteſt ſervatâ lineâ AC, celeritate nempe ipſius radii, <lb />
<ptr xml:id="note-0511-10a" corresp="note-0511-10" type="noteAnchor" />
hujus inclinatio mutari, quo etiam mutatur celeritas juxta <lb />directionem OC, quæ celeritas in totum evaneſcit, ſi mi-<lb />nimus ſit angulus A a G. </s>
          <s xml:space="preserve">In quo caſu ſi poſt ingreſſum <lb />luminis in medium denſius, illius motus in duos reſolvatur, <lb />ita ut unius directio ſit ſuperficiei IL perpendicularis, hu-<lb />jus celeritas in totum tribuenda erit attractioni ſæpius me-<lb />moratæ. </s>
          <s xml:space="preserve">In ingreſſu enim in ſpatium attractionis generatur <lb />motus juxta hanc directionem, &amp; </s>
          <s xml:space="preserve">in tranſitu per hoc ſpatium, <lb />in quo ubique nova actio juxta eandem directionem in lumen <lb />agit, continuò acceleratur. </s>
          <s xml:space="preserve">Quæ acceleratio in omnilumi-<lb />nis tranſitu per ſpatium attractionis obtinet, ſed diverſa eſt, <lb />pro varia celeritate qua lumen perpendiculariter ad ſuperfi-<lb />ciem media dirimentem accedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0511-10" corresp="note-0511-10a" place="margin">635.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si æquabilis foret attractio per totam latitudinem ſpatii at-<lb />tractionis, poſſent, quæ accelerationem memoratam ſpectant,
</s>
          <pb facs="0512" n="(24)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ut de acceleratione gravium dictum eſt poſt n. </s>
          <s xml:space="preserve">130.</s>
          <s xml:space="preserve">, deter-<lb />
<ptr xml:id="note-0512-01a" corresp="note-0512-01" type="noteAnchor" />
minari ope trianguli rectanguli PQR, in quo lineæ pa-<lb />rallelæ ad baſin celeritates repreſentant, dum portiones areæ <lb />trianguli ſpatia percurſa deſignant. </s>
          <s xml:space="preserve">Hìc autem de eo-<lb />dem ſpatio percurſo ſemper agitur, latitudine nempe ſpatii <lb />attractionis, quia ſolum motum ad ſuperficiem Media diri-<lb />mentem perpendicularem conſideramus; </s>
          <s xml:space="preserve">idcirco per por-<lb />tiones æquales areæ trianguli PQR ſpatium hoc percur-<lb />ſum ſemper repreſentatur. </s>
          <s xml:space="preserve">Sit portio hæc Pdc quando <lb />cum celeritate o. </s>
          <s xml:space="preserve">lumen ſpatium attractionis juxta memora-<lb />tam directionem perpendicularemintrat, id eſt, quando ra-<lb />dius incidens cum ſuperficie media ſeparante angulum mini-<lb />mum format; </s>
          <s xml:space="preserve">dc in hoc caſu deſignabit celeritatem attra-<lb />ctione acquiſitam, &amp; </s>
          <s xml:space="preserve">quâ lumen ſpatium attractionis exit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0512-01" corresp="note-0512-01a" place="margin">TAB. IV. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si autem lumen cum celeritate quæ per fg deſignatur <lb />perpendiculariter ſpatium attractionis intret, exibit ſpatium <lb />cum celeritate hi poſitis areis Pdc &amp; </s>
          <s xml:space="preserve">fgih æqualibus <lb />inter ſe, ut ex dictis patet. </s>
          <s xml:space="preserve">Triangula Pdc, Pfg, Phi <lb />ſunt ſimilia, ideoque horum areæ ſunt inter ſe ut quadrata <lb />laterum homologorum dc, fg, hi ſumma autem arearum <lb />Pdc, Pfg æqualis eſt areæ phi, (propter areas æ-<lb />quales Pdc &amp; </s>
          <s xml:space="preserve">fgih); </s>
          <s xml:space="preserve">ergo &amp; </s>
          <s xml:space="preserve">ſumma quadratorum li-<lb />nearum dc &amp; </s>
          <s xml:space="preserve">fg æqualis eſt quadrato lineæ hi; </s>
          <s xml:space="preserve">unde <lb />ſequitur tribus memoratis lineis formari poſſe triangulum re-<lb />ctangulum cujus hypotenuſa erit hi. </s>
          <s xml:space="preserve">Ergo</s>
        </p>
        <p rend="italics">
          <s xml:space="preserve">In triangulo rectangulo, cujus latus unum eſt celeritas quâ <lb />
<ptr xml:id="note-0512-02a" corresp="note-0512-02" type="noteAnchor" />
lumen perpendiculariter ſpatium attractionis intrat, latus <lb />alterum celeritas percurrendo hoc ſpatium acquiſita, quando <lb />lumen celeritate o. </s>
          <s xml:space="preserve">hoc intrat, hypotenuſa trianguli deſignat <lb />celeritatem qua lumen ad partem oppoſitam ſpatium attractio-<lb />nis perpendiculariter exit. </s>
          <s xml:space="preserve">Quod univerſaliter obtinet, quo-<lb />modocunque mutetur attractio in ſpatio attractionis pro va-<lb />ria diſtantia a planis quibus hoc ſpatium terminatur. </s>
          <s xml:space="preserve">Quod <lb />ur probetur,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0512-02" corresp="note-0512-02a" place="margin">636.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus ſpatium attractionis in duas partes, ſive æquales <lb />ſive utcunque inæquales ſecari plano parallelo ad ſuperficies <lb />quibus terminatur. </s>
          <s xml:space="preserve">Ponamus ulterius attractionem dari diver-
</s>
          <pb facs="0513" n="(25)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. VI.</fw>
ſam in his partibus, in eadem tamen illam non variari. </s>
          <s xml:space="preserve">Con-<lb />ſiderandæ ſunt hæ partes ut duo diverſa ſpatia attractionis. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0513-01a" corresp="note-0513-01" type="noteAnchor" />
Sit A celeritas, quam lumen primam partem ſpatii percurren-<lb />do acquirit, quando ſpatium intrat celeritate o.</s>
          <s xml:space="preserve">; ſit B cele-<lb />ritas ſecundam partem ſpatii percurrendo acquiſita, quan-<lb />do itidem lumen hanc partem celeritate o. </s>
          <s xml:space="preserve">intrat. </s>
          <s xml:space="preserve">Notan-<lb />dum in hac demonſtratione ubique agi de motu perpendicu-<lb />lari ad ſuperficiem, qua media ſeparantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0513-01" corresp="note-0513-01a" place="margin">TAB. IV. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Intret lumen primam partem ſpatii memorati celeritate <lb />o. </s>
          <s xml:space="preserve">ad ſecundam partem accedet celeritate A; </s>
          <s xml:space="preserve">ſi ergo lateri-<lb />bus A &amp; </s>
          <s xml:space="preserve">B triangulum formetur rectangulum ECD, hy-<lb />potenuſa ED deſignabit celeritatem qua lumen ex ſpatio <lb />attractionis exibit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">636.</note>
        <p>
          <s xml:space="preserve">Si lumen celeritate FG ſpatium attractionis intret, for-<lb />metur triangulum rectangulum HFG lateribus FG &amp; </s>
          <s xml:space="preserve"><lb />A; </s>
          <s xml:space="preserve">hypotenuſa HG erit celeritas, qua lumen prima par-<lb />
<ptr xml:id="note-0513-03a" corresp="note-0513-03" type="noteAnchor" />
te ſpatii attractionis exit <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in ſecundam penetrat; </s>
          <s xml:space="preserve">for-
mando autem triangulum rectangulum HGI cujus perpen-<lb />dicularis æqualis ſit lineæ B, datur hypotenuſa IG deſignans <lb />celeritatem qua lumen exit, &amp; </s>
          <s xml:space="preserve">poſt totum ſpatium attractio-<lb />nis percurſum motum continuat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0513-03" corresp="note-0513-03a" n="*" anchored="true" place="margin">636.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">636.</note>
        <p>
          <s xml:space="preserve">Demonſtrandum autem eſt celeritatem IG etiam eſſe <lb />hypotenuſam trianguli rectanguli NML, cujus latus ML <lb />æquale eſt FG celeritati, qua lumen ſpatium attractionis <lb />intrat, &amp; </s>
          <s xml:space="preserve">cujus latus alterum LN æquale eſt lineæ ED, <lb />celeritati, quam lumen acquirit totam latitudinem ſpatii re-<lb />fractionis percurrendo, quando hoc intravit celeritateo.</s>
          <s xml:space="preserve">; quo <lb />demonſtrato &amp; </s>
          <s xml:space="preserve">in hoc caſu, in quo duæ diverſæ vires at-<lb />tractionis agunt, propoſitionem n. </s>
          <s xml:space="preserve">636. </s>
          <s xml:space="preserve">obtineri patebit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lineas vero I <ptr type="noteAnchor" /><unclear reason="illegible" /> &amp; </s>
          <s xml:space="preserve">NM æquales eſſe ex conſideratio-
<ptr xml:id="note-0513-05a" corresp="note-0513-05" type="noteAnchor" />
ne triangulorum rectangulorum facile liquet. </s>
          <s xml:space="preserve">Quadratum <lb />lineæ NM valet quadrata linearum NL &amp; </s>
          <s xml:space="preserve">LM aut <lb />FG: </s>
          <s xml:space="preserve">NL æqualis lineæ ED, cujus quadratum valet quadra-<lb />ta linearum EC &amp; </s>
          <s xml:space="preserve">CD, aut linearum A &amp; </s>
          <s xml:space="preserve">B, æqualium <lb />lineis FH &amp; </s>
          <s xml:space="preserve">HI: </s>
          <s xml:space="preserve">Æquale ergo eſt quadratum hypotenu-<lb />ſæ NM tribus quadratis linearum FG, FH, &amp; </s>
          <s xml:space="preserve">HI. </s>
          <s xml:space="preserve">Qui-<lb />bus iiſdem tribus quadratis æquale eſt quadratum lineæ
</s>
          <pb facs="0514" n="26" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
GI; </s>
          <s xml:space="preserve">hoc enim valet quadrata linearum HI &amp; </s>
          <s xml:space="preserve">HG, quod <lb />ultimum æquale eſt quadratis linearum HF &amp; </s>
          <s xml:space="preserve">FG.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0513-05" corresp="note-0513-05a" n="*" anchored="true" place="margin">G</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſpatium refractionis in ſpatia quotcunque dividatur pla-<lb />nis parallelis ſuperficiebus, quibus ſpatium hoc terminatur, &amp; </s>
          <s xml:space="preserve"><lb />in partibus diverſis vires attractionis diverſæ obtineant, ea-<lb />dem demonſtratio locum habebit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">poteſt utcunque etiam <lb />
<ptr xml:id="note-0514-01a" corresp="note-0514-01" type="noteAnchor" />
in infinitum augeri diviſionum numerus; </s>
          <s xml:space="preserve">qui caſus extat in <lb />refractione, quam lumen tranſeundo ex medio quocunque <lb />in aliud diverſæ denſitatis patitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">cui ergo applicari po-
<ptr xml:id="note-0514-02a" corresp="note-0514-02" type="noteAnchor" />
teſt regula n. </s>
          <s xml:space="preserve">636.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0514-01" corresp="note-0514-01a" place="margin">637.</note>
              <note xml:space="preserve" xml:id="note-0514-02" corresp="note-0514-02a" n="*" anchored="true" place="margin">633.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Z medium rarius, X medium denſius, ſeparentur plano <lb />
<ptr xml:id="note-0514-03a" corresp="note-0514-03" type="noteAnchor" />
EF; </s>
          <s xml:space="preserve">detur radius luminis AC obliquè in ſuperficiem EF <lb />incidens; </s>
          <s xml:space="preserve">deſignet AC celeritatem luminis in medio Z, ſit-<lb />que hæc linea AC conſtans; </s>
          <s xml:space="preserve">id eſt, maneat quæcunque <lb />fuerit radii inclinatio. </s>
          <s xml:space="preserve">Centro C ſemidiametro CA deſcriba-<lb />tur circulus; </s>
          <s xml:space="preserve">detur NCM ad EF perpendicularis; </s>
          <s xml:space="preserve">ex A du-<lb />cantur perpendiculares AO ad NC, &amp; </s>
          <s xml:space="preserve">AQ ad EF.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0514-03" corresp="note-0514-03a" place="margin">TAB. IV. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus per AC concipiatur reſolutus in duos alios, unum <lb />juxta AO, alterum juxta AQ aut OC <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">deſignabit linea
<ptr xml:id="note-0514-04a" corresp="note-0514-04" type="noteAnchor" />
OC radii celeritatem perpendicularem ſuperficiei EF, quæ <lb />celeritas ſola ex attractione medii augetur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0514-04" corresp="note-0514-04a" n="*" anchored="true" place="margin">192.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">634.</note>
        <p>
          <s xml:space="preserve">Sit CP celeritas, quam lumen acquirit perpendiculariter <lb />percurrendo ſpatium attractionis medii X; </s>
          <s xml:space="preserve">poſitâ luminis ce-<lb />leritate in ingreſſu o.</s>
          <s xml:space="preserve">; hypotenuſa OP trianguli rectanguli <lb />PCO erit celeritas radii AC in medio X, juxta directio-<lb />nem perpendicularem ſuperficiei EF <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">celeritas luminis jux-
<ptr xml:id="note-0514-06a" corresp="note-0514-06" type="noteAnchor" />
ta directionem AO aut QC, parallelam ſuperficiei EF, non <lb />mutatur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sit ideo CV æqualis AO aut QC, &amp; </s>
          <s xml:space="preserve">VB
<ptr xml:id="note-0514-07a" corresp="note-0514-07" type="noteAnchor" />
perpendicularis ad EF, æqualis hypotenuſæ PO, ducatur-<lb />que CB; </s>
          <s xml:space="preserve">erit motus per CB motus ex ambobus compoſi-<lb />tus, &amp; </s>
          <s xml:space="preserve">determinat linea hæc ſitu ſuo directionem, &amp; </s>
          <s xml:space="preserve">longi-<lb />tudine ſua celeritatem luminis in medio X <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ celeritas
<ptr xml:id="note-0514-08a" corresp="note-0514-08" type="noteAnchor" />
variâ inclinatione radii AC non mutatur. </s>
          <s xml:space="preserve">Quadratum e-<lb />
<ptr xml:id="note-0514-09a" corresp="note-0514-09" type="noteAnchor" />
nim lineæ CB valet quadratum lineæ BV aut PO, &amp; </s>
          <s xml:space="preserve">qua-<lb />dratum lineæ CV aut AO; </s>
          <s xml:space="preserve">quadratum vero lineæ PO valet <lb />quadrata linearum PC &amp; </s>
          <s xml:space="preserve">CO: </s>
          <s xml:space="preserve">æquale ergo eſt quadratum <lb />lineæ CB tribus quadratis linearum PC, CO, &amp; </s>
          <s xml:space="preserve">AO, quæ
</s>
          <pb facs="0515" n="27" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. VI.</fw>
duo ultima ſi jungantur habebimus quadratum ſemi diametri <lb />AC aut CN; </s>
          <s xml:space="preserve">id eſt, CB æqualis eſt PN, cujus quadratum <lb />valet etiam quadrata linearum PC &amp; </s>
          <s xml:space="preserve">CN, &amp; </s>
          <s xml:space="preserve">quæ ex mu-<lb />tata inclinatione radii AC nullam mutationem ſubit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0514-06" corresp="note-0514-06a" n="*" anchored="true" place="margin">637.</note>
              <note xml:space="preserve" xml:id="note-0514-07" corresp="note-0514-07a" n="*" anchored="true" place="margin">634</note>
              <note xml:space="preserve" xml:id="note-0514-08" corresp="note-0514-08a" place="margin">638.</note>
              <note xml:space="preserve" xml:id="note-0514-09" corresp="note-0514-09a" n="*" anchored="true" place="margin">191.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Linea CB ſecat in T circulum ſemidiametro CA de-<lb />ſcriptum; </s>
          <s xml:space="preserve">a punctis B &amp; </s>
          <s xml:space="preserve">T perpendiculares BS &amp; </s>
          <s xml:space="preserve">TR du-<lb />cantur ad CM: </s>
          <s xml:space="preserve">propter triangula ſimilia CBS, CTR, <lb />BC erit ad TC aut CA, ut BS ad TR; </s>
          <s xml:space="preserve">quæ ergo li-<lb />neæ, propter conſtantes BC &amp; </s>
          <s xml:space="preserve">CA, eandem ſemper ratio-<lb />nem habebunt, quicunque fuerit angulus incidentiæ. </s>
          <s xml:space="preserve">TR <lb />eſt ſinus anguli refractionis TCR; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">B æqualis CV, <lb />
<ptr xml:id="note-0515-01a" corresp="note-0515-01" type="noteAnchor" />
æqualis AO, eſt ſinus anguli incidentiæ ACO.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0515-01" corresp="note-0515-01a" place="margin">S<unclear reason="illegible" /></note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In omni ergo radii incidentis inclinatione conſtans &amp; </s>
          <s xml:space="preserve">im-<lb />
<ptr xml:id="note-0515-02a" corresp="note-0515-02" type="noteAnchor" />
mutabilis datur ratio inter ſinus angulorum incidentiæ &amp; </s>
          <s xml:space="preserve">re-<lb />fractionis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0515-02" corresp="note-0515-02a" place="margin">639.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cum autem BC &amp; </s>
          <s xml:space="preserve">CA, quæ ſunt ut memorati ſinus, <lb />etiam deſignent celeritates luminis in mediis X &amp; </s>
          <s xml:space="preserve">Z, ſequi-<lb />tur ſinus hos eſſe inverſè ut ſunt celeritates in iſtis mediis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">640.</note>
        <p>
          <s xml:space="preserve">Si medium Z ſit aër &amp; </s>
          <s xml:space="preserve">X aqua, ſinus prædicti ſunt ut 4. <lb /></s>
          <s xml:space="preserve">ad 3.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">celeritas luminis in aëre ad hujus celeritatem in <lb />aqua, ut 3. </s>
          <s xml:space="preserve">ad 4. </s>
          <s xml:space="preserve">Si vero, manente Z aëre, X ſit vitrum, <lb />ſinus ſunt ut 17. </s>
          <s xml:space="preserve">ad 11. </s>
          <s xml:space="preserve">circa omnia media illud unico expe-<lb />rimento determinaſſe ſufficit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ratio quæ datur inter ſinus angulorum quorumcunque eſt <lb />
<ptr xml:id="note-0515-04a" corresp="note-0515-04" type="noteAnchor" />
inverſa ſecantium comp.</s>
          <s xml:space="preserve">, ut in hac figura patet, conci-<lb />piendo circulum ſemi diametro CQ aut CV ductum: </s>
          <s xml:space="preserve">tunc <lb />enim AC æqualis CT, &amp; </s>
          <s xml:space="preserve">CB ſunt ſecantes angulorum <lb />ACQ &amp; </s>
          <s xml:space="preserve">BCV complementorum angulorum incidentiæ <lb />&amp; </s>
          <s xml:space="preserve">refractionis, &amp; </s>
          <s xml:space="preserve">ſunt inverſè ut BS æqualis AO &amp; </s>
          <s xml:space="preserve">TR, <lb />quæ in majori circulo ſunt ſinus incidentiæ &amp; </s>
          <s xml:space="preserve">refractionis. <lb /></s>
          <s xml:space="preserve">Hæcque ſecantium proportio methodum dat facillimè vo-<lb />candi ad experimentum Propoſitionem N. </s>
          <s xml:space="preserve">639.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0515-04" corresp="note-0515-04a" place="margin">641.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">In hoc Experimento, lumen eodem modo ac in præce-<lb />
<ptr xml:id="note-0515-05a" corresp="note-0515-05" type="noteAnchor" />
dentibus in cubiculum obſcurum per ſciſſuram intromitti-<lb />tur, &amp; </s>
          <s xml:space="preserve">a ſpeculo reflexum per ſciſſuram verticalem in tabella <lb />T tranſmittitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0515-05" corresp="note-0515-05a" place="margin">TAB IV. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0516" n="28" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Datur Pixis P, ejuſdem præterpropter magnitudinis cum <lb />illa, qua in præcedentibus experimentis utimur; </s>
          <s xml:space="preserve">in hac uni-<lb />cum latus, &amp; </s>
          <s xml:space="preserve">quidem ex minoribus, vitreum eſt abcd. <lb /></s>
          <s xml:space="preserve">Ad dimidiam altitudinem aquâ repletur Pixis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Radius luminis verticalis in fg obliquè in latus vitreum <lb />pixidis inpingit; </s>
          <s xml:space="preserve">pars radii ſupra aqua rectâ tranſit &amp; </s>
          <s xml:space="preserve">in h <lb />ad latus majus pixidis pertingit; </s>
          <s xml:space="preserve">pars verò radii in aqua re-<lb />fracta per g i procedit &amp; </s>
          <s xml:space="preserve">in i in idem pixidis latus impin-<lb />git. </s>
          <s xml:space="preserve">Quicunque fuerit angulus a radio cum latere abcd <lb />pixidis formatus, lineæ fh &amp; </s>
          <s xml:space="preserve">gi ſemper ſunt inter ſe ut <lb />3. </s>
          <s xml:space="preserve">ad 4.</s>
          <s xml:space="preserve">; ut commodè oſtenditur in variis inclinationibus, ſi <lb />ſcalæ duæ dentur, ſingulæ in partes exiguas æquales diviſæ, <lb />&amp; </s>
          <s xml:space="preserve">quarum diviſiones ſunt inter ſe ut 3. </s>
          <s xml:space="preserve">ad 4; </s>
          <s xml:space="preserve">tot enim ſem-<lb />per continebit partes majores linea gi, quot minores conti-<lb />net linea fh. </s>
          <s xml:space="preserve">Angulus, quem fh cum plano abcd format, <lb />eſt complementum anguli incidentiæ ad angulum rectum, <lb />&amp; </s>
          <s xml:space="preserve">angulus, a linea gi cum eodem plano formatus, eſt com-<lb />plementum anguli refractionis ad angulum rectum; </s>
          <s xml:space="preserve">ſunt ideo <lb />gh &amp; </s>
          <s xml:space="preserve">gi ſecantes comp. </s>
          <s xml:space="preserve">angulorum incidentiæ &amp; </s>
          <s xml:space="preserve">refra-<lb />ctionis, quas conſtantem inter ſe rationem habere experi-<lb />mento erat confirmandum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hucuſque radium è medio rariori in denſius intrantem <lb />
<ptr xml:id="note-0516-01a" corresp="note-0516-01" type="noteAnchor" />
conſideravimus, ſed eadem conſtans ſinuum proportio, in n. <lb /></s>
          <s xml:space="preserve">639.</s>
          <s xml:space="preserve">, memorata in motu radiorum contrario obtinet; </s>
          <s xml:space="preserve">anguli <lb />ACN, MCB non mutantur quicunque ſit radius inci-<lb />
<ptr xml:id="note-0516-02a" corresp="note-0516-02" type="noteAnchor" />
dens, ſive AC ſive BC <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In hoc caſu ſi BC ſit celeritas
<ptr xml:id="note-0516-03a" corresp="note-0516-03" type="noteAnchor" />
radii incidentis, CA erit celeritas radii refracti; </s>
          <s xml:space="preserve">eodem e-<lb />nim modo, ex attractione verſus medium X, motus radii <lb />ex X in Z tranſeuntis retardatur, ac in motu contrario ac-<lb />celeratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0516-01" corresp="note-0516-01a" place="margin">642.</note>
              <note xml:space="preserve" xml:id="note-0516-02" corresp="note-0516-02a" place="margin">TAB. IV. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0516-03" corresp="note-0516-03a" n="*" anchored="true" place="margin">626.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VII.</head>
        <head rend="italics" xml:space="preserve">De luminis refractione, quando media ſuperficie <lb />planâ ſeparantur.</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio i</hi>.</head>
        <p rend="italics">
          <s xml:space="preserve">RAdii ab eodem puncto, quaſi centro, procedentes &amp; </s>
          <s xml:space="preserve">ſic con-<lb />
<ptr xml:id="note-0516-04a" corresp="note-0516-04" type="noteAnchor" />
tinuo magis a ſe mutuo recedentes, dicuntur divergentes.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0516-04" corresp="note-0516-04a" place="margin">643.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0517" />
        <pb facs="0517a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0517a-01" />
          <label>0517a-01</label>
        </figure>
        <pb facs="0518" />
        <pb facs="0519" n="29" />
        <fw type="head">MATHEMATICA LIB. III. CAP. VII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Magis divergentes ſunt, qui majorem Angulum inter ſe for-<lb />
<ptr xml:id="note-0519-01a" corresp="note-0519-01" type="noteAnchor" />
mant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-01" corresp="note-0519-01a" place="margin">644.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Punctum, a quo radii divergentes procedunt, dicitur Pun-<lb />
<ptr xml:id="note-0519-02a" corresp="note-0519-02" type="noteAnchor" />
ctum radians.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-02" corresp="note-0519-02a" place="margin">645.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quo magis radii ſunt divergentes, poſitâ eâdem inter hos <lb />
<ptr xml:id="note-0519-03a" corresp="note-0519-03" type="noteAnchor" />
diſtantiâ, quo minus diſtat punctum radians &amp; </s>
          <s xml:space="preserve">contra.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-03" corresp="note-0519-03a" place="margin">646.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sæpe per refractionem radii ita moventur, quaſi a puncto <lb />
<ptr xml:id="note-0519-04a" corresp="note-0519-04" type="noteAnchor" />
radiante procederent, licet revera a tali puncto non proce-<lb />dant; </s>
          <s xml:space="preserve">id eſt, ſi radii continuarentur, verſus partem a qua <lb />procedunt, in unum punctum concurrerent. </s>
          <s xml:space="preserve">In hoc caſu <lb />etiam divergentes radii dicuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-04" corresp="note-0519-04a" place="margin">647.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitiones</hi> 4. &amp; 5.</head>
        <p>
          <s xml:space="preserve">Radii qui in unum punctum concurrunt, aut continuati <lb />
<ptr xml:id="note-0519-05a" corresp="note-0519-05" type="noteAnchor" />
concurrerent, vocantur convergentes; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">magis convergen-<lb />
<ptr xml:id="note-0519-06a" corresp="note-0519-06" type="noteAnchor" />
tes, qui majorem angulum formant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-05" corresp="note-0519-05a" place="margin">648.</note>
              <note xml:space="preserve" xml:id="note-0519-06" corresp="note-0519-06a" place="margin">649.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p rend="italics">
          <s xml:space="preserve">Punctum concurſus radiorum convergentium vocatur Focus.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">650.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p>
          <s xml:space="preserve">Punctum, in quo radii convergentes, &amp; </s>
          <s xml:space="preserve">ante concurſum in-<lb />
<ptr xml:id="note-0519-08a" corresp="note-0519-08" type="noteAnchor" />
tercepti aut deflexi, continuati concurrerent, vocatur Focus <lb />imaginarius; </s>
          <s xml:space="preserve">quo nomine etiam datur punctum, ex quo fluere <lb />concipiuntur radii divergentes, qui ex puncto radiante non <lb />procedunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-08" corresp="note-0519-08a" place="margin">651.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">647.</note>
        <p rend="italics">
          <s xml:space="preserve">Quo magis radii convergunt, poſitâ eâdem inter hos di-<lb />
<ptr xml:id="note-0519-10a" corresp="note-0519-10" type="noteAnchor" />
ſtantiâ, eo minus diſtat focus ſive verus ſive imaginarius.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-10" corresp="note-0519-10a" place="margin">652.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si radii paralleli tranſeant è medio quocunque in aliud <lb />
<ptr xml:id="note-0519-11a" corresp="note-0519-11" type="noteAnchor" />
alterius denſitatis, poſt refractionem etiam ſunt paralleli: </s>
          <s xml:space="preserve">quia <lb />omnes æqualiter inflectuntur, in toto enim hoc capite agi-<lb />tur de mediis ſuperficie planâ ſeparatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-11" corresp="note-0519-11a" place="margin">653.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dentur media X &amp; </s>
          <s xml:space="preserve">Z, hoc rarius illud verò denſius, pla-<lb />
<ptr xml:id="note-0519-12a" corresp="note-0519-12" type="noteAnchor" />
no ES ſeparata; </s>
          <s xml:space="preserve">procedant à puncto R radii divergentes <lb />
<ptr xml:id="note-0519-13a" corresp="note-0519-13" type="noteAnchor" />
RC, R o, R n, mediumque denſius intrent: </s>
          <s xml:space="preserve">inter hos ſit <lb />RC, perpendicularis ad ſuperficiem ES; </s>
          <s xml:space="preserve">hic a via non <lb />deflectitur <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">per CG motum continuat. </s>
          <s xml:space="preserve">Radii R o,
<ptr xml:id="note-0519-14a" corresp="note-0519-14" type="noteAnchor" />
R n refractionem patiuntur verſus perpendiculares, quæ in
</s>
          <pb facs="0520" n="30" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
punctis o &amp; </s>
          <s xml:space="preserve">n ad ſuperficiem ES concipiuntur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hi radií in
<ptr xml:id="note-0520-01a" corresp="note-0520-01" type="noteAnchor" />
medio denſiori ita moventur, quaſi procederent omnes a foco <lb />imaginario r, magis a ſuperficie diſtanti, quam ipſum R, ſi <lb />radii non nimium diſpergantur; </s>
          <s xml:space="preserve">quod tamen non mathema-<lb />ticè eſt intelligendum, per punctum enim ſpatium exiguum, <lb />quod aliter punctum phyſicum vocatur, intelligimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0519-12" corresp="note-0519-12a" place="margin">654.</note>
              <note xml:space="preserve" xml:id="note-0519-13" corresp="note-0519-13a" place="margin">TAB. V. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0519-14" corresp="note-0519-14a" n="*" anchored="true" place="margin">629.</note>
              <note xml:space="preserve" xml:id="note-0520-01" corresp="note-0520-01a" n="*" anchored="true" place="margin">624.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut hanc demonſtremus propoſitionem, conſiderandum eſt, <lb />angulum Ro C eſſe complementum anguli incidentiæ ad <lb />angulum rectum, &amp; </s>
          <s xml:space="preserve">angulum roC eſſe etiam complemen-<lb />tum anguli refractionis ad angulum rectum; </s>
          <s xml:space="preserve">ideoque lineas <lb />Ro, ro eſſe ſecantes comp. </s>
          <s xml:space="preserve">angulorum incidentiæ &amp; </s>
          <s xml:space="preserve">refra-<lb />ctionis, poſito ſemidiametro oC; </s>
          <s xml:space="preserve">inter quas ſecantes con-<lb />ſtans datur proportio <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In diſperſione exigua Ro &amp; </s>
          <s xml:space="preserve">RC,
<ptr xml:id="note-0520-02a" corresp="note-0520-02" type="noteAnchor" />
ut &amp; </s>
          <s xml:space="preserve">ro, &amp; </s>
          <s xml:space="preserve">rC, ſenſibiliter non differunt, &amp; </s>
          <s xml:space="preserve">inter RC <lb />&amp; </s>
          <s xml:space="preserve">rC etiam conſtans datur ratio; </s>
          <s xml:space="preserve">id eſt r æquè fixum eſt <lb />ac R, licet inclinatio radii mutetur: </s>
          <s xml:space="preserve">idcirco Rn ita etiam re-<lb />fringitur per nA quaſi ab r procederet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0520-02" corresp="note-0520-02a" n="*" anchored="true" place="margin">641. 639.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nimium diſpergantur radii, hæc demonſttatio locum <lb />
<ptr xml:id="note-0520-03a" corresp="note-0520-03" type="noteAnchor" />
non habet, &amp; </s>
          <s xml:space="preserve">locus concurſus r pro puncto haberi non po-<lb />teſt; </s>
          <s xml:space="preserve">in hoc caſu circellus ibi concipiendus eſt, in quem omnes <lb />radii concurrunt, qui eo major erit, quo majorem angulum <lb />radii divergentes formant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0520-03" corresp="note-0520-03a" place="margin">655.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si radii quidam ex R procedentes non admodum diſper-<lb />
<ptr xml:id="note-0520-04a" corresp="note-0520-04" type="noteAnchor" />
gantur, ſed valdè obliquè incidant in ſuperficiem ES, re-<lb />fringuntur quaſi procederent ex puncto non admodum a pun-<lb />cto r remoto: </s>
          <s xml:space="preserve">ut ex dictis ſatis liquet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0520-04" corresp="note-0520-04a" place="margin">656.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii qui ut An, Bo, GC convergentes ex medio denſiori <lb />
<ptr xml:id="note-0520-05a" corresp="note-0520-05" type="noteAnchor" />
X in rarius Z tranſeunt, citius concurrunt, quam concur-<lb />rerent, ſi in medio denſiori motum continuarent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, ma-
<ptr xml:id="note-0520-06a" corresp="note-0520-06" type="noteAnchor" />
gis convergentes fiunt, &amp; </s>
          <s xml:space="preserve">focus verus minus quam imagina-<lb />rius diſtat. </s>
          <s xml:space="preserve">In hac figura focus imaginarius eſt r, focus autem <lb />verus R <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Propoſitio hæc propriè eſt inverſa propoſitionis
<ptr xml:id="note-0520-07a" corresp="note-0520-07" type="noteAnchor" />
n. </s>
          <s xml:space="preserve">654. </s>
          <s xml:space="preserve">ideoque eodem experimento probantur ambæ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0520-05" corresp="note-0520-05a" place="margin">657.</note>
              <note xml:space="preserve" xml:id="note-0520-06" corresp="note-0520-06a" n="*" anchored="true" place="margin">625.</note>
              <note xml:space="preserve" xml:id="note-0520-07" corresp="note-0520-07a" n="*" anchored="true" place="margin">652.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">626.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Per globum G, in feneſtra mobilem, &amp; </s>
          <s xml:space="preserve">in quo foramen <lb />
<ptr xml:id="note-0520-09a" corresp="note-0520-09" type="noteAnchor" />
per centrum tranſiens datur, radius ſolaris cylindricus in cu-<lb />biculum obſcurum intromittitur, &amp; </s>
          <s xml:space="preserve">a ſpeculo Shorizontaliter
</s>
          <pb facs="0521" n="31" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. VII.</fw>
reflectitur; </s>
          <s xml:space="preserve">tranſmittitur per lentem vitream convexam in <lb />tabella T, &amp; </s>
          <s xml:space="preserve">radii in R colliguntur, &amp; </s>
          <s xml:space="preserve">poſt R moventur quaſi <lb />ab hoc puncto procederent; </s>
          <s xml:space="preserve">quod ergo eſt punctum radians.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0520-09" corresp="note-0520-09a" place="margin">TAB. V. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lentes vitreæ convexæ ſunt admodum vulgares; </s>
          <s xml:space="preserve">de ha-<lb />rum proprietatibus in ſequentibus agam <ptr type="noteAnchor" />, hasque memorare
<ptr xml:id="note-0521-01a" corresp="note-0521-01" type="noteAnchor" />
hujus loci non eſt; </s>
          <s xml:space="preserve">in hoc experimento indigemus puncto ra-<lb />diante, &amp; </s>
          <s xml:space="preserve">ſatis eſt hujus formationem memoraſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0521-01" corresp="note-0521-01a" n="*" anchored="true" place="margin">691. 697.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur Pixis P cujus latus abcd eſt vitreum, aquâ im-<lb />pleatur; </s>
          <s xml:space="preserve">radii, divergentes a puncto R, aquam ingreſſi mi-<lb />nus divergentes erunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando radii convergentes, ut HD, I p, L q, habentes <lb />
<ptr xml:id="note-0521-02a" corresp="note-0521-02" type="noteAnchor" />
focum imaginarium f, è medio rariori Z in denſius X pene-<lb />
<ptr xml:id="note-0521-03a" corresp="note-0521-03" type="noteAnchor" />
trant, minus convergentes fiunt <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in focum F, magis
<ptr xml:id="note-0521-04a" corresp="note-0521-04" type="noteAnchor" />
diſtantem a ſuperficie ES <ptr type="noteAnchor" />, concurrunt ut patet hic appli-
<ptr xml:id="note-0521-05a" corresp="note-0521-05" type="noteAnchor" />
cando demonſtrationem datam in n. </s>
          <s xml:space="preserve">654.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0521-02" corresp="note-0521-02a" place="margin">658.</note>
              <note xml:space="preserve" xml:id="note-0521-03" corresp="note-0521-03a" place="margin">TAB. V. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0521-04" corresp="note-0521-04a" n="*" anchored="true" place="margin">624.</note>
              <note xml:space="preserve" xml:id="note-0521-05" corresp="note-0521-05a" n="*" anchored="true" place="margin">652.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii ex puncto F procedentes, &amp; </s>
          <s xml:space="preserve">ex medio denſiori in <lb />
<ptr xml:id="note-0521-06a" corresp="note-0521-06" type="noteAnchor" />
rarius penetrantes, magis divergentes fiunt, &amp; </s>
          <s xml:space="preserve">moventur <lb />quaſi ex f procederent; </s>
          <s xml:space="preserve">quæ propoſitio eſt inverſa præce-<lb />dentis, &amp; </s>
          <s xml:space="preserve">cum hac eodem Experimento confirmatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0521-06" corresp="note-0521-06a" place="margin">659.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">626.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Eâdem, cum præcedenti Experimento, pixide P inſtituitur; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0521-08a" corresp="note-0521-08" type="noteAnchor" />
in hoc, lumen ſolare in cubiculum obſcurum intromittitur per <lb />duo foramina in orbe mobili O, qui in feneſtra datur; </s>
          <s xml:space="preserve">à ſpeculo <lb />horizontaliter reflectantur radiiambo, &amp; </s>
          <s xml:space="preserve">per lentes convexas, <lb />ſimiles tranſmittantur; </s>
          <s xml:space="preserve">quo radii, ex quibus radii primi con-<lb />ſtant, convergentes fiunt, habentes focos ad eandem diſtan-<lb />tiam; </s>
          <s xml:space="preserve">ſi autem radii convergentes in aquam, pixide conten-<lb />tam, per latus vitreum abcd penetrent, ad majorem di-<lb />ſtantiam colligentur; </s>
          <s xml:space="preserve">quod clarè patet, comparando inter ſe <lb />ſitus punctorum F in aëre &amp; </s>
          <s xml:space="preserve">f in aqua.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0521-08" corresp="note-0521-08a" place="margin">TAB. V. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VIII.</head>
        <head rend="italics" xml:space="preserve">De refractione luminis, poſitis mediis ſuperficie <lb />ſphæricâ ſeparatis.</head>
        <p>
          <s xml:space="preserve">SInt Media denſitate differentia X &amp; </s>
          <s xml:space="preserve">Z, hoc rarius illud <lb />
<ptr xml:id="note-0521-09a" corresp="note-0521-09" type="noteAnchor" />
denſius; </s>
          <s xml:space="preserve">ſeparentur ſuperficie ſphæricâ ES, cujus cen-<lb />trum eſt C, &amp; </s>
          <s xml:space="preserve">cujus convexitas eſt ad partem medii rarioris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0521-09" corresp="note-0521-09a" place="margin">TAB. VI. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0522" n="32" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Ut caſum ſimpliciſſimum ante alios examinemus, ponamus <lb />
<ptr xml:id="note-0522-01a" corresp="note-0522-01" type="noteAnchor" />
radios parallelos ut BO &amp; </s>
          <s xml:space="preserve">An, ex medio rariori in denſius <lb />penetrantes, in memoratam convexam ſuperficiem incidere; <lb /></s>
          <s xml:space="preserve">deturque inter hos BO, qui continuatus per centrum C <lb />tranſit, &amp; </s>
          <s xml:space="preserve">perpendiculariter cadit in ſuperficiem ES; </s>
          <s xml:space="preserve">ideo-<lb />que a recta non deflectitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Radii omnes non nimium ab
<ptr xml:id="note-0522-02a" corresp="note-0522-02" type="noteAnchor" />
hoc diſtantes ad hunc refractione medii denſioris accedunt, <lb />&amp; </s>
          <s xml:space="preserve">in unum punctum F colliguntur. </s>
          <s xml:space="preserve">Sit ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">radius An, <lb />qui refringitur per n F; </s>
          <s xml:space="preserve">per punctum n ducatur ad centrum <lb />C ſemidiameter C n continuata ad p; </s>
          <s xml:space="preserve">cùm hæc perpendicu-<lb />laris ſit ad ſuperficiem media dirimentem, angulus inciden-<lb />tiæ eſt A np, æqualis angulo nCO: </s>
          <s xml:space="preserve">angulus refractionis <lb />eſt C n F. </s>
          <s xml:space="preserve">Si arcus n O fuerit exiguus, anguli hi ſunt ut ho-<lb />rum ſinus, quorum ratio eſt conſtans <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In eadem ergo ra-
<ptr xml:id="note-0522-03a" corresp="note-0522-03" type="noteAnchor" />
tione creſcunt &amp; </s>
          <s xml:space="preserve">minuuntur hi anguli n CO &amp; </s>
          <s xml:space="preserve">CnF, ut &amp; </s>
          <s xml:space="preserve"><lb />horum differentia angulus n FO, qui igitur ſequitur propor-<lb />tionem arcus n O, menſuræ anguli n CO; </s>
          <s xml:space="preserve">Quamdiu arcus <lb />n O, 15. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">non ſuperat, angulus nFO in eadem ratione cum <lb />hoc arcu ſenſibiliter augetur &amp; </s>
          <s xml:space="preserve">minuitur; </s>
          <s xml:space="preserve">ideoque omnes <lb />radii inter A n &amp; </s>
          <s xml:space="preserve">BO, refractione, ſenſibiliter in punctum <lb />F concurrunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0522-01" corresp="note-0522-01a" place="margin">660.</note>
              <note xml:space="preserve" xml:id="note-0522-02" corresp="note-0522-02a" n="*" anchored="true" place="margin">629.</note>
              <note xml:space="preserve" xml:id="note-0522-03" corresp="note-0522-03a" n="*" anchored="true" place="margin">639.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Radius ſolaris cylindricus diametri unius pollicis, ex in-<lb />
<ptr xml:id="note-0522-04a" corresp="note-0522-04" type="noteAnchor" />
numeris aliis parallelis, propter immenſam Solis diſtantiam, <lb />conſtans, in cubiculum obſcurum intromittitur, ut in exp. </s>
          <s xml:space="preserve">1. <lb /></s>
          <s xml:space="preserve">capitis præcedentis, &amp; </s>
          <s xml:space="preserve">a ſpeculo Shorizontaliter reflectitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0522-04" corresp="note-0522-04a" place="margin">TAB. VI. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pixis P, latitudinis ad &amp; </s>
          <s xml:space="preserve">altitudinis ba circiter trium pol-<lb />licum, longitudinis unius pedis, aquâ repletur. </s>
          <s xml:space="preserve">In medio la-<lb />teris abcd datur vitrum V; </s>
          <s xml:space="preserve">eſt hoc ſphæræ portio, tenue, <lb />&amp; </s>
          <s xml:space="preserve">ubique ejuſdem craſſitiei; </s>
          <s xml:space="preserve">vulgo vitris talibus indices ob-<lb />teguntur in horologiis portatilibus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Diſponitur vitrum V, ut pars convexa ſit exterior, &amp; </s>
          <s xml:space="preserve">a-<lb />qua, cavitatem vitri implens, adipiſcatur ſuperficiem ſphæri-<lb />cam convexam. </s>
          <s xml:space="preserve">Si radii memorati pixidem per hoc vitrum <lb />intrent, propter vitri tenuitatem &amp; </s>
          <s xml:space="preserve">quia hoc faciebus pa-<lb />rallelis terminatur, non ſenſibilis datur mutatio in motu lu-<lb />minis ex vitri refractione, &amp; </s>
          <s xml:space="preserve">lumen aquam intrat, eodem
</s>
          <pb facs="0523" />
          <s xml:space="preserve">
<pb facs="0523a" />
<ptr xml:id="fig-0523a-01a" corresp="fig-0523a-01" type="figureAnchor" />
<pb facs="0524" />
<pb facs="0525" n="(33)" /><fw type="head">MATHEMATICA, LIB. III. CAP. VIII.</fw>
modo ac ſi vitrum non daretur. </s>
          <s xml:space="preserve">Diſponatur pixis, ut unus <lb />ex radiis per centrum ſuperficiei ſphæricæ aquæ tranſeat, a-<lb />lii ad hunc accedent, &amp; </s>
          <s xml:space="preserve">in F cum hoc concurrent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0523a-01" corresp="fig-0523a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0523a-01" />
                <label>0523a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur iterum X medium denſius, Z rarius, ſeparentur <lb />
<ptr xml:id="note-0525-01a" corresp="note-0525-01" type="noteAnchor" />
ſuperficie ſphæricâ ES, cujus centrum eſt C, &amp; </s>
          <s xml:space="preserve">cujus con-<lb />vexitas eſt ad partem medii rarioris; </s>
          <s xml:space="preserve">Ex puncto radiante R <lb />
<ptr xml:id="note-0525-02a" corresp="note-0525-02" type="noteAnchor" />
procedant radii, &amp; </s>
          <s xml:space="preserve">in medium denſius per memoratam ſuperfi-<lb />ciem penetrent, ita ut inter hos radius RO continuatus per <lb />centrum C tranſeat; </s>
          <s xml:space="preserve">hic non refringitur dum aquam intrat, <lb />&amp; </s>
          <s xml:space="preserve">ad hunc refractione reliqui omnes accedunt, &amp; </s>
          <s xml:space="preserve">quando <lb />parum diſperguntur in unum punctum, ut F, colliguntur, eo-<lb />dem modo ac de radiis parallelis dictum; </s>
          <s xml:space="preserve">cum hac differen-<lb />tiâ, quod focus F in hoc caſu magis diſtet. </s>
          <s xml:space="preserve">Eadem etiam de-<lb />monſtratio hìc locum habet ac circa radios parallelos, quæ <lb />hoc fundamento nititur, quod angulus incidentiæ, cum ar-<lb />cu n O in eadem ratione creſcat, quod &amp; </s>
          <s xml:space="preserve">hìc obtinet, ſiarcus <lb />n O gradus 15. </s>
          <s xml:space="preserve">non ſuperet. </s>
          <s xml:space="preserve">Detur radius R n, per n ex <lb />centro C ducatur C np: </s>
          <s xml:space="preserve">angulus R np erit angulus inci-<lb />dentiæ; </s>
          <s xml:space="preserve">dividatur hic in duas partes lineâ nq, parallelâ li-<lb />neæ ROC; </s>
          <s xml:space="preserve">pars pnq æqualis eſt angulo n CO, qui arcu <lb />n O menſuratur, &amp; </s>
          <s xml:space="preserve">qui ideo cum hoc arcu eandem ſequitur <lb />proportionem; </s>
          <s xml:space="preserve">quam etiam, poſito hoc exiguo, ſequitur <lb />angulus n RO, æqualis ſecundæ parti anguli incidentiæ, <lb />qui igitur in totum etiam cum arcu n O in eadem ratione <lb />creſcit &amp; </s>
          <s xml:space="preserve">minuitur, quæ enim ratio in ſingulis partibus lo-<lb />cum habet, reſpectu totius etiam obtinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0525-01" corresp="note-0525-01a" place="margin">TAB. VI. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0525-02" corresp="note-0525-02a" place="margin">661.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Similis demonſtratio poteſt applicari radiis quibuſcunque <lb />
<ptr xml:id="note-0525-03a" corresp="note-0525-03" type="noteAnchor" />
divergentibus, aut convergentibus, qui in quocunque caſu <lb />in ſuperficie ſphæricâ refringuntur, &amp; </s>
          <s xml:space="preserve">qui ut hac demonſtra-<lb />tione conſtat, in exiguâ diſperſione, focum habent aut ve-<lb />rum, aut imaginarium, aut paralleli ſunt inter ſe. </s>
          <s xml:space="preserve">Quod in <lb />genere hic notaſſe ſufficiat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0525-03" corresp="note-0525-03a" place="margin">662.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Focus F radiorum ab R procedentium, accedente R rece-<lb />
<ptr xml:id="note-0525-04a" corresp="note-0525-04" type="noteAnchor" />
dit &amp; </s>
          <s xml:space="preserve">vice verſa. </s>
          <s xml:space="preserve">Accedente puncto radiante, ſi maneat <lb />punctum n, augetur angulus incidentiæ, quo creſcente, au-<lb />getur etiam angulus refractionis F n C, &amp; </s>
          <s xml:space="preserve">n F ad majorem <lb />diſtantiam interſecat RC.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0525-04" corresp="note-0525-04a" place="margin">663.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0526" n="(34)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Differt hoc experimentum cum præcedenti in eo ſolo, <lb />
<ptr xml:id="note-0526-01a" corresp="note-0526-01" type="noteAnchor" />
quod radius ſolaris cylindricus, horizontaliter reflexus, tranſ-<lb />mittatur per lentem convexam in tabella T, ut in experi-<lb />mentis capitis præcedentis, quo formatur punctum radians <lb />R. </s>
          <s xml:space="preserve">Radii ab hoc procedentes in aquâ colliguntur in F ad ma-<lb />jorem diſtantiam, quàm ſi paralleli forent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0526-01" corresp="note-0526-01a" place="margin">TAB. VI. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motu tabellæ T movetur punctum R; </s>
          <s xml:space="preserve">recedente hoc a <lb />ſuperficie media dirimente, ad hanc accedit F; </s>
          <s xml:space="preserve">contra ac-<lb />cedente R recedit F.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ita poteſt admoveri punctum radians ad ſuperficiem me-<lb />
<ptr xml:id="note-0526-02a" corresp="note-0526-02" type="noteAnchor" />
dia dirimentem, ut focus ad diſtantiam infinitam recedat, <lb />id eſt, ut radii refracti paralleli fiant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0526-02" corresp="note-0526-02a" place="margin">664.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Rebus, ut in Experimento præcedenti, diſpoſitis; </s>
          <s xml:space="preserve">motu <lb />
<ptr xml:id="note-0526-03a" corresp="note-0526-03" type="noteAnchor" />
tabellæ T admoveatur R ad pixidem, &amp; </s>
          <s xml:space="preserve">in tali ſitu facile <lb />diſponetur, ut refracti radii paralleli ſint.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0526-03" corresp="note-0526-03a" place="margin">TAB. VI. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Iiſdem manentibus, ſi magis accedat ad pixidem punctum <lb />
<ptr xml:id="note-0526-04a" corresp="note-0526-04" type="noteAnchor" />
radians R, divergentes fient radii refracti, minus tamen <lb />
<ptr xml:id="note-0526-05a" corresp="note-0526-05" type="noteAnchor" />
divergentes quam incidentes;</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0526-04" corresp="note-0526-04a" place="margin">665.</note>
              <note xml:space="preserve" xml:id="note-0526-05" corresp="note-0526-05a" place="margin">TAB. VII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si radii, qui ex medio rariori in denſius per ſuperficiem <lb />
<ptr xml:id="note-0526-06a" corresp="note-0526-06" type="noteAnchor" />
convexam intrant, convergentes ſint, &amp; </s>
          <s xml:space="preserve">ad centrum ſuperfi-<lb />ciei dirigantur, nullam patiuntur refractionem <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si ver-
<ptr xml:id="note-0526-07a" corresp="note-0526-07" type="noteAnchor" />
ſus aliud punctum dirigantur, cùm verſus perpendicularem <lb />
<ptr xml:id="note-0526-08a" corresp="note-0526-08" type="noteAnchor" />
refringantur <ptr type="noteAnchor" />, ita inflectuntur radii, ut focus radiorum ho-
<ptr xml:id="note-0526-09a" corresp="note-0526-09" type="noteAnchor" />
rum convergentium ſemper detur inter centrum ſuperficiei <lb />media dirimentis, (ad quod perpendiculares omnes diri-<lb />guntur), &amp; </s>
          <s xml:space="preserve">punctum verſus quod radii incidentes tendunt. <lb /></s>
          <s xml:space="preserve">Id eſt, ſi focus imaginarius incidentium detur ad minorem <lb />diſtantiam quàm centrum, minus convergentes ſunt radii re-<lb />fracti: </s>
          <s xml:space="preserve">ſi ultra centrum detur hicce focus imaginarius, magis <lb />convergentes erunt radii refracti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0526-06" corresp="note-0526-06a" place="margin">666.</note>
              <note xml:space="preserve" xml:id="note-0526-07" corresp="note-0526-07a" n="*" anchored="true" place="margin">629.</note>
              <note xml:space="preserve" xml:id="note-0526-08" corresp="note-0526-08a" place="margin">667.</note>
              <note xml:space="preserve" xml:id="note-0526-09" corresp="note-0526-09a" n="*" anchored="true" place="margin">624.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Iiſdem adhibitis, quæ in experimentis præcedentibus, faci-<lb />
<ptr xml:id="note-0526-10a" corresp="note-0526-10" type="noteAnchor" />
le hæ propoſitiones experimentis confirmantur; </s>
          <s xml:space="preserve">ita enim <lb />diſponi poteſt tabella T, ut radii convergentes aquam in-
</s>
          <pb facs="0527" />
          <s xml:space="preserve">
<pb facs="0527a" />
<ptr xml:id="fig-0527a-01a" corresp="fig-0527a-01" type="figureAnchor" />
<pb facs="0528" />
<pb facs="0529" n="(35)" /><fw type="head">MATHEMATICA. LIB. III. CAP. VIII.</fw>
trent, &amp; </s>
          <s xml:space="preserve">horum focus imaginarius detur ad diſtantiam <lb />quamcunque in aquâ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0526-10" corresp="note-0526-10a" place="margin">TAB. VII. <lb />fig. 2.</note>
              <figure xml:id="fig-0527a-01" corresp="fig-0527a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0527a-01" />
                <label>0527a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hucuſque dictis, quæ in motu radiorum contrario ob <lb />
<ptr xml:id="note-0529-01a" corresp="note-0529-01" type="noteAnchor" />
tinent facile determinamus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, motum radiorum ex
<ptr xml:id="note-0529-02a" corresp="note-0529-02" type="noteAnchor" />
medio denſiori in rarius, manente ſuperficie convexâ ad par-<lb />tem medii rarioris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-01" corresp="note-0529-01a" place="margin">668.</note>
              <note xml:space="preserve" xml:id="note-0529-02" corresp="note-0529-02a" n="*" anchored="true" place="margin">626.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Radii paralleli poſt refractionem in focum concurrunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">664.</note>
        <p rend="italics">
          <s xml:space="preserve">Etiam in punctum aut focum conveniunt radii ex puncto <lb />
<ptr xml:id="note-0529-04a" corresp="note-0529-04" type="noteAnchor" />
radiante manantes, <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">accedente hoc recedit illud, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0529-05a" corresp="note-0529-05" type="noteAnchor" />
contra <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-04" corresp="note-0529-04a" place="margin">669.</note>
              <note xml:space="preserve" xml:id="note-0529-05" corresp="note-0529-05a" n="*" anchored="true" place="margin">661.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">663.</note>
        <p>
          <s xml:space="preserve">Ita poteſt diſponi punctum radians, ut focus ad diſtantiam <lb />
<ptr xml:id="note-0529-07a" corresp="note-0529-07" type="noteAnchor" />
infinitam detur, id eſt, ut radii refracti paralleli ſint. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-07" corresp="note-0529-07a" place="margin">670.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">660.</note>
        <p rend="italics">
          <s xml:space="preserve">Si ulterius accedat punctum radians, refracti divergen-<lb />
<ptr xml:id="note-0529-09a" corresp="note-0529-09" type="noteAnchor" />
tes ſunt; </s>
          <s xml:space="preserve">minus divergentes quam incidentes, ſi punctum <lb />radians magis diſtet à ſuperficie quàm centrum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-09" corresp="note-0529-09a" place="margin">671.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">667.</note>
        <p rend="italics">
          <s xml:space="preserve">Si autem punctum radians detur inter ſuperficiem &amp; </s>
          <s xml:space="preserve">cen-<lb />
<ptr xml:id="note-0529-11a" corresp="note-0529-11" type="noteAnchor" />
trum, radii refracti magis divergentes erunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-11" corresp="note-0529-11a" place="margin">672.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">667.</note>
        <p>
          <s xml:space="preserve">Si radii fuerint convergentes, magis in omni caſu fiunt <lb />
<ptr xml:id="note-0529-13a" corresp="note-0529-13" type="noteAnchor" />
convergentes, quod ex refractione a perpendiculari <ptr type="noteAnchor" /> ſequi-
<ptr xml:id="note-0529-14a" corresp="note-0529-14" type="noteAnchor" />
tur, &amp; </s>
          <s xml:space="preserve">etiam deducitur ex n. </s>
          <s xml:space="preserve">665.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-13" corresp="note-0529-13a" place="margin">673.</note>
              <note xml:space="preserve" xml:id="note-0529-14" corresp="note-0529-14a" n="*" anchored="true" place="margin">625.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus iterum radios ex medio rariori Z in denſius X <lb />
<ptr xml:id="note-0529-15a" corresp="note-0529-15" type="noteAnchor" />
intrare, cavitatem autem ſuperficiei ſphæricæ ES, media ſe-<lb />
<ptr xml:id="note-0529-16a" corresp="note-0529-16" type="noteAnchor" />
parantis, dari ad partem medii rarioris. </s>
          <s xml:space="preserve">Si radii fuerint <lb />paralleli, ut BO, A n; </s>
          <s xml:space="preserve">BO, qui per centrum C ſuperficiei <lb />ES tranſit, nullam patitur refractionem; </s>
          <s xml:space="preserve">A n verò ad per-<lb />pendicularem C p per n G refringitur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">verſus Z conti-
<ptr xml:id="note-0529-17a" corresp="note-0529-17" type="noteAnchor" />
nuatus interſecat BCO in f, quod etiam reſpectu radio-<lb />rum inter BO &amp; </s>
          <s xml:space="preserve">A n obtinet <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">fiunt ergo hi radii diver-
<ptr xml:id="note-0529-18a" corresp="note-0529-18" type="noteAnchor" />
gentes, hàbentes focum imaginarium f in medio rariori.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-15" corresp="note-0529-15a" place="margin">674.</note>
              <note xml:space="preserve" xml:id="note-0529-16" corresp="note-0529-16a" place="margin">TAB. VII. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0529-17" corresp="note-0529-17a" n="*" anchored="true" place="margin">624.</note>
              <note xml:space="preserve" xml:id="note-0529-18" corresp="note-0529-18a" n="*" anchored="true" place="margin">662.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">In eo ſolo experimentum hoc a primo hujus capitis dif-<lb />
<ptr xml:id="note-0529-19a" corresp="note-0529-19" type="noteAnchor" />
fert, quod vitrum V, habeat cavitatem ad partem aëris, de <lb />cætero pixis P à prima pixide non differt; </s>
          <s xml:space="preserve">In hoc caſu ra-<lb />dii, ex quibus radius cylindricus conſtat, in aquâ diſpergun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-19" corresp="note-0529-19a" place="margin">TAB. VII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si à puncto radiante in CB ultra C, radii emanant, mi-<lb />
<ptr xml:id="note-0529-20a" corresp="note-0529-20" type="noteAnchor" />
nuitur angulus incidentiæ A n C, &amp; </s>
          <s xml:space="preserve">idcirco etiam angulus <lb />
<ptr xml:id="note-0529-21a" corresp="note-0529-21" type="noteAnchor" />
</s>
          <pb facs="0530" n="(36)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
refractionis G np; </s>
          <s xml:space="preserve">id eſt, radii refracti magis divergentes <lb />fiunt, &amp; </s>
          <s xml:space="preserve">ad C accedit focus imaginarius f <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">donec acceſſu
<ptr xml:id="note-0530-01a" corresp="note-0530-01" type="noteAnchor" />
puncti radiantis tandem hoc coincidat cum foco imaginario <lb />in C; </s>
          <s xml:space="preserve">in hoc enim caſu radii nullam patiuntur refractionem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0529-20" corresp="note-0529-20a" place="margin">675.</note>
              <note xml:space="preserve" xml:id="note-0529-21" corresp="note-0529-21a" place="margin">TAB. VII. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0530-01" corresp="note-0530-01a" n="*" anchored="true" place="margin">646.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">629.</note>
        <p>
          <s xml:space="preserve">Si ulterius accedat punctum radians, inter C &amp; </s>
          <s xml:space="preserve">O ma-<lb />
<ptr xml:id="note-0530-03a" corresp="note-0530-03" type="noteAnchor" />
gis diſtet focus imaginarius ab O, quàm punctum radians, in-<lb />ter hoc enim &amp; </s>
          <s xml:space="preserve">C ſemper ille datur, propter angulos refra-<lb />ctionis minores angulis incidentiæ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-03" corresp="note-0530-03a" place="margin">676.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">624.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 7.</head>
        <p>
          <s xml:space="preserve">Si eadem dentur, quæ in experimento præcedenti, ad-<lb />hibitâ tabellâ cum lente convexâ, de qua ſæpius jam di-<lb />ctum, ad punctum radians formandum, facilia ſunt experi-<lb />menta circa has propoſitiones.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Si radii fuerint convergentes, &amp; </s>
          <s xml:space="preserve">punctum concurſus detur <lb />
<ptr xml:id="note-0530-05a" corresp="note-0530-05" type="noteAnchor" />
in medio denſiori, in viciniis ſuperficiei media ſeparantis, re-<lb />fracti radii etiam convergunt, ſed minus convergunt, quàm <lb />incidentes.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-05" corresp="note-0530-05a" place="margin">677.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ab O magis ac magis recedat focus imaginarius radio-<lb />rum incidentium, id eſt, ſi hi minus convergant, etiam mi-<lb />
<ptr xml:id="note-0530-06a" corresp="note-0530-06" type="noteAnchor" />
nus convergent radii refracti; </s>
          <s xml:space="preserve">donec, receſſu foci imagina-<lb />rii, refracti paralleli ſint.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-06" corresp="note-0530-06a" place="margin">678.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In ulteriori receſſu foci imaginarii divergentes fiunt refra-<lb />
<ptr xml:id="note-0530-07a" corresp="note-0530-07" type="noteAnchor" />
cti radii.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-07" corresp="note-0530-07a" place="margin">679.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">In hoc ad pixidem ita admovenda eſt tabella T, ut ra-<lb />
<ptr xml:id="note-0530-08a" corresp="note-0530-08" type="noteAnchor" />
dii convergentes aquam intrent; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in motu tabellæ prædi-<lb />cta ad oculum patent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-08" corresp="note-0530-08a" place="margin">TAB. VII. <lb />fig 5.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii, qui e medio denſiori in rarius penetrant, manente <lb />
<ptr xml:id="note-0530-09a" corresp="note-0530-09" type="noteAnchor" />
ſuperficie cavâ ad partem hujus medii, iiſdem fere legibus <lb />ſubjiciuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-09" corresp="note-0530-09a" place="margin">680.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Radii paralleli refractione divergunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">678. 626.</note>
        <p rend="italics">
          <s xml:space="preserve">Si à puncto radianti procedant, magis ſunt divergentes <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">681.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">677.</note>
        <p rend="italics">
          <s xml:space="preserve">Et cum acceſſu puncti radiantis continuo magis ac magïs <lb />
<ptr xml:id="note-0530-13a" corresp="note-0530-13" type="noteAnchor" />
divergunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-13" corresp="note-0530-13a" place="margin">682.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">678.</note>
        <p rend="italics">
          <s xml:space="preserve">Convergentes radii, qui ad centrum ſuperficiei ſphæricæ <lb />
<ptr xml:id="note-0530-15a" corresp="note-0530-15" type="noteAnchor" />
tendunt, nullam ſubeunt mutationem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-15" corresp="note-0530-15a" place="margin">683.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">629.</note>
        <p rend="italics">
          <s xml:space="preserve">Si magis aut minus convergant, focus imaginarius inciden-<lb />
<ptr xml:id="note-0530-17a" corresp="note-0530-17" type="noteAnchor" />
</s>
          <pb facs="0531" />
          <s xml:space="preserve">
<pb facs="0531a" />
<ptr xml:id="fig-0531a-01a" corresp="fig-0531a-01" type="figureAnchor" />
<pb facs="0532" />
<pb facs="0533" n="(37)" /><fw type="head">MATHEMATICA LIB. III. CAP. VIII.</fw>
tium ſemper datur inter centrum ſuperficiei media ſeparan-<lb />
<ptr xml:id="note-0533-01a" corresp="note-0533-01" type="noteAnchor" />
tis, &amp; </s>
          <s xml:space="preserve">focum refractorum <ptr type="noteAnchor" />, qui poteſt in infinitum recedere,
<ptr xml:id="note-0533-02a" corresp="note-0533-02" type="noteAnchor" />
ita ut radii refracti paralleli ſint <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0530-17" corresp="note-0530-17a" place="margin">684.</note>
              <figure xml:id="fig-0531a-01" corresp="fig-0531a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0531a-01" />
                <label>0531a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0533-01" corresp="note-0533-01a" place="margin">685.</note>
              <note xml:space="preserve" xml:id="note-0533-02" corresp="note-0533-02a" n="*" anchored="true" place="margin">675. 676.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">674.</note>
        <p>
          <s xml:space="preserve">Huc uſque conſideravimus radios parum ad ſuperfi-<lb />ciem media ſeparantem inclinatos; </s>
          <s xml:space="preserve">nam de incidentibus <lb />egimus, inter quos datur radius ad ſeparationem mediorum <lb />perpendicularem, &amp; </s>
          <s xml:space="preserve">qui parum diſperguntur. </s>
          <s xml:space="preserve">In radiis <lb />
<ptr xml:id="note-0533-04a" corresp="note-0533-04" type="noteAnchor" />
obliquis fere eædem propoſitiones locum habent, in hoc tamen <lb />caſu omnes inflectuntur, quod in directis non æquè; </s>
          <s xml:space="preserve">radius <lb />enim ad ſuperficiem perpendicularis non inflectitur. </s>
          <s xml:space="preserve">In ob-<lb />
<ptr xml:id="note-0533-05a" corresp="note-0533-05" type="noteAnchor" />
liquis etiam omnes majorem patiuntur refractionem, id eſt, <lb />magis ad ſe mutuò aut à ſe mutuò radii inter ſe vicini infle-<lb />ctuntur, quàm in directis, poſitis iiſdem circumſtantiis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0533-04" corresp="note-0533-04a" place="margin">686.</note>
              <note xml:space="preserve" xml:id="note-0533-05" corresp="note-0533-05a" place="margin">687.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Z medium rarius, X denſius, ES ſuperficies cujus <lb />
<ptr xml:id="note-0533-06a" corresp="note-0533-06" type="noteAnchor" />
centrum C, quæ media ſeparat; </s>
          <s xml:space="preserve">radii A n, B m paralleli <lb />concurrunt in F. </s>
          <s xml:space="preserve">Radii, qui procedunt ex puncto radian-<lb />te R, concurrunt in focum f.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0533-06" corresp="note-0533-06a" place="margin">TAB. VIII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si convertatur ſuperficies, ut cavitas ſit ad partem medii <lb />
<ptr xml:id="note-0533-07a" corresp="note-0533-07" type="noteAnchor" />
rarioris, radii A n &amp; </s>
          <s xml:space="preserve">B m paralleli habebunt focum imagi-<lb />narium in f; </s>
          <s xml:space="preserve">hujus autem diſtantia a ſuperficie ES, ut &amp; </s>
          <s xml:space="preserve"><lb />memoratorum focorum F &amp; </s>
          <s xml:space="preserve">f in fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">minor eſt, quam ſi <lb />radii forent directi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0533-07" corresp="note-0533-07a" place="margin">TAB. VIII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corporis lucidi ſingula puncta ſunt puncta radiantia &amp; </s>
          <s xml:space="preserve">ha-<lb />
<ptr xml:id="note-0533-08a" corresp="note-0533-08" type="noteAnchor" />
bent ſingula ſuum focum. </s>
          <s xml:space="preserve">Quod dat explicationem experi-<lb />menti ſequentis, quod, quæ deradiis obliquis dicta ſunt, con-<lb />firmat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0533-08" corresp="note-0533-08a" place="margin">688.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 9.</head>
        <p>
          <s xml:space="preserve">Detur pixis P, de qua in Exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">aquâ plena; </s>
          <s xml:space="preserve">vitrum V ob-<lb />
<ptr xml:id="note-0533-09a" corresp="note-0533-09" type="noteAnchor" />
tegatur ita, ut pars detecta ſit circularis &amp; </s>
          <s xml:space="preserve">diametri circiter <lb />ſemi pollicis; </s>
          <s xml:space="preserve">in pixide detur tabella T alba &amp; </s>
          <s xml:space="preserve">mobilis. </s>
          <s xml:space="preserve">Si <lb />candela A ad diſtantiam detur trium aut quatuor pedum a <lb />pixide, &amp; </s>
          <s xml:space="preserve">tabella T per aquam moveatur, ubi pervenerit <lb />ad diſtantiam focorum flammæ A, flamma hæc in tabella exa-<lb />ctiſſimè repræſentata apparebit; </s>
          <s xml:space="preserve">focis omnibus picturam for-<lb />mantibus. </s>
          <s xml:space="preserve">Hoc autem obtinet ſive radii à candela obliquè in <lb />vitrum V incidant ſive directè, in ſitu tamen obliquo, manen-<lb />te diſtantia candelæ A, minuitur diſtantia tabellæ T ab V.</s>
          <s xml:space="preserve">
</s>
          <pb facs="0534" n="38" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
In hoc etiam caſu candela &amp; </s>
          <s xml:space="preserve">vitrum V non ſunt in eadem <lb />linea recta cum repreſentatione illius, quod in ſitu directo <lb />obtinet; </s>
          <s xml:space="preserve">quo confirmatur n. </s>
          <s xml:space="preserve">686.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0533-09" corresp="note-0533-09a" place="margin">TAB. VIII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Repræ ſentatur candela in ſitu everſo, quia radii, à diver-<lb />
<ptr xml:id="note-0534-01a" corresp="note-0534-01" type="noteAnchor" />
ſis punctis procedentes, tranſeundo per V. </s>
          <s xml:space="preserve">ſeſe mutuò inter-<lb />ſecant, ut per inſpectionem fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">clarè patet. </s>
          <s xml:space="preserve">Ex qua eadem <lb />cauſa, ſi duæ dentur candelæ ut A &amp; </s>
          <s xml:space="preserve">B, repræſentatio hujus <lb />dabitur in b illius in a.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0534-01" corresp="note-0534-01a" place="margin">689.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omnes mutationes in lumine, de quibus in hoc capite a-<lb />
<ptr xml:id="note-0534-02a" corresp="note-0534-02" type="noteAnchor" />
ctum, eò magis ſunt ſenſibiles, quo ſuperficies media diri-<lb />mens eſt magis curva, id eſt, minoris ſphæræ portio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0534-02" corresp="note-0534-02a" place="margin">690.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IX.</head>
        <head rend="italics" xml:space="preserve">De Motu Luminis trans Medium denſius. Vbi de <lb />Lentium affectionibus.</head>
        <p>
          <s xml:space="preserve">VItrorum frequens uſus eſt, aëre denſiora ſunt, &amp; </s>
          <s xml:space="preserve">ex aëre <lb />
<ptr xml:id="note-0534-03a" corresp="note-0534-03" type="noteAnchor" />
in aërem trans vitrum radii penetrant. </s>
          <s xml:space="preserve">Pro variis ſuper-<lb />ficiebus, quibus terminatur vitrum, diverſas in hoc motu lu-<lb />men mutationes ſubit, quæ ut determinentur, vitra, aut <lb />media quæcunque medio rariori circumdata, &amp; </s>
          <s xml:space="preserve">variis ſuper-<lb />ficiebus terminata, examinanda ſunt. </s>
          <s xml:space="preserve">Conſiderando ſolas ſu-<lb />perficies planas &amp; </s>
          <s xml:space="preserve">ſphæricas, ſex Claſſes dantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0534-03" corresp="note-0534-03a" place="margin">691.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">I. </s>
          <s xml:space="preserve">Medium hoc planum eſt ab utraque parte. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Ab una <lb />parte planum ab altera convexum. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Ab utraque parte <lb />convexum. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Ab una parte planum ab altera cavum. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">ca-<lb />vum utrimque. </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">Terminatur ſuperficie cavâ, &amp; </s>
          <s xml:space="preserve">oppoſita <lb />convexa eſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio i</hi>.</head>
        <p>
          <s xml:space="preserve">Si de vitro agatur &amp; </s>
          <s xml:space="preserve">craſſitiem non magnam habeat in quin-<lb />
<ptr xml:id="note-0534-04a" corresp="note-0534-04" type="noteAnchor" />
que ultimis caſibus, vitrum tale Lens vitrea dicitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0534-04" corresp="note-0534-04a" place="margin">692.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſecundo &amp; </s>
          <s xml:space="preserve">tertio caſu lens dicitur convexa; </s>
          <s xml:space="preserve">ſi tamen <lb />hi caſus diſtinguendi ſint, in ſecundo caſu dicitur plano-con-<lb />vexa. </s>
          <s xml:space="preserve">Eodem modo in quarto caſu dicitur plano-cava; </s>
          <s xml:space="preserve">licèt <lb />&amp; </s>
          <s xml:space="preserve">hicce caſus cum quinto ſequenti ad cavas lentes generali-<lb />ter referatur. </s>
          <s xml:space="preserve">Lens autem cavo-convexa ad cavas aut con-<lb />vexas lentes refertur, pro illa aut hac ſuperficie prævalente;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0535" n="39" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. IX.</fw>
prævalet autem cujus curvatura major eſt, id eſt, quæ mi-<lb />noris ſphæræ portio eſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">In omni lente, aut medio quocunque ut dictum terminato, axis <lb />
<ptr xml:id="note-0535-01a" corresp="note-0535-01" type="noteAnchor" />
vocatur linea recta, quæ ad ambas ſuperficies perpendicularis <lb />eſt. </s>
          <s xml:space="preserve">Quando ambæ ſuperficies ſunt ſphæricæ per ambarum <lb />centra tranſit axis; </s>
          <s xml:space="preserve">poſitâ verò alterâ ſuperficie planâ, per-<lb />pendiculariter ad hanc per aliûs centrum procedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0535-01" corresp="note-0535-01a" place="margin">693.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In tranſitu luminis per medium, duabus ſuperficiebus pla-<lb />nis terminatum, radiorum directio non mutatur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">qui caſus
<ptr xml:id="note-0535-02a" corresp="note-0535-02" type="noteAnchor" />
in vitris planis extat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0535-02" corresp="note-0535-02a" place="margin">694.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">628.</note>
        <p>
          <s xml:space="preserve">Lentium convexarum quarumcunque proprietas eſt, quod <lb />
<ptr xml:id="note-0535-04a" corresp="note-0535-04" type="noteAnchor" />
radii in tranſitu verſus ſe mutuò inflectantur; </s>
          <s xml:space="preserve">eò magis, quo <lb />major eſt convexitas: </s>
          <s xml:space="preserve">cavarum autem quod radii à ſe mu-<lb />
<ptr xml:id="note-0535-05a" corresp="note-0535-05" type="noteAnchor" />
tuo deflectantur; </s>
          <s xml:space="preserve">magis pro majori cavitate. </s>
          <s xml:space="preserve">Nam per vitrum <lb />planum radiorum directio non mutatur <ptr type="noteAnchor" />, inflectendo autem
<ptr xml:id="note-0535-06a" corresp="note-0535-06" type="noteAnchor" />
unam aut ambas ſuperficies, alia datur radiorum directio: </s>
          <s xml:space="preserve">ma-<lb />gis verſus lentis axem inflectuntur ex convexitate ſuperficiei <lb />vitri, &amp; </s>
          <s xml:space="preserve">excavando ſuperficiem ab axe deflectuntur; </s>
          <s xml:space="preserve">ut cla-<lb />rè patet in omni caſu, comparando inflexionem in ſuperfi-<lb />cie plana ad axem perpendiculari, cum inflexione in ſuper-<lb />ficie ſphærica ad diſtantiam quamcunque ab axe. </s>
          <s xml:space="preserve">Et diffe-<lb />rentia inſlexionum, id eſt, directionis radiorum mutatio, <lb />cum diſtantia ab axe creſcit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in quacunque radiorum di-<lb />rectione locum habet; </s>
          <s xml:space="preserve">æquè in radiis obliquis, quàm in di-<lb />rectis; </s>
          <s xml:space="preserve">ſed in radiis obliquis propter majores angulos inci-<lb />
<ptr xml:id="note-0535-07a" corresp="note-0535-07" type="noteAnchor" />
dentiæ mutationes majores ſunt. </s>
          <s xml:space="preserve">Ex quibus Lentium pro-<lb />prietates ſequentes deducimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0535-04" corresp="note-0535-04a" place="margin">695.</note>
              <note xml:space="preserve" xml:id="note-0535-05" corresp="note-0535-05a" place="margin">696.</note>
              <note xml:space="preserve" xml:id="note-0535-06" corresp="note-0535-06a" n="*" anchored="true" place="margin">694.</note>
              <note xml:space="preserve" xml:id="note-0535-07" corresp="note-0535-07a" place="margin">697.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Radios parallelos, tranſeundo per lentem convexam, in fo-<lb />
<ptr xml:id="note-0535-08a" corresp="note-0535-08" type="noteAnchor" />
cum concurrere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0535-08" corresp="note-0535-08a" place="margin">698.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radios divergentes aut minus divergere, aut parallelos <lb />
<ptr xml:id="note-0535-09a" corresp="note-0535-09" type="noteAnchor" />
fieri, aut tandem convergere; </s>
          <s xml:space="preserve">in quo caſu recedente puncto <lb />radiante accedit focus, &amp; </s>
          <s xml:space="preserve">vice verſa: </s>
          <s xml:space="preserve">Caſus autem hic ex-<lb />tat; </s>
          <s xml:space="preserve">quando punctum radians à lente magis removetur, quàm <lb />ab hac diſtat focus radiorum parallelorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0535-09" corresp="note-0535-09a" place="margin">699.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tandem radios convergentes magis in egreſſu luminis con-<lb />
<ptr xml:id="note-0535-10a" corresp="note-0535-10" type="noteAnchor" />
vergere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0535-10" corresp="note-0535-10a" place="margin">700.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0536" n="40" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p rend="italics">
          <s xml:space="preserve">Hæc etiam obtinent in radiis obliquis; </s>
          <s xml:space="preserve">circa quos notan-<lb />
<ptr xml:id="note-0536-01a" corresp="note-0536-01" type="noteAnchor" />
dum diſtantias focorum radiorum exeuntium, minores eſſe quàm <lb />in radiis directis, &amp; </s>
          <s xml:space="preserve">reliquas mutationes magis ſenſibiles eſſe <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0536-01" corresp="note-0536-01a" place="margin">701.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">697.</note>
        <p>
          <s xml:space="preserve">Hæc eadem omnia ex examine duplicis refractionis in in <lb />greſſu &amp; </s>
          <s xml:space="preserve">egreſſu luminis deducuntur. </s>
          <s xml:space="preserve">Hæc autem duplex <lb />refractio in caſu quocunque ſub oculis ponitur, in experi-<lb />mentis ſequentibus; </s>
          <s xml:space="preserve">quibus lentium convexarum affectiones <lb />memoratæ confirmantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pixides ut P variæ dantur, quæ aquam continent, &amp; </s>
          <s xml:space="preserve">per <lb />
<ptr xml:id="note-0536-03a" corresp="note-0536-03" type="noteAnchor" />
quas lumen tranſmittitur per vitra V &amp; </s>
          <s xml:space="preserve">V, quæ dantur in <lb />
<ptr xml:id="note-0536-04a" corresp="note-0536-04" type="noteAnchor" />
lateribus oppoſitis pixidis, a ſe mutuò diſtantibus circiter <lb />pollicem unum. </s>
          <s xml:space="preserve">Vitra hæc ſunt tenuia; </s>
          <s xml:space="preserve">in pixide, quæ re-<lb />præſentat lentem convevam ab utraque parte unum datur, <lb />ſimile illi, de quo in exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">capitis præcedentis, quæ diſpo-<lb />nuntur ut convexitates ſint extra pixidem. </s>
          <s xml:space="preserve">Quando lens plano <lb />convexa repræſentanda eſt, ad unam partem datur vitrum <lb />planum. </s>
          <s xml:space="preserve">Lens cavo-convexa repreſentatur adhibitis duobus <lb />vitris ſphæricis variarum ſphærarum portionibus, &amp; </s>
          <s xml:space="preserve">convexi-<lb />tas portionis majoris ſphæræ, ad interiorem pixidis partem <lb />datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0536-03" corresp="note-0536-03a" place="margin">702.</note>
              <note xml:space="preserve" xml:id="note-0536-04" corresp="note-0536-04a" place="margin">TAB. VIII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum lumen per has pixides tranſit, ad oculum patent lu-<lb />minis mutationes in ingreſſu &amp; </s>
          <s xml:space="preserve">egreſſu medii denſioris, &amp; </s>
          <s xml:space="preserve"><lb />harum ope omnia, quæ lentes convcxas ſpcctant, clarè de-<lb />monſtrantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum i</hi>.</head>
        <p>
          <s xml:space="preserve">Sit una ex memoratis pixidibus P, ex.</s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve">cum vitris V, V, <lb />ſphæricis, poſitis convexitatibus externè; </s>
          <s xml:space="preserve">aquâ repleatur; <lb /></s>
          <s xml:space="preserve">detur in cubiculo obſcuro radius Solis cylindricus a ſpeculo <lb />S horizontaliter reflexus; </s>
          <s xml:space="preserve">intret hic pixidem; </s>
          <s xml:space="preserve">radii paralleli <lb />ex quibus formatur ad ſe mutuò inflectentur, &amp; </s>
          <s xml:space="preserve">convergent; </s>
          <s xml:space="preserve"><lb />in egreſſu magis convergent &amp; </s>
          <s xml:space="preserve">in F concurrent. </s>
          <s xml:space="preserve">Circa ra-<lb />dios incidentes, qui divergunt aut convergunt, experimenta <lb />inſtituuntur, adhibitâ tabellâ cum lente convexa, ut in expe-<lb />rimentis capitis præcedentis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Singula puncta corporis lucidi, ut antea memoratum, ſunt <lb />puncta radiantia <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">poſita juſta diſtantia à convexâ lente,
<ptr xml:id="note-0536-05a" corresp="note-0536-05" type="noteAnchor" />
ſingula focum ſuum habent <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0536-05" corresp="note-0536-05a" n="*" anchored="true" place="margin">688.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">698.</note>
        <pb facs="0537" />
        <pb facs="0537a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0537a-01" />
          <label>0537a-01</label>
        </figure>
        <pb facs="0538" />
        <pb facs="0539" n="41" />
        <fw type="head">MATHEMATICA LIB. III. CAP. IX.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Detur candela lucens, à lente convexâ remota ultra fo-<lb />cum radiorum parallelorum, ad oppoſitam lentis partem ſu-<lb />per plano albo, per focos punctorum flammæ, hæc repræ-<lb />ſentabitur &amp; </s>
          <s xml:space="preserve">quidem inverſa, propter radiorum interſectio. <lb /></s>
          <s xml:space="preserve">nem in tranſitu per vitrum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Lentes convexæ ſunt etiam vitra uſtoria, quia colligunt <lb />
<ptr xml:id="note-0539-01a" corresp="note-0539-01" type="noteAnchor" />
radios ſolares <ptr type="noteAnchor" />, qui, propter Solis immenſam diſtantiam, pro
<ptr xml:id="note-0539-02a" corresp="note-0539-02" type="noteAnchor" />
parallelis habentur. </s>
          <s xml:space="preserve">Radii verò in foco collecti, propter i-<lb />gnem antea diſperſum, nunc collectum, &amp; </s>
          <s xml:space="preserve">propter ignis <lb />motum juxta varias directiones, violenter urunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0539-01" corresp="note-0539-01a" place="margin">703.</note>
              <note xml:space="preserve" xml:id="note-0539-02" corresp="note-0539-02a" n="*" anchored="true" place="margin">698.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Detur lens convexa cujuſcunque magnitudinis, exponatur <lb />hæc radiis ſolaribus ita, ut lentis axis cum directione radio-<lb />rum conveniat; </s>
          <s xml:space="preserve">ſi corpus quodcunque combuſtibile in foco <lb />radiorum ſolarium ponatur, uritur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando propter lentis magnitudinem non ſatis exactè col-<lb />liguntur radii, antequam ad focum perveniant, per ſecun-<lb />dam minorem convexam lentem tranſmittuntur, quo in mi-<lb />nus ſpatium rediguntur, ita ut magis violenter comburant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quod ſpectat lentes cavas, &amp; </s>
          <s xml:space="preserve">harum proprietates ex di-<lb />ctis <ptr type="noteAnchor" /> facile deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">696.</note>
        <p rend="italics">
          <s xml:space="preserve">Radii paralteli divergentes fiunt, per lentem cavam <lb />
<ptr xml:id="note-0539-04a" corresp="note-0539-04" type="noteAnchor" />
tranſeundo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0539-04" corresp="note-0539-04a" place="margin">704.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Divergentes magis divergunt.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">705.</note>
        <p>
          <s xml:space="preserve">Convergentes, aut minus convergunt; </s>
          <s xml:space="preserve">aut paralleli fiunt; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0539-06a" corresp="note-0539-06" type="noteAnchor" />
aut, quod in minus convergentibus obtinet, divergentes <lb />lentem exeunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0539-06" corresp="note-0539-06a" place="margin">706.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quæ omnia, æquè in obliquis radiis, ac in directis locum <lb />
<ptr xml:id="note-0539-07a" corresp="note-0539-07" type="noteAnchor" />
habent, in illis tamen magis ſenſibiliter <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0539-07" corresp="note-0539-07a" place="margin">707.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">697.</note>
        <p>
          <s xml:space="preserve">Pixides, repræſentantes lentes cavas, eodem modo con-<lb />
<ptr xml:id="note-0539-09a" corresp="note-0539-09" type="noteAnchor" />
ſtruuntur, ac illæ cum quibus experimenta circa lentes con-<lb />
<ptr xml:id="note-0539-10a" corresp="note-0539-10" type="noteAnchor" />
vexas inſtituuntur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Sola differentia datur in ſitu vitro-
<ptr xml:id="note-0539-11a" corresp="note-0539-11" type="noteAnchor" />
rum: </s>
          <s xml:space="preserve">In pixide primâ vitrorum duorum ſphæricorum V, V <lb />cavitates externæ ſunt. </s>
          <s xml:space="preserve">In ſecundâ, loco unius illorum vi-<lb />trorum, datur vitrum planum. </s>
          <s xml:space="preserve">In tertiâ, duo quidem vitra <lb />dantur ſphærica, ſed diverſarum ſphærarum ſectiones, majo-
</s>
          <pb facs="0540" n="42" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ris ſphæræ ſectio convexitatem externè habet, aliûs con-<lb />vexitas internè datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0539-09" corresp="note-0539-09a" place="margin">708.</note>
              <note xml:space="preserve" xml:id="note-0539-10" corresp="note-0539-10a" place="margin">TAB. IX. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0539-11" corresp="note-0539-11a" n="*" anchored="true" place="margin">702.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Radii ſolares paralleli, in cubiculo obſcuro à ſpeculo Sho-<lb />rizontaliter reflexi, per pixidem P, lentem utrinque con-<lb />cavam repræſentantem &amp; </s>
          <s xml:space="preserve">aquâ plenam, tranſmittuntur; </s>
          <s xml:space="preserve">in <lb />ingreſſu divergentes fiunt, &amp; </s>
          <s xml:space="preserve">egreſſu magis diſperguntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Reliqua experimenta circa lentes cavas eodem modo in-<lb />ſtituuntur, ac de lentibus convexis in exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">dictum.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT X.</head>
        <head rend="italics" xml:space="preserve">De Viſu, ubi de Oculi conſtructione.</head>
        <p>
          <s xml:space="preserve">QUas luminis proprietates refractioniſque leges explicavi-<lb />mus, mirandum, in objectis menti noſtræ repræſentan-<lb />dis, uſum habent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">His legibus objecta in fundo oculi pulcherrimè, propriis <lb />ſuis coloribus ornata, depinguntur; </s>
          <s xml:space="preserve">hæcque pictura, ut in <lb />ſequentibus dicam <ptr type="noteAnchor" />, occaſio eſt idearum, quæ in mente cir-
<ptr xml:id="note-0540-01a" corresp="note-0540-01" type="noteAnchor" />
ca res viſas excitantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0540-01" corresp="note-0540-01a" n="*" anchored="true" place="margin">716.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quomodo autem hæc pictura in oculo detur explicarinon <lb />poteſt, niſi examinatâ novâ luminis proprietate; </s>
          <s xml:space="preserve">radiorum <lb />nempe diviſibilitate captum noſtrum ſuperante.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p>
          <s xml:space="preserve">Corpus, quod non eſt lucidum &amp; </s>
          <s xml:space="preserve">lumen intercipit, vocatur <lb />
<ptr xml:id="note-0540-02a" corresp="note-0540-02" type="noteAnchor" />
opacum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0540-02" corresp="note-0540-02a" place="margin">709.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpora pleraque inter hæc opaca omnia, exactiſſimè poli-<lb />
<ptr xml:id="note-0540-03a" corresp="note-0540-03" type="noteAnchor" />
ta, ut &amp; </s>
          <s xml:space="preserve">perfectè nigra excipias, ſi quæ dantur, dividendi <lb />luminis proprietatem habent; </s>
          <s xml:space="preserve">repercutiunt lumen ita, ut à <lb />ſingulis punctis radii repercuſſi dividantur, &amp; </s>
          <s xml:space="preserve">verſus omnes <lb />partes recedant, &amp; </s>
          <s xml:space="preserve">ſingula puncta corporis ſint quaſi pun-<lb />cta radiantia, ex quibus lumen verſus omnes partes procedit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0540-03" corresp="note-0540-03a" place="margin">710.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde deducimus Methodum depingendorum objectorum <lb />
<ptr xml:id="note-0540-04a" corresp="note-0540-04" type="noteAnchor" />
in plano albo; </s>
          <s xml:space="preserve">ſingula enim puncta corporis illuminati, ex <lb />quibus radii ad lentem convexam perveniunt, poſt len-<lb />tem focum ſuum habent <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Objectorum diſtantium, li-
<ptr xml:id="note-0540-05a" corresp="note-0540-05" type="noteAnchor" />
cèt inæqualiter, foci ſenſibiliter eandem ad diſtantiam à
</s>
          <pb facs="0541" n="43" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. X.</fw>
lente dantur; </s>
          <s xml:space="preserve">hiſce in eodem plano, objecta hæc, repræ-<lb />ſentari poſſunt; </s>
          <s xml:space="preserve">quæ repræſentatio inverſa eſt, propter ra-<lb />diorum interſectionem tranſeundo per vitrum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſenſi-<lb />bilis, eſt in loco obſcuro, in quo lumen per ſolam len-<lb />tem intrat, &amp; </s>
          <s xml:space="preserve">quidem illud ſolum quo objecta depingun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0540-04" corresp="note-0540-04a" place="margin">711.</note>
              <note xml:space="preserve" xml:id="note-0540-05" corresp="note-0540-05a" n="*" anchored="true" place="margin">699.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc obtinent ubicunque lens ponatur, &amp; </s>
          <s xml:space="preserve">quidem circa <lb />omnia objectorum puncta, luminis radiis illuſtrata, à quibus <lb />lineæ rectæ non interruptæ ad lentem duci poſſunt; </s>
          <s xml:space="preserve">ita ut <lb />ſequenti Experimento probetur diviſibilitas memorata in lu-<lb />mine, &amp; </s>
          <s xml:space="preserve">dividendi luminis capacitas in corporibus lumen <lb />repercutientibus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum i</hi>.</head>
        <p>
          <s xml:space="preserve">In loco obſcuro foramen detur, cui varia reſpondeant <lb />
<ptr xml:id="note-0541-01a" corresp="note-0541-01" type="noteAnchor" />
objecta, ad diſtantiam ad minimum quinquaginta pedum, &amp; </s>
          <s xml:space="preserve"><lb />majorem. </s>
          <s xml:space="preserve">Sit hoc V, &amp; </s>
          <s xml:space="preserve">in hoc detur lens convexa, quæ col-<lb />ligit radios parallelos ad diſtantiam quatuor aut quinque pe-<lb />dum; </s>
          <s xml:space="preserve">ſi ad diſtantiam paululum majorem poſt lentem detur <lb />planum album, in hoc objecta memorata pulcherrimis co-<lb />loribus depinguntur. </s>
          <s xml:space="preserve">Notandum lentem in ſitu ad planum <lb />parallelo ponendam eſſe; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">motu plani aut lentis detegi di-<lb />ſtantiam ad quam objecta exactiſſimè repræſentantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0541-01" corresp="note-0541-01a" place="margin">TAB. IX. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc objectorum repræſentatio magnam cum illa, qua in <lb />fundo oculi objecta viſa depinguntur, affinitatem habet, ut <lb />ex oculi conſtructione patebit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Oculi figura, ſi capite extrahatur, præterpropter eſt <lb />
<ptr xml:id="note-0541-02a" corresp="note-0541-02" type="noteAnchor" />
ſphærica: </s>
          <s xml:space="preserve">nihilominus pars anterior eſt paululum magis con-<lb />vexa.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0541-02" corresp="note-0541-02a" place="margin">712.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Oculi ſectio in hac figurâ repræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">TAB. IX. <lb />fig. 3.</note>
        <p>
          <s xml:space="preserve">Pars magis convexa A A, eſt tranſlucida &amp; </s>
          <s xml:space="preserve">tunica cor-<lb />nea vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Totum oculi integumentum, corneâ exceptâ, vocatur <lb />ſclerotica B A A B; </s>
          <s xml:space="preserve">pars ſcleroticæ quæ corneæ adjacet, <lb />vocatur adnata, ſive album oculi.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ab interiori parte cornea obtegitur tunicâ uvea dictâ, quæ <lb />in medio foramen habet p p, quod nominatur pupilla.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Uvea conſtat ex fibris circularibus concentricis, ad angu-
</s>
          <pb facs="0542" n="44" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
los rectos per rectas fibras interſectis. </s>
          <s xml:space="preserve">Si primæ inflentur <lb />relaxantur ſecundæ, &amp; </s>
          <s xml:space="preserve">pupilla minuitur; </s>
          <s xml:space="preserve">augetur motu fi-<lb />brarum contrario.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In medio oculi, magis tamen verſus partem anteriorem, <lb />datur corpus molle tranſlucidum C C, lenti convexæ ſimi-<lb />le, cujus ſuperficies poſterior convexitate anteriorem ſupe-<lb />rat. </s>
          <s xml:space="preserve">Vocatur humor cryſtallinus. </s>
          <s xml:space="preserve">Axis hujus cum oculi <lb />axe, per centra pupillæ &amp; </s>
          <s xml:space="preserve">totius oculi tranſeunte, coinci-<lb />dit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Suſtinetur cryſtallinus humor filis, quæ in ſingulis punctis <lb />circumferentiæ hujus cohærent, &amp; </s>
          <s xml:space="preserve">interiori parte oculi <lb />annectuntur: </s>
          <s xml:space="preserve">in formam arcus inflectuntur, &amp; </s>
          <s xml:space="preserve">muſculi ſunt; <lb /></s>
          <s xml:space="preserve">nominantur ligamenta ciliaria, duo videntur in l C, l C. </s>
          <s xml:space="preserve"><lb />Omnia inter ſe cohærent, &amp; </s>
          <s xml:space="preserve">cum cryſtallino ſeparationem <lb />in oculo formant, huncque in duas cavitates, unam ante-<lb />riorem p p, alteram poſteriorem SS, dividunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Anterior cavitas repletur liquido aquæ ſimili, dicitur hu-<lb />mor aquens.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cavitas poſterior repletur humore tranſlucido, ejuſdem <lb />circiter denſitatis cum humore aqueo, ſed non æquè fluido; <lb /></s>
          <s xml:space="preserve">humor vitreus vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Superficies poſterior &amp; </s>
          <s xml:space="preserve">interior oculi tunicâ obtegitur, <lb />choroides dictâ, quam iterum obtegit membrana tenuiſſima, <lb />cui nomen retinæ datur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Nervus opticus NN, ad poſteriorem bulbi oculi partem, <lb />paululum ad latus, datur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ita cum oculo jungitur; </s>
          <s xml:space="preserve">ut hic <lb />ſit quaſi expanſio nervi optici; </s>
          <s xml:space="preserve">tunicæ enim nervi expanſæ <lb />choroidem &amp; </s>
          <s xml:space="preserve">ſcleroticam formant; </s>
          <s xml:space="preserve">Fibræ autem ex quibus <lb />retina conſtat concurrunt &amp; </s>
          <s xml:space="preserve">medullam nervi formant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Oculus in capite movetur variis muſculis cum ſclerotica <lb />cohærentibus; </s>
          <s xml:space="preserve">de his hìc non agitur; </s>
          <s xml:space="preserve">oculi conſtructionem <lb />cum relatione ad motum luminis conſidero, de omnibus cæ-<lb />teris loqui conſultò abſtineo.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Radii à puncto quocunque procedentes, &amp; </s>
          <s xml:space="preserve">qui per pupil-<lb />
<ptr xml:id="note-0542-01a" corresp="note-0542-01" type="noteAnchor" />
lam oculum intrant, ex medio rariori in denſius per ſuperfi-<lb />ciem ſphæricam tranſeunt, ideoque poſitâ juſtâ puncti diſtan-<lb />tiâ ab oculo, radii poſt refractionem convergunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">planè eo-
<ptr xml:id="note-0542-02a" corresp="note-0542-02" type="noteAnchor" />
</s>
          <pb facs="0543" n="45" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. X.</fw>
dem modo ac in experimento n. </s>
          <s xml:space="preserve">663. </s>
          <s xml:space="preserve">in quo vitrum V oculi <lb />
<ptr xml:id="note-0543-01a" corresp="note-0543-01" type="noteAnchor" />
tunicam corneam tranſlucidam repræſentat, dum aqua in <lb />pixide humoris aquei vices gerit; </s>
          <s xml:space="preserve">ideoque poſitis corneâ <lb />
<ptr xml:id="note-0543-02a" corresp="note-0543-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">humore aqueo, dabitur pictura inverſa objectorum in <lb />oculo <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0542-01" corresp="note-0542-01a" place="margin">713.</note>
              <note xml:space="preserve" xml:id="note-0542-02" corresp="note-0542-02a" n="*" anchored="true" place="margin">661.</note>
              <note xml:space="preserve" xml:id="note-0543-01" corresp="note-0543-01a" place="margin">TAB. VI. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0543-02" corresp="note-0543-02a" place="margin">714.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">710. 711:</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum 2</hi>.</head>
        <p>
          <s xml:space="preserve">Sit P pixis ſtatim memorata, aquam continens; </s>
          <s xml:space="preserve">detur hæc <lb />
<ptr xml:id="note-0543-04a" corresp="note-0543-04" type="noteAnchor" />
in loco obſcuro, in quo foramen datur diametri circiter ſe-<lb />mi pollicis, &amp; </s>
          <s xml:space="preserve">cui ad certam diſtantiam reſpondent objecta <lb />illuminata ita, ut per hoc foramen viſibilia ſint; </s>
          <s xml:space="preserve">applice-<lb />tur vitrum V pixidis huic foramini, &amp; </s>
          <s xml:space="preserve">pictura inverſa ob-<lb />jectorum, in tabella alba T, dabitur: </s>
          <s xml:space="preserve">motu tabeIlæ diſtantia <lb />ad quam repræſentatio eſt exacta, detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0543-04" corresp="note-0543-04a" place="margin">TAB. IX. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pictura ſtatim memorata in oculo, &amp; </s>
          <s xml:space="preserve">cujus imitationem <lb />in hoc experimento habemus, ad nimiam diſtantiam à cor-<lb />neâ, &amp; </s>
          <s xml:space="preserve">ultra fundum oculi, daretur; </s>
          <s xml:space="preserve">minuitur idcirco <lb />diſtantia ope humoris Cryſtallini denſioris mediis illum cir-<lb />
<ptr xml:id="note-0543-05a" corresp="note-0543-05" type="noteAnchor" />
cumdantibus; </s>
          <s xml:space="preserve">radii enim convergentes in humore aqueo trans <lb />cryſtallinum in humorem vitreum penetrant; </s>
          <s xml:space="preserve">id eſt, ex <lb />medio rariori trans denſius, duabus ſuperficiebus ſphæricis <lb />convexis terminatum, in rarius; </s>
          <s xml:space="preserve">quo motu convergentes <lb />radii magis convergentes fiunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideoque citius concurrunt,
<ptr xml:id="note-0543-06a" corresp="note-0543-06" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">pictura memorata intra oculum cadit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0543-05" corresp="note-0543-05a" place="margin">715.</note>
              <note xml:space="preserve" xml:id="note-0543-06" corresp="note-0543-06a" n="*" anchored="true" place="margin">700.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum 3</hi>.</head>
        <p>
          <s xml:space="preserve">Iiſdem poſitis, quæ in experimento præcedenti, detur lens <lb />
<ptr xml:id="note-0543-07a" corresp="note-0543-07" type="noteAnchor" />
vitrea convexa C inter vitrum V &amp; </s>
          <s xml:space="preserve">tabellam T, multò ta-<lb />men minus à vitro quam à tabellâ diſtans; </s>
          <s xml:space="preserve">ut pictura exacta <lb />detur, verſus V admovenda erit tabella. </s>
          <s xml:space="preserve">In quo experimen-<lb />to Oculum artificialem habemus, qui exactiſſimè quantum <lb />ad motum luminis, naturalem imitatur. </s>
          <s xml:space="preserve">Vitrum V, ut in ex-<lb />perimento præcedenti dictum, corneam repræſentat; </s>
          <s xml:space="preserve">lens <lb />convexa vitrea C cryſtallini vices gerit; </s>
          <s xml:space="preserve">tabella T pro fun-<lb />do oculi habetur; </s>
          <s xml:space="preserve">aqua humorum aquei &amp; </s>
          <s xml:space="preserve">vitrei locum te-<lb />net, in his enim humoribus lumen æqualem patitur refra-<lb />ctionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0543-07" corresp="note-0543-07a" place="margin">TAB. IX. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Objecta, quæ ut explicavi in fundo oculi depinguntur, in <lb />
<ptr xml:id="note-0543-08a" corresp="note-0543-08" type="noteAnchor" />
retinâ delineantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">motu luminis fibræ tenuiſſimæ, ex
</s>
          <pb facs="0544" n="(46)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
quibus retina conſtat, agitantur; </s>
          <s xml:space="preserve">qua agitatione ideæ obje-<lb />ctorum, in oculo depictorum, in mente excitantur. </s>
          <s xml:space="preserve">Nexus in-<lb />ter ideas &amp; </s>
          <s xml:space="preserve">motus quibus excitantur, ut ante dictum <ptr type="noteAnchor" />, nos
<ptr xml:id="note-0544-01a" corresp="note-0544-01" type="noteAnchor" />
latet: </s>
          <s xml:space="preserve">in cauſis ſenſationum determinandis, non ultra ner-<lb />vorum agitationes penetrare poſiumus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0543-08" corresp="note-0543-08a" place="margin">716.</note>
              <note xml:space="preserve" xml:id="note-0544-01" corresp="note-0544-01a" n="*" anchored="true" place="margin">502.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quo pictura memorat a magis eſt exacta, quo objecta diſtin-<lb />
<ptr xml:id="note-0544-02a" corresp="note-0544-02" type="noteAnchor" />
ctius apparent. </s>
          <s xml:space="preserve">Quando radii ab eodem puncto manantes <lb />
<ptr xml:id="note-0544-03a" corresp="note-0544-03" type="noteAnchor" />
non exactè in retinâ junguntur, illius pictura non eſt pun-<lb />ctum ſed macula, quæ confunditur cum picturis punctorum <lb />vicinorum; </s>
          <s xml:space="preserve">in quo caſu viſio confuſa eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0544-02" corresp="note-0544-02a" place="margin">717.</note>
              <note xml:space="preserve" xml:id="note-0544-03" corresp="note-0544-03a" place="margin">718.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cùm autem, pro varíâ puncti radiantis diſtantiâ, hujus <lb />
<ptr xml:id="note-0544-04a" corresp="note-0544-04" type="noteAnchor" />
focus magis aut minus removeatur <ptr type="noteAnchor" />, neceſſe eſt, ut mutatio
<ptr xml:id="note-0544-05a" corresp="note-0544-05" type="noteAnchor" />
detur in oculo, ne locus in quo pictura eſt exacta, ante aut <lb />poſt retinam cadat, &amp; </s>
          <s xml:space="preserve">viſio confuſa ſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0544-04" corresp="note-0544-04a" place="margin">719.</note>
              <note xml:space="preserve" xml:id="note-0544-05" corresp="note-0544-05a" n="*" anchored="true" place="margin">663.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quænam autem hæc ſit mutatio difficulter admodum de-<lb />terminatur, variæque dantur Philoſophorum ſententiæ; </s>
          <s xml:space="preserve">cir-<lb />ca quas in genere notabo, minimè probabile eſſe totius oculi <lb />
<ptr xml:id="note-0544-06a" corresp="note-0544-06" type="noteAnchor" />
figuram mutari, ad removendam aut admovendam retinam, <lb />&amp; </s>
          <s xml:space="preserve">in interiori oculo mutationem quærendam eſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0544-06" corresp="note-0544-06a" place="margin">720.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nam ſi figura oculi mutaretur, cùm in omnibus Animali-<lb />bus æquè neceſſaria ſit mutatio de qua agitur, in omnibus <lb />animalibus oculi figura eaſdem ſubibit mutationes; </s>
          <s xml:space="preserve">ejuſdem <lb />enim effectus cauſas varias in rerum natura non deprehen-<lb />dimus. </s>
          <s xml:space="preserve">In Balenâ verò ſclerotica nimium eſt dura, ut va-<lb />riationi obnoxia ſit. </s>
          <s xml:space="preserve">Ulterius, ſi talis detur mutatio in toto <lb />oculo, orietur hæc ex muſculorum externorum preſſione, <lb />quæ pro variò oculi ſitu diverſa erit, &amp; </s>
          <s xml:space="preserve">tantum regularis in <lb />unico oculi ſitu.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si nunc oculum in interiori examinemus, mutationem in <lb />cryſtallino neceſſariò dari patebit; </s>
          <s xml:space="preserve">qui tranſlatione in ocu-<lb />lo, aut mutatione figuræ, deſideratum effectum præſtabit; <lb /></s>
          <s xml:space="preserve">Radii enim retinam ante concurſum ſecantes, in retinâ con-<lb />current, ſi convexior fiat cryſtallinus humor <ptr type="noteAnchor" />, aut ſi, ſer-
<ptr xml:id="note-0544-07a" corresp="note-0544-07" type="noteAnchor" />
vatâ hujus figurâ, ipſe magis verſus anteriorem oculi partem <lb />feratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0544-07" corresp="note-0544-07a" n="*" anchored="true" place="margin">695.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cryſtallini humoris ſitum facile mutari, illumque ad reti-<lb />
<ptr xml:id="note-0544-08a" corresp="note-0544-08" type="noteAnchor" />
nam accedere &amp; </s>
          <s xml:space="preserve">ab hac recedere, manente illius axe, ex eo
</s>
          <pb facs="0545" n="(47)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. X.</fw>
liquet, quod ligamina ciliaria muſculoſa ſint: </s>
          <s xml:space="preserve">quando hi mu-<lb />ſculi inflantur, &amp; </s>
          <s xml:space="preserve">breviores fiunt, minuitur cavitas quæ exin-<lb />flexione horum ligaminum formatur in C l, C l; </s>
          <s xml:space="preserve">quo com-<lb />primitur humor vitreus, qui ipſe in humorem cryſtallinum <lb />premit &amp; </s>
          <s xml:space="preserve">hunc propellit, hujuſque diſtantiam à retinâ auget; <lb /></s>
          <s xml:space="preserve">quod in viſione objectorum propinquorum requiritur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0544-08" corresp="note-0544-08a" place="margin">721.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">663. 699.</note>
        <p>
          <s xml:space="preserve">Aliam præter hanc in oculo mutationem dari, ex experi-<lb />mento, in ſequentibus memorando <ptr type="noteAnchor" />, demonſtratum fuit,
<ptr xml:id="note-0545-02a" corresp="note-0545-02" type="noteAnchor" />
quæ cum hac contrariè agit; </s>
          <s xml:space="preserve">quod unde deductum fuerit <lb />dicetur. </s>
          <s xml:space="preserve">Mutatio autem ſecunda etiam ad ipſum cryſtalli-<lb />num referenda eſt; </s>
          <s xml:space="preserve">hic quando à ligaminibus ciliaribus tra-<lb />
<ptr xml:id="note-0545-03a" corresp="note-0545-03" type="noteAnchor" />
hitur, quo à fundo oculi recedit, etiam planior fit, quare <lb />ut magis recedat, quàm ſi figuram immutabilem baberet, ne-<lb />
<ptr xml:id="note-0545-04a" corresp="note-0545-04" type="noteAnchor" />
ceſſe eſt: </s>
          <s xml:space="preserve">id eſt, mutationem magis ſenſibilem eſſe, quod <lb />uſum ſuum habere videbimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0545-02" corresp="note-0545-02a" n="*" anchored="true" place="margin">753.</note>
              <note xml:space="preserve" xml:id="note-0545-03" corresp="note-0545-03a" place="margin">722.</note>
              <note xml:space="preserve" xml:id="note-0545-04" corresp="note-0545-04a" place="margin">723.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">730.</note>
        <p>
          <s xml:space="preserve">Limites ſuos habent hæ mutationes in oculo, inde etiam <lb />objecta tantum diſtincta apparent inter certos limites, ad <lb />
<ptr xml:id="note-0545-06a" corresp="note-0545-06" type="noteAnchor" />
varias diſtantias pro variis oculis poſitos; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſæpiſſimè in <lb />
<ptr xml:id="note-0545-07a" corresp="note-0545-07" type="noteAnchor" />
eodem bomine, non pro ſingulis oculis iidem limites dan-<lb />tur, quod ejuſdem ferè eſt utilitatis, ac ſi pro ambobus <lb />oculis limites magis inte ſe diſtarent; </s>
          <s xml:space="preserve">unico enim oculo ob-<lb />jectum diſtinctè videri ſat eſt. </s>
          <s xml:space="preserve">In quibuſdam etiam, proxi-<lb />mus limes reſpectu unius oculi, magis diſtat quàm maximè <lb />remotus reſpectu alterius, in hoc caſu objecta propinqua &amp; </s>
          <s xml:space="preserve"><lb />valdè remota diſtinctè videntur, intermedia confuſa apparent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0545-06" corresp="note-0545-06a" place="margin">724.</note>
              <note xml:space="preserve" xml:id="note-0545-07" corresp="note-0545-07a" place="margin">725.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Pictura in fundo oculi, ut dictum <ptr type="noteAnchor" />, eſt inverſa; </s>
          <s xml:space="preserve">unde
<ptr xml:id="note-0545-08a" corresp="note-0545-08" type="noteAnchor" />
quæſitum, quare objecta erecta appareant? </s>
          <s xml:space="preserve">Quæſtione re-<lb />
<ptr xml:id="note-0545-09a" corresp="note-0545-09" type="noteAnchor" />
ſpondemus, an quis melius concipiat nexum inter ideam in <lb />mente, &amp; </s>
          <s xml:space="preserve">figuram erectam, quàm everſam? </s>
          <s xml:space="preserve">nexum in neu-<lb />tro caſu nos nullum percipere fatemur: </s>
          <s xml:space="preserve">Experientia autem <lb />docet, dari nexum inter picturam inverſam in oculo &amp; </s>
          <s xml:space="preserve">ob-<lb />jecti erecti ideam; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">præterea nihil novimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0545-08" corresp="note-0545-08a" place="margin">726.</note>
              <note xml:space="preserve" xml:id="note-0545-09" corresp="note-0545-09a" n="*" anchored="true" place="margin">714.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ambobus oculis ſi idem objectum intueamur unicum appa-<lb />
<ptr xml:id="note-0545-10a" corresp="note-0545-10" type="noteAnchor" />
ret; </s>
          <s xml:space="preserve">illudque in eo caſu ſolo, quando objectum in punctis re-<lb />ſpondentibus retinæ depingitur; </s>
          <s xml:space="preserve">quod probabiliter ex con-<lb />curſu nervorum opticorum ſequitur. </s>
          <s xml:space="preserve">Obſervatur enim in <lb />omnibus animalibus, quæ idem objectum ambobus oculis
</s>
          <pb facs="0546" n="(48)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
vident, nervos opticos concurrere, antequam ad cerebrum <lb />perveniant, ad quod iterum ſeparati pertingunt; </s>
          <s xml:space="preserve">in animali-<lb />bus verò quæ ſingulis oculis diverſa objecta intuentur, nervi <lb />optici ab oculis ad cerebrum uſque ſeparantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0545-10" corresp="note-0545-10a" place="margin">727.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vnicum tantum punctum eodem tempore diſtinctiſſimè vi-<lb />
<ptr xml:id="note-0546-01a" corresp="note-0546-01" type="noteAnchor" />
deri poteſt, quod nempe in axe oculi repreſentatur; </s>
          <s xml:space="preserve">ſi am-<lb />bobus oculis punctum quis intueatur, ita ſunt dirigendi ocu-<lb />li, ut axes amborum oculorum continuati in illo concur-<lb />rant; </s>
          <s xml:space="preserve">quod obtinet, quando in aliquod punctum intentos <lb />oculos habemus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0546-01" corresp="note-0546-01a" place="margin">728.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc ipſa axium directio in judicio circa diſtantiam obje-<lb />ctorum viſorum uſum habet; </s>
          <s xml:space="preserve">ſitus enim diverſus oculorum <lb />pro vario angulo ab axibus formato datur, &amp; </s>
          <s xml:space="preserve">pendet hic ab <lb />objecti diſtantiâ: </s>
          <s xml:space="preserve">unde, ne quidem ad illud attendendo, uſu <lb />facultatem acquirimus, de diſtantiâ dijudicandi, ex axium di-<lb />
<ptr xml:id="note-0546-02a" corresp="note-0546-02" type="noteAnchor" />
rectione; </s>
          <s xml:space="preserve">quæ nobis ſenſibilis eſt, quia à motu oculi, nobis ſen-<lb />ſibili, pendet. </s>
          <s xml:space="preserve">Videmus ergo uſum duorum oculorum ad <lb />certam â ſe mutuo diſtantiam poſitorum; </s>
          <s xml:space="preserve">quamdiu hæc o-<lb />culorum diſtantia ſenſibilem rationem babet ad objectorum <lb />diſtantiam, de bac judicium ſatis certum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0546-02" corresp="note-0546-02a" place="margin">729.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De minoribus diſtantiis etiam unico oculo dijudicamus; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0546-03a" corresp="note-0546-03" type="noteAnchor" />
quia in variatione exiguæ diſtantiæ mutatio in oculo <ptr type="noteAnchor" /> ſenſi-
<ptr xml:id="note-0546-04a" corresp="note-0546-04" type="noteAnchor" />
bilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0546-03" corresp="note-0546-03a" place="margin">730.</note>
              <note xml:space="preserve" xml:id="note-0546-04" corresp="note-0546-04a" n="*" anchored="true" place="margin">721. 723.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De magnis diſtantiis, ſi de objectis notis agatur, judicium <lb />
<ptr xml:id="note-0546-05a" corresp="note-0546-05" type="noteAnchor" />
ex magnitudine apparente &amp; </s>
          <s xml:space="preserve">colore fertur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0546-05" corresp="note-0546-05a" place="margin">731.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">De maximis impoſſibile eſt judicium, niſi ex diverſis locis <lb />
<ptr xml:id="note-0546-06a" corresp="note-0546-06" type="noteAnchor" />
idem objectum obſervetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0546-06" corresp="note-0546-06a" place="margin">732.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magnitudo apparens objecti, pendet à magnitudine picturæ <lb />
<ptr xml:id="note-0546-07a" corresp="note-0546-07" type="noteAnchor" />
in fundo oculi, quæ ipſa pendet ab angulo ſub quo objectum <lb />videtur, id eſt, qui formatur à lineis ab extremitatibus ob-<lb />jecti ad oculum ductis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0546-07" corresp="note-0546-07a" place="margin">733.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magnitudo hæc apparens diſtinguenda eſt à magnitudine, <lb />
<ptr xml:id="note-0546-08a" corresp="note-0546-08" type="noteAnchor" />
quam mens noſtra tribuit objecto viſo, quæ ultima judicio <lb />nititur, quod non ſolam apparentiam pro fundamento habet. <lb /></s>
          <s xml:space="preserve">Notum eſt unicuique, objectum eo minus apparêre, quo ma-<lb />gis diſtat; </s>
          <s xml:space="preserve">unde pro majori diſtantiâ objecti, ſi nota ſit, ma-<lb />gnitudo apparens objecti augetur in judicio à mente lato,
</s>
          <pb facs="0547" n="(49)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XI.</fw>
quod fit ne quidem ad illud attendendo. </s>
          <s xml:space="preserve">Ideò idem obje-<lb />ctum, ad eandem diſtantiam, diverſae; </s>
          <s xml:space="preserve">apparet magnitudinis, <lb />ſi judicium de diſtantiâ fuerit diverſum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0546-08" corresp="note-0546-08a" place="margin">734.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Exemplum notabile habemus in Sole &amp; </s>
          <s xml:space="preserve">Lunâ, majoribus <lb />
<ptr xml:id="note-0547-01a" corresp="note-0547-01" type="noteAnchor" />
apparentibus propè horizontem, quàm ad majorem altitudi-<lb />nim; </s>
          <s xml:space="preserve">licèt, ut Aſtronomis notum, pictura Solis in fundo oculi <lb />ſit eadem in utroque caſu, &amp; </s>
          <s xml:space="preserve">Lunæ pictura minor ſit, quando <lb />propè horizontem major apparet; </s>
          <s xml:space="preserve">de diſtantiâ in neutro caſu <lb />judicium ferre non poſſumus <ptr type="noteAnchor" />, ſed major, ex interpoſitis
<ptr xml:id="note-0547-02a" corresp="note-0547-02" type="noteAnchor" />
campis &amp; </s>
          <s xml:space="preserve">coelo, hæc videtur propè horizontem. </s>
          <s xml:space="preserve">Per tubum <lb />ſi intueamur corpora memorata, diſtantia apparens evaneſcit, <lb />&amp; </s>
          <s xml:space="preserve">cum hac magnitudo quæ ex ipſà deducitur. </s>
          <s xml:space="preserve">Ab infantiâ <lb />continuò, &amp; </s>
          <s xml:space="preserve">adhucdum omnibus momentis, ideam diſtan-<lb />tiæ cum augmento in magnitudine apparente jungimus, <lb />(quod ad verum de magnitudine judicium ferendum neceſſe <lb />eſt,) quo hæ ideæ ita intimè junguntur, ut ſeparari ne-<lb />queant, ne quidem in illis caſibus, in quibus novimus illas <lb />nos in errorem ducere. </s>
          <s xml:space="preserve">Quòt errores tribuendi ſint ideis <lb />ita junctis norunt logici.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0547-01" corresp="note-0547-01a" place="margin">735.</note>
              <note xml:space="preserve" xml:id="note-0547-02" corresp="note-0547-02a" n="*" anchored="true" place="margin">732.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XI.</head>
        <head rend="italics" xml:space="preserve">De viſione trans vitra, &amp; corrigendis quibuſdam <lb />oculorum vitiis.</head>
        <p>
          <s xml:space="preserve">OBjectum viſibile eſt, quia ſingula hujus puncta ſunt quaſi <lb />puncta radiantia <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Punctum ergo apparet in illo loco,
<ptr xml:id="note-0547-03a" corresp="note-0547-03" type="noteAnchor" />
ex quo radii divergentes emittuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0547-03" corresp="note-0547-03a" place="margin">736.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">713. 714. 715.</note>
        <p>
          <s xml:space="preserve">Si radii utcunque in flexi divergentes oculum intrent, da-<lb />
<ptr xml:id="note-0547-05a" corresp="note-0547-05" type="noteAnchor" />
bitur punctum viſibile in radiorum foco imaginario; </s>
          <s xml:space="preserve">planè e-<lb />nim eodem modo radii hi oculum intrant, ac radii directè <lb />ex illo foco procedentes; </s>
          <s xml:space="preserve">idemque ut in retinâ concur-<lb />rant, cryſtallini ſitus requiritur: </s>
          <s xml:space="preserve">ita ut reſpectu ſpectatoris <lb />non interſit, utrum illi radii refracti, an hi directi oculum <lb />intrent; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">idem motus detur in oculo, cùm ſe conſtituit <lb />ut viſio ſit diſtincta <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0547-05" corresp="note-0547-05a" place="margin">737.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">719. 730.</note>
        <p rend="italics">
          <s xml:space="preserve">Punctum eo magis illuminatum apparet, quo plures radii <lb />
<ptr xml:id="note-0547-07a" corresp="note-0547-07" type="noteAnchor" />
ab boc procedentes oculum intrant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0547-07" corresp="note-0547-07a" place="margin">738.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0548" n="(50)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Objecta viſa trans vitrum planum, ſuperficiebus inter. </s>
          <s xml:space="preserve">ſe <lb />
<ptr xml:id="note-0548-01a" corresp="note-0548-01" type="noteAnchor" />
parallelis terminatum, ad minorem diſtantiam, quàm nudis <lb />
<ptr xml:id="note-0548-02a" corresp="note-0548-02" type="noteAnchor" />
oculis apparent. </s>
          <s xml:space="preserve">Sit A punctum viſibile; </s>
          <s xml:space="preserve">radii ex hoc pro-<lb />cedentes, &amp; </s>
          <s xml:space="preserve">oculum intrantes, dantur inter A b, &amp; </s>
          <s xml:space="preserve">A b; <lb /></s>
          <s xml:space="preserve">hi refracti in vitro V V moventur per b c, b c; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">exeunt <lb />per c d, c d parallelas lineis A b, A b <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">quia autem
<ptr xml:id="note-0548-03a" corresp="note-0548-03" type="noteAnchor" />
b c, b c ad perpendicularem refringuntur <ptr type="noteAnchor" />, c d, c d, in-
<ptr xml:id="note-0548-04a" corresp="note-0548-04" type="noteAnchor" />
ter b A &amp; </s>
          <s xml:space="preserve">b A cadunt; </s>
          <s xml:space="preserve">id eſt, ſeſe mutuò ſecant in a mi-<lb />nus diſtanti quam A; </s>
          <s xml:space="preserve">focus ergo imaginarius radiorum ocu-<lb />lum intrantium eſt a, in quo punctum A apparet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0548-01" corresp="note-0548-01a" place="margin">739.</note>
              <note xml:space="preserve" xml:id="note-0548-02" corresp="note-0548-02a" place="margin">TAB. X. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0548-03" corresp="note-0548-03a" n="*" anchored="true" place="margin">628.</note>
              <note xml:space="preserve" xml:id="note-0548-04" corresp="note-0548-04a" n="*" anchored="true" place="margin">624.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">737.</note>
        <p>
          <s xml:space="preserve">Punctum hoc etiam magis illuminatum apparet, viſum <lb />
<ptr xml:id="note-0548-06a" corresp="note-0548-06" type="noteAnchor" />
trans vitrum memoratum. </s>
          <s xml:space="preserve">Nam omnes radii inter A b &amp; </s>
          <s xml:space="preserve"><lb />A b pupillam intrant inter d &amp; </s>
          <s xml:space="preserve">d; </s>
          <s xml:space="preserve">cùm verò lineæ A b, A b <lb />ſint parallelæ lineis c d, c d, &amp; </s>
          <s xml:space="preserve">hæ dentur inter illas, A b <lb />&amp; </s>
          <s xml:space="preserve">A b continuatæ ultra d &amp; </s>
          <s xml:space="preserve">d caderent; </s>
          <s xml:space="preserve">ideoque ſublato vi-<lb />tro, radii qui nunc pupillam intrant majus ſpatium occupa-<lb />rent, &amp; </s>
          <s xml:space="preserve">non omnes oculum intrarent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0548-06" corresp="note-0548-06a" place="margin">740.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magnitudo apparens objecti augetur interpoſito vitro pla-<lb />
<ptr xml:id="note-0548-07a" corresp="note-0548-07" type="noteAnchor" />
no; </s>
          <s xml:space="preserve">Objectum A E nudo oculo videtur ſub angulo A d E; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0548-08a" corresp="note-0548-08" type="noteAnchor" />
poſito verò vitro V V, ob refractionem per A b c d &amp; </s>
          <s xml:space="preserve">E b c d, <lb />videtur ſub angulo c d c, qui præcedente major eſt. </s>
          <s xml:space="preserve">Non ta-<lb />
<ptr xml:id="note-0548-09a" corresp="note-0548-09" type="noteAnchor" />
men pro ratione auctæ magnitudinis, apparentis objectum <lb />majus videtur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam ad minorem diſtantiam apparet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0548-07" corresp="note-0548-07a" place="margin">741.</note>
              <note xml:space="preserve" xml:id="note-0548-08" corresp="note-0548-08a" place="margin">TAB. X. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0548-09" corresp="note-0548-09a" place="margin">742.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">734.</note>
        <p>
          <s xml:space="preserve">Augmentum magnitudinis apparentis eo major eſt, quo ma-<lb />
<ptr xml:id="note-0548-11a" corresp="note-0548-11" type="noteAnchor" />
<ptr xml:id="note-0548-12a" corresp="note-0548-12" type="noteAnchor" />
gis differunt anguli a d E &amp; </s>
          <s xml:space="preserve">c d c; </s>
          <s xml:space="preserve">quorum differentia creſcit <lb />cum acceſſu interſectionum linearum A d cum b c &amp; </s>
          <s xml:space="preserve">E d <lb />cum b c, verſus puncta b &amp; </s>
          <s xml:space="preserve">b; </s>
          <s xml:space="preserve">quod obtinet in acceſſu objecti <lb />ad vitrum; </s>
          <s xml:space="preserve">ideoque omnium maxima eſt, quando objectum <lb />vitrum tangit; </s>
          <s xml:space="preserve">quod probat objecta in ipſo vitro etiam am-<lb />plificata apparêre.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0548-11" corresp="note-0548-11a" n="*" anchored="true" place="margin">739.</note>
              <note xml:space="preserve" xml:id="note-0548-12" corresp="note-0548-12a" place="margin">743.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Et in genere, poſito oculo in medio rariori, objectum quod <lb />
<ptr xml:id="note-0548-13a" corresp="note-0548-13" type="noteAnchor" />
in medio denſiori videtur majus apparere, quod etiam refra-<lb />ctione appropinquatur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Confirmantur hæc quotidianâ ex-
<ptr xml:id="note-0548-14a" corresp="note-0548-14" type="noteAnchor" />
perientiâ, reſpectu objectorum in aquâ viſorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0548-13" corresp="note-0548-13a" place="margin">744.</note>
              <note xml:space="preserve" xml:id="note-0548-14" corresp="note-0548-14a" n="*" anchored="true" place="margin">659.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur punctum A trans lentem convexam V V viſum, ra-<lb />
<ptr xml:id="note-0548-15a" corresp="note-0548-15" type="noteAnchor" />
dii A b, A b in c d, c d minus divergentes exeunt, quaſi <lb />
<ptr xml:id="note-0548-16a" corresp="note-0548-16" type="noteAnchor" />
nempe ex a procederent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideoque punctum hoc ad majo-
<ptr xml:id="note-0548-17a" corresp="note-0548-17" type="noteAnchor" />
</s>
          <pb facs="0549" n="(51)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XI.</fw>
rem diſtantiam apparet <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Etiam magis illuminatum; </s>
          <s xml:space="preserve">nam
<ptr xml:id="note-0549-01a" corresp="note-0549-01" type="noteAnchor" />
tranſeundo per vitrum ad ſe mutuo accedunt radii, <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">in
<ptr xml:id="note-0549-02a" corresp="note-0549-02" type="noteAnchor" />
minus ſpatium rediguntur, quare etiam majori numero pu-<lb />
<ptr xml:id="note-0549-03a" corresp="note-0549-03" type="noteAnchor" />
pillam intrant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0548-15" corresp="note-0548-15a" place="margin">745.</note>
              <note xml:space="preserve" xml:id="note-0548-16" corresp="note-0548-16a" place="margin">TAB. X. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0548-17" corresp="note-0548-17a" n="*" anchored="true" place="margin">699.</note>
              <note xml:space="preserve" xml:id="note-0549-01" corresp="note-0549-01a" place="margin">746.</note>
              <note xml:space="preserve" xml:id="note-0549-02" corresp="note-0549-02a" n="*" anchored="true" place="margin">737.</note>
              <note xml:space="preserve" xml:id="note-0549-03" corresp="note-0549-03a" n="*" anchored="true" place="margin">695.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magnitudo apparens objecti etiam augetur; </s>
          <s xml:space="preserve">id eſt, Ob-<lb />
<ptr xml:id="note-0549-04a" corresp="note-0549-04" type="noteAnchor" />
jectum ſub majori angulo trans vitrum convexum vide-<lb />
<ptr xml:id="note-0549-05a" corresp="note-0549-05" type="noteAnchor" />
tur, quod ex inſpectione figurarum patet: </s>
          <s xml:space="preserve">Objectum A E <lb />nudis oculis videtur ſub angulo A d E, nunc autem ſub an-<lb />gulo majori c d c; </s>
          <s xml:space="preserve">nam (in fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">radii A b, E b conver-<lb />gentes, magis convergunt ex lente exeuntes <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">aut (in fig. </s>
          <s xml:space="preserve">5.)</s>
          <s xml:space="preserve">
<ptr xml:id="note-0549-06a" corresp="note-0549-06" type="noteAnchor" />
divergentes, convergentes ad oculum perveniunt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Idcir-
<ptr xml:id="note-0549-07a" corresp="note-0549-07" type="noteAnchor" />
co objectum amplificatum apparet, &amp; </s>
          <s xml:space="preserve">ex remotâ apparen-<lb />tiâ <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ex auctâ hujus magnitudine <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideo non ſequitur
<ptr xml:id="note-0549-08a" corresp="note-0549-08" type="noteAnchor" />
magnitudo, quam objecto tribuimus, eandem proportionem <lb />
<ptr xml:id="note-0549-09a" corresp="note-0549-09" type="noteAnchor" />
cum magnitudine apparente; </s>
          <s xml:space="preserve">quare non inhæremus in de-<lb />
<ptr xml:id="note-0549-10a" corresp="note-0549-10" type="noteAnchor" />
monſtrandis quæ hanc ſpectant. </s>
          <s xml:space="preserve">Sed generaliter notamus;</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0549-04" corresp="note-0549-04a" place="margin">747.</note>
              <note xml:space="preserve" xml:id="note-0549-05" corresp="note-0549-05a" place="margin">TAB. X. <lb />fig. 4. &amp; 5.</note>
              <note xml:space="preserve" xml:id="note-0549-06" corresp="note-0549-06a" n="*" anchored="true" place="margin">700.</note>
              <note xml:space="preserve" xml:id="note-0549-07" corresp="note-0549-07a" n="*" anchored="true" place="margin">699.</note>
              <note xml:space="preserve" xml:id="note-0549-08" corresp="note-0549-08a" place="margin">748.</note>
              <note xml:space="preserve" xml:id="note-0549-09" corresp="note-0549-09a" n="*" anchored="true" place="margin">745.</note>
              <note xml:space="preserve" xml:id="note-0549-10" corresp="note-0549-10a" n="*" anchored="true" place="margin">734.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Angulum, ſub quo objectum trans vitrum convexum vide-<lb />
<ptr xml:id="note-0549-11a" corresp="note-0549-11" type="noteAnchor" />
tur, minui in receſſu oculi à vitro; </s>
          <s xml:space="preserve">quamdiu objectum non <lb />diſtat à vitro ultra punctum, in quo radii paralleli colligun-<lb />tur: </s>
          <s xml:space="preserve">poſito verò objecto ad majorem diſtantiam, augetur ma-<lb />gnitudo apparens in oculi receſſu.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0549-11" corresp="note-0549-11a" place="margin">749.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem modo, poſito oculo inter vitrum &amp; </s>
          <s xml:space="preserve">focum radio-<lb />
<ptr xml:id="note-0549-12a" corresp="note-0549-12" type="noteAnchor" />
rum parallelorum, in receſſu objecti minuitur angulus memo-<lb />ratus; </s>
          <s xml:space="preserve">poſito oculo ad majorem diſtantiam, idem angulus in <lb />receſſu objecti augetur; </s>
          <s xml:space="preserve">in quo ultimo caſu ita poteſt remo-<lb />veri objectum, ut trans vitrum non ſit viſibile, ut ſtatim <lb />dicetur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0549-12" corresp="note-0549-12a" place="margin">750.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">754.</note>
        <p>
          <s xml:space="preserve">In ipſis etiam caſibus, in quibus objecta ſunt viſibilia, non <lb />ſemper diſtinctè apparent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Nam ut punctum diſtinctum appareat requiritur, ut ra-<lb />
<ptr xml:id="note-0549-14a" corresp="note-0549-14" type="noteAnchor" />
dii à puncto procedentes divergentes oculum intrent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ut
<ptr xml:id="note-0549-15a" corresp="note-0549-15" type="noteAnchor" />
focus imaginarius borum radiorum detur, reſpectu ſpectato-<lb />ris, inter limites diſtinctæ viſionis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0549-14" corresp="note-0549-14a" place="margin">751.</note>
              <note xml:space="preserve" xml:id="note-0549-15" corresp="note-0549-15a" n="*" anchored="true" place="margin">736.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">737. 724.</note>
        <p>
          <s xml:space="preserve">Si objectum removeatur ultra focum radiorum parallelo-<lb />
<ptr xml:id="note-0549-17a" corresp="note-0549-17" type="noteAnchor" />
rum, radii à puncto objecti manantes convergentes oculum <lb />intrant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">qui caſus nudis oculis impoſſibilis eſt: </s>
          <s xml:space="preserve">in hoc vi-
<ptr xml:id="note-0549-18a" corresp="note-0549-18" type="noteAnchor" />
ſio ſemper confufa datur, &amp; </s>
          <s xml:space="preserve">oculus ſeſe diſponit ut viſio
</s>
          <pb facs="0550" n="(52)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
omnium minimè ſit confuſa; </s>
          <s xml:space="preserve">ex hac diſpoſitione de diſtan-<lb />tià dijudicamus, ut in omni caſu in quo unico oculo de hac <lb />judicium fertur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0549-17" corresp="note-0549-17a" place="margin">752.</note>
              <note xml:space="preserve" xml:id="note-0549-18" corresp="note-0549-18a" n="*" anchored="true" place="margin">699.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">730.</note>
        <p>
          <s xml:space="preserve">Hæc autem diſtantia non ſemper eadem videtur, unde <lb />
<ptr xml:id="note-0550-02a" corresp="note-0550-02" type="noteAnchor" />
deducuntur, quæ de mutatione figuræ cryſtallini dicta ſunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0550-03a" corresp="note-0550-03" type="noteAnchor" />
Si enim, poſito cryſtallino mobili, figuram immutatam ha-<lb />beat, in omni objecti &amp; </s>
          <s xml:space="preserve">oculi ſitu, in quo radii ex puncto <lb />manantes convergentes oculum intrant, minima dabitur <lb />confuſio, ſi cryſtallinus quantum poteſt ad retinam accedat; <lb /></s>
          <s xml:space="preserve">ita ut in omni caſu eadem daretur oculi diſpoſitio, &amp; </s>
          <s xml:space="preserve">idem <lb />judicium circa diſtantiam; </s>
          <s xml:space="preserve">quod ut dictum, experientiæ <lb />adverſatur: </s>
          <s xml:space="preserve">ſi autem in receſſu à retinâ cryſtallinus planior <lb />fiat, mutationes dantur in oculo, quæ congruunt cum variis <lb />judiciis circa diſtantiam in vario objecti &amp; </s>
          <s xml:space="preserve">oculi ſitu.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0550-02" corresp="note-0550-02a" place="margin">753.</note>
              <note xml:space="preserve" xml:id="note-0550-03" corresp="note-0550-03a" n="*" anchored="true" place="margin">722.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si in caſu ultimo, in quo radii à puncto convergunt, ita <lb />
<ptr xml:id="note-0550-04a" corresp="note-0550-04" type="noteAnchor" />
removeatur oculus, ut concurrant radii antequam ad oculum <lb />perveniant, dantur in ſingulis punctis, in quo radii concur-<lb />runt, puncta radiantia; </s>
          <s xml:space="preserve">nempe foci ſingulorum punctorum <lb />objecti, quibus objectum inverſum in plano albo repræſenta-<lb />tur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">qui ſunt puncta viſibilia reſpectu oculi, ad quem
<ptr xml:id="note-0550-05a" corresp="note-0550-05" type="noteAnchor" />
radii poſt interſectionem pervenire poſſunt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In hoc caſu
<ptr xml:id="note-0550-06a" corresp="note-0550-06" type="noteAnchor" />
objectum inverſum apparet, quia objectum ipſum non vide-<lb />mus, ſed hujus repræſentationem poſt vitrum, quam inver-<lb />ſam dari diximus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0550-04" corresp="note-0550-04a" place="margin">754.</note>
              <note xml:space="preserve" xml:id="note-0550-05" corresp="note-0550-05a" n="*" anchored="true" place="margin">711.</note>
              <note xml:space="preserve" xml:id="note-0550-06" corresp="note-0550-06a" n="*" anchored="true" place="margin">736.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">711.</note>
        <p>
          <s xml:space="preserve">Nudis oculis dixi caſum impoſſibilem eſſe, in quo radii à <lb />
<ptr xml:id="note-0550-08a" corresp="note-0550-08" type="noteAnchor" />
puncto convergentes oculum intrant; </s>
          <s xml:space="preserve">ideoque viſionem talem <lb />ſemper confuſam eſſe; </s>
          <s xml:space="preserve">quia nempe ad caſum impoſſibilem <lb />oculorum conſtructio non adaptatur: </s>
          <s xml:space="preserve">aliquando tamen, ſed <lb />rarò, &amp; </s>
          <s xml:space="preserve">in hoc caſu objecta diſtinctè videntur, quod cùm <lb />ex vitio oculi oriatur, quo omnis diſtincta viſio nudis oculis <lb />tollitur, ad has exceptiones regulæ generalis attendendum <lb />non eſle credidi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0550-08" corresp="note-0550-08a" place="margin">755.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Plerorumque ſenum vitium in oculis eſt, quod niſi obje-<lb />
<ptr xml:id="note-0550-09a" corresp="note-0550-09" type="noteAnchor" />
cta longinqua diſtinctè non videant, propinqua confuſe4; <lb /></s>
          <s xml:space="preserve">quod, interpoſitâ lente convexâ, vitium corrigitur. </s>
          <s xml:space="preserve">Radii, <lb />à puncto propinquo manantes, ultra retinam concurrunt; </s>
          <s xml:space="preserve"><lb />per vitrum convexum minus divergunt dum oculum intrant,
</s>
          <pb facs="0551" n="(53)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP XI.</fw>
&amp; </s>
          <s xml:space="preserve">in oculo citius concurrunt; </s>
          <s xml:space="preserve">id eſt ad oculum perveniunt <lb />quaſi à puncto remotiori, quod à ſene diſtinctè videtur, <lb />procederent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0550-09" corresp="note-0550-09a" place="margin">756.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Trans lentem cavam objecta minus diſtantia, minus illumi-<lb />
<ptr xml:id="note-0551-01a" corresp="note-0551-01" type="noteAnchor" />
nata, &amp; </s>
          <s xml:space="preserve">minora, apparent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0551-01" corresp="note-0551-01a" place="margin">757.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii A b, A b, &amp; </s>
          <s xml:space="preserve">omnes intermedii, tranſeundo per <lb />
<ptr xml:id="note-0551-02a" corresp="note-0551-02" type="noteAnchor" />
Ientem cavam magis divergentes fiunt <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">oculum intrant
<ptr xml:id="note-0551-03a" corresp="note-0551-03" type="noteAnchor" />
quaſi à puncto minus diſtanti a procederent <ptr type="noteAnchor" />, in quo pun-
<ptr xml:id="note-0551-04a" corresp="note-0551-04" type="noteAnchor" />
ctum A apparet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0551-02" corresp="note-0551-02a" place="margin">TAB. X. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0551-03" corresp="note-0551-03a" n="*" anchored="true" place="margin">705.</note>
              <note xml:space="preserve" xml:id="note-0551-04" corresp="note-0551-04a" n="*" anchored="true" place="margin">652.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">737.</note>
        <p>
          <s xml:space="preserve">Ex radiorum divergentiâ auctâ magis diſperguntur radii, <lb />&amp; </s>
          <s xml:space="preserve">minori numero oculum intrant, quod minuit puncti illu-<lb />minationem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">738.</note>
        <p>
          <s xml:space="preserve">Minuitur etiam magnitudo apparens, quia radii A b, E b, <lb />
<ptr xml:id="note-0551-07a" corresp="note-0551-07" type="noteAnchor" />
quibus extremitates objecti videntur minus convergentes ad <lb />oculum perveniunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò angulus c d c ſub quo trans
<ptr xml:id="note-0551-08a" corresp="note-0551-08" type="noteAnchor" />
lentem objectum videtur, minor eſt angulo A d E, ſub quo <lb />nudis oculis apparet: </s>
          <s xml:space="preserve">quare &amp; </s>
          <s xml:space="preserve">ex imminutâ diſtantiâ &amp; </s>
          <s xml:space="preserve">ex <lb />imminuto angulo memorato, imminutum apparet objectum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0551-07" corresp="note-0551-07a" place="margin">TAB. X. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0551-08" corresp="note-0551-08a" n="*" anchored="true" place="margin">706.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">734.</note>
        <p>
          <s xml:space="preserve">Illis inſervit lens cava, qui objecta propinqua tantum di-<lb />
<ptr xml:id="note-0551-10a" corresp="note-0551-10" type="noteAnchor" />
ſtinctè vident; </s>
          <s xml:space="preserve">Myopes vocantur; </s>
          <s xml:space="preserve">trans hanc lentem puncta <lb />remota appropinquantur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">radii, qui ante retinam con-
<ptr xml:id="note-0551-11a" corresp="note-0551-11" type="noteAnchor" />
currebant, magis divergentes oculum intrantes, in retinâ <lb />concurrunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0551-10" corresp="note-0551-10a" place="margin">758.</note>
              <note xml:space="preserve" xml:id="note-0551-11" corresp="note-0551-11a" n="*" anchored="true" place="margin">757.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vitra dantur unicâ ſuperſicie planâ ab unâ parte termina-<lb />ta, ad aliam variis ſuperficiebus planis, angulos inter ſe for-<lb />mantibus, per has radii, ab eodem puncto procedentes, di-<lb />verſas patiuntur refractiones; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pro ſingulis ſuperficiebus o-<lb />culum intrant juxta diverſam directionem, &amp; </s>
          <s xml:space="preserve">quaſi à puncto <lb />diverſo procederent: </s>
          <s xml:space="preserve">id eſt, format idem punctum varios <lb />focos imaginarios; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">idcirco multiplicatum apparet: </s>
          <s xml:space="preserve">vide-<lb />tur nempe in ſingulis focis imaginariis <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">quod cùm obti-
<ptr xml:id="note-0551-12a" corresp="note-0551-12" type="noteAnchor" />
neat reſpectu ſingulorum punctorum objecti, per talem len-<lb />
<ptr xml:id="note-0551-13a" corresp="note-0551-13" type="noteAnchor" />
tem polygonam objectum multiplicatum apparet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0551-12" corresp="note-0551-12a" n="*" anchored="true" place="margin">737.</note>
              <note xml:space="preserve" xml:id="note-0551-13" corresp="note-0551-13a" place="margin">759.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0552" n="(54)" />
        <fw type="head">PHYSICES ELEMENTA CAPUT XII.</fw>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">De Microſcopiis &amp; Teleſcopiis.</head>
        <p>
          <s xml:space="preserve">VItrorum, ſphæricis ſuperficiebus terminatorum, uſus, <lb />in corrigendis oculorum Senum &amp; </s>
          <s xml:space="preserve">Myopum vitiis, vi-<lb />dimus <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quantum valeant, in minimis objectis detegen-
<ptr xml:id="note-0552-01a" corresp="note-0552-01" type="noteAnchor" />
dis, &amp; </s>
          <s xml:space="preserve">in longè diſtantibus quaſi ſub oculis ponendis, dicen-<lb />dum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0552-01" corresp="note-0552-01a" n="*" anchored="true" place="margin">756. 758.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vitra convexa objecta amplificare diximus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ ampli-
<ptr xml:id="note-0552-02a" corresp="note-0552-02" type="noteAnchor" />
ficatio pendet à refractione radiorum, tranſeundo per lentem <lb />convexam, unde ſequitur illam augeri, ſi ſervatis iiſdem <lb />conditionibus, refractio augeatur; </s>
          <s xml:space="preserve">quem effectum obtine-<lb />mus, augendo convexitatem lentis; </s>
          <s xml:space="preserve">quæ eò convexior eſt, <lb />quo ſuperficies, hanc terminantes, ſunt portiones minoris <lb />ſphæræ quod niſi in exiguis vitris locum habere non poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0552-02" corresp="note-0552-02a" n="*" anchored="true" place="margin">747.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Tales lentes exiguæ Microſcopia vocantur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">760.</note>
        <p>
          <s xml:space="preserve">Microſcopio exigua objecta in immenſum amplificantur <lb />
<ptr xml:id="note-0552-04a" corresp="note-0552-04" type="noteAnchor" />
ita, ut quæ nudis oculis detegi non poſſunt, hoc median-<lb />te, diſtinctiſſimè videantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0552-04" corresp="note-0552-04a" place="margin">761.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Spatium per Microſcopium viſum, id eſt, circulus in quo <lb />
<ptr xml:id="note-0552-05a" corresp="note-0552-05" type="noteAnchor" />
objecta per Microſcopium viſibilia ſunt, vocatur Microſco-<lb />pii campus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0552-05" corresp="note-0552-05a" place="margin">762.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Per Microſcopium V ſi intueamur objectum exiguum <lb />
<ptr xml:id="note-0552-06a" corresp="note-0552-06" type="noteAnchor" />
A E, in a e amplificatum apparebit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0552-06" corresp="note-0552-06a" place="margin">TAB. IX. <lb />fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">745. 747.</note>
        <p>
          <s xml:space="preserve">Dantur &amp; </s>
          <s xml:space="preserve">Microſcopia compoſita, ex duabus aut tribus <lb />lentibus conſtantia; </s>
          <s xml:space="preserve">quo fundamento nitantur, explicatione <lb />illius, quod ex duabus lentibus conſtat, ſatis patebit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Detur lens exigua, admodum convexa, V V, ad talem ab <lb />
<ptr xml:id="note-0552-08a" corresp="note-0552-08" type="noteAnchor" />
hac diſtantiam detur objectum A E, ut ſingula illius puncta <lb />poſt lentem focum ſuum habeant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">admoveatur ita obje-
<ptr xml:id="note-0552-09a" corresp="note-0552-09" type="noteAnchor" />
ctum, ut foci removeantur ad a e <ptr type="noteAnchor" />, dabitur ibi objecti re-
<ptr xml:id="note-0552-10a" corresp="note-0552-10" type="noteAnchor" />
præſentatio, admodum amplificata, quæ ſuper plano albo <lb />ſi recipiatur ſenſibilis fiet <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0552-08" corresp="note-0552-08a" place="margin">TAB XI. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0552-09" corresp="note-0552-09a" n="*" anchored="true" place="margin">710. 699.</note>
              <note xml:space="preserve" xml:id="note-0552-10" corresp="note-0552-10a" n="*" anchored="true" place="margin">699.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">711.</note>
        <pb facs="0553" />
        <pb facs="0553a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0553a-01" />
          <label>0553a-01</label>
        </figure>
        <pb facs="0554" />
        <pb facs="0555" n="55" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Lens memorata in tubi extremitate firmatur in V, altera <lb />
<ptr xml:id="note-0555-01a" corresp="note-0555-01" type="noteAnchor" />
latior tubi extremitas, chartâ tenuiſſimâ CC obtegitur; </s>
          <s xml:space="preserve">ob-<lb />jectum AE ita diſponitur, ut foci punctorum hujus objecti <lb />dentur ad chartæ diſtantiam; </s>
          <s xml:space="preserve">ſi tunc objectum probè fuerit <lb />illuminatum, dabitur hujus repræſentatio inverſa, trans char-<lb />tam viſibilis, in a e. </s>
          <s xml:space="preserve">Motu objecti detegitur hujus ſitus ut <lb />repræſentatio in chartâ ſit exacta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0555-01" corresp="note-0555-01a" place="margin">TAB. XI. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Puncta ſingula repræſentationis a e ſunt puncta radiantia, <lb />
<ptr xml:id="note-0555-02a" corresp="note-0555-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">viſibilia <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ per microſcopium majus VV viſa, auctam
<ptr xml:id="note-0555-03a" corresp="note-0555-03" type="noteAnchor" />
repræſentationem a e exhibent in a e <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, radii ab ob-
<ptr xml:id="note-0555-04a" corresp="note-0555-04" type="noteAnchor" />
jecto AE procedentes, poſt refractionem per ambas lentes <lb />VV, VV, oculum intrabunt, quaſi ex objecto in a e pro-<lb />cederent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0555-02" corresp="note-0555-02a" place="margin">TAB. XI. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0555-03" corresp="note-0555-03a" n="*" anchored="true" place="margin">736. 754.</note>
              <note xml:space="preserve" xml:id="note-0555-04" corresp="note-0555-04a" n="*" anchored="true" place="margin">761.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Objectum itaque inverſum, &amp; </s>
          <s xml:space="preserve">multò magis amplificatum, <lb />
<ptr xml:id="note-0555-05a" corresp="note-0555-05" type="noteAnchor" />
per hoc Microſcopium compoſitum apparet, quàm per Mi-<lb />croſcopium ſimplex.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0555-05" corresp="note-0555-05a" place="margin">763.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3. &amp; 4.</head>
        <p rend="italics">
          <s xml:space="preserve">In hoc Microſcopio lens minima objecto vicina vocatur <lb />
<ptr xml:id="note-0555-06a" corresp="note-0555-06" type="noteAnchor" />
objectiva, alia ocularis dicitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0555-06" corresp="note-0555-06a" place="margin">764.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ne hæc nimium ſit exigua requiritur: </s>
          <s xml:space="preserve">nam puncta repræ-<lb />ſentationis ab, licèt ſint puncta radiantia, non tamen verſus <lb />omnes partes lumen emittunt; </s>
          <s xml:space="preserve">radii ſoli, qui per lentem ob-<lb />jectivam tranſeunt, ſeſe mutuò interſecant in ſingulis pun-<lb />ctis repræſentationis a b; </s>
          <s xml:space="preserve">quæ ergo per lentem ocularem vi-<lb />ſibilis non erit, niſi radii, per lentem objectivam tranſeun-<lb />tes, ad lentem ocularem perveniant. </s>
          <s xml:space="preserve">Campus ideò pendet <lb />
<ptr xml:id="note-0555-07a" corresp="note-0555-07" type="noteAnchor" />
à magnitudine hujus lentis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0555-07" corresp="note-0555-07a" place="margin">765.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Oculus etiam ita diſponendus eſt, ut omnes radii, qui ad <lb />
<ptr xml:id="note-0555-08a" corresp="note-0555-08" type="noteAnchor" />
lentem ocularem pertingunt, per hanc tranſeundo, ad o-<lb />culum perveniant; </s>
          <s xml:space="preserve">quod obtinemus, diſponendo oculum <lb />in d, puncto, in quo radii à centro lentis objectivæ provenien-<lb />tes, ocularem tranſeundo, colliguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0555-08" corresp="note-0555-08a" place="margin">766.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Per Microſcopia objecta ſatis illuminata apparent; </s>
          <s xml:space="preserve">quia <lb />parum à vitro diſtant, &amp; </s>
          <s xml:space="preserve">ita radii iidem per exiguam len-<lb />tem tranſeunt, qui ad diſtantiam majorem, niſi per majus fo-<lb />ramen, non tranſirent. </s>
          <s xml:space="preserve">Sæpe tamen, in maximis amplifica-<lb />
<ptr xml:id="note-0555-09a" corresp="note-0555-09" type="noteAnchor" />
</s>
          <pb facs="0556" n="56" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tionibus, neceſſe eſt, ut objecta illuminentur radiis, tranſeun-<lb />do per lentem convexam, collectis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0555-09" corresp="note-0555-09a" place="margin">767.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magnam cum Microſcopio compoſito affinitatem habet <lb />Teleſcopium Aſtronomicum.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Teleſcopia vocantur, inſtrumenta ad objecta longinqua vi-<lb />
<ptr xml:id="note-0556-01a" corresp="note-0556-01" type="noteAnchor" />
denda adaptata.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0556-01" corresp="note-0556-01a" place="margin">768.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De quo nunc agimus, vocatur Aſtronomicum, quia rebus <lb />
<ptr xml:id="note-0556-02a" corresp="note-0556-02" type="noteAnchor" />
terreſtribus videndis minimè eſt aptum, objecta enim inver-<lb />ſa repræſentat: </s>
          <s xml:space="preserve">de ſitu autèm apparentiæ minimè ſolliciti <lb />ſunt Aſtronomi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0556-02" corresp="note-0556-02a" place="margin">769.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Teleſcopium hoc conſtat ex duabus lentibus convexis, unâ <lb />objectivâ, quæ verſus objecta diſponitur, alterâ oculari, quæ <lb />ad partem oculi datur. </s>
          <s xml:space="preserve">Ope primæ, objecta longinqua ad <lb />certam diſtantiam poſt lentem repræſentantur <ptr type="noteAnchor" />, ut in mi-
<ptr xml:id="note-0556-03a" corresp="note-0556-03" type="noteAnchor" />
croſcopio compoſito objecta propinqua. </s>
          <s xml:space="preserve">Per lentem ocula-<lb />rem ſi obſervetur hæc repræſentatio, amplificata &amp; </s>
          <s xml:space="preserve">inverſa <lb />apparet, ut de Microſcopio dictum. </s>
          <s xml:space="preserve">Campum etiam in hoc <lb />
<ptr xml:id="note-0556-04a" corresp="note-0556-04" type="noteAnchor" />
caſu, ut in Microſcopio, à magnitudine lentis ocularis pen-<lb />dere, clarè liquet; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">ſitum oculi eodem modo pro Teleſco-<lb />
<ptr xml:id="note-0556-05a" corresp="note-0556-05" type="noteAnchor" />
pio, quàm pro Microſcopio, determinari <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">differt enim Te-
<ptr xml:id="note-0556-06a" corresp="note-0556-06" type="noteAnchor" />
leſcopium Aſtronomicum à Microſcopio compoſito in eo ſo-<lb />lo, quod in hoc lentes ſint magis convexæ, quæ objectis lon-<lb />ginquis videndis minimè ſunt aptæ, præcipuè quod ſpectat <lb />lentes objectivas. </s>
          <s xml:space="preserve">In Microſcopio lens objectiva ocularem <lb />convexitate ſuperat; </s>
          <s xml:space="preserve">in Teleſcopio contrarium obtinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0556-03" corresp="note-0556-03a" n="*" anchored="true" place="margin">711.</note>
              <note xml:space="preserve" xml:id="note-0556-04" corresp="note-0556-04a" place="margin">770.</note>
              <note xml:space="preserve" xml:id="note-0556-05" corresp="note-0556-05a" place="margin">771.</note>
              <note xml:space="preserve" xml:id="note-0556-06" corresp="note-0556-06a" n="*" anchored="true" place="margin">766.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Teleſcopia, quantumvis longa, ſideribus obſervandis apta <lb />ſunt: </s>
          <s xml:space="preserve">quæ viginti pedes excedunt, ad objecta, in terræ ſuper-<lb />ſicie, videnda nullius uſus ſunt; </s>
          <s xml:space="preserve">propter aëris continuam agita-<lb />tionem, in tantâ objectorum amplificatione nimium ſenſibilem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Brevius autem Teleſcopium Aſtronomicum, rebus terreſtri-<lb />
<ptr xml:id="note-0556-07a" corresp="note-0556-07" type="noteAnchor" />
bus videndis, adaptatur, additis duabus lentibus convexis, <lb />quæ etiam oculares dicuntur; </s>
          <s xml:space="preserve">tres autèm oculares ſimiles <lb />ſunt, &amp; </s>
          <s xml:space="preserve">minus convexæ quàm in Teleſcopio Aſtronomico, <lb />ſervatâ eâdem lente objectivâ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0556-07" corresp="note-0556-07a" place="margin">772.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Detur lens objectiva VV, quæ objectum longinquum in-<lb />
<ptr xml:id="note-0556-08a" corresp="note-0556-08" type="noteAnchor" />
verſum repræſentat in e a; </s>
          <s xml:space="preserve">Dentur ulterius lentes oculares <lb />
<ptr xml:id="note-0556-09a" corresp="note-0556-09" type="noteAnchor" />
</s>
          <pb facs="0557" />
          <s xml:space="preserve">
</s>
          <pb facs="0557a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0557a-01a" corresp="fig-0557a-01" type="figureAnchor" />
</s>
          <pb facs="0558" />
          <s xml:space="preserve">
</s>
          <pb facs="0559" n="57" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. XII.</fw>
tres DD, DD, DD. </s>
          <s xml:space="preserve">Prima diſponitur, ut radii, à punctis <lb />repræſentationis e a procedentes, paralleli lentem exeant <ptr type="noteAnchor" />:</s>
          <s xml:space="preserve">
<ptr xml:id="note-0559-01a" corresp="note-0559-01" type="noteAnchor" />
in hoc caſu radii, qui à puncto medio lentis objectivæ pro. <lb /></s>
          <s xml:space="preserve">cedunt, colliguntur in G; </s>
          <s xml:space="preserve">ſecunda lens diſponitur, ut ra-<lb />dii hi in G collecti, ibique ſeſe mutuo interſecantes, &amp; </s>
          <s xml:space="preserve">quaſi <lb />ex illo puncto procedentes, paralleli exeant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quibus poſitis,
<ptr xml:id="note-0559-02a" corresp="note-0559-02" type="noteAnchor" />
radii à vitro objectivo ad e provenientes, ibique ſeſe mutuo <lb />interſecantes, &amp; </s>
          <s xml:space="preserve">punctum hoc repræſentationis objecti for-<lb />mantes, per primam lentem refracti, per G paralleli inter <lb />ſe moventur; </s>
          <s xml:space="preserve">per ſecundam lentem refringuntur juxta dire-<lb />ctionem D e &amp; </s>
          <s xml:space="preserve">in e colliguntur <ptr type="noteAnchor" /> ita, ut hoc punctum ſit
<ptr xml:id="note-0559-03a" corresp="note-0559-03" type="noteAnchor" />
punctum novæ repræſentationis. </s>
          <s xml:space="preserve">Eodem modo puncto a <lb />primæ repræſentationis reſpondet punctum a ſecundæ repræ-<lb />ſentationis; </s>
          <s xml:space="preserve">quod cùm etiam locum habeat reſpectu puncto-<lb />rum intermediorum, datur objecti repræſentatio erecta in a e.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0556-08" corresp="note-0556-08a" place="margin">773.</note>
              <note xml:space="preserve" xml:id="note-0556-09" corresp="note-0556-09a" place="margin">TAB. XI. <lb />fig. 3.</note>
              <figure xml:id="fig-0557a-01" corresp="fig-0557a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0557a-01" />
                <label>0557a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0559-01" corresp="note-0559-01a" n="*" anchored="true" place="margin">699.</note>
              <note xml:space="preserve" xml:id="note-0559-02" corresp="note-0559-02a" n="*" anchored="true" place="margin">699.</note>
              <note xml:space="preserve" xml:id="note-0559-03" corresp="note-0559-03a" n="*" anchored="true" place="margin">698.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Tres tabellæ D, D, D, cum vitris ocularibus, quæ ad <lb />
<ptr xml:id="note-0559-04a" corresp="note-0559-04" type="noteAnchor" />
diſtantiam quinque circiter pollicum radios parallelos colli-<lb />gunt, ſuper plano inter duas regulas moventur ita, ut tria <lb />vitra ſint in eadem lineâ, in quâ etiam foramen datur V, <lb />per quod ſolum in cubiculum lumen intrat, &amp; </s>
          <s xml:space="preserve">in quo datur <lb />lens objectiva, quæ tubo brevi continetur, ad excludendum <lb />lumen laterale.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0559-04" corresp="note-0559-04a" place="margin">TAB. XI. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lens hæc objectiva talis eſt, ut ad diſtantiam circiter trium <lb />pedum ab V, repræſentet objecta longinqua inverſa in F, <lb />quæ repræſentatio videtur, ſi plano albo radii intercipian-<lb />tur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ad diſtantiam quinque pollicum ab F datur prima
<ptr xml:id="note-0559-05a" corresp="note-0559-05" type="noteAnchor" />
lens ocularis, à qua decem pollices diſtat lens ſecunda; </s>
          <s xml:space="preserve">in f, <lb />ad diſtantiam quinque pollicum ab hac, datur repræſentatio <lb />erecta eorundèm objectorum, quæ etiam interpoſito plano <lb />albo ſenſibilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0559-05" corresp="note-0559-05a" n="*" anchored="true" place="margin">711.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si repræſentatio a e videatur per tertiam lentem ocula-<lb />
<ptr xml:id="note-0559-06a" corresp="note-0559-06" type="noteAnchor" />
rem, poſito oculo in o, in quo colliguntur radii paralleli <lb />a D, e D, amplificatum, appropinquatum &amp; </s>
          <s xml:space="preserve">erectum, obje-<lb />
<ptr xml:id="note-0559-07a" corresp="note-0559-07" type="noteAnchor" />
ctum apparet; </s>
          <s xml:space="preserve">videtur enim ſub angulo D o D, dum nudis <lb />oculis ſub angulo exiguo apparet; </s>
          <s xml:space="preserve">etiam objectum appro-<lb />pinquatum habemus, quia, licèt ultra a e videatur, diſtantia
</s>
          <pb facs="0560" n="58" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tamen ad quam apparet, relationem ſenſibilem non habet ad <lb />objecti longinqui diſtantiam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0559-06" corresp="note-0559-06a" place="margin">TAB. XI. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0559-07" corresp="note-0559-07a" place="margin">774.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Poſitis quæ in Experimento præcedenti; </s>
          <s xml:space="preserve">ad diſtantiam <lb />
<ptr xml:id="note-0560-01a" corresp="note-0560-01" type="noteAnchor" />
decem pollicum à ſecundâ lente oculari detur tertia, à qua <lb />quinque pollices diſtet tabella O cum foramine; </s>
          <s xml:space="preserve">ſi oculus de-<lb />tur in O, objectum, ut dictum, erectum, amplificatum, &amp; </s>
          <s xml:space="preserve">ap-<lb />propinquatum, apparet. </s>
          <s xml:space="preserve">Si tabella O tranſponatur, id eſt, <lb />accedat aut recedat, campus Teleſcopii minuitur; </s>
          <s xml:space="preserve">quia uni-<lb />cus tantum oculi datur ſitus, in quo omnes radii, per lentes <lb />oculares tranſeuntes ad oculum, perveniunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0560-01" corresp="note-0560-01a" place="margin">TAB. XI. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Notandum lentes oculares, hìc adhibitas, non ſatis eſſe <lb />convexas reſpectu lentis objectivæ V; </s>
          <s xml:space="preserve">ſed hæ in experimen-<lb />to 3. </s>
          <s xml:space="preserve">magis ſunt commodæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Singula etiam objecti puncta magis illuminata apparent; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0560-02a" corresp="note-0560-02" type="noteAnchor" />
radii enim qui, ab aliquo puncto ad ſingula lentis objectivæ <lb />puncta advenientes, in puncto repræſentationis ſeſe mutuò <lb />interſecant, propter exiguam lentis ocularis ab hac repræ-<lb />ſentatione diſtantiam, parum diſperguntur antequam ad o-<lb />culum perveniant; </s>
          <s xml:space="preserve">ita ut omnes hunc intrent. </s>
          <s xml:space="preserve">Eſt itaque <lb />illuminatio, per Teleſcopium, ad hanc, nudis oculis, ut ſuper-<lb />ficies lentis objectivæ, per quam radii tranſeunt, ad pupillæ <lb />ſuperficiem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0560-02" corresp="note-0560-02a" place="margin">775.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">738.</note>
        <p>
          <s xml:space="preserve">Conſtruuntur etiam ex duabus lentibus Teleſcopia, per quæ <lb />
<ptr xml:id="note-0560-04a" corresp="note-0560-04" type="noteAnchor" />
objecta erecta, illuminata, &amp; </s>
          <s xml:space="preserve">amplificata, apparent. </s>
          <s xml:space="preserve">Bre-<lb />viora hæc ſunt, nam propter arctum campum, ſi longitudine <lb />pedem unicum excedant, ferè nullius uſus ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0560-04" corresp="note-0560-04a" place="margin">776.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit VV lens objectiva; </s>
          <s xml:space="preserve">repræſentatio inverſa objecti di-<lb />
<ptr xml:id="note-0560-05a" corresp="note-0560-05" type="noteAnchor" />
ſtantis datur in e a <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">lente cavâ DD intercipiuntur radii
<ptr xml:id="note-0560-06a" corresp="note-0560-06" type="noteAnchor" />
ita, ut qui à centro lentis VV procedunt, inflectantur quaſi <lb />à puncto f procederent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eâdem refractione radii concur-
<ptr xml:id="note-0560-07a" corresp="note-0560-07" type="noteAnchor" />
rentes in a, divergentes fiunt <ptr type="noteAnchor" />, habentes focum imaginarium
<ptr xml:id="note-0560-08a" corresp="note-0560-08" type="noteAnchor" />
in a; </s>
          <s xml:space="preserve">quod idem in ſingulis punctis repræſentationis e a obti-<lb />net, &amp; </s>
          <s xml:space="preserve">loco hujus datur repræſentatio imaginaria, erecta, <lb />in a e; </s>
          <s xml:space="preserve">id eſt, radii oculum intrant, quaſi ex objecto in a e <lb />procederent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0560-05" corresp="note-0560-05a" place="margin">TAB. XI. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0560-06" corresp="note-0560-06a" n="*" anchored="true" place="margin">711.</note>
              <note xml:space="preserve" xml:id="note-0560-07" corresp="note-0560-07a" n="*" anchored="true" place="margin">705.</note>
              <note xml:space="preserve" xml:id="note-0560-08" corresp="note-0560-08a" n="*" anchored="true" place="margin">706.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii, omni reſpectu, divergentes ex lente oculari <lb />
<ptr xml:id="note-0560-09a" corresp="note-0560-09" type="noteAnchor" />
</s>
          <pb facs="0561" />
          <s xml:space="preserve">
<pb facs="0561a" />
<ptr xml:id="fig-0561a-01a" corresp="fig-0561a-01" type="figureAnchor" />
<pb facs="0562" />
<pb facs="0563" n="59" /><fw type="head">MATHEMATICA LIB. III. CAP. XIII.</fw>
exeunt; </s>
          <s xml:space="preserve">ideò quantum poteſt oculus huic lenti admovendus <lb />eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0560-09" corresp="note-0560-09a" place="margin">777.</note>
              <figure xml:id="fig-0561a-01" corresp="fig-0561a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0561a-01" />
                <label>0561a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Campus in hoc Teleſcopio pendet à magnitudine lentis ob-<lb />
<ptr xml:id="note-0563-01a" corresp="note-0563-01" type="noteAnchor" />
jectivæ; </s>
          <s xml:space="preserve">radii enim, qui à puncto obliquè ad centrum hujus <lb />lentis perveniunt, ſæpe oculum non intrant, dum radii ab <lb />eodem puncto, qui per lentem verſus periferiam tranſeunt, <lb />ad oculum pertingunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0563-01" corresp="note-0563-01a" place="margin">778.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIII.</head>
        <head rend="italics" xml:space="preserve">De Reflexione Luminis.</head>
        <p>
          <s xml:space="preserve">LUmen à corporibus opacis repercuti vidimus, &amp; </s>
          <s xml:space="preserve">quidem <lb />in omnibus punctis verſus omnes partes <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In cauſâ eſt
<ptr xml:id="note-0563-02a" corresp="note-0563-02" type="noteAnchor" />
inæqualitas ſuperficierum, quæ conſtant ex innumeris pla-<lb />nis minimis, quæ, in omnibus punctis ſenſibilibus, ver-<lb />ſus omnes partes diriguntur; </s>
          <s xml:space="preserve">quod facilè concipitur, ſi ſuper-<lb />ficiem innumeris hemiſphæriis minimis obtectam concipia-<lb />mus. </s>
          <s xml:space="preserve">Hoc revera ſic ſe haberi deducimus, ex reflexione lu-<lb />minis, â ſuperficie politâ, id eſt, cujus æqualitates ſunt <lb />
<ptr xml:id="note-0563-03a" corresp="note-0563-03" type="noteAnchor" />
ſublatæ; </s>
          <s xml:space="preserve">quæ verſus unicam tantum partem in ſingulis pun-<lb />ctis lumen reflectit; </s>
          <s xml:space="preserve">quod æquè in curvis ac planis ſuperfi-<lb />ciebus locum habet. </s>
          <s xml:space="preserve">Etiam, à ſuperficiebus minimé politis, <lb />lumen maximâ copiâ reflecti verſus illam partem, verſus <lb />quam, ſi politæ forent, in totum reflecteretur, quotidianis <lb />experimentis extra dubium eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0563-02" corresp="note-0563-02a" n="*" anchored="true" place="margin">710.</note>
              <note xml:space="preserve" xml:id="note-0563-03" corresp="note-0563-03a" place="margin">779.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit radius luminis AC, obliquè in ſuperficiem planam im-<lb />
<ptr xml:id="note-0563-04a" corresp="note-0563-04" type="noteAnchor" />
pingens; </s>
          <s xml:space="preserve">ſit ad hanc perpendicularis CO, &amp; </s>
          <s xml:space="preserve">reflectatur ra-<lb />dius per CB,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0563-04" corresp="note-0563-04a" place="margin">TAB. XII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Radius CB, vocatur Radius reflexus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <note xml:space="preserve" place="margin">780.</note>
        <p>
          <s xml:space="preserve">Angulus OCB vocatur angulus reflexionis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">781.</note>
        <p rend="italics">
          <s xml:space="preserve">Radius reflexus eſt cum incidente in eodem plano perpendi-<lb />
<ptr xml:id="note-0563-07a" corresp="note-0563-07" type="noteAnchor" />
culari ad planum reflectens.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0563-07" corresp="note-0563-07a" place="margin">782.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hujus enim plani actio, qua lumen repercutitur, perpen-<lb />
<ptr xml:id="note-0563-08a" corresp="note-0563-08" type="noteAnchor" />
diculariter dirigitur ad hoc planum, quod ſibi ſimile ponitur <lb />in omnibus punctis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0563-08" corresp="note-0563-08a" place="margin">783.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0564" n="60" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p rend="italics">
          <s xml:space="preserve">Angulus reflexionis æqualis eſt angulo incidentiæ.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">784.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Detur in loco obſcuro ſpeculum planum S, quod, ope <lb />
<ptr xml:id="note-0564-02a" corresp="note-0564-02" type="noteAnchor" />
globi mobilis pede ſuſtentati, ad libitum conſtituitur; </s>
          <s xml:space="preserve">per fo-<lb />ramen in laminâ metallicâ L, quæ in feneſtrâ datur, radius <lb />ſolaris diametri circiter quartæ partis pollicis, in cubiculum <lb />intromittitur; </s>
          <s xml:space="preserve">ita ſpeculum diſponitur ut radius tranſeat per <lb />cavitatem cylindricam obliquam, (cujus diameter radii dia-<lb />metrum æquat,) in tabellâ T: </s>
          <s xml:space="preserve">ſi hæc tranſponatur, reflexus <lb />radius per eandem cavitatem tranſibit. </s>
          <s xml:space="preserve">Obtinet hoc quæ-<lb />cunque fuerit cavitatis inclinatio, ut adhibitis variis tabellis <lb />demonſtratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0564-02" corresp="note-0564-02a" place="margin">TAB. XII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quo experimento cum n. </s>
          <s xml:space="preserve">784. </s>
          <s xml:space="preserve">etiam probatur n. </s>
          <s xml:space="preserve">779.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Siradius reflexus fiat radius incidens, id eſt, ſi lumen ac-<lb />
<ptr xml:id="note-0564-03a" corresp="note-0564-03" type="noteAnchor" />
cedat per lineam BC, redibit per CA, id eſt, primus in-<lb />
<ptr xml:id="note-0564-04a" corresp="note-0564-04" type="noteAnchor" />
cidens fiet reflexus; </s>
          <s xml:space="preserve">ut patet ex æqualitate angulorum BCO, <lb />OCA.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0564-03" corresp="note-0564-03a" place="margin">785.</note>
              <note xml:space="preserve" xml:id="note-0564-04" corresp="note-0564-04a" place="margin">TAB. XII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hac æqualitate angulorum incidentiæ &amp; </s>
          <s xml:space="preserve">reflectionis, <lb />ulterius deducimus, lumen eâdem cum vi à corpore poſt im-<lb />
<ptr xml:id="note-0564-05a" corresp="note-0564-05" type="noteAnchor" />
pactum recedere, qua acceſſit. </s>
          <s xml:space="preserve">Reſolvatur motus per AC, <lb />in duos motus per AO &amp; </s>
          <s xml:space="preserve">OC <ptr type="noteAnchor" />, poſitis AO ad planum
<ptr xml:id="note-0564-06a" corresp="note-0564-06" type="noteAnchor" />
reflectens parallelâ, &amp; </s>
          <s xml:space="preserve">OC ad hoc perpendiculari. </s>
          <s xml:space="preserve">Con-<lb />tinuetur AO; </s>
          <s xml:space="preserve">motus juxta hanc directionem non mutatur <lb />ex plani actione: </s>
          <s xml:space="preserve">ſint ideò AO &amp; </s>
          <s xml:space="preserve">OB æquales; </s>
          <s xml:space="preserve">ſi lumen re-<lb />cedat â plano eâ cum vi, cum qua acceſſit, motus ex repul-<lb />ſione repræſentatur per CO, &amp; </s>
          <s xml:space="preserve">in hoc caſu radius reflexus <lb />tranſit per B <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt, angulus OCB æqualis eſt angulo
<ptr xml:id="note-0564-07a" corresp="note-0564-07" type="noteAnchor" />
OCA, quod cum experimento congruit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0564-05" corresp="note-0564-05a" place="margin">786.</note>
              <note xml:space="preserve" xml:id="note-0564-06" corresp="note-0564-06a" n="*" anchored="true" place="margin">192.</note>
              <note xml:space="preserve" xml:id="note-0564-07" corresp="note-0564-07a" n="*" anchored="true" place="margin">191.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa luminis reflexionem notatu digniſſimum eſt, lumen <lb />
<ptr xml:id="note-0564-08a" corresp="note-0564-08" type="noteAnchor" />
non incurrere in partes ſolidas corporum, dum ab his refle-<lb />ctitur, ſed ibi reflecti, ubi liberrimè pertranſire poteſt. </s>
          <s xml:space="preserve">Va-<lb />riis illud probabo experimentis, quibus aliæ miræ reflexionis <lb />proprietates deteguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0564-08" corresp="note-0564-08a" place="margin">787.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quotidianum eſt experimentum à nemine non obſerva-<lb />tum, lumen dum per medium quodcunque movetur, ex. </s>
          <s xml:space="preserve">gr. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0564-09a" corresp="note-0564-09" type="noteAnchor" />
vitrum, aquam, aërem, ſenſibilem &amp; </s>
          <s xml:space="preserve">regularem non pati re-<lb />flexionem; </s>
          <s xml:space="preserve">ibi autem reflecti, ubi media duo diverſæ denſi-
</s>
          <pb facs="0565" n="61" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XIII.</fw>
tatis ſeparantur; </s>
          <s xml:space="preserve">ſic in ſuperficie aquæ aut vitri reflectitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0564-09" corresp="note-0564-09a" place="margin">788.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">An tantâ copiâ lumen, ubi media ſeparantur, in horum <lb />particulas poteſt incurrere, dum per utrumque per ſpatium <lb />magnum in has non incurrendo movetur? </s>
          <s xml:space="preserve">An tales particu-<lb />læ majori numero verſus ſuperficiem dantur quam alibi?</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Lumen etiam majori copiâ reflectitur, in denſiori medio, <lb />
<ptr xml:id="note-0565-01a" corresp="note-0565-01" type="noteAnchor" />
incurrendo in ſuperficiem rarioris, quàm contra in rariori, <lb />impingendo in ſuperficiem denſioris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0565-01" corresp="note-0565-01a" place="margin">789.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 2.</head>
        <p>
          <s xml:space="preserve">In loco obſcuro, in quo lumen per foramen in lamina L <lb />
<ptr xml:id="note-0565-02a" corresp="note-0565-02" type="noteAnchor" />
intrat, detur priſma triangulare vitreum AB; </s>
          <s xml:space="preserve">lumen prif-<lb />ma intret per latus unum; </s>
          <s xml:space="preserve">ſi ad vicinum latus perveniat, &amp; </s>
          <s xml:space="preserve"><lb />efficiat angulum incidentiæ majorem grad. </s>
          <s xml:space="preserve">40. </s>
          <s xml:space="preserve">in totum re-<lb />flectitur, &amp; </s>
          <s xml:space="preserve">nihil in aërem penetrat; </s>
          <s xml:space="preserve">lumen autem in aëre à <lb />vitro nunquam in totum reflectitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0565-02" corresp="note-0565-02a" place="margin">TAB. XII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si verò reflexio fiat ex impactu luminis in partes ſolidas <lb />corporum, plures tales dantur partes in aëre, quàm in vitro, <lb />nam ſi ab ipſo vitro in hoc lumen reflecteretur, ad ſepara-<lb />tionem mediorum lumen nunquam pertingeret; </s>
          <s xml:space="preserve">ex vitro e-<lb />tiam lumen poſſe exire, ubi reflectitur, in Exp. </s>
          <s xml:space="preserve">ſequentibus <lb />probatur. </s>
          <s xml:space="preserve">In viciniis idcirco vitri tot requiruntur partes in <lb />aëre, ut lumini via non detur, ita ut in totum in vitrum re-<lb />flectatur; </s>
          <s xml:space="preserve">tales tamen non dari patet, quia per aërem juxta <lb />omnes directiones ad vitrum uſque pervenit lumen &amp; </s>
          <s xml:space="preserve">vitrum <lb />intrat. </s>
          <s xml:space="preserve">Etiam in eodem loco ſuperficiei, ſeparantis vitrum <lb />&amp; </s>
          <s xml:space="preserve">aërem, lumen ab unâ parte accedens reflectitur, dum <lb />quod à parte oppoſitâ advenit, tranſmittitur. </s>
          <s xml:space="preserve">Quod clarè <lb />probat lumen ibi reflecti, ubi pertranſire poteſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Iiſdem poſitis, quæ in Experimento præcedenti, fi mi <lb />
<ptr xml:id="note-0565-03a" corresp="note-0565-03" type="noteAnchor" />
nuatur luminis obliquitas, pro parte in aërem tranſibit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0565-03" corresp="note-0565-03a" place="margin">790.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XII. <lb />fig. 3.</note>
        <p>
          <s xml:space="preserve">Quis concipiet lumen, quod ex vitro in aërem tranſit &amp; </s>
          <s xml:space="preserve"><lb />in partes ſolidas non incurrit, illud totum, ſi paululum au-<lb />geatur obliquitas, incurrere in tales partes; </s>
          <s xml:space="preserve">cùm in utroque <lb />medio, ut dictum, meatus juxta omnes directiones dentur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Priſma vitreum triangulare AB, volubile eſt circa axem; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0565-05a" corresp="note-0565-05" type="noteAnchor" />
<ptr xml:id="note-0565-06a" corresp="note-0565-06" type="noteAnchor" />
</s>
          <pb facs="0566" n="62" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
quod præſtatur baſibus jungendo laminas æneas, quibus fila <lb />ænea perpendiculariter cohærent; </s>
          <s xml:space="preserve">pixidi P ſuperimponitur <lb />priſma ita, ut memorata fila ab oris pixidis ſuſtineantur; </s>
          <s xml:space="preserve">oræ <lb />etiam paululum excavantur, ad fila recipienda; </s>
          <s xml:space="preserve">quæ facilè <lb />circumaguntur, quo motu priſma circa axem revolvitur, &amp; </s>
          <s xml:space="preserve"><lb />facilè diſponitur, ut lumen reflectat eodem modo, ac in <lb />exp. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Pixis impletur aquâ, quæ ad priſma pertingit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">lu-<lb />men, quod in aërem impingendo, in totum reflectebatur, <lb />nunc in aquam incurrens, pro parte in hanc penetrat, &amp; </s>
          <s xml:space="preserve"><lb />pro parte tantum reflectitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0565-05" corresp="note-0565-05a" place="margin">791.</note>
              <note xml:space="preserve" xml:id="note-0565-06" corresp="note-0565-06a" place="margin">TAB. XII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quod experimentum cum reflexione, ex impactu in par-<lb />tes ſolidas, minimè congruit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In parte tertiâ hujus libri etiam videbimus, tenues lami-<lb />nas, quæ lumen reflectunt, illud tranſmittere, ſi craſſiores <lb />fiant <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">894.</note>
        <p>
          <s xml:space="preserve">Probat etiam Exp. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">vim reflectentem eo eſſe majorem, quo <lb />
<ptr xml:id="note-0566-02a" corresp="note-0566-02" type="noteAnchor" />
media, quæ à ſuperficie reflectente ſeparantur, magis denſita-<lb />te differant; </s>
          <s xml:space="preserve">vitrum enim &amp; </s>
          <s xml:space="preserve">aër, magis quàm illud cum a-<lb />quâ, denſitate differunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0566-02" corresp="note-0566-02a" place="margin">792.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In hoc Experimento etiam videmus reflexionem fieri ex <lb />
<ptr xml:id="note-0566-03a" corresp="note-0566-03" type="noteAnchor" />
eâdem vi, qua radii refringuntur, quæ in diverſis circum-<lb />ſtantiis varios edit effectus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0566-03" corresp="note-0566-03a" place="margin">793.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radius, qui ex medio denſiori in rarius tranſit, attractio-<lb />ne illius medii à perpendiculari recedit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi incidentis obli-
<ptr xml:id="note-0566-04a" corresp="note-0566-04" type="noteAnchor" />
quitas augeatur, augetur &amp; </s>
          <s xml:space="preserve">refracti obliquitas, donec tan-<lb />dem hic, in ipſâ ſuperficie media dirimente, moveatur. <lb /></s>
          <s xml:space="preserve">Quod obtinet, quando ſinus anguli incidentiæ eſt ad ſi-<lb />num totum, ut ſinus incidentiæ in medio denſiori, ad ſi-<lb />num refractionis in rariori; </s>
          <s xml:space="preserve">in hoc enim caſu angulus refra-<lb />ctionis eſt rectus. </s>
          <s xml:space="preserve">Si ulterius incidentis radii obliquitas au-<lb />geatur, radium in rarius non poſſe penetrare clarè patet; </s>
          <s xml:space="preserve"><lb />hicce eſt caſus, in quo lumen in totum reflectitur; </s>
          <s xml:space="preserve">quæ re-<lb />flexio pendet ab attractione qua radii refringuntur. </s>
          <s xml:space="preserve">Nam <lb />radius, dum per ſpatium attractionis movetur, incurvatur <lb />verſus medium denſius <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi in denſiori medio detur &amp; </s>
          <s xml:space="preserve">ita
<ptr xml:id="note-0566-05a" corresp="note-0566-05" type="noteAnchor" />
incurvetur, ut antequam per totum penetraverit ſpatium at-<lb />tractionis, tangens ad curvam parallela ſit ſuperficiei media
</s>
          <pb facs="0567" n="63" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XIII.</fw>
ſeparanti, curva continuata regreditur, idèoque radius refle-<lb />ctitur ex attractione medii denſioris, hæcque curvæ conti-<lb />nuatio ſimilis &amp; </s>
          <s xml:space="preserve">æqualis eſt primæ portioni, &amp; </s>
          <s xml:space="preserve">efficit angu-<lb />lum reflexionis æqualem angulo incidentiæ; </s>
          <s xml:space="preserve">quia per ean-<lb />dem partem ſpatii attractionis lumen redit, &amp; </s>
          <s xml:space="preserve">eædem vires <lb />attrahentes in punctis reſpondentibus portionum curvæ in <lb />lumen agunt. </s>
          <s xml:space="preserve">Sic corpus projectum, in aſcenſu &amp; </s>
          <s xml:space="preserve">deſcen-<lb />ſu, curvas ſimiles &amp; </s>
          <s xml:space="preserve">æquales deſcribit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0566-04" corresp="note-0566-04a" n="*" anchored="true" place="margin">625.</note>
              <note xml:space="preserve" xml:id="note-0566-05" corresp="note-0566-05a" n="*" anchored="true" place="margin">619.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non tamen omnem reflectionem ab hac attractione eodem <lb />
<ptr xml:id="note-0567-01a" corresp="note-0567-01" type="noteAnchor" />
modo pendêre, clarum eſt; </s>
          <s xml:space="preserve">nam in eo caſu in quo refractio <lb />datur, lumen pro parte reflectitur; </s>
          <s xml:space="preserve">ne quidem in totum ex <lb />rariori medio in denſius penetrat lumen; </s>
          <s xml:space="preserve">nam &amp; </s>
          <s xml:space="preserve">in hoc ca-<lb />ſu, in quo attractio quam maximè reflectioni opponitur, <lb />quidam radii repercutiuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0567-01" corresp="note-0567-01a" place="margin">794.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reflexionem tamen, in omni caſu, cum vi refringente re-<lb />
<ptr xml:id="note-0567-02a" corresp="note-0567-02" type="noteAnchor" />
lationem habere, in dubium vocari non poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0567-02" corresp="note-0567-02a" place="margin">795.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vbi lumen ſine refractione tranſit, ibi non reflectitur<ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0567-03a" corresp="note-0567-03" type="noteAnchor" />
<ptr xml:id="note-0567-04a" corresp="note-0567-04" type="noteAnchor" />
ubi autem refractio maxima eſt, ibi etiam reflexio fortior <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0567-05a" corresp="note-0567-05" type="noteAnchor" />
quod non modo obtinet, quando lumen, in medio denſiori <lb />motum, in rarius impingit, ut in exp. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve">, ſed idem obſerva-<lb />tur, quando lumen in denſius medium impingit: </s>
          <s xml:space="preserve">ſic poſito <lb />lumine in aëre, ſuperficies vitri fortius reflectit, quam aquæ; <lb /></s>
          <s xml:space="preserve">adamantis ſuperficies iterum fortius. </s>
          <s xml:space="preserve">Immerſis, aquâ, vitro &amp; </s>
          <s xml:space="preserve"><lb />adamante, in ſeparatione horum corporum cum aquâ vis re-<lb />fringens minor eſt, quàm in viciniis aëris, &amp; </s>
          <s xml:space="preserve">eorundem cor-<lb />porum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">minus etiam fortiter in aquâ, quàm in aëre, re-
<ptr xml:id="note-0567-06a" corresp="note-0567-06" type="noteAnchor" />
flectunt lumen hæc corpora. </s>
          <s xml:space="preserve">Ex hac relatione vis reflecten-<lb />tis cum vi refringente deducimus, lumen repercuti ad certam <lb />
<ptr xml:id="note-0567-07a" corresp="note-0567-07" type="noteAnchor" />
diſtantiam à corporibus, eodem modo ac vis refringens ad <lb />certam à corpore diſtantiam agit; </s>
          <s xml:space="preserve">confirmatur hæc propoſitio <lb />ex demonſtratis circa reflexionem, quæ non pendet ab im-<lb />pactu in partes ſolidas corporum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">pleniſſimè evincitur ſi <lb />conſideremus, corpora polita regulariter lumen reflectere, <lb />
<ptr xml:id="note-0567-08a" corresp="note-0567-08" type="noteAnchor" />
quod in ſpeculis obſervamus, licèt in horum ſuperficiebus in-<lb />numeræ dentur raſuræ: </s>
          <s xml:space="preserve">nam pulveris attritu poliuntur, &amp; </s>
          <s xml:space="preserve"><lb />quantumvis ſint exiguæ hujus particulæ, reſpectu luminis ra-<lb />ſuras magnas in ſuperficie relinquunt; </s>
          <s xml:space="preserve">unde in ipſâ ſuperfi-
</s>
          <pb facs="0568" n="64" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cie reflectio neceſſario irregularis eſt; </s>
          <s xml:space="preserve">ſi autem ad exiguam <lb />à ſuperficie diſtantiam reflexionem fieri concipiamus, minu-<lb />untur, &amp; </s>
          <s xml:space="preserve">ferè in totum tolluntur irregularitates, ut atten-<lb />dendo facilè liquet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0567-03" corresp="note-0567-03a" place="margin">796.</note>
              <note xml:space="preserve" xml:id="note-0567-04" corresp="note-0567-04a" n="*" anchored="true" place="margin">617. 788.</note>
              <note xml:space="preserve" xml:id="note-0567-05" corresp="note-0567-05a" n="*" anchored="true" place="margin">631. 792.</note>
              <note xml:space="preserve" xml:id="note-0567-06" corresp="note-0567-06a" n="*" anchored="true" place="margin">631.</note>
              <note xml:space="preserve" xml:id="note-0567-07" corresp="note-0567-07a" place="margin">797.</note>
              <note xml:space="preserve" xml:id="note-0567-08" corresp="note-0567-08a" place="margin">798.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIV.</head>
        <head rend="italics" xml:space="preserve">De Speculis planis.</head>
        <p>
          <s xml:space="preserve">SIt bc ſuperficies ſpeculi plani; </s>
          <s xml:space="preserve">A punctum radians. </s>
          <s xml:space="preserve">Con-<lb />
<ptr xml:id="note-0568-01a" corresp="note-0568-01" type="noteAnchor" />
tinuetur planum ſpeculi, &amp; </s>
          <s xml:space="preserve">ad hoc à radiante A dimitta-<lb />tur perpendicularis AC; </s>
          <s xml:space="preserve">ſi continuetur hæc, &amp; </s>
          <s xml:space="preserve">fiat C a <lb />æqualis CA, a erit focus imaginarius reflexorum radiorum <lb />ex A procedentium. </s>
          <s xml:space="preserve">Sit A b radius incidens; </s>
          <s xml:space="preserve">b f radius re-<lb />flexus; </s>
          <s xml:space="preserve">continuetur hoc ultra ſpeculum; </s>
          <s xml:space="preserve">propter angulos in-<lb />cidentiæ &amp; </s>
          <s xml:space="preserve">reflexionis æquales inter ſe <ptr type="noteAnchor" />, æquantur etiam
<ptr xml:id="note-0568-02a" corresp="note-0568-02" type="noteAnchor" />
horum complementa anguli A b C, f b d; </s>
          <s xml:space="preserve">huic æqualis <lb />eſt oppoſitus ad verticem ab C: </s>
          <s xml:space="preserve">Triangula A b C, ab C <lb />rectangula habent latus commune C b &amp; </s>
          <s xml:space="preserve">angulos æquales <lb />C b a, C b A; </s>
          <s xml:space="preserve">in omnibus ergo conveniunt, &amp; </s>
          <s xml:space="preserve">ſunt æ-<lb />quales inter ſe CA &amp; </s>
          <s xml:space="preserve">C a: </s>
          <s xml:space="preserve">quæ demonſtratio omnibus a-<lb />liis radiis, ex A profluentibus, competit, in quocunque <lb />plano perpendiculari ad planum ſpeculi concipiantur. </s>
          <s xml:space="preserve">ld-<lb />circo ubicunque oculus detur, ſi ad hunc radii reflexi per-<lb />veniant, oculum intrabunt quaſi ex a procederent; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in hoc <lb />puncto apparebit punctum A <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hujus autem puncti appa-
<ptr xml:id="note-0568-03a" corresp="note-0568-03" type="noteAnchor" />
rentia eundem ſitum habet reſpectu ſpeculi, ad partem poſti-<lb />
<ptr xml:id="note-0568-04a" corresp="note-0568-04" type="noteAnchor" />
cam, quâm habet ipſum punctum radians ad partem anticam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0568-01" corresp="note-0568-01a" place="margin">799.</note>
              <note xml:space="preserve" xml:id="note-0568-02" corresp="note-0568-02a" n="*" anchored="true" place="margin">384.</note>
              <note xml:space="preserve" xml:id="note-0568-03" corresp="note-0568-03a" place="margin">800.</note>
              <note xml:space="preserve" xml:id="note-0568-04" corresp="note-0568-04a" n="*" anchored="true" place="margin">737.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quod ſi applicetur ad ſingula puncta objecti, patebit, ob-<lb />
<ptr xml:id="note-0568-05a" corresp="note-0568-05" type="noteAnchor" />
jectum poſt ſpeculum apparêre, in eo ſitu, in quo reverâ da-<lb />tur ante ſpeculum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0568-05" corresp="note-0568-05a" place="margin">801.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XV.</head>
        <head rend="italics" xml:space="preserve">De Speculis ſphæricis.</head>
        <p>
          <s xml:space="preserve">OMnis ſuperficies ſphærica conſiderari poteſt, quaſi for-<lb />mata ex innumeris ſuperficiebus planis minimis; </s>
          <s xml:space="preserve">pla-<lb />numque, ſphæram in puncto quocunque tangens, eſt quaſi <lb />continuatio talis plani exigui.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0569" n="65" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XV.</fw>
        <p>
          <s xml:space="preserve">Specula ſphærica ſunt aut cava aut convexa.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Prima formantur ex portione ſphæræ cavæ &amp; </s>
          <s xml:space="preserve">politæ.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Secunda ſunt portiones ſphærarum ab exteriori parte po-<lb />litarum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Radius in ſpeculum quodcunque ſphæricum impingens, cum <lb />
<ptr xml:id="note-0569-01a" corresp="note-0569-01" type="noteAnchor" />
ſuo reflexo, dantur in plano, quod continuatum per ſphæræ cen-<lb />trum tranſit <ptr type="noteAnchor" />, eſt enim tale planum ad ſuperficiem ſphæræ
<ptr xml:id="note-0569-02a" corresp="note-0569-02" type="noteAnchor" />
perpendiculare. </s>
          <s xml:space="preserve">Linea, quæ per centrum ſphæræ &amp; </s>
          <s xml:space="preserve">punctum <lb />
<ptr xml:id="note-0569-03a" corresp="note-0569-03" type="noteAnchor" />
incidentiæ ducitur, continuata, cum radio incidente &amp; </s>
          <s xml:space="preserve">re-<lb />flexo angulos æquales format <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam linea hæc eſt perpen-
<ptr xml:id="note-0569-04a" corresp="note-0569-04" type="noteAnchor" />
dicularis ad ſuperficiem &amp; </s>
          <s xml:space="preserve">hi ſunt anguli incidentiæ &amp; </s>
          <s xml:space="preserve">re-<lb />flexionis: </s>
          <s xml:space="preserve">ideoque radius per centrum tranſiens, aut qui con-<lb />
<ptr xml:id="note-0569-05a" corresp="note-0569-05" type="noteAnchor" />
tinuatus per centrum tranſiret, reflexus in ſe redit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0569-01" corresp="note-0569-01a" place="margin">804.</note>
              <note xml:space="preserve" xml:id="note-0569-02" corresp="note-0569-02a" n="*" anchored="true" place="margin">782;</note>
              <note xml:space="preserve" xml:id="note-0569-03" corresp="note-0569-03a" place="margin">805.</note>
              <note xml:space="preserve" xml:id="note-0569-04" corresp="note-0569-04a" n="*" anchored="true" place="margin">784.</note>
              <note xml:space="preserve" xml:id="note-0569-05" corresp="note-0569-05a" place="margin">806.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">TAB. XII. <lb />fig. 5.</note>
        <p>
          <s xml:space="preserve">Sit b c portio ſpeculi convexi; </s>
          <s xml:space="preserve">punctum radians A; </s>
          <s xml:space="preserve">ſint <lb />A b, A d, A e, radii incidentes; </s>
          <s xml:space="preserve">reflexi erunt b f, d g, <lb />
<ptr xml:id="note-0569-07a" corresp="note-0569-07" type="noteAnchor" />
e b; </s>
          <s xml:space="preserve">ſi à puncto radiante A ducatur tangens ad ſpeculum, <lb />radius reflexus erit continuatio incidentis, aut potius in <lb />puncto contactus terminatur radiorum reflexio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0569-07" corresp="note-0569-07a" place="margin">807.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si radii à ſpeculo convexo reflexi b f, d g, e b continuentur, <lb />
<ptr xml:id="note-0569-08a" corresp="note-0569-08" type="noteAnchor" />
cum omnibus intermediis, interſectionibus ſuis formant cur-<lb />vam a a, quam omnes hi radii tangunt, &amp; </s>
          <s xml:space="preserve">radii vicini ſeſe <lb />mutuo interſecant in ipſa periferia curvæ; </s>
          <s xml:space="preserve">ita ut ſemper ocu-<lb />lum intrent quaſi à puncto periferiæ procederent; </s>
          <s xml:space="preserve">in qua <lb />ideò punctum A ſemper apparet <ptr type="noteAnchor" />, quamdiu reflexi ad ocu-
<ptr xml:id="note-0569-09a" corresp="note-0569-09" type="noteAnchor" />
lum pervenire poſſunt, &amp; </s>
          <s xml:space="preserve">oculus movetur in plano, quod <lb />per centrum ſphæræ tranſit: </s>
          <s xml:space="preserve">remoto verò oculo ex hoc pla-<lb />no, in aliâ curvâ apparet radians, quia tales curvæ dantur in <lb />ſingulis planis, quæ per A &amp; </s>
          <s xml:space="preserve">C concipi poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0569-08" corresp="note-0569-08a" place="margin">808.</note>
              <note xml:space="preserve" xml:id="note-0569-09" corresp="note-0569-09a" n="*" anchored="true" place="margin">737.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cùm omnes hæ curvæ &amp; </s>
          <s xml:space="preserve">quidem integræ dentur poſt <lb />ſpeculum, omnia etiam objecta poſt ſpeculi ſuperficiem appa-<lb />
<ptr xml:id="note-0569-10a" corresp="note-0569-10" type="noteAnchor" />
rent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0569-10" corresp="note-0569-10a" place="margin">809.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Objecta etiam apparent erecta. </s>
          <s xml:space="preserve">Nam ſi punctum A mo-<lb />
<ptr xml:id="note-0569-11a" corresp="note-0569-11" type="noteAnchor" />
veatur circa ſpeculum, eodem motu fertur tota curva a a; <lb /></s>
          <s xml:space="preserve">quod probat, quantum ad ſitum erectum aut inverſum, pun-<lb />cta repræſentationis eandem inter ſe habere relationem, <lb />quam ipſius objecti puncta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0569-11" corresp="note-0569-11a" place="margin">810.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Recedente puncto A à ſpeculo, recedit &amp; </s>
          <s xml:space="preserve">tota curva mo-
</s>
          <pb facs="0570" n="66" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tu contrario; </s>
          <s xml:space="preserve">poſito autem A ad diſtantiam infinitam, pun-<lb />ctum curvæ à ſuperficie maximè remotum, ab hac diſtabit <lb />quartam partem diametri: </s>
          <s xml:space="preserve">Unde ſequitur imminuta appare-<lb />
<ptr xml:id="note-0570-01a" corresp="note-0570-01" type="noteAnchor" />
re objecta; </s>
          <s xml:space="preserve">repræſentationes enim omnes inter arctos limites <lb />continentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0570-01" corresp="note-0570-01a" place="margin">811.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si moveatur oculus, movetur &amp; </s>
          <s xml:space="preserve">objecti apparentia, cujus <lb />
<ptr xml:id="note-0570-02a" corresp="note-0570-02" type="noteAnchor" />
figura etiam mutatur: </s>
          <s xml:space="preserve">ſingula enim puncta per ſuas curvas <lb />moventur, &amp; </s>
          <s xml:space="preserve">quidem inæqualiter pro diverſo oculi ſitu, re-<lb />ſpectu ſingularum curvarum; </s>
          <s xml:space="preserve">unde neceſſario ſigura mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0570-02" corresp="note-0570-02a" place="margin">812.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Si, in ſpeculo ſphærico convexo, aliquis ut A ſe ipſum in-<lb />tueatur, faciem ſuam in a, erectam, imminutam, &amp; </s>
          <s xml:space="preserve">à vera <lb />
<ptr xml:id="note-0570-03a" corresp="note-0570-03" type="noteAnchor" />
diſſimilem, videbit; </s>
          <s xml:space="preserve">motu oculi reliqua memorata obſerva-<lb />bit reſpectu objectorum fixorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0570-03" corresp="note-0570-03a" place="margin">TAB. XII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit b d ſpeculum cavum, portio ſphæræ cujus centrum <lb />
<ptr xml:id="note-0570-04a" corresp="note-0570-04" type="noteAnchor" />
eſt C; </s>
          <s xml:space="preserve">cadant in ſpeculi ſuperficiem radii paralleli, inter <lb />
<ptr xml:id="note-0570-05a" corresp="note-0570-05" type="noteAnchor" />
quos detur C d per centrum tranſiens; </s>
          <s xml:space="preserve">reflexione hic in ſe <lb />redit <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">radii vicini, reflexi, convergentes fiunt, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0570-06a" corresp="note-0570-06" type="noteAnchor" />
cum hoc concurrunt in focum F, punctum medium inter <lb />d &amp; </s>
          <s xml:space="preserve">C. </s>
          <s xml:space="preserve">Sit A b radius parum à C d diſtans; </s>
          <s xml:space="preserve">ducatur ſemi-<lb />diameter C b; </s>
          <s xml:space="preserve">angulus incidentiæ erit A b C, cui æqualis <lb />eſt angulus reflexionis C b F <ptr type="noteAnchor" />, ut &amp; </s>
          <s xml:space="preserve">angulus alternus b C
<ptr xml:id="note-0570-07a" corresp="note-0570-07" type="noteAnchor" />
F; </s>
          <s xml:space="preserve">Eſt ergo iſoſceles triangulum b FC, &amp; </s>
          <s xml:space="preserve">latera FC &amp; </s>
          <s xml:space="preserve"><lb />F b ſunt æqualia: </s>
          <s xml:space="preserve">propter exiguum b d, F d &amp; </s>
          <s xml:space="preserve">F b ſenſibi-<lb />liter non differunt; </s>
          <s xml:space="preserve">idè FC &amp; </s>
          <s xml:space="preserve">F d ſunt æquales: </s>
          <s xml:space="preserve">quæ de-<lb />monſtratio omnibus radiis à C d parum diſtantibus competit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0570-04" corresp="note-0570-04a" place="margin">813.</note>
              <note xml:space="preserve" xml:id="note-0570-05" corresp="note-0570-05a" place="margin">TAB. XIII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0570-06" corresp="note-0570-06a" n="*" anchored="true" place="margin">806.</note>
              <note xml:space="preserve" xml:id="note-0570-07" corresp="note-0570-07a" n="*" anchored="true" place="margin">805.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si radii paralleli magis à C d diſtent, in F non conve-<lb />niunt; </s>
          <s xml:space="preserve">omnes tamen in circellum exiguum concurrunt, ſi <lb />ſpeculi diametrum non excedat ſextam aut quintam partem <lb />diametri ſphæræ, cujus portio eſt ſpeculum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hoc fundamento nituntur ſpecula uſtoria, quæ radios ſo-<lb />
<ptr xml:id="note-0570-08a" corresp="note-0570-08" type="noteAnchor" />
lares parallelos in focum colligunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0570-08" corresp="note-0570-08a" place="margin">814.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Detur ſpeculum concavum S, ex metallo, aut vitro hy-<lb />
<ptr xml:id="note-0570-09a" corresp="note-0570-09" type="noteAnchor" />
drargyro à poſteriori parte induto; </s>
          <s xml:space="preserve">ſuſtineatur hoc pede li-<lb />gneo P, in cujus ſuperiori parte datur cavitas cylindrica, <lb />quæ cylindro ligneo impletur, qui cum tranſverſo ligno
</s>
          <pb facs="0571" />
          <s xml:space="preserve">
</s>
          <pb facs="0571a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0571a-01a" corresp="fig-0571a-01" type="figureAnchor" />
<pb facs="0572" />
<pb facs="0573" n="67" /><fw type="head">MATHEMATICA LIB. III. CAP. XV.</fw>
AA cohœret, quod ope cylindri hujus circa punctum <lb />ſuum medium horizontaliter rotatur; </s>
          <s xml:space="preserve">inter ſuſtentacula <lb />AB, AB, ſpeculum utcunque inclinatur, &amp; </s>
          <s xml:space="preserve">ope cochlea-<lb />rum in B, B, in ſitu quocunque firmatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0570-09" corresp="note-0570-09a" place="margin">TAB. XIII. <lb />fig. 2.</note>
              <figure xml:id="fig-0571a-01" corresp="fig-0571a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0571a-01" />
                <label>0571a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Expoſito ſpeculo radiis ſolaribus ita, ut radius, qui ad ſpe-<lb />culi punctum medium pertingit, ad ſuperficiem ſit perpen-<lb />dicularis, cùm omnes alii huic ſint paralleli, colliguntur in <lb />focum, ad diſtantiam à ſpeculo quartæ partis diametri ſphæ-<lb />ræ, ibique violenter urunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si diameter ſuperficiei ſpeculi, ut in noſtro, ſit circiter <lb />quindecim pollicum, &amp; </s>
          <s xml:space="preserve">focus detur ad diſtantiam ſeſqui pe-<lb />dis, lignum ſtatim flammam concpiit, &amp; </s>
          <s xml:space="preserve">laminæ tenues <lb />plumbi brevi liqueſcunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si conſideremus radios à C d remotos &amp; </s>
          <s xml:space="preserve">huic parallelos, <lb />ſi vicini fuerint, reflexi ſeſe mutuo interſecant antequam ad <lb />C d perveniant, &amp; </s>
          <s xml:space="preserve">in hoc caſu, id eſt, ubi incidentes pa-<lb />
<ptr xml:id="note-0573-01a" corresp="note-0573-01" type="noteAnchor" />
ralleli obliquè in ſpeculum impingunt, parum diſperſi refle-<lb />ctione in unum punctum colliguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0573-01" corresp="note-0573-01a" place="margin">815.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si focus, in quo radii paralleli â ſpeculo cavo colligun-<lb />
<ptr xml:id="note-0573-02a" corresp="note-0573-02" type="noteAnchor" />
tur, fiat punctum radians, radii parum diſperſi, reflectun-<lb />tur paralleli inter ſe <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0573-02" corresp="note-0573-02a" place="margin">816.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">813. 785.</note>
        <p>
          <s xml:space="preserve">Ex hiſce ſpeculi cavi proprietatibus deducimus metho-<lb />
<ptr xml:id="note-0573-04a" corresp="note-0573-04" type="noteAnchor" />
dum repræſentandi objecta in loco obſcuro, ſimilem illi, de <lb />qua antèa, adhibitâ lente convexâ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0573-04" corresp="note-0573-04a" place="margin">817.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">711.</note>
        <p>
          <s xml:space="preserve">Detur foramen F in pariete; </s>
          <s xml:space="preserve">ſit a b ſpeculum cavum ita <lb />
<ptr xml:id="note-0573-06a" corresp="note-0573-06" type="noteAnchor" />
diſpoſitum, ut colligat in F radios parallelos, &amp; </s>
          <s xml:space="preserve">ad parie-<lb />tem perpendiculares: </s>
          <s xml:space="preserve">juxta hanc directionem radii ex F pro-<lb />cedentes reflectuntur <ptr type="noteAnchor" />, quales ſunt radii, qui ab objectis re-
<ptr xml:id="note-0573-07a" corresp="note-0573-07" type="noteAnchor" />
percuſſi in F ſeſe mutuò interſecant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0573-06" corresp="note-0573-06a" place="margin">TAB. XIII. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0573-07" corresp="note-0573-07a" n="*" anchored="true" place="margin">816.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint AF radii à puncto objecti longinqui manantes; </s>
          <s xml:space="preserve">re-<lb />flectuntur hi à ſpeculo perpendiculariter ad parietem; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />quia radii ex puncto longinquo, per exiguum foramen tran-<lb />ſeuntes, pro parallelis haberi poſſunt, colliguntur hi, poſt <lb />reflexionem, in unum punctum a, ad diſtantiam parietis <ptr type="noteAnchor" />,
<ptr xml:id="note-0573-08a" corresp="note-0573-08" type="noteAnchor" />
id eſt, in ſuperficie hujus; </s>
          <s xml:space="preserve">ubi idcirco punctum repræſen-<lb />tatur. </s>
          <s xml:space="preserve">Eodem modo radii per BF, à puncto profluentes, <lb />colliguntur in b, quod cùm reſpectu omnium punctorum
</s>
          <pb facs="0574" n="(68)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
objecti locum habeat, datur hujus repræſentatio in pariete; <lb /></s>
          <s xml:space="preserve">qui ſi albus fuerit, &amp; </s>
          <s xml:space="preserve">objectum Solis radiis illuſtratum, vivi-<lb />dis coloribus depictum objectum erit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0573-08" corresp="note-0573-08a" n="*" anchored="true" place="margin">815.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">In loco obſcuro feneſtra chartâ albâ obtegitur, in cujus <lb />
<ptr xml:id="note-0574-01a" corresp="note-0574-01" type="noteAnchor" />
medio foramen datur, cujus diameter ſemi pollicem paulu-<lb />lum excedit, &amp; </s>
          <s xml:space="preserve">quod cum foramine in feneſtrâ congruit, cui <lb />ad dìſtantiam ad minimum quinquaginta pedum reſpondent <lb />objecta varia à Sole illuminata; </s>
          <s xml:space="preserve">ſpeculum concavum cujus <lb />ſuperficiei diameter eſt quindecim pollicum, &amp; </s>
          <s xml:space="preserve">quod ad di-<lb />ſtantiam octodecim pollicum colligit radios parallelos, ad <lb />hanc diſtantiam à feneſtrâ diſponitur ita, ut linea, per cen-<lb />trum foraminis, &amp; </s>
          <s xml:space="preserve">centrum ſuperficiei ſpeculi tranſiens, ad <lb />planum chartæ, &amp; </s>
          <s xml:space="preserve">ſpeculi ſuperficiem perpendicularis ſit. <lb /></s>
          <s xml:space="preserve">Objecta tunc ſuper chartâ repræſentantur in circulo concen-<lb />trico cum foramine, &amp; </s>
          <s xml:space="preserve">cujus diameter æqualis eſt diametro <lb />ſpeculi. </s>
          <s xml:space="preserve">Conus truncatus excavatus cum foramine extra <lb />cubiculum jungitur ad excludendum lumen, quod non ab <lb />objectis repræſentandis advenit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0574-01" corresp="note-0574-01a" place="margin">TAB. XIII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit ſpeculum cavum b e; </s>
          <s xml:space="preserve">centrum cavitatis C; </s>
          <s xml:space="preserve">punctum <lb />
<ptr xml:id="note-0574-02a" corresp="note-0574-02" type="noteAnchor" />
radians A, ultra centrum C à ſpeculo diſtans; </s>
          <s xml:space="preserve">radii inci-<lb />
<ptr xml:id="note-0574-03a" corresp="note-0574-03" type="noteAnchor" />
dentes A b, A d, A e, quorum reflexi b f, dg, eb, cum <lb />intermediis, mutuis interſectionibus, formant curvam a a, <lb />quam omnes tangunt; </s>
          <s xml:space="preserve">Punctum ideo A in hac curvâ appa-<lb />ret <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">moto oculo in plano curvæ apparentia per hanc
<ptr xml:id="note-0574-04a" corresp="note-0574-04" type="noteAnchor" />
curvam transfertur. </s>
          <s xml:space="preserve">In ſingulis autem planis quæ per C A <lb />concipi poſſunt talis datur curva, omnes concurrunt in linea <lb />C A, nempe in a. </s>
          <s xml:space="preserve">In hoc puncto a ergo maximâ copiâ col-<lb />
<ptr xml:id="note-0574-05a" corresp="note-0574-05" type="noteAnchor" />
liguntur radii reflexi, quod ideò vocatur focus radiorum ex <lb />A profluentium. </s>
          <s xml:space="preserve">Vice verſa A eſt focus, poſito radiante <lb />in a <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0574-02" corresp="note-0574-02a" place="margin">818.</note>
              <note xml:space="preserve" xml:id="note-0574-03" corresp="note-0574-03a" place="margin">TAB. XIII. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0574-04" corresp="note-0574-04a" n="*" anchored="true" place="margin">808.</note>
              <note xml:space="preserve" xml:id="note-0574-05" corresp="note-0574-05a" place="margin">819.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">785.</note>
        <p>
          <s xml:space="preserve">In hac figura pars curvæ, quæ ab unâ parte lineæ A C <lb />datur, tantum delineata eſt; </s>
          <s xml:space="preserve">pars ſimilis ad aliam partem <lb />concipi debet; </s>
          <s xml:space="preserve">ambæ junguntur in foco puncti radiantis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Recedente puncto radiante ad ſpeculum accedit curva.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">820.</note>
        <p>
          <s xml:space="preserve">Accedente radiante recedit à ſpeculo curva &amp; </s>
          <s xml:space="preserve">verſus <lb />ipſum radians movetur; </s>
          <s xml:space="preserve">donec in centro C concurrant; </s>
          <s xml:space="preserve">in <lb />
<ptr xml:id="note-0574-08a" corresp="note-0574-08" type="noteAnchor" />
</s>
          <pb facs="0575" n="(69)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. XV.</fw>
quo ſi detur radians, omnes radii reflexi cum incidentibus <lb />coincidunt <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">tota curva quaſi coacta eſt in ipſo centro.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0574-08" corresp="note-0574-08a" place="margin">821.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">806.</note>
        <p>
          <s xml:space="preserve">Si ulterius accedat radians, ut inter centrum &amp; </s>
          <s xml:space="preserve">ſpeculum <lb />
<ptr xml:id="note-0575-02a" corresp="note-0575-02" type="noteAnchor" />
detur, magis etiam recedit curva, quæ tunc ultra centrum <lb />datur, &amp; </s>
          <s xml:space="preserve">in curvâ omnium maximè recedit punctum, in quo <lb />omnes curvæ quæ in variis planis concipiuntur concurrunt, <lb />id eſt, focus puncti radiantis, qui ad diſtantiam infinitam <lb />datur, quando radians diſtat à ſpeculo quartam partem diame-<lb />
<ptr xml:id="note-0575-03a" corresp="note-0575-03" type="noteAnchor" />
tri ſphæræ <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Tuncque curva in infinitum extenditur &amp; </s>
          <s xml:space="preserve">duæ
<ptr xml:id="note-0575-04a" corresp="note-0575-04" type="noteAnchor" />
partes quæ in foco radiantis concurrunt ſeparantur; </s>
          <s xml:space="preserve">talis <lb />pars ſeparata videtur in a a; </s>
          <s xml:space="preserve">ſi magis accedat radians magis <lb />
<ptr xml:id="note-0575-05a" corresp="note-0575-05" type="noteAnchor" />
à ſe mutuo declinant curvæ partes, quia radii ut A b cum <lb />
<ptr xml:id="note-0575-06a" corresp="note-0575-06" type="noteAnchor" />
vicinis reflexi curvam non tangunt, ſed divergentes ſunt; <lb /></s>
          <s xml:space="preserve">id eſt, reflexi ultra ſpeculum continuati ſeſe mutuo interſe-<lb />cant, &amp; </s>
          <s xml:space="preserve">formant novam curvam poſt ſpeculum, quæ conſtat <lb />ex duobus cruribus, quorum unum videtur in a a; </s>
          <s xml:space="preserve">concur-<lb />runt in lineâ C A continuatâ, nempe in a, &amp; </s>
          <s xml:space="preserve">recedendo à <lb />ſpeculo in infinitum porriguntur. </s>
          <s xml:space="preserve">Daturque ab utraque <lb />parte puncti radiantis, in ſuperficie punctum ut d, quod ſe-<lb />parat radios formantes curvas a a &amp; </s>
          <s xml:space="preserve">a a; </s>
          <s xml:space="preserve">radiuſque A d re-<lb />flexus in d g neutram curvam tangit, ſi verſus utramque <lb />partem g, g, in infinitum continuetur, licèt continuò ma-<lb />gis ac magis ad utramque curvam accedat. </s>
          <s xml:space="preserve">Si tota ſphæra <lb />abſolveretur, reſpectu partis oppoſitæ ſphæræ, ultra cen-<lb />trum diſtaret radians, &amp; </s>
          <s xml:space="preserve">radii reflexi formarent curvam, <lb />de qua antea <ptr type="noteAnchor" />, qua conjungerentur crura ſeparata ut a a.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0575-07a" corresp="note-0575-07" type="noteAnchor" />
His præ miſſis phænomena ſpeculorum concavorum expli-<lb />canda ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0575-02" corresp="note-0575-02a" place="margin">822.</note>
              <note xml:space="preserve" xml:id="note-0575-03" corresp="note-0575-03a" place="margin">823.</note>
              <note xml:space="preserve" xml:id="note-0575-04" corresp="note-0575-04a" n="*" anchored="true" place="margin">813. 816.</note>
              <note xml:space="preserve" xml:id="note-0575-05" corresp="note-0575-05a" place="margin">824.</note>
              <note xml:space="preserve" xml:id="note-0575-06" corresp="note-0575-06a" place="margin">TAB. XIII. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0575-07" corresp="note-0575-07a" n="*" anchored="true" place="margin">818.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si corpore lucido illuminetur ſpeculum, radii à ſingulis <lb />
<ptr xml:id="note-0575-08a" corresp="note-0575-08" type="noteAnchor" />
punctis corporis manantes reflexi, curvas formant, ſed maxi-<lb />mâ copiâ in horum punctorum focis colliguntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi idèo foci
<ptr xml:id="note-0575-09a" corresp="note-0575-09" type="noteAnchor" />
hi in ſuperficie plani albi dentur, dabitur ibi corporis lucidi <lb />
<ptr xml:id="note-0575-10a" corresp="note-0575-10" type="noteAnchor" />
repræſentatio, ut in exp. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">9.</s>
          <s xml:space="preserve">; &amp; </s>
          <s xml:space="preserve">quidem inverſa, <lb />nam linea quæ jungit punctum radians cum ſuo foco, tranſit <lb />per centrum ſphæræ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in quo idcirco omnes tales lineæ
<ptr xml:id="note-0575-11a" corresp="note-0575-11" type="noteAnchor" />
ſeſe mutuo interſecant; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hæc interſectio, datur inter pun-<lb />ctum radians &amp; </s>
          <s xml:space="preserve">focum <ptr type="noteAnchor" />, in quo punctum repræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0575-08" corresp="note-0575-08a" place="margin">825.</note>
              <note xml:space="preserve" xml:id="note-0575-09" corresp="note-0575-09a" place="margin">826.</note>
              <note xml:space="preserve" xml:id="note-0575-10" corresp="note-0575-10a" n="*" anchored="true" place="margin">819.</note>
              <note xml:space="preserve" xml:id="note-0575-11" corresp="note-0575-11a" n="*" anchored="true" place="margin">819.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">818.</note>
        <pb facs="0576" n="(70)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">Accedente autem ad ſpeculum corpore lucido, recedit ap-<lb />parentia <ptr type="noteAnchor" />, quæ in eo caſu major eſt.</head>
        <note xml:space="preserve" n="*" anchored="true" place="margin">820.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Candela lucens ponitur inter ſpeculum cavum &amp; </s>
          <s xml:space="preserve">centrum <lb />ſphæræ, cujus ſectio ſpeculum eſt, ita tamen, ut magis à <lb />ſpeculo quàm ab hoc centro diſtet: </s>
          <s xml:space="preserve">ſi tunc planum album <lb />detur perpendiculare ad lineam, quæ per candelam &amp; </s>
          <s xml:space="preserve">cen-<lb />trum ſphæræ tranſit, &amp; </s>
          <s xml:space="preserve">ultra centrum ponatur, dabitur in <lb />illo repræſentatio candelæ inverſa; </s>
          <s xml:space="preserve">plani diſtantia à ſpeculo <lb />movendo illud, detegitur; </s>
          <s xml:space="preserve">etiam hac proportione; </s>
          <s xml:space="preserve">ut dif-<lb />ferentia diſtantiarum candelæ â centro ſphæræ &amp; </s>
          <s xml:space="preserve">â ſpecu-<lb />lo, ſe habet ad quartam partem diametri ſphæræ, ita di-<lb />ſtantia candelæ à ſpeculo ad diſtantiam quæſitam. </s>
          <s xml:space="preserve">Dum <lb />candela accedit ad ſpeculum, planum removendum eſt, <lb />&amp; </s>
          <s xml:space="preserve">augetur repræſentatio.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Objecta, ultra centrum poſita, inter ſpeculum &amp; </s>
          <s xml:space="preserve">cen-<lb />
<ptr xml:id="note-0576-02a" corresp="note-0576-02" type="noteAnchor" />
trum apparent, nam ſingula puncta in curvâ ut a a appa-<lb />
<ptr xml:id="note-0576-03a" corresp="note-0576-03" type="noteAnchor" />
rent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">etiam imminuta &amp; </s>
          <s xml:space="preserve">inverſa ſunt objectorum idola:</s>
          <s xml:space="preserve">
<ptr xml:id="note-0576-04a" corresp="note-0576-04" type="noteAnchor" />
nam in arctum ſpatium rediguntur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in deſcenſu puncti <lb />
<ptr xml:id="note-0576-05a" corresp="note-0576-05" type="noteAnchor" />
A adſcendit repræſentatio hujus; </s>
          <s xml:space="preserve">linea enim a a eundem <lb />ſervat ſitum reſpectu A C a rotantis circa centrum C.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0576-02" corresp="note-0576-02a" place="margin">827.</note>
              <note xml:space="preserve" xml:id="note-0576-03" corresp="note-0576-03a" place="margin">TAB. XIII. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0576-04" corresp="note-0576-04a" place="margin">828</note>
              <note xml:space="preserve" xml:id="note-0576-05" corresp="note-0576-05a" n="*" anchored="true" place="margin">818.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Ne lumine extraneo minus vivida ſit objectorum repræ-<lb />
<ptr xml:id="note-0576-06a" corresp="note-0576-06" type="noteAnchor" />
ſentatio, pixide includendum ſpeculum. </s>
          <s xml:space="preserve">Detur ſpeculum <lb />cujus ſuperficiei diameter eſt circiter octo pollicum, &amp; </s>
          <s xml:space="preserve">quod <lb />eſt portio ſphæræ diametri unius pedis cum ſemiſſe; </s>
          <s xml:space="preserve">inclu-<lb />datur hoc pixide P, in cujus anteriori parte datur foramen <lb />diametri circiter ſex pollicum, &amp; </s>
          <s xml:space="preserve">â quo ſpeculum diſtat <lb />pollices ſex aut ſeptem; </s>
          <s xml:space="preserve">ut apertura hæc à lumine ſit aver-<lb />ſa neceſſe eſt. </s>
          <s xml:space="preserve">Si nunc quis, ut A ad diſtantiam circiter <lb />duorum pedum à ſpeculo, ſe ipſum intueatur; </s>
          <s xml:space="preserve">facies ejus <lb />inverſa in pixide verſus aperturam apparebit, ſi accedat <lb />ſpectator, caput ex pixide prominens videbit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0576-06" corresp="note-0576-06a" place="margin">TAB. XIII. <lb />fig. 7.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Repræſentatio puncti, in centro ſphæræ poſiti, cum ipſo <lb />
<ptr xml:id="note-0576-07a" corresp="note-0576-07" type="noteAnchor" />
puncto radiante coincidit, &amp; </s>
          <s xml:space="preserve">ab hoc quaſi abſorbetur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0576-07" corresp="note-0576-07a" place="margin">829.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">821.</note>
        <p>
          <s xml:space="preserve">Poſuo oculo in hoc centro nullum objectum ab hoc poterit <lb />
<ptr xml:id="note-0576-09a" corresp="note-0576-09" type="noteAnchor" />
videri; </s>
          <s xml:space="preserve">ſoli enim radii ab oculo provenientes ad ipſum re-<lb />flectuntur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0576-09" corresp="note-0576-09a" place="margin">830.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">806.</note>
        <pb facs="0577" n="(71)" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XV.</fw>
        <p>
          <s xml:space="preserve">Si objectum detur inter centrum &amp; </s>
          <s xml:space="preserve">punctum, in quo radii <lb />
<ptr xml:id="note-0577-01a" corresp="note-0577-01" type="noteAnchor" />
paralleli reflexi colliguntur; </s>
          <s xml:space="preserve">apparet etiam objectum extra <lb />ſpeculum, ad majorem diſtantiam à ſpeculo, quàm ipſum obje-<lb />ctum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">inverſa eſt repræſentatio, quod eodem modo pro-
<ptr xml:id="note-0577-02a" corresp="note-0577-02" type="noteAnchor" />
batur ac in n. </s>
          <s xml:space="preserve">828; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">amplificatur, quia hæc magis remo <lb />vetur â centro, quàm ipſum objectum ab hoc diſtat; </s>
          <s xml:space="preserve">in <lb />infinitum enim à centro recedit repræſentatio, dum obje-<lb />ctum quartam partem diametri ſphæræ percurrit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0577-01" corresp="note-0577-01a" place="margin">831.</note>
              <note xml:space="preserve" xml:id="note-0577-02" corresp="note-0577-02a" n="*" anchored="true" place="margin">822.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si objectum non diſtet â ſpeculo quartam partem diametri <lb />
<ptr xml:id="note-0577-03a" corresp="note-0577-03" type="noteAnchor" />
ſphæræ, pro diver ſo oculi ſitu, aut ante aut poſt ſpeculum <lb />
<ptr xml:id="note-0577-04a" corresp="note-0577-04" type="noteAnchor" />
objectum apparet. </s>
          <s xml:space="preserve">Poſito oculo, ut radii reflexi ad hunc <lb />perveniant, qui formant curvam a a, ut verſus f, videbit <lb />objecti apparentiam ultra ſpeculum <ptr type="noteAnchor" />, amplificatam; </s>
          <s xml:space="preserve">quia
<ptr xml:id="note-0577-05a" corresp="note-0577-05" type="noteAnchor" />
curvæ ut a a, quæ ad varia puncta pertinent divergentes <lb />ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0577-03" corresp="note-0577-03a" place="margin">832.</note>
              <note xml:space="preserve" xml:id="note-0577-04" corresp="note-0577-04a" place="margin">TAB. XIII. <lb />fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0577-05" corresp="note-0577-05a" n="*" anchored="true" place="margin">824.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ad oculum perveniant radii formantes curvam a a, ob-<lb />jectum extra ſpeculum apparet: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in utroque caſu repræ-<lb />
<ptr xml:id="note-0577-06a" corresp="note-0577-06" type="noteAnchor" />
ſentatio eſt erecta; </s>
          <s xml:space="preserve">adſcendente enim aut deſcendente <lb />puncto A, eodem motu curvæ a a, a a, in quibus repræ-<lb />ſentatur, agitantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0577-06" corresp="note-0577-06a" place="margin">833.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si oculus detur in puncto, in quo radii reflexi pertinentes <lb />
<ptr xml:id="note-0577-07a" corresp="note-0577-07" type="noteAnchor" />
ad utramque curvam ſeſe mutuo interſecant, ut in O, duplex <lb />dabitur objecti apparentia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0577-07" corresp="note-0577-07a" place="margin">834.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Facilè patet in omni caſu apparentiæ, puncta non ean-<lb />dem inter ſe habere relationem, quam habent objecti pun-<lb />cta; </s>
          <s xml:space="preserve">ideoque ſpeculum cavum nunquam objectum exactè re-<lb />
<ptr xml:id="note-0577-08a" corresp="note-0577-08" type="noteAnchor" />
præſentare: </s>
          <s xml:space="preserve">maximè tamen irregularis repræſentatio eſt, <lb />quæ datur in lineis ut a a.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0577-08" corresp="note-0577-08a" place="margin">835.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dantur &amp; </s>
          <s xml:space="preserve">ſpæcula cylindrica convexa &amp; </s>
          <s xml:space="preserve">cava, uno re-<lb />
<ptr xml:id="note-0577-09a" corresp="note-0577-09" type="noteAnchor" />
ſpectu ſunt plana, alio reſpectu ſphærica; </s>
          <s xml:space="preserve">idcirco objecto-<lb />rum repræſentatio admodum irregularis eſt, quæ irregula-<lb />ritas, cùm à regulari figurâ pendeat, determinari poteſt ita, <lb />ut ſiguræ delineantur, quæ dum revera irregulares ſunt, <lb />in tali ſpeculo, in determinato oculi ſitu, regulares vi-<lb />dentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0577-09" corresp="note-0577-09a" place="margin">836.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0578" n="(72)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVI.</head>
        <head rend="italics" xml:space="preserve">De Lucerna Magica.</head>
        <p>
          <s xml:space="preserve">VAriæ conſtruuntur Machinæ, in quibus, ſpeculis &amp; </s>
          <s xml:space="preserve"><lb />lentibus conjunctis, &amp; </s>
          <s xml:space="preserve">utilia &amp; </s>
          <s xml:space="preserve">amoena videntur ſpecta-<lb />cula; </s>
          <s xml:space="preserve">quorum explicatio ex ante dictis haud difficulter de-<lb />ducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Unicam explicandam inter cæteras eligam, quâ in vitro <lb />exiguo figuræ depictæ, giganteæ in plano albo repræſentan-<lb />tur. </s>
          <s xml:space="preserve">Phoenomenon ſatis ſtupendum, ut peculiarem merea-<lb />tur explicationem! Lucerna Magica vocatur machina, quâ <lb />exhibetur, à ſcriptoribus opticis non quidem intacta, ſa-<lb />tis tamen neglecta.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Pixis datur lignea, longitudinis circiter unius pedis cum <lb />
<ptr xml:id="note-0578-01a" corresp="note-0578-01" type="noteAnchor" />
ſemiſſe, lata &amp; </s>
          <s xml:space="preserve">alta quatuordecim pollices; </s>
          <s xml:space="preserve">in hac datur <lb />
<ptr xml:id="note-0578-02a" corresp="note-0578-02" type="noteAnchor" />
ſpeculum cavum S, diametri octo pollicum, &amp; </s>
          <s xml:space="preserve">ſectio ſphæ-<lb />ræ diametri ſeſquipedalis: </s>
          <s xml:space="preserve">ſpeculum hoc ſuſtentaculo ap-<lb />plicatur, quod inter regulas juxta longitudinem pixidis <lb />movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0578-01" corresp="note-0578-01a" place="margin">837.</note>
              <note xml:space="preserve" xml:id="note-0578-02" corresp="note-0578-02a" place="margin">TAB. XIV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datur &amp; </s>
          <s xml:space="preserve">in hac lampas L, quæ pede ligneo ſuſtinetur, <lb />inter regulas ad latus pixidis, juxta hujus longitudinem <lb />mobili. </s>
          <s xml:space="preserve">Prominet lampadis tubus ita, ut centrum flammæ <lb />reſpondeat centro ſuperficiei ſpeculi; </s>
          <s xml:space="preserve">conſtat hæc flamma <lb />ex quatuor flammis, quæ cum ſeſe mutuò tangant flammam <lb />quadratam formant, cujus latus excedit duos pollices.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Oblonga datur apertura in ſuperiori pixidis plano, quæ <lb />operculo inter regulas mobili obtegitur; </s>
          <s xml:space="preserve">per hoc tranſit ca-<lb />minus C, qui (ut in fig. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">videtur) ſupra pixidem ad alti-<lb />tudinem circiter ſeſquipedis prominet. </s>
          <s xml:space="preserve">Caminus cum oper-<lb />culo eſt mobilis, aperturâ memoratâ manente clauſâ; </s>
          <s xml:space="preserve">ut <lb />lampadi reſpondeat diſponitur caminus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In Pixidis latere minori datur foramen rotundum, dia-<lb />metri quinque pollicum; </s>
          <s xml:space="preserve">in quo datur vitrum convexum <lb />ejuſdem diametri V: </s>
          <s xml:space="preserve">terminatur hoc utrimque convexâ ſu-<lb />perficie, portione ſphæræ, cujus diameter pedem unum æ-<lb />quat: </s>
          <s xml:space="preserve">axis hujus vitri ſi concipiatur, ad ſpeculi ſuperficiem in
</s>
          <pb facs="0579" />
          <s xml:space="preserve">
<pb facs="0579a" />
<ptr xml:id="fig-0579a-01a" corresp="fig-0579a-01" type="figureAnchor" />
<pb facs="0580" />
<pb facs="0581" n="(73)" /><fw type="head">MATHEMATICA LIB. III. CAP. XVI.</fw>
hujus centro perpendicularis erit, ut &amp; </s>
          <s xml:space="preserve">ad planum flammæ <lb />per cujus punctum medium tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0579a-01" corresp="fig-0579a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0579a-01" />
                <label>0579a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Clauditur &amp; </s>
          <s xml:space="preserve">reſeratur hoc foramen plano inter regulas <lb />mobili, quod cylindro, in E ex pixide prominente, agi-<lb />tatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Huic foramini extra pixidem reſpondet tubus T, longitu-<lb />dinis &amp; </s>
          <s xml:space="preserve">diametri circiter ſex pollicum, in cujus extremo da-<lb />tur annulus, in quo movetur tubus ſecundus t, diametri cir-<lb />citer quatuor pollicum, &amp; </s>
          <s xml:space="preserve">longitudinis quinque aut ſex pol-<lb />licum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hoc tubo minori dantur lentes duæ; </s>
          <s xml:space="preserve">prima in extre-<lb />mitate quæ tubo T intruditur, &amp; </s>
          <s xml:space="preserve">eſt ejuſdem convexitatis <lb />cum vitro V, &amp; </s>
          <s xml:space="preserve">diametri trium pollicum cum ſemiſſe. </s>
          <s xml:space="preserve">Se-<lb />cunda lens pollices tres à primâ diſtat, planior eſt, termina-<lb />tur portionibus ſphæræ diametri quatuor pedum. </s>
          <s xml:space="preserve">Inter has <lb />lentes, diſtans à ſecundâ pollicem unum, diſponitur an-<lb />nulus ligneus, quo tubus clauditur, relictâ aperturâ circula-<lb />ri, cujus diameter quartâ parte pollicem unum excedit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Objecta repræſentanda in vitro plano &amp; </s>
          <s xml:space="preserve">tenui depingun-<lb />tur, quod extra pixidem juxta vitrum V, inter hoc &amp; </s>
          <s xml:space="preserve">tu-<lb />bum T movetur, poſitâ picturâ in ſitu inverſo. </s>
          <s xml:space="preserve">Si vitra hæc <lb />fuerint rotunda, habent diametrum quinque pollicum; </s>
          <s xml:space="preserve">ut <lb />commodè moveantur, in plano ligneo firmantur, &amp; </s>
          <s xml:space="preserve">tres in <lb />eodem plano poſſunt conjungi. </s>
          <s xml:space="preserve">Etiam in vitris longioribus <lb />depinguntur figuræ, quæ ſucceſſivè juxta vitrum V tran-<lb />ſeunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tota hæc pixis pede ſuſtinetur, quo, inter certos limites, <lb />
<ptr xml:id="note-0581-01a" corresp="note-0581-01" type="noteAnchor" />
ad altitudinem quamcunque firmatur; </s>
          <s xml:space="preserve">Plana lignea cum <lb />pixide cohoerent, &amp; </s>
          <s xml:space="preserve">inter regulas juxta plana quæ pedem <lb />formant moventur; </s>
          <s xml:space="preserve">in utroque illorum datur ſciſſura; </s>
          <s xml:space="preserve">ad <lb />altitudinem deſideratam, ope cochlearum in pede fixarum, <lb />&amp; </s>
          <s xml:space="preserve">per ſciſſuras mobilium, conſtituitur pixis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0581-01" corresp="note-0581-01a" place="margin">TAB. XIV. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diſponitur tota machina ad diſtantiam, quindecim, viginti, <lb />aut triginta pedum à plano albo, diverſam pro magnitudine <lb />plani; </s>
          <s xml:space="preserve">hæc enim diſtantia poteſt plani longitudinem æquare; <lb /></s>
          <s xml:space="preserve">ad talem altitudinem firmatur pixis ut tubi, in latere pixidis, <lb />medio plani reſpondeant. </s>
          <s xml:space="preserve">Accenſâ lampade pixis clauditur
</s>
          <pb facs="0582" n="(74)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
&amp; </s>
          <s xml:space="preserve">figuræ, in vitro depictæ, in plano albo repræſentantur. <lb /></s>
          <s xml:space="preserve">Motu tubi, in quo lentes duæ dantur, detegitur hujus ſitus, <lb />ad repræſentationem diſtinctam exhibendam, requiſitus. </s>
          <s xml:space="preserve"><lb />Diſpoſitio autem partium machinæ, quæ immediatè huic <lb />ſpectaculo exhibendo inſerviunt, peculiarius eſt explicanda.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sint hæ partes ſeparatæ; </s>
          <s xml:space="preserve">S S ſpeculum; </s>
          <s xml:space="preserve">flamma in l l, <lb />
<ptr xml:id="note-0582-01a" corresp="note-0582-01" type="noteAnchor" />
conſtat hæc ex quatuor flammis in lineâ l l; </s>
          <s xml:space="preserve">V V eſt vitrum <lb />
<ptr xml:id="note-0582-02a" corresp="note-0582-02" type="noteAnchor" />
V. </s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">I.</s>
          <s xml:space="preserve">; O O pictura in vitro plano tenui; </s>
          <s xml:space="preserve">a a lens major; <lb /></s>
          <s xml:space="preserve">d d lens planior; </s>
          <s xml:space="preserve">b b annulus ligneus inter lentes; </s>
          <s xml:space="preserve">f apertura <lb />annuli, id eſt, foramen in medio hujus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0582-01" corresp="note-0582-01a" place="margin">838.</note>
              <note xml:space="preserve" xml:id="note-0582-02" corresp="note-0582-02a" place="margin">TAB. XIV. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hiſce omnibus ut jam explicatum, &amp; </s>
          <s xml:space="preserve">ut in hac figurâ vi-<lb />detur diſpoſitis; </s>
          <s xml:space="preserve">radii, qui à puncto picturæ O O procedunt, <lb />per lentem a a tranſeundo, minus divergentes ſunt, &amp; </s>
          <s xml:space="preserve">quaſi <lb />à puncto remotiori procederent, ad lentem d d perveniunt <ptr type="noteAnchor" />,
<ptr xml:id="note-0582-03a" corresp="note-0582-03" type="noteAnchor" />
ex qua convergentes exeunt <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in ſuperficie plani albi col-
<ptr xml:id="note-0582-04a" corresp="note-0582-04" type="noteAnchor" />
liguntur, &amp; </s>
          <s xml:space="preserve">picturam puncti, figuræ in vitro, exhibent <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0582-05a" corresp="note-0582-05" type="noteAnchor" />
Figura in vitro illuminatur &amp; </s>
          <s xml:space="preserve">à radiis à flammâ l l proceden-<lb />tibus &amp; </s>
          <s xml:space="preserve">à radiis à ſpeculo S S reflexis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0582-03" corresp="note-0582-03a" n="*" anchored="true" place="margin">699.</note>
              <note xml:space="preserve" xml:id="note-0582-04" corresp="note-0582-04a" n="*" anchored="true" place="margin">699.</note>
              <note xml:space="preserve" xml:id="note-0582-05" corresp="note-0582-05a" n="*" anchored="true" place="margin">711.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ad perfectionem hujus machinæ requiritur; </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">ut figura <lb />
<ptr xml:id="note-0582-06a" corresp="note-0582-06" type="noteAnchor" />
O O quantum fieri poteſt ſit illuminata; </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">ut in omnibus <lb />punctis æqualiter illuminetur; </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">ut omne lumen, quo ſingu-<lb />la picturæ puncta illuminantur, per lentes a a &amp; </s>
          <s xml:space="preserve">d d ad pla-<lb />num album perveniat &amp; </s>
          <s xml:space="preserve">repræſentationi exhibendæ inſer-<lb />viat; </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">tandem ut ſolum hoc lumen ex pixide exeat, ne <lb />lumine extraneo minus vivida ſit repræſentatio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0582-06" corresp="note-0582-06a" place="margin">839.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">A magnitudine flammæ &amp; </s>
          <s xml:space="preserve">ſpeculi, ut &amp; </s>
          <s xml:space="preserve">hujus cavitate, <lb />pendet requiſitum primum; </s>
          <s xml:space="preserve">quo magis excavatur ſpeculum, <lb />eo propius flammæ admovendum eſt, &amp; </s>
          <s xml:space="preserve">majori numero <lb />radii intercipiuntur, &amp; </s>
          <s xml:space="preserve">reflectuntur; </s>
          <s xml:space="preserve">cavendum tamen, ne <lb />nimium incaleſcat ſpeculum, quod optimè ex vitro confla-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Datis autem flammâ &amp; </s>
          <s xml:space="preserve">ſpeculo, ut quantum fieri poteſt <lb />maximè illuminetur pictura, &amp; </s>
          <s xml:space="preserve">ubique æqualiter, ita flamma <lb />&amp; </s>
          <s xml:space="preserve">ſpeculum conſtituuntur, ut repræſentatio inverſa flammæ <ptr type="noteAnchor" />
<ptr xml:id="note-0582-07a" corresp="note-0582-07" type="noteAnchor" />
cadat in ipſam picturam: </s>
          <s xml:space="preserve">cùm autem repræſentatio flammæ <lb />augeri &amp; </s>
          <s xml:space="preserve">minui poſſit <ptr type="noteAnchor" />, ita ſpeculum &amp; </s>
          <s xml:space="preserve">flamma diſponenda
<ptr xml:id="note-0582-08a" corresp="note-0582-08" type="noteAnchor" />
ſunt, ut flammæ repræſentatio totam picturam in vitro obte-
</s>
          <pb facs="0583" n="(75)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. XVII.</fw>
gat &amp; </s>
          <s xml:space="preserve">hanc non excedat. </s>
          <s xml:space="preserve">Tunc enim pictura quantum poteſt <lb />fieri maximè à lumine reflexo illuminatur, &amp; </s>
          <s xml:space="preserve">ſingula illius <lb />puncta æqualiter illuſtrantur; </s>
          <s xml:space="preserve">directè etiam in ſingula pictu-<lb />ræ puncta lumen, ſenſibiliter æquale, cadit; </s>
          <s xml:space="preserve">admotâ flam-<lb />mâ, lumen hoc quidem augeretur, ſed minueretur reflexum, <lb />&amp; </s>
          <s xml:space="preserve">diminutio hujus augmentum illius ſuperaret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0582-07" corresp="note-0582-07a" n="*" anchored="true" place="margin">826.</note>
              <note xml:space="preserve" xml:id="note-0582-08" corresp="note-0582-08a" n="*" anchored="true" place="margin">826.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Uſus vitri V V eſt inflexio luminis, quo pictura O O il-<lb />luminatur, antequam illud ad hanc perveniat; </s>
          <s xml:space="preserve">qua infle-<lb />ctione lumen omne ad lentem a a pervenit, &amp; </s>
          <s xml:space="preserve">repræſenta-<lb />tioni in plano albo inſervit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Omne lumen, quod huic repræſentationi utile eſt, tranſit <lb />per foramen f; </s>
          <s xml:space="preserve">radiique à variis punctis procedentes ibi ſeſe <lb />mutuo interſecant; </s>
          <s xml:space="preserve">quare pictura inverſa in vitro, erecta da-<lb />tur in plano albo; </s>
          <s xml:space="preserve">annulo b b omnes radii, qui repræſenta-<lb />tioni formandæ non inſerviunt, intercipiuntur, ne cubiculum <lb />intrent &amp; </s>
          <s xml:space="preserve">minus vivida ſit pictura. </s>
          <s xml:space="preserve">Annulus etiam hicce <lb />intercipit radios, quibus unum punctum magis quàm aliud il-<lb />luminatur, quo lumen, quod ex ante dictis quidem æqua-<lb />bile ſatis eſt, magis adhucdum æquabile fit. </s>
          <s xml:space="preserve">Niſi exactè <lb />detur annulus b b in radiorum interſectione, magnoperè <lb />nocet.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">LIBRI III. Pars III.</head>
        <head xml:space="preserve">De Opaco &amp; Coloribus.</head>
        <head xml:space="preserve">CAPUT XVII.</head>
        <head rend="italics" xml:space="preserve">De Corporum Opacitate</head>
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p>
          <s xml:space="preserve">COrpora quæ lumen tranſmittunt vocantur pellucida. </s>
          <s xml:space="preserve">Ta-<lb />
<ptr xml:id="note-0583-01a" corresp="note-0583-01" type="noteAnchor" />
lia ſunt omnia media <ptr type="noteAnchor" />, vacuo excepto.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0583-01" corresp="note-0583-01a" place="margin">840.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">615.</note>
        <p>
          <s xml:space="preserve">Nullum datur corpus, cujus partes minimæ non ſint pelluci-<lb />
<ptr xml:id="note-0583-03a" corresp="note-0583-03" type="noteAnchor" />
dæ; </s>
          <s xml:space="preserve">hoc in dubium nemo vocabit, qui mycroſcopiis ſæpe u-<lb />ſus eſt: </s>
          <s xml:space="preserve">partes quædam metallicæ, quæ licèt exiguæ, lumen <lb />non tranſmittunt, ſi in menſtruis diſſolvantur, id eſt, in
</s>
          <pb facs="0584" n="(76)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
partes multò minores dividantur, tranſlucidæ fiunt. </s>
          <s xml:space="preserve">Facili <lb />etiam experimento probatur, lumen per pleraque corpora o-<lb />paca tranſire poſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0583-03" corresp="note-0583-03a" place="margin">841.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 1.</head>
        <p>
          <s xml:space="preserve">In cubiculo obſcuro, in quo lumen ſolare per foramen in-<lb />trat, obtegatur foramen hoc laminâ tenui corporis opaci, <lb />per hanc tranſibit lumen; </s>
          <s xml:space="preserve">lignum craſſitiei decimæ partis pol-<lb />licis lumen omne non intercipit. </s>
          <s xml:space="preserve">Hoc autem experimento <lb />perfecta partium tranſluciditas in corporibus opacis non pro-<lb />batur, talis enim in minimis partibus tantum obtinet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Opacitas non oritur, ut vulgò creditur, ex eo, quod viæ, <lb />
<ptr xml:id="note-0584-01a" corresp="note-0584-01" type="noteAnchor" />
per quas lumen tranſire poſſet, obturentur à materiæ parti-<lb />culis, per ſingulas enim corporis partes minores lumen tran-<lb />ſit; </s>
          <s xml:space="preserve">inutilis etiam ad opacitatem talis eſt luminis interceptio; <lb /></s>
          <s xml:space="preserve">ad opacitatem requiritur luminis reflectio &amp; </s>
          <s xml:space="preserve">deflectio à lineâ <lb />rectâ, ad quod ſeparatio duorum mediorum tantum requi-<lb />ritur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0584-01" corresp="note-0584-01a" place="margin">842.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">631. 796.</note>
        <p>
          <s xml:space="preserve">Concipiamus corpus conſtans ex particulis minimis, per-<lb />fectè tranſlucidis, (quales ſunt particulæ ex quibus corpora <lb />conſtant <ptr type="noteAnchor" />) poris inter ſe ſeparatis; </s>
          <s xml:space="preserve">interſtitiaque aut vacua
<ptr xml:id="note-0584-03a" corresp="note-0584-03" type="noteAnchor" />
dari aut repleta medio denſitate differente cum ipſis parti-<lb />culis; </s>
          <s xml:space="preserve">lumen ſi intret hoc corpus, omnibus momentis incidet <lb />in ſuperficiem media, denſitate differentia, ſeparantem; </s>
          <s xml:space="preserve">in-<lb />numeras ergo patietur reflectiones &amp; </s>
          <s xml:space="preserve">refractiones in illo cor-<lb />pore <ptr type="noteAnchor" />, ita ut pertranſire non poterit. </s>
          <s xml:space="preserve">Videmus ergo opa-
<ptr xml:id="note-0584-04a" corresp="note-0584-04" type="noteAnchor" />
citatem à poris pendêre; </s>
          <s xml:space="preserve">Repletis enim poris, medio ejuſdem <lb />denſitatis cum particulis ipſis corporis, nullam in corpore <lb />lumen patietur reflectionem, aut refractionem, ſed rectâ <lb />tranſibit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">corpus erit tranſlucidum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0584-03" corresp="note-0584-03a" n="*" anchored="true" place="margin">841.</note>
              <note xml:space="preserve" xml:id="note-0584-04" corresp="note-0584-04a" n="*" anchored="true" place="margin">631. 796. <lb />843.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">841. 631. 796.</note>
        <p>
          <s xml:space="preserve">Licèt non poſſimus experimenta inſtituere, in quibus pori <lb />exactiſſimè medio ejuſdem denſitatis cum particulis replean-<lb />tur, ſequentia nihilominus, ſatis clarè doctrinam Newto-<lb />nianam, de opacitate, evincunt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Charta, ſi aquâ madefiat magis fit tranſlucida; </s>
          <s xml:space="preserve">hæc im-<lb />plet poros &amp; </s>
          <s xml:space="preserve">minus quàm aër denſitate cum particulis <lb />chartæ differt. </s>
          <s xml:space="preserve">Oleum eundem edit effectum.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0585" />
        <pb facs="0585a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0585a-01" />
          <label>0585a-01</label>
        </figure>
        <pb facs="0586" />
        <pb facs="0587" n="(77)" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XVII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Detur fruſtum vitri, craſſitiei duorum pollicum; </s>
          <s xml:space="preserve">dentur <lb />variæ laminæ ejuſdem vitri, quæ, ad ſe mutuo applicatæ, <lb />omnes ſimul craſſitie duos pollices non æquant; </s>
          <s xml:space="preserve">hæ minus <lb />erunt tranſlucidæ, propter aërem interjectum inter laminas, <lb />quàm fruſtum cujus omnes partes cohoerent.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Dentur, ex eodem vitro, duodecim laminæ, quantum <lb />fieri poteſt ejuſdem craſſitiei; </s>
          <s xml:space="preserve">ſex &amp; </s>
          <s xml:space="preserve">ſex ad ſe invicem ap-<lb />plicentur; </s>
          <s xml:space="preserve">ex duabus hiſce congeriebus ſi minus tranſlucida <lb />aquæ immergatur, extracta, tranſluciditate, aliam vincet; <lb /></s>
          <s xml:space="preserve">quia aqua, quæ in hoc caſu interſtitia inter plana replet, <lb />denſitate cum vitro minus differt quàm aër.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Confirmantur ulterius, &amp; </s>
          <s xml:space="preserve">extra omne dubium ponuntur, <lb />quæ de opacitate dicta ſunt innumeris experimentis, quibus <lb />corpora perfectè tranſlucida, ſeparatione partium, non in-<lb />
<ptr xml:id="note-0587-01a" corresp="note-0587-01" type="noteAnchor" />
terveniente corpore ullo opaco, opaca fiunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0587-01" corresp="note-0587-01a" place="margin">844.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Agitetur liquidum quodcunque, perfectè tranſlucidum, <lb />quod in ſpumam poteſt converti, donec in bullas extenſum <lb />ſit; </s>
          <s xml:space="preserve">ſtatim opacum erit, ex interſtitiis aëre repletis.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">Reſina terebinthina, &amp; </s>
          <s xml:space="preserve">aqua, ſunt corpora tranſlucida; <lb /></s>
          <s xml:space="preserve">commixta corpus formant opacum.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Aqua &amp; </s>
          <s xml:space="preserve">oleum commixta ſunt opaca; </s>
          <s xml:space="preserve">licèt ſeparata ſint <lb />tranſlucida.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 8.</head>
        <p>
          <s xml:space="preserve">Vitrum quantumvis tranſlucidum, ſi in pulverem redi-<lb />gatur fit opacum. </s>
          <s xml:space="preserve">Etiam ex rimis in vitro hoc opa-<lb />cum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hiſce omnibus clarè videmus opacitatem dari, quia <lb />inter partes tranſlucidas interjacet medium diverſæ denſi-<lb />tatis; </s>
          <s xml:space="preserve">quod etiam in nubibus obſervatur, quæ opacæ ſunt <lb />ex aëre inter aquæ particulas interpoſito.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si hiſce addamus, quæ de tenuium laminarum coloribus <lb />in capite 22. </s>
          <s xml:space="preserve">ſequenti dicuntur; </s>
          <s xml:space="preserve">nova habebimus experi-
</s>
          <pb facs="0588" n="(78)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
menta, quibus ſolis pleniſſimè probatur corpora lumen in-<lb />tercipere, quia ex particulis tenuibus, medio, denſitate cum <lb />ipſis particulis differente, circumdatis, conſtant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpora quædam opaca exiguam luminis copiam refle-<lb />ctunt, reliquum lumen, innumeris diviſionibus, quas in re-<lb />flectionibus &amp; </s>
          <s xml:space="preserve">refractionibus memoratis patitur, in corpore <lb />extinguitur; </s>
          <s xml:space="preserve">talia funt corpora nigra; </s>
          <s xml:space="preserve">ſi perfectè nigra da-<lb />
<ptr xml:id="note-0588-01a" corresp="note-0588-01" type="noteAnchor" />
rentur, nullum reflecterent lumen; </s>
          <s xml:space="preserve">corpus enim omne, ſi <lb />nullo illuſtretur lumine, &amp; </s>
          <s xml:space="preserve">ita nullos radios reflectat, nigrum <lb />apparet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0588-01" corresp="note-0588-01a" place="margin">845.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpora reliqua opaca coloribus variis induta videntur, <lb />quædam etiam tranſlucida coloribus tinguntur: </s>
          <s xml:space="preserve">Unde hi <lb />oriantur examinandum nunc eſt.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVIII.</head>
        <head rend="italics" xml:space="preserve">De diverſâ radiorum ſolarium refrangibilitate.</head>
        <p>
          <s xml:space="preserve">COrpora variè colorata apparent, licèt iiſdem radiis ſo-<lb />laribus, qui ab illis reflectuntur, illuminentur: </s>
          <s xml:space="preserve">multa <lb />præterea lucis phoenomena, circa colores, minimè negli-<lb />genda dantur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In his ad tria attendendum eſt: </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Ipſi radii examinandi <lb />
<ptr xml:id="note-0588-02a" corresp="note-0588-02" type="noteAnchor" />
ſunt. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Animadvertenda eſt radiorum reflectio. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">Inqui-<lb />rendum in conſtitutionem ſuperficierum corporum diverſè <lb />coloratorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0588-02" corresp="note-0588-02a" place="margin">846.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quod radios ſpectat, prima harum proprietas, hìc no-<lb />tanda, eſt, non omnes radios, in circumſtantiis ſimilibus, <lb />
<ptr xml:id="note-0588-03a" corresp="note-0588-03" type="noteAnchor" />
eandem pati refractionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0588-03" corresp="note-0588-03a" place="margin">847.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Radii, qui talem diverſam refractionem patiuntur, di-<lb />
<ptr xml:id="note-0588-04a" corresp="note-0588-04" type="noteAnchor" />
verſæ refrangibilitatis dicuntur, &amp; </s>
          <s xml:space="preserve">magis refrangibiles, qui <lb />magis refractione inflectuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0588-04" corresp="note-0588-04a" place="margin">848.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Homogenei radii dicuntur, qui refrangibilitate inter ſe <lb />
<ptr xml:id="note-0588-05a" corresp="note-0588-05" type="noteAnchor" />
non differunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0588-05" corresp="note-0588-05a" place="margin">849.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Heterogenei, qui non omnes æqualiter, in iiſdem circum-<lb />
<ptr xml:id="note-0588-06a" corresp="note-0588-06" type="noteAnchor" />
ſtantiis, refractione inflectuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0588-06" corresp="note-0588-06a" place="margin">850.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0589" n="(79)" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XVIII.</fw>
        <p>
          <s xml:space="preserve">Sit inter A B &amp; </s>
          <s xml:space="preserve">C D radius ſolaris, ex innumeris aliis, <lb />
<ptr xml:id="note-0589-01a" corresp="note-0589-01" type="noteAnchor" />
inter ſe parallelis, formatus; </s>
          <s xml:space="preserve">non omnes hi æqualem patiun-<lb />tur refractionem, ſi enim obliquè in ſuperficiem BD me-<lb />dii denſioris incidant, quidam inter BE &amp; </s>
          <s xml:space="preserve">DG refringun-<lb />tur, &amp; </s>
          <s xml:space="preserve">juxta hanc directionem in denſiori medio moventur; <lb /></s>
          <s xml:space="preserve">alii magis inflectuntur, &amp; </s>
          <s xml:space="preserve">inter BF &amp; </s>
          <s xml:space="preserve">DH, juxta harum <lb />linearum ſitum, motum dirigunt; </s>
          <s xml:space="preserve">nulla denique directio <lb />concipi poteſt inter media juxta quam radii quidam non mo-<lb />ventur, in ſingulis punctis inter B &amp; </s>
          <s xml:space="preserve">D: </s>
          <s xml:space="preserve">ita ut radius quan-<lb />tumvis exiguus refractione in innumeros alios dividatur, quia <lb />omnis radius, ut à Sole profluit, quantumvis exiguus hete-<lb />rogeneus eſt, &amp; </s>
          <s xml:space="preserve">conſtans ex innumeris minoribus radiis re-<lb />frangibilibus juxta omnes gradus refrangibilitatis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0589-01" corresp="note-0589-01a" place="margin">TAB. XV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii memorati paralleli, incidentes in ſuperficiem pla-<lb />nam, refractione moventur inter BE &amp; </s>
          <s xml:space="preserve">DH; </s>
          <s xml:space="preserve">quæ lineæ <lb />divergunt inter ſe, &amp; </s>
          <s xml:space="preserve">continuatæ magis ac magis ſeparan-<lb />tur; </s>
          <s xml:space="preserve">ita ut radii memorati refractione diſpergantur. </s>
          <s xml:space="preserve">In <lb />n. </s>
          <s xml:space="preserve">653. </s>
          <s xml:space="preserve">radios conſideravimus homogeneos, ut ubique in tota <lb />
<ptr xml:id="note-0589-02a" corresp="note-0589-02" type="noteAnchor" />
parte præcedenti; </s>
          <s xml:space="preserve">ſatis eſt exigua differentia refrangibilita-<lb />tis in radiis ſolaribus, ut in præcedentibus negligi potuit. <lb /></s>
          <s xml:space="preserve">Quid in homogeneis radiis obtineat etiam prius fuit exami-<lb />nandum, &amp; </s>
          <s xml:space="preserve">quid ex diverſâ refrangibilitate in propoſitioni-<lb />bus mutandum ſit unuſquiſque facile videbit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0589-02" corresp="note-0589-02a" place="margin">851.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut hæc radiorum refrangibilitas ad oculum pateat, au-<lb />
<ptr xml:id="note-0589-03a" corresp="note-0589-03" type="noteAnchor" />
genda eſt divergentia memorata; </s>
          <s xml:space="preserve">quod fit, ſi radii memora-<lb />ti incidant in ſuperficiem EH, medium denſius terminan-<lb />tem, &amp; </s>
          <s xml:space="preserve">hoc à rariori ſeparantem, quæ cum ſuperficie BD <lb />angulum quemcunque format, &amp; </s>
          <s xml:space="preserve">ad hanc ita inclinatur, ut <lb />in illam radii magis refrangibiles obliquius incidant, quàm <lb />minus refrangibiles; </s>
          <s xml:space="preserve">ita ut illi, tranſeundo in medium ra-<lb />rius, ex duplici cauſa, majori refrangibilitate &amp; </s>
          <s xml:space="preserve">majori in-<lb />clinatione, magis detorqueantur, &amp; </s>
          <s xml:space="preserve">ab aliis magis diver-<lb />gant. </s>
          <s xml:space="preserve">Radii minus refrangibiles inter BE &amp; </s>
          <s xml:space="preserve">DG, ſecun-<lb />dò refracti inter EI &amp; </s>
          <s xml:space="preserve">GL motum continuant; </s>
          <s xml:space="preserve">alii inter <lb />FM &amp; </s>
          <s xml:space="preserve">HN: </s>
          <s xml:space="preserve">in quo caſu, ſi, ad diſtantiam quindecim <lb />aut viginti pedum, in plano hi radii cadant, ſenſibiliter <lb />maximè &amp; </s>
          <s xml:space="preserve">minimè refrangibiles ſeparantur, &amp; </s>
          <s xml:space="preserve">totum in-
</s>
          <pb facs="0590" n="(80)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
termedium ſpatium radiis mediâ refrangibilitate præditis il-<lb />luminatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0589-03" corresp="note-0589-03a" place="margin">852.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Detur in laminâ metallicâ in feneſtrâ foramen, diametri <lb />
<ptr xml:id="note-0590-01a" corresp="note-0590-01" type="noteAnchor" />
quartæ partis pollicis, per quod radii ſolares cubiculum <lb />obſcurum intrent, cadant hi in priſma vitreum triangulare <lb />AA, ut in totum ab inferiori ſuperficie reflectantur, (vi-<lb />de exp. </s>
          <s xml:space="preserve">n. </s>
          <s xml:space="preserve">789.) </s>
          <s xml:space="preserve">Duabus refractionibus, quas lumen pati-<lb />tur, radii diverſè refrangibiles non divergunt, &amp; </s>
          <s xml:space="preserve">reflexi ad <lb />ſecundum priſma, etiam vitreum &amp; </s>
          <s xml:space="preserve">triangulare, BB per-<lb />veniunt, eodem modo ac ſi directè à Sole procederent. <lb /></s>
          <s xml:space="preserve">Priſmata hæc ambo circa axes ſunt volubilia, ut ante expli-<lb />catum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">primum AA ligno imponitur &amp; </s>
          <s xml:space="preserve">huic alligatur, ita
<ptr xml:id="note-0590-02a" corresp="note-0590-02" type="noteAnchor" />
tamen, ut rotatio circa axem non impediatur; </s>
          <s xml:space="preserve">lignum hoc <lb />cum globo mobili conjungitur, qui â tripode ſuſtinetur, <lb />quæ machina in praxi geometriæ vulgaris eſt. </s>
          <s xml:space="preserve">Priſma ſe-<lb />cundum BB imponitur ſuſtentaculo S, in cujus lateribus <lb />ſciſſuræ variæ dantur, reſpondentes inter ſe in ſingulis lateri-<lb />bus; </s>
          <s xml:space="preserve">illis priſma ad varias altitudines ſuſtinetur, ſemper ta-<lb />men horizontaliter, ambabus axeos extremitatibus in ſciſſu-<lb />ris reſpondentibus poſitis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0590-01" corresp="note-0590-01a" place="margin">TAB. XV. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0590-02" corresp="note-0590-02a" n="*" anchored="true" place="margin">791.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lumen ad priſma BB perpendiculariter ad axem accedit <lb />&amp; </s>
          <s xml:space="preserve">tranſmittitur, ut in fig. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">demonſtratur, in qua BD &amp; </s>
          <s xml:space="preserve"><lb />EH latera priſmatis deſignant; </s>
          <s xml:space="preserve">etiam ad utrumque latus <lb />æqualiter inclinatur lumen: </s>
          <s xml:space="preserve">quod obtinetur, ſi circa axem <lb />priſma agitetur, lumen enim Solis in hac agitatione adſcen-<lb />dit iterumque deſcendit, ſituſque quæſitus, eſt ubi lumen <lb />maximè elevatur: </s>
          <s xml:space="preserve">ita autem ambo ſunt diſponenda priſma-<lb />ta, ut in hoc caſu lumen horizontaliter ex priſmate BB <lb />exeat. </s>
          <s xml:space="preserve">Radius hicce horizontalis, ad diſtantiam quindecim <lb />aut viginti pedum, cadit in tabulam T, chartâ albâ obte-<lb />ctam, quæ pede ſuſtinetur, quo ad varias altitudines eleva-<lb />tur &amp; </s>
          <s xml:space="preserve">firmatur. </s>
          <s xml:space="preserve">Radii divergentes ad tabulam perveniunt <lb />&amp; </s>
          <s xml:space="preserve">in hac formant imaginem oblongam RV, terminatam, <lb />ad latera, lineis parallelis, in R &amp; </s>
          <s xml:space="preserve">V verò ſemicirculis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Radii ſolares, per foramen rotundum tranſeuntes, ſi ad <lb />certam diſtantiam in planum cadant, in hoc videtur macula
</s>
          <pb facs="0591" n="(81)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XVIII.</fw>
illuminata rotunda, eo major, quo planum magis à foramine <lb />diſtat, quod oritur ex radiis à lateribus Solis provenientibus, <lb />cum illis, qui à centro ad foramen perveniunt angulum <lb />formantibus, &amp; </s>
          <s xml:space="preserve">in foramine hos interſecantibus, ita ut in <lb />plano quaſi imago Solis detur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si radii per priſma BB non tranſirent, &amp; </s>
          <s xml:space="preserve">ad diſtantiam <lb />tabulæ T in planum caderent, Solis imago haberet diametrum <lb />æqualem latitudini imaginis RV; </s>
          <s xml:space="preserve">quæ latitudo refractione <lb />non mutatur; </s>
          <s xml:space="preserve">quia radii, perpendiculariter ad axem, priſma <lb />intrant, &amp; </s>
          <s xml:space="preserve">ad hoc, reſpectu latitudinis imaginis, non in-<lb />clinantur. </s>
          <s xml:space="preserve">Cum autem alio reſpectu oblonga ſit Solis imago, <lb />
<ptr xml:id="note-0591-01a" corresp="note-0591-01" type="noteAnchor" />
clarè inde ſequitur, non omnes radios æqualem paſſos re-<lb />fractionem; </s>
          <s xml:space="preserve">radiis homogeneis rotundam, licèt refractis, <lb />dantibus Solis imaginem. </s>
          <s xml:space="preserve">Minimè refrangibiles radii pertin-<lb />gunt ad R, maximè refrangibiles ad V; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſemicirculis in <lb />R &amp; </s>
          <s xml:space="preserve">V terminatur tota imago RV; </s>
          <s xml:space="preserve">quia ex circularibus <lb />imaginibus tota conſtat: </s>
          <s xml:space="preserve">inter R &amp; </s>
          <s xml:space="preserve">V autem dantur imagi-<lb />nes circulares innumeræ, ex radiis refrangibilitatum inter-<lb />mediarum omnium poſſibilium; </s>
          <s xml:space="preserve">aliter ad latera non lineis <lb />rectis imago RV terminaretur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0591-01" corresp="note-0591-01a" place="margin">853.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In plurimis experimentis, per ſciſſuram aut foramen lu-<lb />men intromitti in locum obſcurum, vidimus, quod ad arbi-<lb />trium artificis reliquimus; </s>
          <s xml:space="preserve">nos autem hac methodo uſi ſumus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In plano ligneo, quo feneſtræ apertura obturatur, datur <lb />
<ptr xml:id="note-0591-02a" corresp="note-0591-02" type="noteAnchor" />
foramen quadratum, cujus latus eſt quatuor pollicum; </s>
          <s xml:space="preserve">cir-<lb />
<ptr xml:id="note-0591-03a" corresp="note-0591-03" type="noteAnchor" />
cumdatur hoc tribus regulis ligneis AB, BC, CD, quæ <lb />retinent tabellam ligneam quadratam R, longitudinis &amp; </s>
          <s xml:space="preserve">la-<lb />titudinis ſex pollicum. </s>
          <s xml:space="preserve">Extrahi poteſt hæc, &amp; </s>
          <s xml:space="preserve">variæ dantur <lb />variis experimentis inſervientes. </s>
          <s xml:space="preserve">Quæ in experimento ſe-<lb />quenti adhibetur, à parte poſteriori in medio excavatur, ut <lb />contineat lentem convexam, objectivam Teleſcopii ſedecim <lb />aut viginti pedum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in medio datur foramen rotundum f, <lb />cujus diameter ſemi pollicem ſuperat, per quod, tranſeun-<lb />do per vitrum, radii ſolares cubiculum intrant. </s>
          <s xml:space="preserve">In ante-<lb />riori parte quoque excavatur tabella Q, non tamen in medio; <lb /></s>
          <s xml:space="preserve">continet cavitas hæc orbem æneum rotundum L, verſus pe-<lb />ripheriam perforatum in f, quod foramen æquale eſt foramini
</s>
          <pb facs="0592" n="(82)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
in ipſâ tabellâ Q, &amp; </s>
          <s xml:space="preserve">cum hoc congruit. </s>
          <s xml:space="preserve">Cum orbe L alius <lb />minor concentricus &amp; </s>
          <s xml:space="preserve">circa centrum mobilis conjungitur; <lb /></s>
          <s xml:space="preserve">Continet hicce foramina varia inæqualia, quæ ſucceſſivè <lb />dum orbis rotatur tranſeunt in f; </s>
          <s xml:space="preserve">ita ut ad libitum, per fo-<lb />ramen majus aut minus, lumen locum obſcurum intret; </s>
          <s xml:space="preserve">quod <lb />in multis experimentis, quæ, ſublatâ lente memoratâ, inſti-<lb />tuuntur, uſu venit. </s>
          <s xml:space="preserve">Clavulo m cum orbe conjuncto, in gy-<lb />rum hicce rotatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0591-02" corresp="note-0591-02a" place="margin">854.</note>
              <note xml:space="preserve" xml:id="note-0591-03" corresp="note-0591-03a" place="margin">TAB. XV. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Trans lentem memoratam radii ſolares, per foramen dia-<lb />metri quartæ partis pollicis, in cubiculum obſcurum intrant; <lb /></s>
          <s xml:space="preserve">his, ad diſtantiam ad quam radii paralleli à lente colliguntur, <lb />Sol exactiſſimè repræſentatur, &amp; </s>
          <s xml:space="preserve">hujus imago circìnatis li-<lb />mitibus terminatur. </s>
          <s xml:space="preserve">Nam radii à ſingulis punctis Solis, qui, <lb />propter hujus immenſam diſtantiam, pro parallelis haberi <lb />poſſunt, ad talem diſtantiam in unum punctum colliguntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si nunc hiſce radiis experimentum ſtatim memoratum in-<lb />
<ptr xml:id="note-0592-01a" corresp="note-0592-01" type="noteAnchor" />
ſtituatur, ſingulæ imagines ex radiis homogeneis, poſitâ ta-<lb />bulâ T ad juſtam diſtantiam, exactè terminantur, ideòque <lb />imago oblonga RV, quæ ex omnibus illis imaginibus for-<lb />matur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0592-01" corresp="note-0592-01a" place="margin">TAB. XV. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Procedit eodem modo hoc experimentum, ſi radii tran-<lb />ſeant per priſma cujuſcunque materiæ aëre denſioris.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Detur ex ligno &amp; </s>
          <s xml:space="preserve">duobus planis vitreis, priſma triangula-<lb />
<ptr xml:id="note-0592-02a" corresp="note-0592-02" type="noteAnchor" />
re, quod aquâ repletur; </s>
          <s xml:space="preserve">tale videtur in BB, (Tab. </s>
          <s xml:space="preserve">XVII. <lb /></s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">hoc ſi adhibeatur loco priſmatis BB in hac fig.</s>
          <s xml:space="preserve">, ex-<lb />perimentum eodem modo procedit; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, tranſeundo per a-<lb />quam, radii heterogenei eodem modo refractionibus ſepa-<lb />rantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0592-02" corresp="note-0592-02a" place="margin">TAB. XV. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Si ſpectator ad diſtantiam quindecim, aut viginti pedum, <lb />intueatur foramen, per quod lumen in cubiculum intromit-<lb />titur, rotundum illud apparet; </s>
          <s xml:space="preserve">ſi priſma triangulare vitreum, <lb />aut aqueum in ultimo experimento memoratum, ante oculos <lb />ponatur ita, ut radii à foramine procedentes, poſt refractio-<lb />nes, ſimiles illis quas lumen in experimentis præcedentibus
</s>
          <pb facs="0593" n="(83)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. III. CAP. XVIII.</fw>
patitur, ad oculos perveniant, foramen oblongum apparebit. <lb /></s>
          <s xml:space="preserve">Situs priſmatis detegitur, ſi, poſito hoc in ſitu horizontali <lb />&amp; </s>
          <s xml:space="preserve">acie ſupernè, paululum circa axem agitetur, quo mo-<lb />tu adſcendit &amp; </s>
          <s xml:space="preserve">deſcendit imago foraminis, &amp; </s>
          <s xml:space="preserve">priſma re-<lb />tineatur in ſitu, in quo foramen maximè depreſſum ap-<lb />paret.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Probat hoc experimentum, æquè ac præcedentia, diver-<lb />ſam radiorum refrangibilitatem; </s>
          <s xml:space="preserve">nam, radiis homogeneis u-<lb />nius cujuſque refrangibilitatis, foramen apparet in focis ima-<lb />ginariis radiorum à ſingulis punctis foraminis procedentium <ptr type="noteAnchor" />,
<ptr xml:id="note-0593-01a" corresp="note-0593-01" type="noteAnchor" />
quæ imago rotunda eſt; </s>
          <s xml:space="preserve">radii, qui variam patiuntur refra-<lb />ctionem, juxta varias directiones oculos intrant, &amp; </s>
          <s xml:space="preserve">imagi-<lb />nes dantur diverſæ, quæ omnes imaginem oblongam, quæ <lb />reverâ videtur, formant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0593-01" corresp="note-0593-01a" n="*" anchored="true" place="margin">737.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hanc autem diverſam refrangibilitatem non à medio re-<lb />
<ptr xml:id="note-0593-02a" corresp="note-0593-02" type="noteAnchor" />
fringente pendere, ſed ab ipſorum radiorum conſtitutione, ex <lb />eo probatur, quod radii, qui in uno caſu maximam patiun-<lb />tur refractionem, in tefractione quacunque à viâ maximè <lb />deflectantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0593-02" corresp="note-0593-02a" place="margin">855.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Iiſdem poſitis quæ in Experimento 1, ad diſtantiam quam-<lb />
<ptr xml:id="note-0593-03a" corresp="note-0593-03" type="noteAnchor" />
cunque à priſmate BB, cadat oblonga Solis imago in priſma <lb />CC verticale, etiam circa axem volubile; </s>
          <s xml:space="preserve">dum radii tran-<lb />ſeunt, agitetur hoc circa axem, ſixumque relinquatur ubi <lb />radii quantum poteſt minimè, per refractiones trans priſma, <lb />à rectâ viâ deflectuntur; </s>
          <s xml:space="preserve">in hoc caſu radii eodem modo per <lb />hoc priſma ac per primum refranguntur; </s>
          <s xml:space="preserve">non autem eo-<lb />dem modo diſperguntur, quod quadratam formaret imagi-<lb />nem. </s>
          <s xml:space="preserve">Hæc autem, manente hujus latitudine, inclinatur in <lb />RV, radiis in V maximè ex viâ deſlexis, ut in refractione <lb />per primum priſma BB.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0593-03" corresp="note-0593-03a" place="margin">TAB. XV. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Demonſtratio, antea data <ptr type="noteAnchor" />, de conſtanti ratione inter
<ptr xml:id="note-0593-04a" corresp="note-0593-04" type="noteAnchor" />
ſinus angulorum incidentiæ &amp; </s>
          <s xml:space="preserve">refractionis, ad radios quoſcun-<lb />
<ptr xml:id="note-0593-05a" corresp="note-0593-05" type="noteAnchor" />
que homogeneos referri debet, poſitâ verò diverſâ refrangi-<lb />bilitate, proportio hæc variat, ut ex experimentis hujus <lb />capitis clarè ſequitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0593-04" corresp="note-0593-04a" place="margin">856.</note>
              <note xml:space="preserve" xml:id="note-0593-05" corresp="note-0593-05a" n="*" anchored="true" place="margin">639.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Refrangibilitatem autem, in ſingulis radiis, omni modo eſſe <lb />
<ptr xml:id="note-0593-06a" corresp="note-0593-06" type="noteAnchor" />
</s>
          <pb facs="0594" n="(84)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
immutabilem experimentis, in ſequentibus memorandis, ex-<lb />tra omne dubium erit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0593-06" corresp="note-0593-06a" place="margin">857.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIX.</head>
        <head rend="italics" xml:space="preserve">De Radiorum Coloribus &amp; horum immutabilitate.</head>
        <p rend="italics">
          <s xml:space="preserve">Diverſa radiorum refrangibilitas cum diverſo colore con-<lb />
<ptr xml:id="note-0594-01a" corresp="note-0594-01" type="noteAnchor" />
juncta eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſinguli radii, pro ut magis aut minus refra-<lb />ctione inflectuntur, colorem ſibi peculiarem, &amp; </s>
          <s xml:space="preserve">omnino im-<lb />mutabilem, habent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0594-01" corresp="note-0594-01a" place="margin">858.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa colores notandum, quod circa alias ſenſationes jam <lb />fuit notatum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">colores ſunt ideæ, quæ nihil cum radiis,
<ptr xml:id="note-0594-02a" corresp="note-0594-02" type="noteAnchor" />
quibus excitantur, commune habent: </s>
          <s xml:space="preserve">definiendum ideo, <lb />quid per radios coloratos &amp; </s>
          <s xml:space="preserve">objecta colorata intelligamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0594-02" corresp="note-0594-02a" n="*" anchored="true" place="margin">502. 580. 716.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Objectum illo colore tinctum dicitur, cujus idea, radiis ab <lb />
<ptr xml:id="note-0594-03a" corresp="note-0594-03" type="noteAnchor" />
objecto reflexis, in mente excitatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0594-03" corresp="note-0594-03a" place="margin">859.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Radii homogenei, qui in retinam impingentes, ideam ali-<lb />
<ptr xml:id="note-0594-04a" corresp="note-0594-04" type="noteAnchor" />
cujus coloris in mente excitant, vocantur radii illius coloris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0594-04" corresp="note-0594-04a" place="margin">860.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dicimus radios ideam excitare, intelligimus radios ſi-<lb />bras agitare, &amp;</s>
          <s xml:space="preserve">, occaſione hujus agitationis, ideam in men-<lb />te dari.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex experimentis capitis præcedentis, diverſum colorem <lb />
<ptr xml:id="note-0594-05a" corresp="note-0594-05" type="noteAnchor" />
habere radios diverſæ refrangibilitatis pleniſſimè conſtat; <lb /></s>
          <s xml:space="preserve">Variis enim coloribus tincta eſt imago Solis, oblonga in illis <lb />experimentis demonſtrata. </s>
          <s xml:space="preserve">Qui radii minimè refractione à <lb />
<ptr xml:id="note-0594-06a" corresp="note-0594-06" type="noteAnchor" />
viâ deflectuntur rubri ſunt, reliqui colores hoc ordine ſequun-<lb />tur, aureus, flavus, viridis, cæruleus, indicus, violaceus, <lb />cujus ultimi coloris ſunt radii maximâ refrangibilitate præ-<lb />diti. </s>
          <s xml:space="preserve">Oblonga memorata Solis imago, ut dictum <ptr type="noteAnchor" />, for-
<ptr xml:id="note-0594-07a" corresp="note-0594-07" type="noteAnchor" />
matur innumeris imaginibus rotundis, ſi harum diametri mi-<lb />nuantur, quod fit interceptis radiis ſolaribus ita, ut ſoli per <lb />priſma tranſeant à centro Solis manantes, non mutantur cen-<lb />tra imaginum peculiarium oblongam formantium; </s>
          <s xml:space="preserve">idcirco <lb />longitudo ah imaginis inter lineas parallelas non mutatur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />hæc ſola ſupereſſet ſi infinitè parva daretur imaginis latitu-
</s>
          <pb facs="0595" />
          <s xml:space="preserve">
<pb facs="0595a" />
<ptr xml:id="fig-0595a-01a" corresp="fig-0595a-01" type="figureAnchor" />
<pb facs="0596" />
<pb facs="0597" n="(85)" /><fw type="head">MATHEMATICA LIB. III. CAP. XIX.</fw>
do: </s>
          <s xml:space="preserve">ita, ut hæc longitudo ſola conſideranda ſit in determi-<lb />nandis colorum limitibus, in ipſâ imagine, hi in hac figurâ <lb />litteris a, b, c, d, e, f, g, h, notantur, &amp; </s>
          <s xml:space="preserve">numerus uni-<lb />cuique colori adſcriptus ſpatium ab hoc in imagine occupa-<lb />tum deſignat, diviſâ totâ imaginis longitudine in partes 360.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0594-05" corresp="note-0594-05a" place="margin">TAB. XVI. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0594-06" corresp="note-0594-06a" place="margin">861.</note>
              <note xml:space="preserve" xml:id="note-0594-07" corresp="note-0594-07a" n="*" anchored="true" place="margin">853.</note>
              <figure xml:id="fig-0595a-01" corresp="fig-0595a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0595a-01" />
                <label>0595a-01</label>
              </figure>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si latitudo imaginis Solis oblonga minuatur, magis in i-<lb />
<ptr xml:id="note-0597-01a" corresp="note-0597-01" type="noteAnchor" />
magine colores heterogenei ſeparantur, quia in ſingulis pun-<lb />ctis minori numero confunduntur imagines peculiares, ex <lb />radiis variarum refrangibilitatum parum inter ſe differentium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0597-01" corresp="note-0597-01a" place="margin">862.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Color cujuſcunque radii, ut &amp; </s>
          <s xml:space="preserve">hujus refrangibilitas, nul-<lb />
<ptr xml:id="note-0597-02a" corresp="note-0597-02" type="noteAnchor" />
lis refractionibus, neque reflexionibus, aut per mixtionibus <lb />quibuſcunque mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0597-02" corresp="note-0597-02a" place="margin">863.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De refractione &amp; </s>
          <s xml:space="preserve">reflectione in hoc capite, de permixtio-<lb />ne in ſequenti, agam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Refrangibilitatem refractione non mutari in exp. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">cap. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0597-03a" corresp="note-0597-03" type="noteAnchor" />
præcedentis probatur; </s>
          <s xml:space="preserve">quod &amp; </s>
          <s xml:space="preserve">etiam ad colorem referri po-<lb />teſt; </s>
          <s xml:space="preserve">hæc eadem experimento ſequenti clariùs evincuntur. <lb /></s>
          <s xml:space="preserve">Circa quod notandum, quod &amp; </s>
          <s xml:space="preserve">de ſequentibus etiam dicen-<lb />dum eſt, experimenta inſtituenda eſſe cum priſmatibus ex <lb />vitro puro venulis immune, his enim irregulariter lumen in <lb />priſmate movetur &amp; </s>
          <s xml:space="preserve">radii refractionibus non ritè ſeparantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0597-03" corresp="note-0597-03a" place="margin">864.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Rebus diſpoſitis ut in exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">capitis præcedentis, inſti-<lb />
<ptr xml:id="note-0597-04a" corresp="note-0597-04" type="noteAnchor" />
tuitur experimentum cum radio ſolari per foramen intrante, <lb />cujus diameter eſt ſemi pollicis; </s>
          <s xml:space="preserve">ſuſtentaculum autem S <lb />priſmatis tale eſt, ut inter latera moveatur tabella t, quæ in <lb />hoc experimento uſu venit, in hac datur foramen F diame-<lb />tri octavæ partis unius pollicis, per hoc tranſmittitur lumen <lb />à priſmate refractum, quo radii in oblongâ imagine melius <lb />inter ſe ſeparantur, radiis magnâ parte interceptis; </s>
          <s xml:space="preserve">imago <lb />hæc oblonga RV, ad diſtantiam decem aut duodecim pe-<lb />dum à priſmate, cadit in tabellam t, ſuſtentaculi ſimilis <lb />priori, in quâ tabellâ etiam exiguum, ut in primâ, datur <lb />foramen F; </s>
          <s xml:space="preserve">per quod radii tranſeunt, qui in ſecundum ca-<lb />dunt priſma, huic ſuſtentaculo impoſitum, &amp; </s>
          <s xml:space="preserve">refringuntur <lb />eodem modo ac per primum; </s>
          <s xml:space="preserve">paululum circa axem agitan-<lb />do primum priſma, adſcendit aut deſcendit imago RV, quo
</s>
          <pb facs="0598" n="(86)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſucceſſivè per foramen radii varii tranſmittuntur; </s>
          <s xml:space="preserve">in omni <lb />caſu radii, per ſecundum priſma refracti, &amp; </s>
          <s xml:space="preserve">in tabulam T, <lb />chartâ albâ obtectam, impingentes, in H non diſperguntur <lb />ſed rotunda eſt imago, ſi radii perpendiculariter in chartam <lb />cadant, etiam ejuſdem coloris cum radiis in ſecundum priſ-<lb />ma cadentibus. </s>
          <s xml:space="preserve">Imago tamen Heo magis elevatur, quo ra-<lb />dii, in refractione, per priſma primum magis à viâ deflectun-<lb />tur, id eſt, magis refrangibiles in uno caſu, in alio caſu <lb />etiam majorem patiuntur refractionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0597-04" corresp="note-0597-04a" place="margin">TAB. XVI. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Refrangibilitatem &amp; </s>
          <s xml:space="preserve">colorem neque reflectione mutari <lb />
<ptr xml:id="note-0598-01a" corresp="note-0598-01" type="noteAnchor" />
experimentis ſequentibus patebit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0598-01" corresp="note-0598-01a" place="margin">865.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Radii partem, ex. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">rubram, imaginis oblongæ colora-<lb />tæ ſæpius memoratæ formantes, à quocunque corpore re-<lb />flectantur, rubri ſunt; </s>
          <s xml:space="preserve">id eſt, omnia corpora in illo lumine <lb />rubra ſunt: </s>
          <s xml:space="preserve">in lumine violaceo ſunt violacea; </s>
          <s xml:space="preserve">in viride ſunt <lb />viridia; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſic de cæteris. </s>
          <s xml:space="preserve">Patet hoc, ſi illud tentetur cum <lb />minio, auripigmento, cœruleo montano, panno utcunque <lb />tincto, &amp;</s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Intret lumen cubiculum obſcurum per duo foramina, dia-<lb />
<ptr xml:id="note-0598-02a" corresp="note-0598-02" type="noteAnchor" />
metri quartæ partis pollicis, in laminâ retundâ volubili, quæ <lb />in feneſtrâ datur; </s>
          <s xml:space="preserve">ſit diſtantia inter hæc circiter duorum pol-<lb />licum; </s>
          <s xml:space="preserve">radii à ſpeculo plano S reflectantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0598-02" corresp="note-0598-02a" place="margin">TAB. XVI. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ita diſponenda lamina &amp; </s>
          <s xml:space="preserve">ſpeculum, ut radii in duo priſma-<lb />ta AA, AA, quæ eidem ſuſtentaculo horizontaliter im-<lb />ponuntur, incidant; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ut imagines oblongæ, refractionibus <lb />horum priſmatum formatæ, ad latus ſeſe mutuo tangant. </s>
          <s xml:space="preserve">Pau-<lb />lulum circa axem agitetur priſma unum, ut color ruber u-<lb />nius imaginis detur ad latus violacei alterius. </s>
          <s xml:space="preserve">Intercipiantur <lb />hi colores, &amp; </s>
          <s xml:space="preserve">quidem ſoli, regulâ ligneâ LL, chartâ albâ <lb />obtectâ, in qua color ille in R hicce in V videtur, dum reli-<lb />quum utriuſque imaginis in parietem, panno nigro obte-<lb />ctum, cadit. </s>
          <s xml:space="preserve">Si ſpectator in O, per priſma BB, intueatur <lb />colores hos R &amp; </s>
          <s xml:space="preserve">V, ut de foramine in exp. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">capitis præ-<lb />cedentis dictum, videbit colores, inter ſe ſeparatos, ru-<lb />brum in r, violaceum in v; </s>
          <s xml:space="preserve">qui ergo reflexus, tranſeundo per
</s>
          <pb facs="0599" n="(87)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XIX.</fw>
priſma BB, majorem patitur refractionem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In experimento 1. </s>
          <s xml:space="preserve">hujus capitis dedimus methodum, qua <lb />radii heterogenei melius ſeparantur quàm in aliis experimen-<lb />tis; </s>
          <s xml:space="preserve">in ſequenti experimento lumina diverſorum colorum <lb />
<ptr xml:id="note-0599-01a" corresp="note-0599-01" type="noteAnchor" />
multò magis homogenea fiunt, quod in ſexto hujus capitis <lb />experimento requiritur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0599-01" corresp="note-0599-01a" place="margin">866.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Intret lumen cubiculum tenebricoſum per foramen, cujus <lb />
<ptr xml:id="note-0599-02a" corresp="note-0599-02" type="noteAnchor" />
diameter ſit pars octava pollicis; </s>
          <s xml:space="preserve">radius Solis, priſmate AA, <lb />ad lentem convexam V, pede ſuſtentatam &amp; </s>
          <s xml:space="preserve">cujus diameter <lb />eſt trium aut quatuor pollicum, reflectitur; </s>
          <s xml:space="preserve">longitudo ra-<lb />diorum incidentis &amp; </s>
          <s xml:space="preserve">reflexi conjunctorum, eſt circiter ſe-<lb />ptem pedum; </s>
          <s xml:space="preserve">lentis convexitas talis eſt, ut, ad diſtantiam <lb />decem aut duodecim pedum à lente, dentur foci radiorum à <lb />ſingulis punctis foraminis procedentium, quibus focis fora-<lb />men poteſt in chartâ repræſentari <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Immediatè poſt len-
<ptr xml:id="note-0599-03a" corresp="note-0599-03" type="noteAnchor" />
tem ponitur priſma BB, quo radii, ut in exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">præceden-<lb />tis, diſperguntur; </s>
          <s xml:space="preserve">poſitâ autem tabulâ T, ad diſtantiam ad <lb />quam à ſingulis punctis foraminis radii colliguntur, dabitur <lb />circinata imago oblonga colorata RV, cujus longitudo ad <lb />latitudinem majorem proportionem habebit, quàm in aliis ex-<lb />perimentis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quæ ideò conſtat ex radiis magis homoge-<lb />neis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eo minus permixtis, quo foramen in feneſtrâ mi-
<ptr xml:id="note-0599-04a" corresp="note-0599-04" type="noteAnchor" />
nus eſt. </s>
          <s xml:space="preserve">Admovendo &amp; </s>
          <s xml:space="preserve">removendo tabulam T, detegitur <lb />diſtantia, ad quam imago maximè eſt diſtincta &amp; </s>
          <s xml:space="preserve">ſine penum-<lb />brâ terminata.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0599-02" corresp="note-0599-02a" place="margin">TAB. XVII. <lb />fig 1.</note>
              <note xml:space="preserve" xml:id="note-0599-03" corresp="note-0599-03a" n="*" anchored="true" place="margin">711.</note>
              <note xml:space="preserve" xml:id="note-0599-04" corresp="note-0599-04a" n="*" anchored="true" place="margin">862.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radios autèm in hoc Experimento ſeparatos, ſatis eſſe <lb />homogeneos, ex eo probatur, quod novâ refractione non <lb />diſpergantur; </s>
          <s xml:space="preserve">hanc autem eſſe homogeneorum proprietatem, <lb />ex æquali refrangibilitate ſequitur; </s>
          <s xml:space="preserve">quod jam experimento <lb />fuit confirmatum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">plenius ſequenti demonſtratur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">864.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Si duo circuli chartacei, diametri circiter unius pollicis, <lb />illuminentur, unus radiis homogeneis coloris cujuſcunque, <lb />alter radiis ſolaribus; </s>
          <s xml:space="preserve">ſi ambo per priſma ad diſtantiam ali-<lb />quot pedum obſerventur, ut in exp. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">hujus capitis; </s>
          <s xml:space="preserve">circu-<lb />lus, colore heterogeneo illuminatus, oblongus apparet, &amp; </s>
          <s xml:space="preserve">va-
</s>
          <pb facs="0600" n="(88)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
riis coloribus tinctus, ut in Exp. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">capitis præceden-<lb />tis; </s>
          <s xml:space="preserve">alterius verò circuli neque color neque figura mu-<lb />tatur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 6.</head>
        <p>
          <s xml:space="preserve">In chartâ albâ ducantur lineæ nigræ inter ſe parallelæ, &amp; </s>
          <s xml:space="preserve"><lb />latæ circiter decimam ſextam pollicis partem; </s>
          <s xml:space="preserve">illuminentur <lb />hæ oblongâ imagine, de qua in experimento quarto, ita, <lb />ut lineæ juxta imaginis longitudinem dirigantur. </s>
          <s xml:space="preserve">Detur ul-<lb />terius lens convexa, diametri quinque aut ſex pollicum, pe-<lb />de ſuſtentata, qualis datur in V (Tab. </s>
          <s xml:space="preserve"><hi rend="small caps">XIX</hi>. </s>
          <s xml:space="preserve">fig. </s>
          <s xml:space="preserve">2.)</s>
          <s xml:space="preserve">, quæ ra-<lb />dios rubros, à puncto radiante emiſſos à vitro ſex pedes di-<lb />ſtanti, ad diſtantiam æqualem colligit. </s>
          <s xml:space="preserve">Si lens hæc detur ad <lb />diſtantiam ſex pedum ab imagine memoratâ, partes linea-<lb />rum, quæ in colore rubro dantur, in chartâ, per radios à <lb />lente collectos, ad diſtantiam etiam ſex pedum exactè re-<lb />præſentantur, in imagine rubrâ; </s>
          <s xml:space="preserve">admovenda autem eſt char-<lb />ta circiter tres pollices cum ſemiſle, ut partes linearum, <lb />colore indico illuminatæ, dìſtinctæ appareant, in imagine <lb />ejuſdem coloris; </s>
          <s xml:space="preserve">colores intermedii dant imagines ad di-<lb />ſtantias intermedias; </s>
          <s xml:space="preserve">violaceus adeo eſt debilis, ut fila in hoc <lb />repræſentari nequeant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Confirmat ergo &amp; </s>
          <s xml:space="preserve">hoc experimentum, reflexorum radio-<lb />rum colorem novâ refractione per lentem non mutari; </s>
          <s xml:space="preserve">ut <lb />&amp; </s>
          <s xml:space="preserve">radios maximè refrangibiles, tranſeundo per lentem aliis <lb />magis inflecti.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Probat etiam Experimentum hoc ultimum, diverſam ra-<lb />
<ptr xml:id="note-0600-01a" corresp="note-0600-01" type="noteAnchor" />
diorum refrangibilitatem in cauſâ eſſe, quo minus Teleſcopia <lb />ſint perfecta. </s>
          <s xml:space="preserve">Foci enim punctorum æquè diſtantium, ad <lb />varias à lente diſtantias dantur, pro vario colore; </s>
          <s xml:space="preserve">unde e-<lb />tiam inæqualiter, â lente oculari diſtant, punctorum repræ-<lb />ſentationes; </s>
          <s xml:space="preserve">quæ ideo per hanc non omnes perfectè videri <lb />queunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0600-01" corresp="note-0600-01a" place="margin">867.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa reflexionem radiorum notandum, radios in totum <lb />
<ptr xml:id="note-0600-02a" corresp="note-0600-02" type="noteAnchor" />
facilius reflecti, qui majorem habent refrangibilitatem; </s>
          <s xml:space="preserve">nam <lb />quo major datur radiorum refractio, quo minor requiritur <lb />obliquitas ut omnes reflectantur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0600-02" corresp="note-0600-02a" place="margin">868.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">793.</note>
        <pb facs="0601" n="(89)" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XX.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Detur priſma diſpoſitum ut ante memoratum <ptr type="noteAnchor" />, ubi vi-
<ptr xml:id="note-0601-01a" corresp="note-0601-01" type="noteAnchor" />
dimus, agitando priſma circa axem, radios primò tranſeun-<lb />tes, auctâ horum inclinatione, in totum reflecti; </s>
          <s xml:space="preserve">ſi autem <lb />lentè in hoc caſu priſma moveatur, videmus radios violaceos <lb />ante omnes alios in totum reflecti, deinde indicos; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">cæ-<lb />teros alios eo ordine, quo in imagine Solis oblongâ, ſæpiſſi-<lb />mè memorata, diſponuntur: </s>
          <s xml:space="preserve">quod patet ſi reflexi, priſmatis <lb />refractione, ſeparentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0601-01" corresp="note-0601-01a" n="*" anchored="true" place="margin">790.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XX.</head>
        <head rend="italics" xml:space="preserve">De Colorum permixtione, ubi de Albore.</head>
        <p>
          <s xml:space="preserve">RAdiorum refrangibilitatem, &amp; </s>
          <s xml:space="preserve">colorem, permixtione <lb />
<ptr xml:id="note-0601-02a" corresp="note-0601-02" type="noteAnchor" />
radiorum variæ refrangibilitatis non mutari dictum <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0601-03a" corresp="note-0601-03" type="noteAnchor" />
quod experimentis probandum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0601-02" corresp="note-0601-02a" place="margin">869.</note>
              <note xml:space="preserve" xml:id="note-0601-03" corresp="note-0601-03a" n="*" anchored="true" place="margin">863.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Inſtituitur hoc, ut tertium capitis præcedentis; </s>
          <s xml:space="preserve">in hoc co-<lb />
<ptr xml:id="note-0601-04a" corresp="note-0601-04" type="noteAnchor" />
lor ruber R, &amp; </s>
          <s xml:space="preserve">violaceus V, confunduntur, in eodem lo-<lb />co regulæ LL cadentes, quæ purpurea in eo loco appa-<lb />ret. </s>
          <s xml:space="preserve">Spectatori tamen, qui hos per priſma BB intuetur, <lb />ſeparati apparent colores, &amp; </s>
          <s xml:space="preserve">neque color, neque refran-<lb />gibilitas, hac colorum confuſione mutantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0601-04" corresp="note-0601-04a" place="margin">TAB. XVI. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Si oblonga colorata Solis imago, (de qua in exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">18.) <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0601-05a" corresp="note-0601-05" type="noteAnchor" />
cadat in RV in lentem convexam L, in exp. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">præ-<lb />cedentis memoratam, &amp; </s>
          <s xml:space="preserve">ad diſtantiam ſex aut ſeptem pe-<lb />dum à priſmate BB diſpoſitam, radii divergentes refra-<lb />ctione lentis convergunt, &amp; </s>
          <s xml:space="preserve">ad diſtantiam novem aut de-<lb />cem pedum ſeſe mutuo interſecant in A; </s>
          <s xml:space="preserve">ſi ad majorem di-<lb />ſtantiam detur Tabula T, radii, qui poſt interſectionem ite-<lb />rum divergunt, diſperſi ad hanc perveniunt; </s>
          <s xml:space="preserve">daturque ite-<lb />rum imago oblonga colorata, ſed colores, propter interſe-<lb />ctionem in A, contrario ordine diſponuntur, non tamen, <lb />permixtione in A, mutantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0601-05" corresp="note-0601-05a" place="margin">TAB. XVII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Omnibus manentibus, ut in Exp. </s>
          <s xml:space="preserve">præcedenti; </s>
          <s xml:space="preserve">ſi chartâ <lb />
<ptr xml:id="note-0601-06a" corresp="note-0601-06" type="noteAnchor" />
</s>
          <pb facs="0602" n="(90)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
nigrâ radii quidam imaginis RV intercipiantur, quod mu-<lb />tat permixtionem, quæ hac methodo ad libitum variatur, <lb />radiorum cæterorum iterum ſeparatorum colores non mu-<lb />tantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0601-06" corresp="note-0601-06a" place="margin">TAB. XVII <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si radii ſolares, ut ad nos perveniunt, in totum ab ali-<lb />
<ptr xml:id="note-0602-01a" corresp="note-0602-01" type="noteAnchor" />
quo corpore reflectantur, hoc album apparet; </s>
          <s xml:space="preserve">radii autem hi <lb />ſunt congeries radiorum variorum colorum <ptr type="noteAnchor" />, unde deduci-
<ptr xml:id="note-0602-02a" corresp="note-0602-02" type="noteAnchor" />
mus permixtionem colorum variorum conſtituere albedinem; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0602-03a" corresp="note-0602-03" type="noteAnchor" />
ſi enim colores, qui obſervantur in oblongâ Solis imagine, <lb />ſæpius memoratâ, eâ proportione, qua in illâ imagine dantur, <lb />inter ſe confundantur, conflatur albedo: </s>
          <s xml:space="preserve">quod &amp; </s>
          <s xml:space="preserve">eo reſpectu <lb />radios immutabiles probat. </s>
          <s xml:space="preserve">A Sole procedentes radii albi ap-<lb />parent, ſi ſeparantur horum colores deteguntur, iterum per-<lb />mixti reſtituitur albor.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0602-01" corresp="note-0602-01a" place="margin">870.</note>
              <note xml:space="preserve" xml:id="note-0602-02" corresp="note-0602-02a" n="*" anchored="true" place="margin">847. 858.</note>
              <note xml:space="preserve" xml:id="note-0602-03" corresp="note-0602-03a" place="margin">871.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Omnibus manentibus, ut in Experimentis duobus præce-<lb />
<ptr xml:id="note-0602-04a" corresp="note-0602-04" type="noteAnchor" />
dentibus; </s>
          <s xml:space="preserve">ponatur tabula T in A, in ipſo loco ubi omnes <lb />radii imaginis RV confunduntur; </s>
          <s xml:space="preserve">albedo dabitur in A; </s>
          <s xml:space="preserve">ſi <lb />color ruber imaginis RV chartâ nigrâ intercipiatur, eva-<lb />neſcit albedo, &amp; </s>
          <s xml:space="preserve">color in A ad cæruleum vergit; </s>
          <s xml:space="preserve">interceptis <lb />verò radiis violaceis &amp; </s>
          <s xml:space="preserve">cæruleis, rubeſcit albor.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0602-04" corresp="note-0602-04a" place="margin">TAB. XVII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Dentur priſmata triangularia tria, ex ligno, &amp; </s>
          <s xml:space="preserve">laminis vi-<lb />
<ptr xml:id="note-0602-05a" corresp="note-0602-05" type="noteAnchor" />
treis, conſtructa, aquam continentia, BB, DD, DD; <lb /></s>
          <s xml:space="preserve">laminæ vitreæ in ſingulis inter ſe formant angulos æquales, <lb />circiter 70. </s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve">; longitudo laminarum eſt ſex aut ſeptem <lb />pollicum, latitudo trium pollicum; </s>
          <s xml:space="preserve">hæ aliter in priſmati-<lb />bus DD, DD, quâm in priſmate BB, diſponuntur; </s>
          <s xml:space="preserve">ita <lb />ut illorum baſes majores ſint. </s>
          <s xml:space="preserve">Refringuntur radii ſolares per <lb />priſma BB, ut in Exp. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">capitis 18.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">ad diſtantiam trium <lb />aut quatuor pedum cadit oblonga Solis imàgo in faciem <lb />priſmatis DD, poſitam in ſitu parallelo faciei priſmatis BB <lb />ex qua radii exeunt. </s>
          <s xml:space="preserve">In ſecundo priſmate radii contrariam <lb />patiuntur refractionem, quàm in primo; </s>
          <s xml:space="preserve">proprer paralle-<lb />liſmum memoratum, &amp; </s>
          <s xml:space="preserve">quia acies anguli à planis vitreis for-<lb />mati in priſmate BB ſurſum, in DD deorſum datur. </s>
          <s xml:space="preserve">Id-<lb />circo ſecundâ refractione deſtruitur prima, &amp; </s>
          <s xml:space="preserve">radii paralleli
</s>
          <pb facs="0603" />
          <s xml:space="preserve">
</s>
          <pb facs="0603a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0603a-01a" corresp="fig-0603a-01" type="figureAnchor" />
</s>
          <pb facs="0604" />
          <s xml:space="preserve">
</s>
          <pb facs="0605" n="91" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XX.</fw>
inter ſe ex priſmate DD in RV exeunt, nam admotis <lb />priſmatibus ita, ut facies parallelæ ſeſe mutuo tangant, tran-<lb />ſibit lumen per medium planis parallelis terminatum, quod <lb />ambo priſmata conjuncta formant, per quod lumen cu-<lb />juſcunque refrangibilitatis ſine directionis mutatione tran-<lb />ſit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Separantur autem priſmata, ut radii heterogenei ſe-
<ptr xml:id="note-0605-01a" corresp="note-0605-01" type="noteAnchor" />
parentur, antequam paralleli iterum fiant; </s>
          <s xml:space="preserve">ſi hi radii colora-<lb />ti cadant in tertium priſma DD, &amp;</s>
          <s xml:space="preserve">, per hoc tranſeundo, <lb />patiantur refractionem ſimilem illi, quàm in primo aut ſecun-<lb />do priſmate paſſi ſunt; </s>
          <s xml:space="preserve">radii in rv exeuntes convergunt, <lb />ex inæqualibus refractionibus in radiis diverſorum colorum, <lb />&amp; </s>
          <s xml:space="preserve">in A concurrunt, in quo loco etiam albor datur, ut in <lb />Experimento præcedenti.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0602-05" corresp="note-0602-05a" place="margin">TAB. XVII. <lb />fig. 3.</note>
              <figure xml:id="fig-0603a-01" corresp="fig-0603a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0603a-01" />
                <label>0603a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0605-01" corresp="note-0605-01a" n="*" anchored="true" place="margin">628.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi>. 6.</head>
        <p>
          <s xml:space="preserve">Si imago Solis oblonga colorata, ut in Exp. </s>
          <s xml:space="preserve"><hi rend="small caps">I</hi>. </s>
          <s xml:space="preserve">Cap. </s>
          <s xml:space="preserve">18.</s>
          <s xml:space="preserve">; <lb />detur, &amp; </s>
          <s xml:space="preserve">ſpectator ad diſtantiam priſmatis, lumen refrin-<lb />gentis, imaginem intueatur, ut de formaine in Exp. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">ejuſ-<lb />dem Capitis dictum, rotundam &amp; </s>
          <s xml:space="preserve">albam videbit imagi-<lb />nem; </s>
          <s xml:space="preserve">ſecundâ refractione primam deſtruente; </s>
          <s xml:space="preserve">quo radii <lb />iterum permixti oculum intrant, quibus in hoc caſu ima-<lb />go alba apparet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Non omnium, qui in imagine Solis oblongâ obſervantur, <lb />
<ptr xml:id="note-0605-02a" corresp="note-0605-02" type="noteAnchor" />
colorum permixtio ad albedinem conflandam neceſſaria eſt, <lb />ipſe radiorum ſolarium albor paululum ad flavum vergit, <lb />radiis flavis pro parte ex permixtione ſublatis albor datur <lb />magis perfectus. </s>
          <s xml:space="preserve">Ex quatuor aut quinque colorum permix-<lb />tione, juſtâ ſervatâ proportione, albedo naſcitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0605-02" corresp="note-0605-02a" place="margin">872.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Colores etiam innumeros primarii, id eſt, homogenei, <lb />
<ptr xml:id="note-0605-03a" corresp="note-0605-03" type="noteAnchor" />
permixti generant, ab homogeneis aut primariis, diverſos. <lb /></s>
          <s xml:space="preserve">Sæpe color homogeneo ſimilis ex aliorum permixtione con-<lb />flatur; </s>
          <s xml:space="preserve">ſed quando nudis oculis inter homogeneum &amp; </s>
          <s xml:space="preserve">permix-<lb />
<ptr xml:id="note-0605-04a" corresp="note-0605-04" type="noteAnchor" />
tum differentia nulla obſervatur, trans priſma ſenſibilis <lb />hæc eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0605-03" corresp="note-0605-03a" place="margin">873.</note>
              <note xml:space="preserve" xml:id="note-0605-04" corresp="note-0605-04a" place="margin">874.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 7.</head>
        <p>
          <s xml:space="preserve">Trans priſma obſerventur objecta quæcunque exigua, ut <lb />litteræ in chartâ, muſcæ &amp; </s>
          <s xml:space="preserve">alia ſimilia; </s>
          <s xml:space="preserve">ſi lumini aperto <lb />exponantur, confuſa apparent; </s>
          <s xml:space="preserve">ſi lumine homogeneo, Fx-
</s>
          <pb facs="0606" n="92" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
perimenti 4, hujus capitis, illuminentur, trans priſma viſa, <lb />diſtinctis limitibus terminantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXI.</head>
        <head rend="italics" xml:space="preserve">De Iride.</head>
        <p>
          <s xml:space="preserve">PEractis quæ radios, quibus corpora illuminantur, ſpe-<lb />ctant, antequam hanc materiam miſſam faciamus, expli-<lb />candum eſt phænomenon, nimium notabile &amp; </s>
          <s xml:space="preserve">vulgare ut <lb />ſilentio prætereatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Arcus cæleſtis, aut Iris, à nemine ſæpiſſimè non fuit ob-<lb />ſervatus; </s>
          <s xml:space="preserve">quibuſdam præmiſſis, explicandum erit unde oria-<lb />tur</s>
        </p>
        <p>
          <s xml:space="preserve">Detur medium denſius, rariori circumdatum, circulo BD <lb />
<ptr xml:id="note-0606-01a" corresp="note-0606-01" type="noteAnchor" />
FH terminatum. </s>
          <s xml:space="preserve">Incidant in illud radii homogenei paralle-<lb />
<ptr xml:id="note-0606-02a" corresp="note-0606-02" type="noteAnchor" />
li inter ſe, quorum unus eſt AB; </s>
          <s xml:space="preserve">ducatur ſemidiameter <lb />CB continuata ad N; </s>
          <s xml:space="preserve">perpendicularis eſt hæc ad ſuperfi-<lb />ciem media dirimentem; </s>
          <s xml:space="preserve">ABN eſt ergo angulus inciden-<lb />tiæ hic æqualis eſt angulo oppoſito ad verticem CBL, cu-<lb />jus ſinus eſt CL, per centrum ad BL perpendicularis; </s>
          <s xml:space="preserve">re-<lb />fringitur radius ad perpendicularem <ptr type="noteAnchor" />, eſtque angulus re-
<ptr xml:id="note-0606-03a" corresp="note-0606-03" type="noteAnchor" />
fractionis CBM, cujus ſinus eſt CM, à C ad BD perpen-<lb />dicularis: </s>
          <s xml:space="preserve">pro ſingulis radiis, ut AB, datur eadem ratio in-<lb />ter lineas, ut CL &amp; </s>
          <s xml:space="preserve">CM <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Radius BD pro parte in me-
<ptr xml:id="note-0606-04a" corresp="note-0606-04" type="noteAnchor" />
dium rarius penetrat juxta DE, pro parte reflectitur per <lb />DF; </s>
          <s xml:space="preserve">efficitque angulum reflectionis CDF æqualem angulo <lb />incidentiæ BDC<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">unde BD &amp; </s>
          <s xml:space="preserve">DF æquales ſunt. </s>
          <s xml:space="preserve">Ra-
<ptr xml:id="note-0606-05a" corresp="note-0606-05" type="noteAnchor" />
dius DF pro parte etiam ex denſiori medio exit per FG, <lb />pro parte reflectitur per FH; </s>
          <s xml:space="preserve">qui eodem modo pro parte <lb />exit per HI, &amp; </s>
          <s xml:space="preserve">pro parte reflectitur: </s>
          <s xml:space="preserve">hanc autem refle-<lb />ctionem, ulterioresque reflectiones &amp; </s>
          <s xml:space="preserve">refractiones non <lb />conſideramus; </s>
          <s xml:space="preserve">nimium debiles ſunt, propter varias quas lu-<lb />men paſſum eſt diviſiones.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0606-01" corresp="note-0606-01a" place="margin">875.</note>
              <note xml:space="preserve" xml:id="note-0606-02" corresp="note-0606-02a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0606-03" corresp="note-0606-03a" n="*" anchored="true" place="margin">624.</note>
              <note xml:space="preserve" xml:id="note-0606-04" corresp="note-0606-04a" n="*" anchored="true" place="margin">639.</note>
              <note xml:space="preserve" xml:id="note-0606-05" corresp="note-0606-05a" n="*" anchored="true" place="margin">805.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radius FG, qui poſt unicam reflectionem medium den-<lb />ſius exit, cum radio incidente AB format angulum GPA, <lb />qui variat in diverſis radiis incidentibus; </s>
          <s xml:space="preserve">Ideò, licèt hi paral-<lb />leli fuerint, diſperguntur, poſt unicam reflectionem exeuntes, <lb />
<ptr xml:id="note-0606-06a" corresp="note-0606-06" type="noteAnchor" />
ut ex inſpectione figuræ patet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0606-06" corresp="note-0606-06a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0607" />
        <pb facs="0607a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0607a-01" />
          <label>0607a-01</label>
        </figure>
        <pb facs="0608" />
        <pb facs="0609" n="93" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XXI.</fw>
        <p>
          <s xml:space="preserve">Radius EE, qui continuatus per centrum C tranſit, neque <lb />reflectione neque refractione à viâ deflectitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0609-01a" corresp="note-0609-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0609-01" corresp="note-0609-01a" n="*" anchored="true" place="margin">806. 629.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Recedendo ab hoc radio, ad incidentem continuò minus <lb />ac minus inclinatur radius, qui redit. </s>
          <s xml:space="preserve">Sic radius DD, qui <lb />per dd exit ex medio denſiori, &amp; </s>
          <s xml:space="preserve">per hanc lineam regredi-<lb />tur, cum dd majorem angulum format, quàm, cum ſuis re-<lb />deuntibus, &amp; </s>
          <s xml:space="preserve">ex medio denſiori exeuntibus, efficiunt radii <lb />intermedii inter DD &amp; </s>
          <s xml:space="preserve">EE.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Datur radius ut BB, cujus reſpectu inclinatio hæc eſt <lb />
<ptr xml:id="note-0609-02a" corresp="note-0609-02" type="noteAnchor" />
omnium minima, id eſt, qui efficit angulum ut GPA <lb />(fig. </s>
          <s xml:space="preserve">1.) </s>
          <s xml:space="preserve">omnium maximum. </s>
          <s xml:space="preserve">Ultra BB, magis ad inci-<lb />dentes inclinantur radii redeuntes; </s>
          <s xml:space="preserve">ſic AA per aa redit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0609-02" corresp="note-0609-02a" place="margin">876.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hac radiorum redeuntium diſperſione, recedendo à <lb />medio denſiori debiliores continuò ſunt, &amp; </s>
          <s xml:space="preserve">horum color non, <lb />
<ptr xml:id="note-0609-03a" corresp="note-0609-03" type="noteAnchor" />
per totum ſpatium quod implent, percipi poteſt, licèt inciden-<lb />tium color vividus ſit. </s>
          <s xml:space="preserve">Color, in radiis redeuntibus, ſenſibilis <lb />tantùm eſt, ubi radii vicini paralleli ſunt &amp; </s>
          <s xml:space="preserve">adjacentes pa-<lb />rum admodum divergunt, ita ut ad magnam diſtantiam ſatis <lb />denſi ſint, ut percipiantur. </s>
          <s xml:space="preserve">Hi ſoli efficaces dicuntur, &amp; </s>
          <s xml:space="preserve"><lb />dantur, ubi radii vicini incidentes refracti concurrunt in <lb />ipſo puncto reflectionis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0609-03" corresp="note-0609-03a" place="margin">877.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint AB, ab radii vicini, paralleli inter ſe, incidentes <lb />
<ptr xml:id="note-0609-04a" corresp="note-0609-04" type="noteAnchor" />
in ſuperficiem circularem medium denſius terminantem; </s>
          <s xml:space="preserve">ſi <lb />hi refracti, per BD, bd, concurrant in D, puncto reflexio-<lb />nis, reflexi, DF, D f, æquales angulos cum F f formabunt, <lb />ac DB, D b cum B b; </s>
          <s xml:space="preserve">ideoque refracti FG, f g paralleli <ptr type="noteAnchor" />
<ptr xml:id="note-0609-05a" corresp="note-0609-05" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">efficaces erunt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In hoc caſu ſequenti methodo deter-
<ptr xml:id="note-0609-06a" corresp="note-0609-06" type="noteAnchor" />
minatur angulus ab incidente cum redeunte formatus, id eſt, <lb />angulus APG, qui hìc eſt omnium maximus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0609-04" corresp="note-0609-04a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0609-05" corresp="note-0609-05a" n="*" anchored="true" place="margin">627.</note>
              <note xml:space="preserve" xml:id="note-0609-06" corresp="note-0609-06a" n="*" anchored="true" place="margin">877.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus inter ſinus angulorum incidentiæ &amp; </s>
          <s xml:space="preserve">refractionis, <lb />
<ptr xml:id="note-0609-07a" corresp="note-0609-07" type="noteAnchor" />
quando lumen ex medio rariori, quo denſius circumdatur, <lb />in denſius, ipſo circulo contentum, penetrat, rationem <lb />dari, quæ datur inter J &amp; </s>
          <s xml:space="preserve">R. </s>
          <s xml:space="preserve">Eſt ergo, ductis perpendicu-<lb />lari C m ad b D, &amp; </s>
          <s xml:space="preserve">arcu mn centro C, &amp; </s>
          <s xml:space="preserve">ſemidiametro <lb />C m,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0609-07" corresp="note-0609-07a" place="margin">878.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">J, R:: CL, CM:: C l, C m:: CL--C l = L l, <lb />CM--C m = M n.</head>
        <pb facs="0610" n="94" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Ducatur B o ad BL perpendicularis; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">B p ad BD nor-<lb />malis; </s>
          <s xml:space="preserve">deturque bp, quæ cum B p angulum rectum format; <lb /></s>
          <s xml:space="preserve">tandem lineis jungantur puncta B, C, &amp; </s>
          <s xml:space="preserve">M, m.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Triangula B bo, BCL ſunt ſimilia; </s>
          <s xml:space="preserve">ſunt enium rectangula, <lb />&amp; </s>
          <s xml:space="preserve">anguli o B b &amp; </s>
          <s xml:space="preserve">CBL, quorum ſingulorum differentia cum <lb />angulo recto eſt angulus o BC, ſunt æquales.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Eodem modo probatur, ſimilia eſſe triangula BMC &amp; </s>
          <s xml:space="preserve"><lb />B bp; </s>
          <s xml:space="preserve">huic etiam ſimile eſt triangulum M mn rectangulum <lb />in n, nam latera M n, B p, perpendicularia lineæ BD, ſunt <lb />parallela; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">M m &amp; </s>
          <s xml:space="preserve">B b, quia in partes æquales, in M <lb />&amp; </s>
          <s xml:space="preserve">m, biſecantur lineæ BD, b D. </s>
          <s xml:space="preserve">Idcirco etiam B b eſt <lb />dupla M m, &amp; </s>
          <s xml:space="preserve">B p dupla mn. </s>
          <s xml:space="preserve">Ex hiſce deducimus</s>
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">BC, BL:: B b, B o.</head>
        <head xml:space="preserve">BC, BM:: B b, B p.</head>
        <p>
          <s xml:space="preserve">ergo</s>
        </p>
        <p>
          <s xml:space="preserve">BL, BM:</s>
          <s xml:space="preserve">: B o = L l, B p = 2 M n:</s>
          <s xml:space="preserve">: J, 2R:</s>
          <s xml:space="preserve">: CL, <lb />2 CM, conferendo haſce proportiones cum ante memo-<lb />ratâ proportione.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Cùm proportionalium quantitatum, quadrata proportio-<lb />nalia ſint, datur</s>
        </p>
        <p>
          <s xml:space="preserve">B L<hi rend="superscript">q</hi>, CL<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: BM<hi rend="superscript">q</hi>, 4CM<hi rend="superscript">q</hi>.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Unde deducimus</s>
        </p>
        <p>
          <s xml:space="preserve">BL<hi rend="superscript">q</hi> + CL<hi rend="superscript">q</hi> = BC<hi rend="superscript">q</hi>, BL<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: BM<hi rend="superscript">q</hi> + 4CM<hi rend="superscript">q</hi> = BC<hi rend="superscript">q</hi> +  <lb />3CM<hi rend="superscript">q</hi>, BM<hi rend="superscript">q</hi> = BC<hi rend="superscript">q</hi>-CM<hi rend="superscript">q</hi> = BL<hi rend="superscript">q</hi> + LC<hi rend="superscript">q</hi>-CM<hi rend="superscript">q</hi>.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Subtrahendo primum &amp; </s>
          <s xml:space="preserve">ſecundum terminum è tertio &amp; </s>
          <s xml:space="preserve"><lb />quarto, quo proportio non mutatur, habemus <lb />BC<hi rend="superscript">q</hi>, BL<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: 3CM<hi rend="superscript">q</hi>, LC<hi rend="superscript">q</hi>-CM<hi rend="superscript">q</hi>:</s>
          <s xml:space="preserve">: 3R<hi rend="superscript">q</hi>, J<hi rend="superscript">q</hi>-R<hi rend="superscript">q</hi>; <lb /></s>
          <s xml:space="preserve">datur enim inter CM &amp; </s>
          <s xml:space="preserve">LC eadem ratio ac inter <lb />R &amp; </s>
          <s xml:space="preserve">J.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si ergo nota ſit ratio inter R &amp; </s>
          <s xml:space="preserve">J, innoteſcit ratio inter <lb />ſemidiametrum BC, &amp; </s>
          <s xml:space="preserve">lineam BL, quæ eſt ſinus anguli <lb />BCL, qui angulus idcirco datur; </s>
          <s xml:space="preserve">notus eſt igitur arcus <lb />BN, ut &amp; </s>
          <s xml:space="preserve">FG, ſunt enim hi æquales.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dato ſinu BL, datur &amp; </s>
          <s xml:space="preserve">BM ſinus anguli BCM; </s>
          <s xml:space="preserve">quia ut <lb />ante vidimus</s>
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">BL, BM:: J, 2 R.</head>
        <p>
          <s xml:space="preserve">Determinatur ergo arcus BD cui æqualis eſt DF.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0611" n="95" />
        <fw type="head">MATHEMATICA LIB. III. CAP. XXI.</fw>
        <p>
          <s xml:space="preserve">Ex hiſce facilè deducimus arcus NH &amp; </s>
          <s xml:space="preserve">BF; </s>
          <s xml:space="preserve">ſi ex hoc <lb />
<ptr xml:id="note-0611-01a" corresp="note-0611-01" type="noteAnchor" />
ille ſubtrahatur, &amp; </s>
          <s xml:space="preserve">reſiduum in duas partes æquales divida-<lb />tur, habetur, ut notum eſt, menſura anguli APG.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0611-01" corresp="note-0611-01a" place="margin">879.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando ratio inter J &amp; </s>
          <s xml:space="preserve">R variat, mutatur angulus APG; <lb /></s>
          <s xml:space="preserve">qui idèo diverſus eſt pro variâ radiorum refrangibilitate.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Si Radiis hæterogeneis, ut à Sole profluunt, illuſtretur ſu-<lb />
<ptr xml:id="note-0611-02a" corresp="note-0611-02" type="noteAnchor" />
perficies memorata, efficaces diverſorum colorum non angulos <lb />æquales cum incidentibus efficiunt, &amp; </s>
          <s xml:space="preserve">ſic ope hujus refractionis <lb />ſeparantur colores.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0611-02" corresp="note-0611-02a" place="margin">880.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> I.</head>
        <p>
          <s xml:space="preserve">Intret lumen ſolare in cubiculum obſcurum, per ſciſluram in <lb />
<ptr xml:id="note-0611-03a" corresp="note-0611-03" type="noteAnchor" />
orbe mobili O, &amp; </s>
          <s xml:space="preserve">à ſpeculo S horizontaliter reflexum, tranſeat <lb />per ſciſſuram in tabellâ T; </s>
          <s xml:space="preserve">ut ante explicatum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Detur phiala
<ptr xml:id="note-0611-04a" corresp="note-0611-04" type="noteAnchor" />
exactè cylindrica, ex vitro puro, aquâ repleta. </s>
          <s xml:space="preserve">Incidat ra-<lb />dius in phialæ ſuperficiem in fg, in aquâ refringitur verſus <lb />hi, &amp; </s>
          <s xml:space="preserve">ibi reflectitur, &amp; </s>
          <s xml:space="preserve">in lm phialam exit. </s>
          <s xml:space="preserve">Facilè ita di-<lb />ſponitur hæc, ut radii hi ſint efficaces; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, propter latitudi-<lb />nem radii incidentis, efficaces omnium colorum eodem <lb />tempore exeunt; </s>
          <s xml:space="preserve">nam parum hi in incidentiâ diſtant. </s>
          <s xml:space="preserve">Si hi <lb />radii efficaces in chartam albam, ad diſtantiam quatuor aut <lb />quinque pedum à phialâ, impingant, dantur in chartâ faſciæ <lb />verticales, variorum colorum homogeneorum, ex radiis ef-<lb />ficacibus ſingulorum colorum oriundæ, ſi etiam, ad diſtan-<lb />tiam aliquot pedum à phialâ, oculus detur ubicunque ut in <lb />N, in radiis hiſce efficacibus, videt in phialâ illum colorem, <lb />cujus radii oculum intrant; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">motu oculi ſucceſſivè omnes <lb />percipit colores antea memoratos <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0611-05a" corresp="note-0611-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0611-03" corresp="note-0611-03a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0611-04" corresp="note-0611-04a" n="*" anchored="true" place="margin">630.</note>
              <note xml:space="preserve" xml:id="note-0611-05" corresp="note-0611-05a" n="*" anchored="true" place="margin">861.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quod autem ſpectat radios, qui poſt duplam in medio den-<lb />
<ptr xml:id="note-0611-06a" corresp="note-0611-06" type="noteAnchor" />
ſiori reflectionem hoc exeunt, efficaces erunt, ſi poſt pri-<lb />
<ptr xml:id="note-0611-07a" corresp="note-0611-07" type="noteAnchor" />
mam reflectionem paralleli ſint: </s>
          <s xml:space="preserve">tunc enim FH, fh ad <lb />H h eodem modo inclinantur ac BD, bd ad B b; </s>
          <s xml:space="preserve">ideòque <lb />poſitis incidentibus AB, ab parallelis, exeuntes HI, hi, e-<lb />tiam paralleli erunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0611-08a" corresp="note-0611-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0611-06" corresp="note-0611-06a" place="margin">881.</note>
              <note xml:space="preserve" xml:id="note-0611-07" corresp="note-0611-07a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0611-08" corresp="note-0611-08a" n="*" anchored="true" place="margin">627.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc caſu d D eſt dimidium differentiæ inter arcus <lb />DF &amp; </s>
          <s xml:space="preserve">df, aut DB &amp; </s>
          <s xml:space="preserve">db; </s>
          <s xml:space="preserve">horum autem differentia eſt <lb />B b minus D d; </s>
          <s xml:space="preserve">ſi ergo hicce ex illo ſubtrahatur, ſupere-<lb />rit duplum arcus D d, cujus triplum eſt idcirco B b. </s>
          <s xml:space="preserve">Si
</s>
          <pb facs="0612" n="96" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
lineis jungantur puncta D, d, &amp; </s>
          <s xml:space="preserve">B, b, triangula BE b &amp; </s>
          <s xml:space="preserve"><lb />DE d erunt ſimilia, ut notum eſt; </s>
          <s xml:space="preserve">quod ergo etiam obti-<lb />net, ſi ipſi arcus B b, D d fuerint minimi, ita ut pro lineis <lb />rectis haberi poſſint.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Datur idcirco inter ED &amp; </s>
          <s xml:space="preserve">E b ratio, quæ inter hos ar-<lb />cus obtinet, id eſt ED eſt pars tertia ipſius E b, aut EB; <lb /></s>
          <s xml:space="preserve">quia exiguum admodum ponimus arcum B b. </s>
          <s xml:space="preserve">Dividitur <lb />igitur MD in duas partes æquales in E; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ME eſt pars <lb />tertia ipſius EB.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si nunc, ut in fig. </s>
          <s xml:space="preserve">3.</s>
          <s xml:space="preserve">, formentur triangula B ob, B pb <lb />&amp; </s>
          <s xml:space="preserve">M mn, erit M m pars tertia B b, &amp; </s>
          <s xml:space="preserve">B p triplum ipſius <lb />M n; </s>
          <s xml:space="preserve">ſi nunc, mutatis mutandis, ad hanc figuram appli-<lb />cemus quæ reſpectu fig. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">demonſtrata ſunt <ptr type="noteAnchor" />, quia in hac
<ptr xml:id="note-0612-01a" corresp="note-0612-01" type="noteAnchor" />
B p valet 3 M n, cujus quadratum eſt 9 M n<hi rend="superscript">9</hi>, habe-<lb />mus</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0612-01" corresp="note-0612-01a" n="*" anchored="true" place="margin">878.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">BC<hi rend="superscript">q</hi>, BL<hi rend="superscript">q</hi>:: 8 R<hi rend="superscript">q</hi>, J<hi rend="superscript">q</hi>-R<hi rend="superscript">q</hi></head>
        <p>
          <s xml:space="preserve">Ex qua proportione, ut de fig. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">dictum, detegitur ar-<lb />cus BN, cui æqualis HG; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quia in hoc caſu</s>
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">BL, BM:: J, 3R,</head>
        <p>
          <s xml:space="preserve">Innoteſcit etiam arcus BD, cui propter angulos reflectio-<lb />nis, æquales angulis incidentiæ <ptr type="noteAnchor" />, æquales ſunt DF &amp; </s>
          <s xml:space="preserve">FH.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0612-02a" corresp="note-0612-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0612-02" corresp="note-0612-02a" n="*" anchored="true" place="margin">805.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex quibus datis, facilè eliciuntur arcus GFDN &amp; </s>
          <s xml:space="preserve">BH, <lb />
<ptr xml:id="note-0612-03a" corresp="note-0612-03" type="noteAnchor" />
quorum ſemi differentia eſt menſura anguli HPB, ab ex-<lb />eunte radio cum incidente formato; </s>
          <s xml:space="preserve">qui angulus in hoc <lb />caſu omnium ſimilium eſt minimus, &amp; </s>
          <s xml:space="preserve">pro diversâ radiorum <lb />refrangibilitâte diverſus. </s>
          <s xml:space="preserve">Unde etiam in hoc caſu poſt du-<lb />
<ptr xml:id="note-0612-04a" corresp="note-0612-04" type="noteAnchor" />
plicem reflectionem efficaces variorum colorum, poſitis inci-<lb />dentibus parallelis, ſeparantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0612-03" corresp="note-0612-03a" place="margin">882.</note>
              <note xml:space="preserve" xml:id="note-0612-04" corresp="note-0612-04a" place="margin">883.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Eodem modo ac præcedens experimentum hoc inſtitui-<lb />
<ptr xml:id="note-0612-05a" corresp="note-0612-05" type="noteAnchor" />
tur, ſitus phialæ tantum paululum mutatur, ut, poſt duas in <lb />phialâ reflexiones, radii ad oculum aut chartam verſus N per-<lb />veniant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0612-05" corresp="note-0612-05a" place="margin"><hi rend="small caps">TAB. XVIII</hi>. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Huc uſque explicata ad Iridem applicari poſſunt; </s>
          <s xml:space="preserve">ad quod <lb />
<ptr xml:id="note-0612-06a" corresp="note-0612-06" type="noteAnchor" />
phænomenon guttæ aqueæ in aëre ſuſpenſæ requiruntur; </s>
          <s xml:space="preserve">ut <lb />ſpectator, adverſo Sole inter hunc &amp; </s>
          <s xml:space="preserve">guttas collocetur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ut <lb />poſt guttas nubes detur obſcura, ut magis ſenſibiles ſint colo-
</s>
          <pb facs="0613" n="97" />
          <s xml:space="preserve"><fw type="head">MATHEMATIC A LIB. III. CAP. XXI.</fw>
res, qui vix percipiuntur, ſi lumen vividum eodem tempo-<lb />re oculos intret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0612-06" corresp="note-0612-06a" place="margin">884.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si, hiſce poſitis, concipiamus ſingulas guttas ſecari planis, <lb />per Solem &amp; </s>
          <s xml:space="preserve">oculum ſpectatoris tranſeuntibus, quæ de me-<lb />dio, ſuperficie circulari terminato, demonſtrata ſunt <ptr type="noteAnchor" />, ad
<ptr xml:id="note-0613-01a" corresp="note-0613-01" type="noteAnchor" />
ſingulas haſce ſectiones poterunt applicari.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0613-01" corresp="note-0613-01a" n="*" anchored="true" place="margin">878. 879. 880. <lb />881. 882. 883.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hìc autem agitur de radiis ex aëre in aquam penetranti-<lb />bus. </s>
          <s xml:space="preserve">In radiis rubris, id eſt, minimè omnium refrangibili-<lb />bus, ratio inter ſinum anguli incidentiæ &amp; </s>
          <s xml:space="preserve">ſinum anguli re-<lb />fractionis, id eſt, inter J &amp; </s>
          <s xml:space="preserve">R, eſt 108. </s>
          <s xml:space="preserve">ad 81. </s>
          <s xml:space="preserve">aut quæ ea-<lb />dem eſt, 4. </s>
          <s xml:space="preserve">ad 3.</s>
          <s xml:space="preserve">; cum quibus numeris ſi computatio inea-<lb />tur, angulus APG (fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">erit 42. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">2 <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">angulus
<ptr xml:id="note-0613-02a" corresp="note-0613-02" type="noteAnchor" />
API (fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">erit 50. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">57′. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi de radiis violaceis aga-
<ptr xml:id="note-0613-03a" corresp="note-0613-03" type="noteAnchor" />
tur, J eſt ad R, ut 109. </s>
          <s xml:space="preserve">ad 81.</s>
          <s xml:space="preserve">; qui numeri dant angulos <lb />APG (fig. </s>
          <s xml:space="preserve">3.) </s>
          <s xml:space="preserve">40. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">17′. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">API (fig. </s>
          <s xml:space="preserve">4.) </s>
          <s xml:space="preserve">54. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">7′. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0613-04a" corresp="note-0613-04" type="noteAnchor" />
<ptr xml:id="note-0613-05a" corresp="note-0613-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0613-02" corresp="note-0613-02a" n="*" anchored="true" place="margin">879.</note>
              <note xml:space="preserve" xml:id="note-0613-03" corresp="note-0613-03a" n="*" anchored="true" place="margin">882.</note>
              <note xml:space="preserve" xml:id="note-0613-04" corresp="note-0613-04a" n="*" anchored="true" place="margin">879.</note>
              <note xml:space="preserve" xml:id="note-0613-05" corresp="note-0613-05a" n="*" anchored="true" place="margin">882.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sint nunc guttæ per aërem diffuſæ, &amp; </s>
          <s xml:space="preserve">radiis ſolaribus <lb />
<ptr xml:id="note-0613-06a" corresp="note-0613-06" type="noteAnchor" />
illuſtratæ, parallelis inter ſe &amp; </s>
          <s xml:space="preserve">lineæ OF, per oculum ſpe-<lb />ctatoris tranſeunti. </s>
          <s xml:space="preserve">Concipiantur lineæ e O, EO, b O, <lb />BO &amp; </s>
          <s xml:space="preserve">ſint anguli e OF 40. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">17′.</s>
          <s xml:space="preserve">, EOF 42. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">2′.</s>
          <s xml:space="preserve">, <lb />b OF 50. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">57′.</s>
          <s xml:space="preserve">, BOF 54. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">7′.</s>
          <s xml:space="preserve">: eædem hæ lineæ cum radiis <lb />incidentibus de, DE, ab, AB, angulos formant memo-<lb />ratis reſpectivè æquales; </s>
          <s xml:space="preserve">ideò, ſi guttæ concipiantur in e, E, <lb />b, B, radii efficaces violacei, poſt unicam reflectionem in gut-<lb />tâ e, oculum intrant; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ad oculum efficaces rubri ex guttâ E <lb />perveniunt; </s>
          <s xml:space="preserve">itidem poſt unicam reflectionem, reliqui colo-<lb />res intermedii inter e &amp; </s>
          <s xml:space="preserve">E obſervantur, ordine antea memo-<lb />rato <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Poſt duas in guttâ reflectiones ex guttâ b radii ef-
<ptr xml:id="note-0613-07a" corresp="note-0613-07" type="noteAnchor" />
ficaces rubri ad oculum perveniunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">violacei efficaces ex <lb />guttâ B; </s>
          <s xml:space="preserve">inter has guttas colores intermedii apparent, eo-<lb />dem modo ac inter E, e, ſed ordine contrario diſpo-<lb />nuntur, &amp; </s>
          <s xml:space="preserve">propter duplicem reflectionem etiam debiliores <lb />ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0613-06" corresp="note-0613-06a" place="margin"><hi rend="small caps">TAB. XIX</hi>. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0613-07" corresp="note-0613-07a" n="*" anchored="true" place="margin">861.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus lineam ut O e, circa lineam OF fixam, ſer-<lb />vato angulo e OF, revolvi, &amp; </s>
          <s xml:space="preserve">conum aut partem ſuperficiei <lb />coni formare; </s>
          <s xml:space="preserve">in omni ſitu linea e O cum radiis ſolaribus, <lb />parallelis inter ſe &amp; </s>
          <s xml:space="preserve">lineæ OF, formabit angulum 40. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">17′. <lb /></s>
          <s xml:space="preserve">Siergo guttæ juxta partem ſuperficiei hujus coni ſive ad ean-<lb />
<ptr xml:id="note-0613-08a" corresp="note-0613-08" type="noteAnchor" />
</s>
          <pb facs="0614" n="(98)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
dem ſive ad diverſas diſtantias diffuſæ fuerint, videbit oculus <lb />arcum violaceum: </s>
          <s xml:space="preserve">idem dicendum eſt de cæteris coloribus; <lb /></s>
          <s xml:space="preserve">ideòque, datis guttis, in aëre ſuſpenſis, videt arcum latitudinis <lb />eE, coloribus homogeneis, ante memoratis <ptr type="noteAnchor" />, tinctum, eodem
<ptr xml:id="note-0614-01a" corresp="note-0614-01" type="noteAnchor" />
ordine diſpoſitis ac in experimentis cum priſmatibus; </s>
          <s xml:space="preserve">quia <lb />in guttis æquè ac inpriſmate radii hæterogenii ſeparantur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0614-02a" corresp="note-0614-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0613-08" corresp="note-0613-08a" place="margin">885.</note>
              <note xml:space="preserve" xml:id="note-0614-01" corresp="note-0614-01a" n="*" anchored="true" place="margin">861.</note>
              <note xml:space="preserve" xml:id="note-0614-02" corresp="note-0614-02a" n="*" anchored="true" place="margin">852. 880.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simili ratiocinio patet dari arcum, latiorem, primum cir-<lb />
<ptr xml:id="note-0614-03a" corresp="note-0614-03" type="noteAnchor" />
cumdantem, in quo colores iidem, ſed contrario ordine, &amp; </s>
          <s xml:space="preserve"><lb />debiliores, apparent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0614-03" corresp="note-0614-03a" place="margin">886.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Panno nigro ſuſpenſo, radiis ſolaribus expoſito; </s>
          <s xml:space="preserve">detur, <lb />inter hunc &amp; </s>
          <s xml:space="preserve">Solem, ſpectator pannum reſpiciens; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">inter <lb />pannum &amp; </s>
          <s xml:space="preserve">ſpectatorem diſpergatur aqua, ut in guttas exi-<lb />guas reſolvatur, videbit ſpectator Iridem ſaltem interiorem.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXII. <lb />De tenuium Laminarum Coloribus.</head>
        <p>
          <s xml:space="preserve">TRanſimus ad corporum naturalium colores, &amp; </s>
          <s xml:space="preserve">ante <lb />omnia examinandas credimus tenues lamellas. </s>
          <s xml:space="preserve">Qui vi-<lb />trum tenue, aut globos ex aquâ cum ſapone formatos, atten-<lb />tè conſideravit, varios colores in illis obſervare facillimè potuit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Radii luminis, ope laminæ tenuis &amp; </s>
          <s xml:space="preserve">tranſlucidæ, inter ſe <lb />ſeparantur, &amp; </s>
          <s xml:space="preserve">pro variâ craſſitie laminæ, radii quorundam co-<lb />
<ptr xml:id="note-0614-04a" corresp="note-0614-04" type="noteAnchor" />
lorum tranſmittuntur, aliorum reflectuntur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eadem lamina <lb />tenuiſſima aliûs coloris eſt, ſiradiis tranſmiſſis, quàm ſi reflexis <lb />videatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0614-04" corresp="note-0614-04a" place="margin">887.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">Si duo vitra objectiva, majoribus teleſcopiis inſervientia, <lb />
<ptr xml:id="note-0614-05a" corresp="note-0614-05" type="noteAnchor" />
AB &amp; </s>
          <s xml:space="preserve">CD, ſuper ſe mutuo imponantur, &amp; </s>
          <s xml:space="preserve">arctè compri-<lb />mantur, in medio ubi vitra ſeſe mutuo tangunt datur macu-<lb />la tranſlucida, quæ circulis coloratis circumdatur. </s>
          <s xml:space="preserve">Si lumen <lb />reflexum ab aëre, inter vitra interjacente, ad oculum in Oper-<lb />veniat, macula tranſlucida nigra apparet, &amp; </s>
          <s xml:space="preserve">colores, quià cen-<lb />tro recedendo ita diſponuntur ut ad varios ordines, propter co-<lb />lores repetitos, referri poſſint, ſequentes ſunt; </s>
          <s xml:space="preserve">NIGER, cœ-<lb />ruleus, albus, flavus, rubeus: </s>
          <s xml:space="preserve">VIOLACEUS, cœruleus, viri-<lb />dis, flavus, rubeus: </s>
          <s xml:space="preserve">PURPUREUS, cœruleus, viridis, flavus,
</s>
          <pb facs="0615" n="(99)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XXII.</fw>
rubeus: </s>
          <s xml:space="preserve">VIRIDIS, rubeus: </s>
          <s xml:space="preserve">qui colores etiam aliis circum-<lb />dantur, ſed recedendo à centro continuò debiliores.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0614-05" corresp="note-0614-05a" place="margin">TAB. XVIII. <lb />fig. 6.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si lumen trans vitra ad oculum Operveniat, macula trans-<lb />lucida, omnes tranſmittens radios, alba eſt, &amp; </s>
          <s xml:space="preserve">juxta hanc ſe-<lb />riem recedendo à centro apparent colores, qui etiam ad <lb />varios ordines referuntur, ordinibus memoratis oppoſitos: <lb /></s>
          <s xml:space="preserve">ALBUS, rubeus flaveſcens, niger, violaceus, cœruleus: </s>
          <s xml:space="preserve">AL-<lb />BUS, flavus, rubeus, violaceus, cœruleus: </s>
          <s xml:space="preserve">VIRIDIS, flavus, <lb />rubeus, viridis ſubcœruleus: </s>
          <s xml:space="preserve">RUBEUS, viridis ſubcœruleus: </s>
          <s xml:space="preserve"><lb />qui etiam colores aliis debilioribus circumdantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Lamina tenuis ex aquâ formatur, ſi hæc paululum ſapo-<lb />ne incraſſata fuerit, &amp; </s>
          <s xml:space="preserve">in bullam infletur. </s>
          <s xml:space="preserve">Obtegatur hæc <lb />vitro admodum tranſlucido, ne, aëris agitatione, colores <lb />qui in hac bullâ obſervantur, motu aquæ, confundantur. <lb /></s>
          <s xml:space="preserve">Bulla talis, quia aqua continuò verſus omnes partes defluit, <lb />tenuiſſima eſt in ſupremâ parte, &amp; </s>
          <s xml:space="preserve">craſſities deſcendendo con-<lb />tinuò augetur, &amp; </s>
          <s xml:space="preserve">totius craſſities ex eâdem cauſa de mo-<lb />mento in momentum minuitur. </s>
          <s xml:space="preserve">Antequam bulla diſrumpa-<lb />tur, ſummitas ipſius ita tenuis fit, ut omne lumen tranſmit-<lb />tat, &amp; </s>
          <s xml:space="preserve">nigra appareat. </s>
          <s xml:space="preserve">Si in hoc caſu bulla hæc reflexo lu-<lb />mine obſervetur, dum cœli ſubalbidioris reflectione illuſtra-<lb />tur, &amp; </s>
          <s xml:space="preserve">lumen extraneum intercipitur, corpore quocunque <lb />nigro ultra bullam poſito; </s>
          <s xml:space="preserve">macula nigra ſtatim memorata <lb />iiſdem circulis coloratis circumdatur &amp; </s>
          <s xml:space="preserve">eodem ordine di-<lb />ſpoſitis, quàm circa maculam nigram in præcedenti ex peri-<lb />mento. </s>
          <s xml:space="preserve">Deſcenſu aquæ continuò dilatantur annuli colorati <lb />donec frangatur bulla.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si, ubi extremus bullæ circuitus, reflexis radiis, rubeus <lb />apparet, ſpectator illum, tranſmiſſis radiis, intueatur, cæru-<lb />leus erit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in genere colores, tranſmiſſis &amp; </s>
          <s xml:space="preserve">reflexis radiis, eo-<lb />dem modo ac in præcedenti experimento, ſibi mutuo op-<lb />ponuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hiſce experimentis coliatis, ſequitur augendo tenuiſſimæ <lb />
<ptr xml:id="note-0615-01a" corresp="note-0615-01" type="noteAnchor" />
laminæ craſſitiem; </s>
          <s xml:space="preserve">hujus colorem mutari, &amp; </s>
          <s xml:space="preserve">quidem mutationes <lb />dari ſucceſſivè eaſdem, eodem ordine, ſive ex rarioriaut denſiori <lb />medio formetur lamella. </s>
          <s xml:space="preserve">Nam in laminâ aëreâ inter vitra &amp; </s>
          <s xml:space="preserve">a-
</s>
          <pb facs="0616" n="(100)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
queâ in bullâ, quarum craſſities recedendoà medio creſcunt, <lb />eodem ordine colores diſponuntur. </s>
          <s xml:space="preserve">In laminâ tamen den-<lb />
<ptr xml:id="note-0616-01a" corresp="note-0616-01" type="noteAnchor" />
ſiori minor craſſities requiritur, quàm in rariori, ut eodem <lb />colore tingantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0615-01" corresp="note-0615-01a" place="margin">888.</note>
              <note xml:space="preserve" xml:id="note-0616-01" corresp="note-0616-01a" place="margin">889.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Iiſdem poſitis quæ in Experimento 1.</s>
          <s xml:space="preserve">; madefactis paulu-<lb />lum ab unâ parte vitrorum marginibus, aqua paulatim inter <lb />vitra penetrabit; </s>
          <s xml:space="preserve">in aquâ non alii, quàm in aëre, circulorum <lb />colores obſervantur, neque horum ordo mutatur, ſed circuli <lb />contrahuntur; </s>
          <s xml:space="preserve">ubi ad centrum pervenit aqua, omnes circu-<lb />lorum portiones in aquâ à portionìbus in aëre ſeparantur, &amp; </s>
          <s xml:space="preserve"><lb />in minus ſpatium rediguntur.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Laminæ color ab illius craſſitie <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">denſitate <ptr type="noteAnchor" />, pen-
<ptr xml:id="note-0616-02a" corresp="note-0616-02" type="noteAnchor" />
<ptr xml:id="note-0616-03a" corresp="note-0616-03" type="noteAnchor" />
<ptr xml:id="note-0616-04a" corresp="note-0616-04" type="noteAnchor" />
det, non à medio circumdante.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0616-02" corresp="note-0616-02a" place="margin">890.</note>
              <note xml:space="preserve" xml:id="note-0616-03" corresp="note-0616-03a" n="*" anchored="true" place="margin">887.</note>
              <note xml:space="preserve" xml:id="note-0616-04" corresp="note-0616-04a" n="*" anchored="true" place="margin">889.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Si lamella ex lapide ſpeculari ita tenuis detur, ut colorata <lb />appareat, colores non mutantur ſi madefacta fuerit, id eſt, <lb />ſi, loco aëris, aquâ circumdetur lamella.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ejuſdem lamellæ color eſt eo magis vividus, quo illius denſitas <lb />
<ptr xml:id="note-0616-05a" corresp="note-0616-05" type="noteAnchor" />
magis differt cum denſitate medii circumambientis. </s>
          <s xml:space="preserve">Hoc præ-<lb />cedenti Experimento probatur, in quo colores laminæ made-<lb />factæ languidiores ſunt, quàm laminæ aëre circumdatæ. </s>
          <s xml:space="preserve">Etiam <lb />in Exp. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">minus vividi ſunt colores quàm in ſecundo; </s>
          <s xml:space="preserve">in utroque <lb />lamina aquea datur, in hoc aëre, in illo vitro circumdata; </s>
          <s xml:space="preserve">minus <lb />autem aqua &amp; </s>
          <s xml:space="preserve">vitrum denſitate differunt, quàm aër &amp; </s>
          <s xml:space="preserve">aqua.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0616-05" corresp="note-0616-05a" place="margin">891.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si media denſitate æqualiter differant, colores vividiores <lb />
<ptr xml:id="note-0616-06a" corresp="note-0616-06" type="noteAnchor" />
erunt, ſi denſius rariori circumdetur: </s>
          <s xml:space="preserve">nam in laminâ vitreâ <lb />tenuiſſimâ, quæ coloribus ex tenuitate tingitur, aëre circum-<lb />datâ, colores magis vividi erunt, quàm in Exper. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">in quo <lb />lamina aërea vitro circumdatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0616-06" corresp="note-0616-06a" place="margin">892.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ejuſdem denſitatis lamina, eodem medio circumdata, eo <lb />
<ptr xml:id="note-0616-07a" corresp="note-0616-07" type="noteAnchor" />
majori copiâ lumen reflectit, quo tenuior eſt. </s>
          <s xml:space="preserve">Nimium tamen <lb />
<ptr xml:id="note-0616-08a" corresp="note-0616-08" type="noteAnchor" />
ſi minuatur craſſities, non reflectit lumen. </s>
          <s xml:space="preserve">Patent hæc expe-<lb />rimentis præcedentibus; </s>
          <s xml:space="preserve">in tribus primis circuli colorati mi-<lb />nores, qui etiam ſunt tenuiores, omnium optimè lumen re-<lb />flectunt; </s>
          <s xml:space="preserve">in centro verò, ubi lamina eſt omnium tenuiſſi-<lb />ma, nulla ſenſibilis datur reflectio; </s>
          <s xml:space="preserve">ut illud in ſecundo clarè
</s>
          <pb facs="0617" n="(101)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XXII.</fw>
patet: </s>
          <s xml:space="preserve">in primo datur etiam lamina tenuiſſima aërea, quæ lu-<lb />men non reflectit; </s>
          <s xml:space="preserve">nam macula in centro tranſlucida ſuperat <lb />magnitudine ſuperficies vitrorum, quæ ex introceſſione par-<lb />tium immediatè ſeſe mutuo tangunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0616-07" corresp="note-0616-07a" place="margin">893.</note>
              <note xml:space="preserve" xml:id="note-0616-08" corresp="note-0616-08a" place="margin">894.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si dentur laminæ ejuſdem medii, quarum craſſities ſint in <lb />
<ptr xml:id="note-0617-01a" corresp="note-0617-01" type="noteAnchor" />
progreſſione arithmeticâ numerorum naturalium 1. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">5. <lb /></s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve">, ſi omnium tenuiſſima reflectat radios homogeneos <lb />quoſcunque, ſecunda eoſdem tranſmittet, tertia iterum re-<lb />flectet, &amp; </s>
          <s xml:space="preserve">alternis vicibus radiir eflectuntur &amp; </s>
          <s xml:space="preserve">tranſmit-<lb />tuntur: </s>
          <s xml:space="preserve">id eſt, laminæ, quarum craſſities in progreſſione <lb />memoratâ reſpondent numeris imparibus 1. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve">, re-<lb />flectunt radios, quos tranſmittunt reliquæ, quarum craſſities <lb />reſpondent numeris paribus 2. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">8. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0617-01" corresp="note-0617-01a" place="margin">895.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc laminarum proprietas obtinet reſpectu radiorum ho-<lb />mogeneorum quorumcunque: </s>
          <s xml:space="preserve">cum hac differentiâ, quod craſ-<lb />ſities diverſæ pro coloribus diverſis requirantur, ut ante di-<lb />ctum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">omnium minima eſt in coloris violacei reflectione;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0617-02a" corresp="note-0617-02" type="noteAnchor" />
in rubri reflectione omnium maxima; </s>
          <s xml:space="preserve">poſitis craſſitiebus in-<lb />termediis, radii refrangibilitatis intermediæ reflectuntur, <lb />id eſt, creſcente radii refrangibilitate etiam minuitur craſ-<lb />
<ptr xml:id="note-0617-03a" corresp="note-0617-03" type="noteAnchor" />
ſities laminæ, quæ illum reflectit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0617-02" corresp="note-0617-02a" n="*" anchored="true" place="margin">887.</note>
              <note xml:space="preserve" xml:id="note-0617-03" corresp="note-0617-03a" place="margin">896.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Inſtituatur experimentum in loco obſcuro, in quo imago <lb />Solis oblonga, in Exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">18. </s>
          <s xml:space="preserve">memorata, in chartâ re-<lb />præſentatur. </s>
          <s xml:space="preserve">Dentur, ut in exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">hujus cap. </s>
          <s xml:space="preserve">duo vitra ob-<lb />jectiva, teleſcopiorum majorum, ſuper ſe mutuo compreſ-<lb />ſorum, &amp; </s>
          <s xml:space="preserve">ita diſponantur, ut in his, quaſi in ſpeculo, ſuc-<lb />ceſſivè videantur colores ſinguli imaginis memoratæ id eſt, <lb />vitra ſucceſſivè illuminentur radiis homogeneis diverſis; <lb /></s>
          <s xml:space="preserve">quod obtinetur paululum circa axem agitando priſma, quo <lb />radii in imagine oblongâ ſeparantur. </s>
          <s xml:space="preserve">Annuli, in experimen-<lb />to primo memorati, apparent, ſed majori numero, &amp; </s>
          <s xml:space="preserve">unius <lb />tantum coloris; </s>
          <s xml:space="preserve">propter coloris immutabilitatem in radiis <lb />homogeneis <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">in interſtitiis horum annulorum radii tranſ-
<ptr xml:id="note-0617-04a" corresp="note-0617-04" type="noteAnchor" />
mittuntur ut in chartâ, diſpoſitâ poſt vitra, in quam radii <lb />tranſmiſſi impingunt, clarè patet; </s>
          <s xml:space="preserve">annuli omnium ſunt mi-<lb />nimi, quando ſunt violacei; </s>
          <s xml:space="preserve">dilatantur ſucceſſivè conſideran-
</s>
          <pb facs="0618" n="(102)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
do colores ſequentes ad rubrum uſque. </s>
          <s xml:space="preserve">Si, poſitis annulis <lb />coloris cujuſcunque, diametri exactè menſurentur ci culo-<lb />rum, qui in medio latitudinis ſingulorum annulorum conci-<lb />piuntur, quadrata diametrorum erunt inter ſe ut numeri im-<lb />pares 1. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eodem modo, menſuratis diametris cir-<lb />culorum, in medio ſingulorum interſtitiorum inter annu-<lb />los, illarum quadrata erunt, ut numeri pares 2. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">c. <lb /></s>
          <s xml:space="preserve">Cùm autem agatur de vitris ſphæricis, craſſities laminæ aëreæ, <lb />in circulis memoratis, ſunt ut numeri pares &amp; </s>
          <s xml:space="preserve">impares.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0617-04" corresp="note-0617-04a" n="*" anchored="true" place="margin">863.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi></head>
        <p>
          <s xml:space="preserve">Color homogencus, in laminâ medii cujuſcunque, dicitur <lb />
<ptr xml:id="note-0618-01a" corresp="note-0618-01" type="noteAnchor" />
primi ordinis, ſi lamina fuerit omnium tenuiſſima, quæ talem <lb />colorem reflectit; </s>
          <s xml:space="preserve">in laminâ, cujus craſſities tripla eſt, dici-<lb />tur ſecundi ordinis, &amp;</s>
          <s xml:space="preserve">c.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0618-01" corresp="note-0618-01a" place="margin">897.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Color primi ordinis eſt omnium maximè vividus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſucceſ-<lb />
<ptr xml:id="note-0618-02a" corresp="note-0618-02" type="noteAnchor" />
ſivè, in ordinibus ſequentibus, ſecundo, tertio, &amp;</s>
          <s xml:space="preserve">c, minus <lb />ac minus vividus eſt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0618-03a" corresp="note-0618-03" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0618-02" corresp="note-0618-02a" place="margin">898.</note>
              <note xml:space="preserve" xml:id="note-0618-03" corresp="note-0618-03a" n="*" anchored="true" place="margin">893.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando radiis hæterogeneis illuſtratur lamina aërea, inter <lb />vitra Teleſcopiorum, aut lamina ſimilis ex aliâ quacunque <lb />materiá, ut in Exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">varii ex annulis, in ultimo ex-<lb />perimento viſis, inter ſe confunduntur, &amp; </s>
          <s xml:space="preserve">color videtur, <lb />qui ex horum permixtione conflatur; </s>
          <s xml:space="preserve">nam eadem laminæ <lb />
<ptr xml:id="note-0618-04a" corresp="note-0618-04" type="noteAnchor" />
craſſities, ad colores diverſos, variorum or dinum, reflecten-<lb />dos, ſæpè requiritur: </s>
          <s xml:space="preserve">ſic lamina, quæ violaceum tertii ordi-<lb />nis reflectit, etiam repercutit rubrum ſecundi ordinis, ut, <lb />ad hoc attendendo, ex ultimo experimento deducitur: </s>
          <s xml:space="preserve">ideò-<lb />que in Exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">2.</s>
          <s xml:space="preserve">, violaceus annulus tertius cum parte ex-<lb />teriori annuli rubri ſecundi confunditur, &amp; </s>
          <s xml:space="preserve">color datur pur-<lb />pureus; </s>
          <s xml:space="preserve">non tamen omnis ruber color ſecundi ordinis abſor-<lb />betur; </s>
          <s xml:space="preserve">quia annulus ruber violaceum latitudine ſuperat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0618-04" corresp="note-0618-04a" place="margin">899.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quo magis augetur laminæ craſſities, eo plures colores re-<lb />
<ptr xml:id="note-0618-05a" corresp="note-0618-05" type="noteAnchor" />
flectit, varios, ex diverſis ordinibus. </s>
          <s xml:space="preserve">Lamina violacea de-<lb />cimi ordinis, congruit cum cæruleâ noni ordinis, &amp; </s>
          <s xml:space="preserve">flavâ <lb />octavi ordinis, &amp; </s>
          <s xml:space="preserve">tandem cum rubrâ ſeptimi ordinis, &amp; </s>
          <s xml:space="preserve">color <lb />laminæ ex permixtione horum colorum conflatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0618-05" corresp="note-0618-05a" place="margin">900.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si, in Exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">2.</s>
          <s xml:space="preserve">, obliquè ſpectator intueatur laminas, <lb />
<ptr xml:id="note-0618-06a" corresp="note-0618-06" type="noteAnchor" />
aëream, &amp; </s>
          <s xml:space="preserve">aqueam, dilantantur annuli cum oculi obliquitate,
</s>
          <pb facs="0619" n="(103)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. III. CAP. XXIII.</fw>
id eſt, in hcc motu oculi laminæ color in determinato loco <lb />mutatur: </s>
          <s xml:space="preserve">major tamen eſt in Exp. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">dilatatio; </s>
          <s xml:space="preserve">quod pro-<lb />bat obliquitate radiorum colorem magis mutari, ſilamina den-<lb />
<ptr xml:id="note-0619-01a" corresp="note-0619-01" type="noteAnchor" />
ſiori medio, quàm ſi rariori circumdetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0618-06" corresp="note-0618-06a" place="margin">901.</note>
              <note xml:space="preserve" xml:id="note-0619-01" corresp="note-0619-01a" place="margin">902.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cujus propoſitionis demonſtrationem ex refractionis legi-<lb />
<ptr xml:id="note-0619-02a" corresp="note-0619-02" type="noteAnchor" />
bus facile deducimus. </s>
          <s xml:space="preserve">Sint L &amp; </s>
          <s xml:space="preserve">l laminæ tenues; </s>
          <s xml:space="preserve">hæc me-<lb />dio denſiori, illa medio rariori circumdata; </s>
          <s xml:space="preserve">ſint ambæ ejuſ-<lb />dem craſſitiei: </s>
          <s xml:space="preserve">ſi in has incidant radii AB, ab, æqualiter <lb />ad laminas inclinati; </s>
          <s xml:space="preserve">in L refractio fiet, accedendo ad per-<lb />pendicularem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">in l contra refringitur radius recedendo a
<ptr xml:id="note-0619-03a" corresp="note-0619-03" type="noteAnchor" />
perpendiculari <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">licèt BD &amp; </s>
          <s xml:space="preserve">bd ſint æquales, bc longitudi-
<ptr xml:id="note-0619-04a" corresp="note-0619-04" type="noteAnchor" />
ne ſuperat BC, ideòque major datur mutatio in motu lu-<lb />minis in laminâ l quàm in L. </s>
          <s xml:space="preserve">Auctâ denſitate laminæ L, <lb />
<ptr xml:id="note-0619-05a" corresp="note-0619-05" type="noteAnchor" />
manente medio rariori quo circumdatur, minor dabitur diffe-<lb />rentia inter BC &amp; </s>
          <s xml:space="preserve">BD, ideoque minor mutatio coloris; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />ſi ita augeatur vis refringens laminæ, ut radii refracti, quæ-<lb />
<ptr xml:id="note-0619-06a" corresp="note-0619-06" type="noteAnchor" />
cunque fuerit incidentis obliquitas, ſenſibiliter inter ſe non <lb />differant, ſenſibilis non dabitur differentia in colore laminæ, <lb />in quocunque ſitu oculus ponatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0619-02" corresp="note-0619-02a" place="margin">TAB. XVIII. <lb />fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0619-03" corresp="note-0619-03a" n="*" anchored="true" place="margin">624.</note>
              <note xml:space="preserve" xml:id="note-0619-04" corresp="note-0619-04a" n="*" anchored="true" place="margin">625.</note>
              <note xml:space="preserve" xml:id="note-0619-05" corresp="note-0619-05a" place="margin">903.</note>
              <note xml:space="preserve" xml:id="note-0619-06" corresp="note-0619-06a" place="margin">904.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce facile deducimus, quarundam laminarum colorem <lb />
<ptr xml:id="note-0619-07a" corresp="note-0619-07" type="noteAnchor" />
ex mutato oculi ſitu variari, aliarum colorem permanere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0619-07" corresp="note-0619-07a" place="margin">905.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XXIII. <lb />De Corporum naturalium Coloribus.</head>
        <p>
          <s xml:space="preserve">QUæ Corporum quorumcunque colores ſpectant, ex huc <lb />uſque explicatis facilè deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vidimus radios luminis colores ſibi peculiares &amp; </s>
          <s xml:space="preserve">im-<lb />mutabiles habere, ita ut reflectione non mutentur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0619-08a" corresp="note-0619-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0619-08" corresp="note-0619-08a" n="*" anchored="true" place="margin">863.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ideò radii à corporibus reflexi, pro majori aut minori re-<lb />
<ptr xml:id="note-0619-09a" corresp="note-0619-09" type="noteAnchor" />
frangibilitate, quæ competit colori ipſius corporis, majorem <lb />aut minorem refrangibilitatem habent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0619-09" corresp="note-0619-09a" place="margin">906.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 1.</head>
        <p>
          <s xml:space="preserve">In medio chartæ nigræ duo fruſta quadrata, duorum cir-<lb />citer pollicum, vittæ ſericæ, unum rubeum alterum viola-<lb />ceum, junguntur ita, ut ſeſe mutuo ad latera tangant, eo-<lb />dem modo ac colores ruber &amp; </s>
          <s xml:space="preserve">violaceus in Exp. </s>
          <s xml:space="preserve">3. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">19.</s>
          <s xml:space="preserve">;
</s>
          <pb facs="0620" n="(104)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
diſponintur charta nigra, ut à lumine per feneſtram cubicu-<lb />lum intranti vittæ probè illuminentur: </s>
          <s xml:space="preserve">ſi ſpectator trans <lb />priſma vittas intueatur, ut in exp. </s>
          <s xml:space="preserve">ſtatim memorato, eodem <lb />modo, ac in illo experimento, colores ſeparati apparent.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 2.</head>
        <p>
          <s xml:space="preserve">Dentur in R &amp; </s>
          <s xml:space="preserve">V vittæ ſericæ in Experimento præceden-<lb />
<ptr xml:id="note-0620-01a" corresp="note-0620-01" type="noteAnchor" />
ti memoratæ hæc violacea, illa rubra eſt; </s>
          <s xml:space="preserve">flammâ candelæ <lb />illuminentur; </s>
          <s xml:space="preserve">ad ſex pedum diſtantiam detur lens convexa <lb />V, de qua in Exp. </s>
          <s xml:space="preserve">6. </s>
          <s xml:space="preserve">cap. </s>
          <s xml:space="preserve">19; </s>
          <s xml:space="preserve">ad diſtantiam circiter ſex <lb />pedum, in chartâ albâ dabitur in r repræſentatio vittæ R, <lb />ad minorem diſtantiam in v aliûs repræſentationem exactam <lb />habemus. </s>
          <s xml:space="preserve">Determinatur ubi repræſentationes ſunt exactæ, <lb />ſi fila nigra trajiciant ſuperficiem vittarum, nam hæc fila di-<lb />ſtincta apparent in exactâ repræſentatione.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0620-01" corresp="note-0620-01a" place="margin">TAB. XIX. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corporum colores varios dari, quia radii diverſi à corpori-<lb />
<ptr xml:id="note-0620-02a" corresp="note-0620-02" type="noteAnchor" />
bus diverſê coloratis reflectuntur, &amp; </s>
          <s xml:space="preserve">corpus illius coloris ap-<lb />parere, qui oritur ex permixtione radiorum reflexorum, <lb />non modo ex præcedentibus experimentis deducitur, ſed <lb />etiam directis demonſtratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0620-02" corresp="note-0620-02a" place="margin">907.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 3.</head>
        <p>
          <s xml:space="preserve">Dentur duo corpora quæcunque unum rubrum, alterum <lb />cœruleum, illuminentur hæc ſucceſſivè, in loco obſcuro, <lb />coloribus imaginis coloratæ, refractione priſmatis formatæ, <lb />ſinguli colores ab ambobus quidem reflectuntur, ſed radii <lb />rubri magnâ copia à corpore rubro repercutiuntur, dum pau-<lb />cos ex his reflectit corpus cœruleum, ut ex collatione coloris <lb />rubri amborum corporum clarè patet; </s>
          <s xml:space="preserve">contrarium obſer-<lb />vatur in radiis cœruleis, qui à corpore cœruleo magnâ co-<lb />piâ reflectuntur, dum à corpore rubro pauci tantum, re-<lb />flectione redeunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Radii, qui à corpore non reflectuntur, in hoc penetrant, ibi-<lb />que innumeras reflectiones &amp; </s>
          <s xml:space="preserve">refractiones patiuntur, ut inter <lb />num. </s>
          <s xml:space="preserve">842. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">843. </s>
          <s xml:space="preserve">explicavimus; </s>
          <s xml:space="preserve">donec tandem ſeſe jungant <lb />
<ptr xml:id="note-0620-03a" corresp="note-0620-03" type="noteAnchor" />
particulis ipſius corporis <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Idèo corpus eo citius incaleſcit,
<ptr xml:id="note-0620-04a" corresp="note-0620-04" type="noteAnchor" />
quo minori copiâ reflectit lumen. </s>
          <s xml:space="preserve">Idcirco corpus album, <lb />
<ptr xml:id="note-0620-05a" corresp="note-0620-05" type="noteAnchor" />
quod ferè omnes radios quibus illuſtratur reflectit <ptr type="noteAnchor" />, omnium,
<ptr xml:id="note-0620-06a" corresp="note-0620-06" type="noteAnchor" />
lentiſſimè incaleſcit, dum corpus nigrum, in quod ferè omnes
</s>
          <pb facs="0621" />
          <s xml:space="preserve">
<pb facs="0621a" />
<ptr xml:id="fig-0621a-01a" corresp="fig-0621a-01" type="figureAnchor" />
<pb facs="0622" />
<pb facs="0623" n="(105)" /><fw type="head">MATHEMATICA LIB. III. CAP. XXIII.</fw>
radii penetrant, quia pauci tantùm reflectuntur <ptr type="noteAnchor" />, citius aliis
<ptr xml:id="note-0623-01a" corresp="note-0623-01" type="noteAnchor" />
calorem acquirit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0620-03" corresp="note-0620-03a" n="*" anchored="true" place="margin">546.</note>
              <note xml:space="preserve" xml:id="note-0620-04" corresp="note-0620-04a" place="margin">908.</note>
              <note xml:space="preserve" xml:id="note-0620-05" corresp="note-0620-05a" place="margin">909.</note>
              <note xml:space="preserve" xml:id="note-0620-06" corresp="note-0620-06a" n="*" anchored="true" place="margin">870.</note>
              <figure xml:id="fig-0621a-01" corresp="fig-0621a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0621a-01" />
                <label>0621a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0623-01" corresp="note-0623-01a" n="*" anchored="true" place="margin">845.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut autem determinemus conſtitutionem ſuperficierum <lb />corporum, à qua color pendet, debemus attendere ad mi-<lb />nimas particulas, ex quibus hæ ſuperficies formantur; </s>
          <s xml:space="preserve">Par-<lb />ticulæ hæ ſunt tranſlucidæ <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſeparantur medio, denſitate
<ptr xml:id="note-0623-02a" corresp="note-0623-02" type="noteAnchor" />
differente cum ipſis particulis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſunt etiam tenues, aliter
<ptr xml:id="note-0623-03a" corresp="note-0623-03" type="noteAnchor" />
ſuperficies quaſi corpore tranſlucido obtegeretur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">color à
<ptr xml:id="note-0623-04a" corresp="note-0623-04" type="noteAnchor" />
particulis infra has pendêret. </s>
          <s xml:space="preserve">In omni ergo ſuperficie cor-<lb />poris colorati dantur laminæ innumeræ exiguæ tenues; </s>
          <s xml:space="preserve">mi-<lb />nuendo autem laminam, ſervatâ hujus craſſitie, non hujus <lb />proprietates, quantum ad luminis reflectionem, mutantur; <lb /></s>
          <s xml:space="preserve">nam lamina minima, cum relatione ad radios luminis, magna <lb />admodum eſt: </s>
          <s xml:space="preserve">Idcirco demonſtrata in Capite præcedenti, ad <lb />haſce laminas in ſuperficiebus corporum applicari poſſunt. </s>
          <s xml:space="preserve"><lb />Unde ſequentes deducimus concluſiones.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0623-02" corresp="note-0623-02a" n="*" anchored="true" place="margin">841.</note>
              <note xml:space="preserve" xml:id="note-0623-03" corresp="note-0623-03a" n="*" anchored="true" place="margin">843.</note>
              <note xml:space="preserve" xml:id="note-0623-04" corresp="note-0623-04a" n="*" anchored="true" place="margin">843.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Pendet color corporis à craſſitie, &amp; </s>
          <s xml:space="preserve">denſitate partium cor-<lb />
<ptr xml:id="note-0623-05a" corresp="note-0623-05" type="noteAnchor" />
poris, quæ in ſuperficie interjacent meatus in corpore <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0623-06a" corresp="note-0623-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0623-05" corresp="note-0623-05a" place="margin">910.</note>
              <note xml:space="preserve" xml:id="note-0623-06" corresp="note-0623-06a" n="*" anchored="true" place="margin">890.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Eo magis vividus &amp; </s>
          <s xml:space="preserve">magis homogeneus eſt color, quo par-<lb />
<ptr xml:id="note-0623-07a" corresp="note-0623-07" type="noteAnchor" />
tes ſunt tenuiores <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0623-08a" corresp="note-0623-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0623-07" corresp="note-0623-07a" place="margin">911.</note>
              <note xml:space="preserve" xml:id="note-0623-08" corresp="note-0623-08a" n="*" anchored="true" place="margin">898. 899. 900.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Cæteris paribus, partes memoratæ craſſitiem omnium <lb />
<ptr xml:id="note-0623-09a" corresp="note-0623-09" type="noteAnchor" />
maximam habent, ſi corpus fuerit rubrum, omnium minimam <lb />ſi violaceum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0623-10a" corresp="note-0623-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0623-09" corresp="note-0623-09a" place="margin">912.</note>
              <note xml:space="preserve" xml:id="note-0623-10" corresp="note-0623-10a" n="*" anchored="true" place="margin">896. 861.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Partes corporum denſitate medium in interſtitiis multum <lb />
<ptr xml:id="note-0623-11a" corresp="note-0623-11" type="noteAnchor" />
ſuperant <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0623-12a" corresp="note-0623-12" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0623-11" corresp="note-0623-11a" place="margin">913.</note>
              <note xml:space="preserve" xml:id="note-0623-12" corresp="note-0623-12a" n="*" anchored="true" place="margin">902. 903. 904.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Denſitas hæc minor eſt in caudis pavonum &amp; </s>
          <s xml:space="preserve">in quibuſdam <lb />
<ptr xml:id="note-0623-13a" corresp="note-0623-13" type="noteAnchor" />
pannis ſericis, &amp; </s>
          <s xml:space="preserve">in genere in omnibus corporibus, quorum co-<lb />lor pro diverſo oculi ſitu variat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0623-14a" corresp="note-0623-14" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0623-13" corresp="note-0623-13a" place="margin">914.</note>
              <note xml:space="preserve" xml:id="note-0623-14" corresp="note-0623-14a" n="*" anchored="true" place="margin">901. 903.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Color corporis obſcurior &amp; </s>
          <s xml:space="preserve">fuſcior eſt, ſi medium denſius po-<lb />
<ptr xml:id="note-0623-15a" corresp="note-0623-15" type="noteAnchor" />
ros intret <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">tunc enim partes à quibus color pendet, medio
<ptr xml:id="note-0623-16a" corresp="note-0623-16" type="noteAnchor" />
denſiori quàm ante, circumdantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0623-15" corresp="note-0623-15a" place="margin">915.</note>
              <note xml:space="preserve" xml:id="note-0623-16" corresp="note-0623-16a" n="*" anchored="true" place="margin">891.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Experimur hoc in omnibus corporibus, quæ intimè ab aquâ <lb />aut oleo penetrantur: </s>
          <s xml:space="preserve">exſiccatis corporibus priſtinum recu-<lb />perant colorem, niſi in quibuſdam occaſionibus, in quibus, <lb />actione aquæ aut olei, quædam partes ſunt ſublatæ, aut quan-<lb />do partes quædam aquæ aut olei, cum partibus corporis ita <lb />conjunguntur, ut lamellarum craſſities mutetur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0624" n="(106)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p rend="italics">
          <s xml:space="preserve">Ex ſimili cauſà deducuntur mutationes in coloribus quo-<lb />rundam liquidorum, ex permixtione cum aliis liquidis. </s>
          <s xml:space="preserve">Sæ-<lb />
<ptr xml:id="note-0624-01a" corresp="note-0624-01" type="noteAnchor" />
pè particulæ ſalinæ, natantes inuno liquido, ſeſe jungunt par-<lb />ticulis ſalinis natantibus in alio; </s>
          <s xml:space="preserve">aut, ex actione particularum <lb />ſupervenientium, ſeparantur particulæ junctæ, quibus omnibus <lb />mutatur particularum craſſities, &amp; </s>
          <s xml:space="preserve">cum hac liquidorum co-<lb />lor <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0624-02a" corresp="note-0624-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0624-01" corresp="note-0624-01a" place="margin">916.</note>
              <note xml:space="preserve" xml:id="note-0624-02" corresp="note-0624-02a" n="*" anchored="true" place="margin">888.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Liquidi aliquando diverſus eſt color, ſiradiis reflexis, quàm <lb />
<ptr xml:id="note-0624-03a" corresp="note-0624-03" type="noteAnchor" />
ſi tranſmiſſis, videatur: </s>
          <s xml:space="preserve">unde hoc oriatur antea vidimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0624-03" corresp="note-0624-03a" place="margin">917.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">887.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 4.</head>
        <p>
          <s xml:space="preserve">Infuſio ligni nephritici, non nimium ſatura, reflexis radiis, <lb />coerulea apparet, flava videtur, ſi inter lumen &amp; </s>
          <s xml:space="preserve">oculum de-<lb />tur phiala infuſionem continens.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Experimentum</hi> 5.</head>
        <p>
          <s xml:space="preserve">Si in infuſione ligni nephritici infundatur ſpiritus aceti vi-<lb />ni, flava apparet quomodocunque videatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In hoc caſu particularum craſſities mutatur, &amp; </s>
          <s xml:space="preserve">radii per <lb />ſingulas particulas tranſmiſſi intercipiuntur; </s>
          <s xml:space="preserve">licèt verò liquor <lb />inter oculum &amp; </s>
          <s xml:space="preserve">lumen ponatur radiis reflexis videtur, nam <lb />tales radios ad oculum pervenire ex variis reflectionibus, quas <lb />lumen in liquido patitur, facile concipimus. </s>
          <s xml:space="preserve">Hicce autem <lb />color ſolus ſenſibilis eſt, quia radii directè per liquidum pe-<lb />netrare non poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hoc ipſo deducimus, quare liquidum coloratum, in vi-<lb />
<ptr xml:id="note-0624-05a" corresp="note-0624-05" type="noteAnchor" />
tro figuræ coni inverſi, ſi detur inter oculum &amp; </s>
          <s xml:space="preserve">lumen, di-<lb />verſi coloris appareat, in variis vaſeos partibus; </s>
          <s xml:space="preserve">Inferiori <lb />parte non omnes radii per particulas tranſmiſſi intercipiun-<lb />tur, magis ac magis intercipiuntur, quo majori copiâ liqui-<lb />dum inter oculum &amp; </s>
          <s xml:space="preserve">lumen detur; </s>
          <s xml:space="preserve">donec tandem omnes in-<lb />tercipiantur &amp; </s>
          <s xml:space="preserve">ſoli à particulis reflexi liquidum penetrent; </s>
          <s xml:space="preserve">in <lb />quo calu color coincidit cum colore liquidi, radiis reflexis viſi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0624-05" corresp="note-0624-05a" place="margin">918.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nubes ſæpe pulcherrimè coloratæ apparent; </s>
          <s xml:space="preserve">conſtant ex <lb />
<ptr xml:id="note-0624-06a" corresp="note-0624-06" type="noteAnchor" />
particulis aqueis quibus interjacet aër, pro variâ idèo partï-<lb />cularum aquearum craſſitie, color diverſus in nube dabitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0624-07a" corresp="note-0624-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0624-06" corresp="note-0624-06a" place="margin">920.</note>
              <note xml:space="preserve" xml:id="note-0624-07" corresp="note-0624-07a" n="*" anchored="true" place="margin">888.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">FINIS LIBRI TERTII.</head>
        <pb facs="0625" />
        <pb facs="0625a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0625a-01" />
          <label>0625a-01</label>
        </figure>
        <pb facs="0626" />
        <pb facs="0627" n="(107)" />
      </div>
      <div type="section">
        <head xml:space="preserve">PHYSICES</head>
        <head xml:space="preserve">ELEMENTA MATHEMATICA, <lb />EXPERIMENTIS CONFIRMATA.</head>
        <head rend="italics" xml:space="preserve">LIBER IV. <lb />Pars I. De Mundi Syſtemate.</head>
        <head xml:space="preserve">CAPUT I. <lb />Idea Generalis Syſtematis Planetarii.</head>
        <p>
          <s xml:space="preserve">Spatium nullis limitibus terminari poſſe <ptr type="noteAnchor" /> qui atten-
<ptr xml:id="note-0627-01a" corresp="note-0627-01" type="noteAnchor" />
tè conſideraverit, vix inficias ire poterit, ſupre-<lb />mam omnipotentem intelligentiam, quam terri-<lb />colis arcto in campo demonſtravit, ſapientiam <lb />ubique manifeſtam feciſſe. </s>
          <s xml:space="preserve">Quem hìc arctum dico campum, <lb />in immenſum captum noſtrum ſuperat; </s>
          <s xml:space="preserve">arctum tamen cum <lb />ſpatio infinito collatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0627-01" corresp="note-0627-01a" n="*" anchored="true" place="margin">15.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tellus noſtra cum ſedecim aliis corporibus, (non plura no-<lb />
<ptr xml:id="note-0627-02a" corresp="note-0627-02" type="noteAnchor" />
vimus) in determinato ſpatio movetur; </s>
          <s xml:space="preserve">non ultra determina-<lb />tos limites, neque à ſe mutuo recedunt; </s>
          <s xml:space="preserve">neque ad ſe mutuo <lb />accedunt hæc corpora; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">immutatis legibus motus horum <lb />ſubjiciuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0627-02" corresp="note-0627-02a" place="margin">921.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> I.</head>
        <p rend="italics">
          <s xml:space="preserve">Congeries hæc ſeptemdecim corporum vocatur Syſtema <lb />
<ptr xml:id="note-0627-03a" corresp="note-0627-03" type="noteAnchor" />
Planetarium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0627-03" corresp="note-0627-03a" place="margin">922.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa hæc ſola ferè tota verſatur ars Aſtronomica; </s>
          <s xml:space="preserve">de his <lb />etiam præcipuè acturus ſum in hoc opere: </s>
          <s xml:space="preserve">reliqua Univer-<lb />ſum conſtituentia corpora nimium à nobis diſtant, ut horum <lb />motus, ſi moventur, à nobis obſervari poſſint; </s>
          <s xml:space="preserve">inter hæc <lb />nobis ſenſibilia ſunt ſola lucida, &amp; </s>
          <s xml:space="preserve">quidem inſigniora tan-<lb />tùm, &amp; </s>
          <s xml:space="preserve">quæ à nobis cæteris minus diſtant: </s>
          <s xml:space="preserve">etiam illorum, <lb />quæ Teleſcopio deteguntur, plurima oculo inermi viſibilia <lb />non ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0628" n="(108)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Corpora hæc omnia dicuntur Stellæ fixæ.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">923.</note>
        <p>
          <s xml:space="preserve">Fixæ vocantur, quia eundem ſitum inter ſe ſenſibiliter ſer-<lb />vant; </s>
          <s xml:space="preserve">circa hæc peculiaria quædam, in ſequentibus, memo-<lb />randa erunt.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Quod autem Syſtema Planetarium ſpectat; </s>
          <s xml:space="preserve">In hoc ſe-<lb />
<ptr xml:id="note-0628-02a" corresp="note-0628-02" type="noteAnchor" />
ptemdecim dari corpora diximus: </s>
          <s xml:space="preserve">Omnia ſunt ſphærica: </s>
          <s xml:space="preserve">V-<lb />nicum proprio lumine lucet; </s>
          <s xml:space="preserve">reliqua ſunt opaca, &amp; </s>
          <s xml:space="preserve">mutuato <lb />lumine viſibilia ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0628-02" corresp="note-0628-02a" place="margin">924.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Sol eſt corpus illud lucidum, &amp; </s>
          <s xml:space="preserve">omnium in Syſtemate Pla-<lb />
<ptr xml:id="note-0628-03a" corresp="note-0628-03" type="noteAnchor" />
netario longè maximum; </s>
          <s xml:space="preserve">in hujus medio quieſcit, ſaltem exi-<lb />guo motu tantùm agitatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0628-03" corresp="note-0628-03a" place="margin">925.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Reliqua ſedecim vocantur Planetæ.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">926.</note>
        <p>
          <s xml:space="preserve">Hi in duas claſſes dividuntur; </s>
          <s xml:space="preserve">ſex dicuntur Planetæ pri-<lb />marii; </s>
          <s xml:space="preserve">decem vocantur Planetæ ſecundarii. </s>
          <s xml:space="preserve">Quando de <lb />Planetis, nullâ adjectâ diſtinctione, loquimur, primarios in-<lb />telligimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Primarii Planetæ motibus ſuis Solem cingunt, &amp; </s>
          <s xml:space="preserve">ad di-<lb />
<ptr xml:id="note-0628-05a" corresp="note-0628-05" type="noteAnchor" />
verſas ab hoc diſtantias, in curvis, in ſe redeuntibus, feruntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0628-05" corresp="note-0628-05a" place="margin">927.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planeta ſecundarius circa primarium revolvitur, &amp; </s>
          <s xml:space="preserve">hunc <lb />
<ptr xml:id="note-0628-06a" corresp="note-0628-06" type="noteAnchor" />
in motu ſuo circa Solem comitatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0628-06" corresp="note-0628-06a" place="margin">928.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planetæ in motibus ſuis lineas Ellipticas, à circulis non <lb />
<ptr xml:id="note-0628-07a" corresp="note-0628-07" type="noteAnchor" />
admodum differentes, deſcribunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0628-07" corresp="note-0628-07a" place="margin">929.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Et ſingulæ lineæ hæ fixæ ſunt, ſaltem, niſi poſt longum <lb />tempus, exigua in ſitu mutatio obſervatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Linea Elliptica formatur, ſi filum, cujus extremitates in <lb />
<ptr xml:id="note-0628-08a" corresp="note-0628-08" type="noteAnchor" />
duobus punctis F &amp; </s>
          <s xml:space="preserve">f fixæ ſunt, moveatur manens tenſum; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0628-09a" corresp="note-0628-09" type="noteAnchor" />
ut in hac figura videtur, in qua filum repræſentatur in F d f, <lb />FE f, FB f. </s>
          <s xml:space="preserve">Puncta F, f, vocantur foci; </s>
          <s xml:space="preserve">linea A a, quæ <lb />per hos tranſit, &amp; </s>
          <s xml:space="preserve">ab utraque parte, in peripheriâ Ellipſeos <lb />terminatur, vocatur axis major; </s>
          <s xml:space="preserve">eſt recta omnium maxima <lb />quæ in Ellipſi duci poteſt. </s>
          <s xml:space="preserve">Punctum hujus axeos medium C, <lb />eſt Ellipſeos centrum; </s>
          <s xml:space="preserve">per hoc, ad axem majorem normalis, <lb />tranſit axis minor D d.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0628-08" corresp="note-0628-08a" place="margin">930.</note>
              <note xml:space="preserve" xml:id="note-0628-09" corresp="note-0628-09a" place="margin"><hi rend="small caps">TAB. XXIV.</hi> <lb />fig 3.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Ita ſingulorum Planetarum primariorum orbitæ diſponun-<lb />
<ptr xml:id="note-0628-10a" corresp="note-0628-10" type="noteAnchor" />
tur, ut focorum alter cadat in centro Solis; </s>
          <s xml:space="preserve">ſi Ellipſis AD a d <lb />repræſentet orbitam Planetæ, centrum Solis eſt F.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0628-10" corresp="note-0628-10a" place="margin">931.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0629" n="(109)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. I.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p rend="italics">
          <s xml:space="preserve">Diſtantia, inter centrum Solis &amp; </s>
          <s xml:space="preserve">centrum orbitæ, vocatur <lb />
<ptr xml:id="note-0629-01a" corresp="note-0629-01" type="noteAnchor" />
Planetæ Excentricitas: </s>
          <s xml:space="preserve">ut FC.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-01" corresp="note-0629-01a" place="margin">932.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſingulis revolutionibus Planeta ſemel ad Solem accedit, <lb />
<ptr xml:id="note-0629-02a" corresp="note-0629-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">ſemel ab hoc recedit; </s>
          <s xml:space="preserve">daturque ad diſtantiam omnium <lb />maximam in extremitate a axeos majoris orbitæ; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ad di-<lb />ſtantiam omnium minimam in extremitate oppoſitâ A.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-02" corresp="note-0629-02a" place="margin">933.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p>
          <s xml:space="preserve">Diſtantia Planetæ à Sole vocatur Media, quæ æqualiter <lb />
<ptr xml:id="note-0629-03a" corresp="note-0629-03" type="noteAnchor" />
cum maximâ &amp; </s>
          <s xml:space="preserve">minimâ differt. </s>
          <s xml:space="preserve">Ad hanc datur Planeta in <lb />extremitatibus D, d, axeos minoris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-03" corresp="note-0629-03a" place="margin">934.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p rend="italics">
          <s xml:space="preserve">Punctum orbitæ, in quo Planeta à Sole maximè diſtat, <lb />
<ptr xml:id="note-0629-04a" corresp="note-0629-04" type="noteAnchor" />
vocatur Aphelium. </s>
          <s xml:space="preserve">Ut a.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-04" corresp="note-0629-04a" place="margin">935.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p rend="italics">
          <s xml:space="preserve">Punctum orbitæ, in quo planeta minimè à Solè diſtat, vo-<lb />
<ptr xml:id="note-0629-05a" corresp="note-0629-05" type="noteAnchor" />
catur Perihelium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-05" corresp="note-0629-05a" place="margin">936.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 8.</head>
        <p>
          <s xml:space="preserve">Nomine communi puncta hæc vocantur Auges ſeu Apſi-<lb />
<ptr xml:id="note-0629-06a" corresp="note-0629-06" type="noteAnchor" />
des.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-06" corresp="note-0629-06a" place="margin">937.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 9.</head>
        <p>
          <s xml:space="preserve">Linea quæ aplides conjungit, id eſt, axis major orbitæ, <lb />
<ptr xml:id="note-0629-07a" corresp="note-0629-07" type="noteAnchor" />
vocatur linea Apſidum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-07" corresp="note-0629-07a" place="margin">938.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Orbita unaquæque in plano datur, quod per centrum Solis <lb />
<ptr xml:id="note-0629-08a" corresp="note-0629-08" type="noteAnchor" />
tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-08" corresp="note-0629-08a" place="margin">939.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 10.</head>
        <p rend="italics">
          <s xml:space="preserve">Planum orbitæ Telluris vocatur Planum Eclipticæ.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">940.</note>
        <p>
          <s xml:space="preserve">Hoc quaquaverſum continuatum concipitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ad ſitum <lb />planorum reliquarum orbitarum, reſpectu hujus, attendunt <lb />Aſtronomi.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 11.</head>
        <p rend="italics">
          <s xml:space="preserve">Puncta in quibus orbitæ ſecant planum Eclipticæ vo-<lb />
<ptr xml:id="note-0629-10a" corresp="note-0629-10" type="noteAnchor" />
cantur Nodi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-10" corresp="note-0629-10a" place="margin">941.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 12.</head>
        <p>
          <s xml:space="preserve">Linea quæ jungit orbitæ cujuſcunque Nodos, id eſt, co-<lb />
<ptr xml:id="note-0629-11a" corresp="note-0629-11" type="noteAnchor" />
munis ſectio plani orbitæ, cum Plano Eclipticæ, vocatur <lb />Linea Nodorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0629-11" corresp="note-0629-11a" place="margin">942.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0630" n="(110)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p rend="italics">
          <s xml:space="preserve">Planeta non æquali celeritate in omnibus punctis orbitæ ſuæ <lb />
<ptr xml:id="note-0630-01a" corresp="note-0630-01" type="noteAnchor" />
fertur; </s>
          <s xml:space="preserve">quo minus à Sole diſtat, eo celerius movetur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tem-<lb />
<ptr xml:id="note-0630-02a" corresp="note-0630-02" type="noteAnchor" />
pora, in quibus arcus varii orbitæ percurruntur, ſunt inter ſe <lb />ut areæ, lineis ad centrum Solis ductis, formatæ; </s>
          <s xml:space="preserve">Arcus AB <lb />&amp; </s>
          <s xml:space="preserve">a E percurruntur in temporibus, quæ ſunt inter ſe, ut areæ <lb />triangulorum mixtorum AFB, a FE.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-01" corresp="note-0630-01a" place="margin">943.</note>
              <note xml:space="preserve" xml:id="note-0630-02" corresp="note-0630-02a" place="margin">944.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omnes Planetæ verſus eandem partem feruntur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ho-<lb />
<ptr xml:id="note-0630-03a" corresp="note-0630-03" type="noteAnchor" />
rum motus, in orbitis ſuis, eſt contrarius motui, quem quoti-<lb />die in omnibus corporibus cœleſtibus obſervamus, quo in <lb />uno die tellurem circumferri videntur, de quo in ſequen-<lb />tibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-03" corresp="note-0630-03a" place="margin">945.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 13.</head>
        <p>
          <s xml:space="preserve">Motus, qualis eſt Planetarum in orbitis, dicitur in conſe-<lb />
<ptr xml:id="note-0630-04a" corresp="note-0630-04" type="noteAnchor" />
quentiâ, &amp; </s>
          <s xml:space="preserve">directus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-04" corresp="note-0630-04a" place="margin">946.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 14.</head>
        <p rend="italics">
          <s xml:space="preserve">Motus contrarius dicitur in antecedentiâ; </s>
          <s xml:space="preserve">aliquando etiam <lb />
<ptr xml:id="note-0630-05a" corresp="note-0630-05" type="noteAnchor" />
retrogradus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-05" corresp="note-0630-05a" place="margin">947.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quo à Sole magis removentur Planetæ, eo in orbitis lentiùs <lb />
<ptr xml:id="note-0630-06a" corresp="note-0630-06" type="noteAnchor" />
feruntur; </s>
          <s xml:space="preserve">ita ut tempora periodica magis diſtantium majora <lb />ſint, &amp; </s>
          <s xml:space="preserve">ex majori orbitâ percurſâ, &amp; </s>
          <s xml:space="preserve">ex lentiori motu.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-06" corresp="note-0630-06a" place="margin">948.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 15.</head>
        <p rend="italics">
          <s xml:space="preserve">Axis Planetæ dicitur linea, quæ per centrum Planetæ tran-<lb />
<ptr xml:id="note-0630-07a" corresp="note-0630-07" type="noteAnchor" />
ſit, &amp; </s>
          <s xml:space="preserve">circa quam hicce rotatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-07" corresp="note-0630-07a" place="margin">949.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planetæ, ſaltem plerique, &amp; </s>
          <s xml:space="preserve">Sol ipſer circa axes revol-<lb />
<ptr xml:id="note-0630-08a" corresp="note-0630-08" type="noteAnchor" />
vuntur: </s>
          <s xml:space="preserve">duo dantur circa quos, hujus reſpectu, obſervationes <lb />inſtituere non licuit, qui hoc motu probabiliter non deſti-<lb />tuuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-08" corresp="note-0630-08a" place="margin">950.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus hicce conſpirat cum motu Planetarum in orbitis, <lb />
<ptr xml:id="note-0630-09a" corresp="note-0630-09" type="noteAnchor" />
id eſt, eſt in antecedentiâ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-09" corresp="note-0630-09a" place="margin">951.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Axes ipſi motu parallelo feruntur, ita, ut ſingula axeos <lb />
<ptr xml:id="note-0630-10a" corresp="note-0630-10" type="noteAnchor" />
Planetæ puncta lineas æquales &amp; </s>
          <s xml:space="preserve">ſimiles deſcribant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-10" corresp="note-0630-10a" place="margin">952.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 16.</head>
        <p rend="italics">
          <s xml:space="preserve">Axeos extremitates dicuntur Planetæ Poli.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">953.</note>
        <p>
          <s xml:space="preserve">Planetarum à Sole diſtantias ſatis accuratè inter ſe con-<lb />
<ptr xml:id="note-0630-12a" corresp="note-0630-12" type="noteAnchor" />
ferunt Aſtronomi; </s>
          <s xml:space="preserve">ita ut totius Syſtematis ideam habeamus. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0630-13a" corresp="note-0630-13" type="noteAnchor" />
Orbium dimenſiones in hoc ſchemate repræſentantur, in quo <lb />puncta NN, ſingulorum orbium Nodos deſignant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0630-12" corresp="note-0630-12a" place="margin">954.</note>
              <note xml:space="preserve" xml:id="note-0630-13" corresp="note-0630-13a" place="margin"><hi rend="small caps">TAB. XX.</hi> <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0631" n="(111)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. I.</fw>
        <p rend="italics">
          <s xml:space="preserve">Nondum tamen hujus ſyſtematis dimenſiones, cum ullâ <lb />
<ptr xml:id="note-0631-01a" corresp="note-0631-01" type="noteAnchor" />
menſurâ nobis notâ, in ſuperficie Telluris, conferre poſſu-<lb />mus; </s>
          <s xml:space="preserve">obſervationes enim, circa talem collationem inſtitutas, <lb />erroris expertes eſſe Aſtronomus non aſſeret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-01" corresp="note-0631-01a" place="margin">955.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut autem variæ ſyſtematis partes inter ſe conferantur, <lb />
<ptr xml:id="note-0631-02a" corresp="note-0631-02" type="noteAnchor" />
ponimus mediam Telluris à Sole diſtantiam, dividi in 1000. <lb /></s>
          <s xml:space="preserve">partes æquales, quæ, in menſurandis reliquis dimenſionibus, <lb />adhibentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-02" corresp="note-0631-02a" place="margin">956.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Solo in medio ſyſtematis, ut ante dictum, exiguo motu agi-<lb />
<ptr xml:id="note-0631-03a" corresp="note-0631-03" type="noteAnchor" />
tatur; </s>
          <s xml:space="preserve">circa axem revolvitur in ſpatio 25. </s>
          <s xml:space="preserve">dierum: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">axis ad <lb />planum Eclipticæ inclinatur, efficiens angulum 87. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">30′.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-03" corresp="note-0631-03a" place="margin">957.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planetarum omnium minimè à Sole diſtat Mercurius ☿; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0631-04a" corresp="note-0631-04" type="noteAnchor" />
Hujus diſtantia media à Sole eſt 387: </s>
          <s xml:space="preserve">Excentricitas eſt 80.</s>
          <s xml:space="preserve">; <lb />Inclinatio orbitæ, id eſt, angulus à plano orbitæ cum plano <lb />Eclipticæ formatus, eſt 6. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">52′.</s>
          <s xml:space="preserve">: In tempore 87. </s>
          <s xml:space="preserve">dierum, <lb />23. </s>
          <s xml:space="preserve">horarum, revolutionem circa Solem peragit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-04" corresp="note-0631-04a" place="margin">958.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inſequitur Venus ♀; </s>
          <s xml:space="preserve">cujus diſtantia media à Sole eſt 723: <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0631-05a" corresp="note-0631-05" type="noteAnchor" />
Excentricitas 5: </s>
          <s xml:space="preserve">Inclinatio orbitæ 3. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">23′: </s>
          <s xml:space="preserve">Tempus pe-<lb />riodicum 224. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">17. </s>
          <s xml:space="preserve">hor.</s>
          <s xml:space="preserve">: Circa axem rotatur in 23. <lb /></s>
          <s xml:space="preserve">horis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-05" corresp="note-0631-05a" place="margin">959.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planeta tertius ordine à Sole, eſt Tellus noſtra ♁, hujus <lb />
<ptr xml:id="note-0631-06a" corresp="note-0631-06" type="noteAnchor" />
diſtantia media à Sole eſt 1000.</s>
          <s xml:space="preserve">: Excentricitas 169: </s>
          <s xml:space="preserve">In ipſo <lb />plano Eclipticæ movetur. </s>
          <s xml:space="preserve">Tempus periodicum eſt 365. </s>
          <s xml:space="preserve">dier. <lb /></s>
          <s xml:space="preserve">5. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">51′: </s>
          <s xml:space="preserve">Circa axem in ſpatio 23. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">56′. </s>
          <s xml:space="preserve">4″. </s>
          <s xml:space="preserve">revolvi-<lb />tur: </s>
          <s xml:space="preserve">Axis cum plano Eclipticæ efficit angulum 66. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">31′.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-06" corresp="note-0631-06a" place="margin">960.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Mars ♂ à Sole in mediâ diſtantiâ removetur 1524.</s>
          <s xml:space="preserve">: Ex-<lb />
<ptr xml:id="note-0631-07a" corresp="note-0631-07" type="noteAnchor" />
centricitas eſt 141.</s>
          <s xml:space="preserve">: Inclinatio orbitæ 1. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">52′.</s>
          <s xml:space="preserve">: Tempus <lb />periodicum 686. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">23. </s>
          <s xml:space="preserve">hor.</s>
          <s xml:space="preserve">. Circa axem revolutionem <lb />peragit in 24. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">40′.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-07" corresp="note-0631-07a" place="margin">961.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Jupiter ♃ Planetarum maximus, à Sole diſtat mediâ re-<lb />
<ptr xml:id="note-0631-08a" corresp="note-0631-08" type="noteAnchor" />
motione 5201.</s>
          <s xml:space="preserve">: Excentricitas 250.</s>
          <s xml:space="preserve">: Inclinatio orbitæ, <lb />1. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">20′.</s>
          <s xml:space="preserve">: Tempus periodicum 4332. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">12. </s>
          <s xml:space="preserve">hor.</s>
          <s xml:space="preserve">: Circa <lb />axem revolvitur in 9. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">56′.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-08" corresp="note-0631-08a" place="margin">962.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Saturni ♄ Planetarum remotiſſimi à Sole diſtantia media <lb />
<ptr xml:id="note-0631-09a" corresp="note-0631-09" type="noteAnchor" />
eſt 9538.</s>
          <s xml:space="preserve">: Excentricitas 547.</s>
          <s xml:space="preserve">: Orbitæ inclinatio 2. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">30′.</s>
          <s xml:space="preserve">: <lb />Tempus periodicum 10759. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">hor.</s>
          <s xml:space="preserve">. Hic annulo cir-<lb />cumdatur, qui Planetam non tangit, &amp; </s>
          <s xml:space="preserve">hunc nunquam de-
</s>
          <pb facs="0632" n="(112)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſerit: </s>
          <s xml:space="preserve">niſi adhibito Teleſcopio viſibilis non eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0631-09" corresp="note-0631-09a" place="margin">963.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Datâ diſtantiâ mediâ, addendo excentricitatem, detegitur <lb />maxima diſtantia; </s>
          <s xml:space="preserve">ſubtractâ verò excentricitate ex mediâ di-<lb />ſtantiâ, determinatur diſtantia minima <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0632-01a" corresp="note-0632-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0632-01" corresp="note-0632-01a" n="*" anchored="true" place="margin">836.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">T@es Planetæ, Mars, Jupiter, &amp; </s>
          <s xml:space="preserve">Saturnus, qui ultra <lb />
<ptr xml:id="note-0632-02a" corresp="note-0632-02" type="noteAnchor" />
Tellurem à Sole removentur, dicuntur ſuperiores. </s>
          <s xml:space="preserve">Inferio-<lb />res Planetæ vocantur Venus &amp; </s>
          <s xml:space="preserve">Mercurius.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0632-02" corresp="note-0632-02a" place="margin">964.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Inter primarios Planetas tres ſecundariis ſtipantur.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">965.</note>
        <p>
          <s xml:space="preserve">Circa Saturnum quinque Planetæ, ſatellites dicti, moventur: <lb /></s>
          <s xml:space="preserve">Circa Jovem quatuor: </s>
          <s xml:space="preserve">Circa Tellurem unus, Luna nempe.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Planetæ ſecundarii, Lunâ exceptâ, nudis oculis non dete-<lb />guntur.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Satellites circa primarios deſcribunt areas, lineis ad cen-<lb />
<ptr xml:id="note-0632-04a" corresp="note-0632-04" type="noteAnchor" />
tra primariorum, ductis, temporibus proportionales; </s>
          <s xml:space="preserve">ut re-<lb />ſpectu centri Solis de primariis dictum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0632-05a" corresp="note-0632-05" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0632-04" corresp="note-0632-04a" place="margin">966.</note>
              <note xml:space="preserve" xml:id="note-0632-05" corresp="note-0632-05a" n="*" anchored="true" place="margin">944.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Luna circa Tellurem in ellipſi movetur, cujus focorum al-<lb />
<ptr xml:id="note-0632-06a" corresp="note-0632-06" type="noteAnchor" />
ter occupat Telluris centrum, à quo Lunæ diſtantia media <lb />eſt ſemidiametrorum Telluris 60 {2/9}.</s>
          <s xml:space="preserve">: Excentricitas mutatio-<lb />
<ptr xml:id="note-0632-07a" corresp="note-0632-07" type="noteAnchor" />
ni obnoxia eſt, media eſt ſemidiametrorum 3 {1/3}.</s>
          <s xml:space="preserve">: Planum or-<lb />
<ptr xml:id="note-0632-08a" corresp="note-0632-08" type="noteAnchor" />
bitæ, cum plano Eclipticæ, efficit angulum circiter 5. </s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve">, ſed <lb />non conſtans eſt hæc inclinatio. </s>
          <s xml:space="preserve">In motu Lunæ circa Tellurem, <lb />
<ptr xml:id="note-0632-09a" corresp="note-0632-09" type="noteAnchor" />
non motu parallelo feruntur, neque linea Apſidum, neque li-<lb />nea Nodorum; </s>
          <s xml:space="preserve">ſed hæc in antecedentia, illa in conſequentia <lb />fertur; </s>
          <s xml:space="preserve">prima in 9. </s>
          <s xml:space="preserve">circiter annis revolutionem peragit, ſe-<lb />cunda in 19. </s>
          <s xml:space="preserve">Annis. </s>
          <s xml:space="preserve">Lunæ tempus periodicum, circa tellu-<lb />rem eſt 27. </s>
          <s xml:space="preserve">dierum &amp; </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">circiter horarum; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">exactiſſimè in <lb />eodem tempore circa axem rotatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0632-06" corresp="note-0632-06a" place="margin">967.</note>
              <note xml:space="preserve" xml:id="note-0632-07" corresp="note-0632-07a" place="margin">968.</note>
              <note xml:space="preserve" xml:id="note-0632-08" corresp="note-0632-08a" place="margin">969.</note>
              <note xml:space="preserve" xml:id="note-0632-09" corresp="note-0632-09a" place="margin">970</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planetarum circumjovialium primus ſeu intimus, à Jovis <lb />
<ptr xml:id="note-0632-10a" corresp="note-0632-10" type="noteAnchor" />
centro diſtat diametros Jovis 2 {5/6}.</s>
          <s xml:space="preserve">: circa Jovem circumvol-<lb />
<ptr xml:id="note-0632-11a" corresp="note-0632-11" type="noteAnchor" />
vitur in uno die 18. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">28′.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0632-10" corresp="note-0632-10a" place="margin">971.</note>
              <note xml:space="preserve" xml:id="note-0632-11" corresp="note-0632-11a" place="margin"><hi rend="small caps">TAB. XX.</hi> <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Secundi diſtantia eſt diametrorum Jovis 4 {1/2}.</s>
          <s xml:space="preserve">: tempus pe-<lb />riodicum 3. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">13. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">18′.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tertii diſtantia eſt 7 {1/6}. </s>
          <s xml:space="preserve">diam.</s>
          <s xml:space="preserve">: Tempus periodicum 7. </s>
          <s xml:space="preserve">dier. <lb /></s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">hor.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quartus diſtat 12 {2/3}. </s>
          <s xml:space="preserve">diam.</s>
          <s xml:space="preserve">: Revolvitur in tempore 16. </s>
          <s xml:space="preserve">dier. <lb /></s>
          <s xml:space="preserve">18. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">5′.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Primus ſeu intimus Saturni Satelles, à centro Saturni di-<lb />
<ptr xml:id="note-0632-12a" corresp="note-0632-12" type="noteAnchor" />
</s>
          <pb facs="0633" n="(113)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. I.</fw>
ſtat {39/40}. </s>
          <s xml:space="preserve">diam. </s>
          <s xml:space="preserve">Annuli: </s>
          <s xml:space="preserve">Tempus periodicum 1. </s>
          <s xml:space="preserve">diei, 21. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">18′.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0632-12" corresp="note-0632-12a" place="margin">972. <lb /><hi rend="small caps">TAB. XX.</hi> <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Secundi diſtantia eſt diam. </s>
          <s xml:space="preserve">Ann. </s>
          <s xml:space="preserve">1 {1/4}.</s>
          <s xml:space="preserve">: Tempus periodicum <lb />2. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">17. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">41′.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Tertii diſtantia eſt 1 {3/4}. </s>
          <s xml:space="preserve">diam. </s>
          <s xml:space="preserve">Ann.</s>
          <s xml:space="preserve">: Tempus periodicum <lb />4. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">13. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">47′.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quarti diſtantia 4. </s>
          <s xml:space="preserve">diam. </s>
          <s xml:space="preserve">Ann.</s>
          <s xml:space="preserve">: Tempus periodicum <lb />15. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">22. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">41′.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quinti diſtantia 12. </s>
          <s xml:space="preserve">diam. </s>
          <s xml:space="preserve">Ann.</s>
          <s xml:space="preserve">: Tempus periodicum <lb />79. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">53′.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Demotu horum, ut &amp; </s>
          <s xml:space="preserve">Jovialium Satellitum, circa axes, nil certi <lb />
<ptr xml:id="note-0633-01a" corresp="note-0633-01" type="noteAnchor" />
huc uſque ex obſervationibus Aſtronomicis determinari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0633-01" corresp="note-0633-01a" place="margin">973.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ad diſtantias &amp; </s>
          <s xml:space="preserve">Tempora periodica Planetarum attenda-<lb />mus, hanc regulam in noſtro Syſtemate, ubicunque plurima <lb />corpora circa idem punctum revolvuntur, id eſt, circa So-<lb />
<ptr xml:id="note-0633-02a" corresp="note-0633-02" type="noteAnchor" />
lem, Saturnum, &amp; </s>
          <s xml:space="preserve">Jovem, obtinêre videmus; </s>
          <s xml:space="preserve">Quadrata <lb />Temporum periodicorum eſſe inter ſe, ut ſunt cubi diſtantia-<lb />rum mediarum à centro.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0633-02" corresp="note-0633-02a" place="margin">974.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dimenſionum ipſorum corporum, in noſtro ſyſtemate, i-<lb />
<ptr xml:id="note-0633-03a" corresp="note-0633-03" type="noteAnchor" />
deam damus in fig. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve">, in qua omnes Planetæ primarii, ut &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0633-04a" corresp="note-0633-04" type="noteAnchor" />
Saturni annulus, ſecundum dimenſiones ſuas, delineantur; <lb /></s>
          <s xml:space="preserve">Sol, cujus magnitudo omnes alias excedit, repræſentatur cir-<lb />culo maximo fig. </s>
          <s xml:space="preserve">1.</s>
          <s xml:space="preserve">, id eſt, figuram terminante.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0633-03" corresp="note-0633-03a" place="margin">975.</note>
              <note xml:space="preserve" xml:id="note-0633-04" corresp="note-0633-04a" place="margin"><hi rend="small caps">TAB. XX.</hi> <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæ dimenſiones ſatis exactè proportiones corporum inter <lb />ſe exhibent, ſi tellurem excipiamus, quæ, ex ratione jam <lb />tradita <ptr type="noteAnchor" />, cum cæteris corporibus ita conferri non poteſt, ut
<ptr xml:id="note-0633-05a" corresp="note-0633-05" type="noteAnchor" />
de errore dubium nullum ſuperſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0633-05" corresp="note-0633-05a" n="*" anchored="true" place="margin">955.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Menſuratur tamen Telluris diameter, &amp; </s>
          <s xml:space="preserve">eſt 340069. </s>
          <s xml:space="preserve">per-<lb />
<ptr xml:id="note-0633-06a" corresp="note-0633-06" type="noteAnchor" />
ticarum, quarum ſingulæ continent 12. </s>
          <s xml:space="preserve">pedes Rhynlandicos; <lb /></s>
          <s xml:space="preserve">ſed licèt inter ſe, &amp; </s>
          <s xml:space="preserve">cumSolis diametro, conferantur cætero-<lb />rum Planetarum diametri, quot pedes hæ contineant exactè, <lb />niſi poſt, in tempore opportuno, inſtituendas obſervationes, <lb />determinari non poterit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0633-06" corresp="note-0633-06a" place="margin">976.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inter corpora Syſtema Planetarium componentia, ſola Lu-<lb />
<ptr xml:id="note-0633-07a" corresp="note-0633-07" type="noteAnchor" />
na cum Tellure confertur; </s>
          <s xml:space="preserve">hujus diameter eſt ad Lunæ dia-<lb />metrum, ut 40. </s>
          <s xml:space="preserve">ad 11.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0633-07" corresp="note-0633-07a" place="margin">977.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planetæ ſecundarii reliqui, ab Aſtronomis non menſuran-<lb />
<ptr xml:id="note-0633-08a" corresp="note-0633-08" type="noteAnchor" />
tur, quoſdam tamen magnitudine Tellurem excedere, in du-<lb />bium vix vocari poterit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0633-08" corresp="note-0633-08a" place="margin">978.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0634" n="(114)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Præter corpora huc uſque memorata, in ſyſtemate plane-<lb />tario, quædam alia per tempus videntur, quæ ad Solem ac-<lb />cedunt, deinde ab hoc recedunt, &amp; </s>
          <s xml:space="preserve">inviſibilia fiunt; </s>
          <s xml:space="preserve">Come-<lb />
<ptr xml:id="note-0634-01a" corresp="note-0634-01" type="noteAnchor" />
tæ dicuntur. </s>
          <s xml:space="preserve">Hi plerumque caudati apparent, &amp; </s>
          <s xml:space="preserve">cauda <lb />ſemper à Sole averſa datur. </s>
          <s xml:space="preserve">In motu ſuo deſcribunt areas, <lb />
<ptr xml:id="note-0634-02a" corresp="note-0634-02" type="noteAnchor" />
lineis ad centrum Solis ductis, temporibus proportionales, <lb />ut de Planetis dictum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0634-03a" corresp="note-0634-03" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0634-01" corresp="note-0634-01a" place="margin">979.</note>
              <note xml:space="preserve" xml:id="note-0634-02" corresp="note-0634-02a" place="margin">980.</note>
              <note xml:space="preserve" xml:id="note-0634-03" corresp="note-0634-03a" n="*" anchored="true" place="margin">944. 966.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa Cometas probabile eſt, illos in orbitis ellipticis ad-<lb />
<ptr xml:id="note-0634-04a" corresp="note-0634-04" type="noteAnchor" />
modum excontricis moveri; </s>
          <s xml:space="preserve">ita ut inviſibiles ſint, quando â <lb />Sole remotiorem orbitæ partem occupant; </s>
          <s xml:space="preserve">quod ex quo-<lb />rundam periodis ſatis regularibus deducitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ex obſer-<lb />vationibus conſtat, quoſdam pertiones Ellipſium valdè ex-<lb />
<ptr xml:id="note-0634-05a" corresp="note-0634-05" type="noteAnchor" />
centricarum, in quarum foco centrum Solis erat, in motu <lb />ſuo deſcripſiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0634-04" corresp="note-0634-04a" place="margin">981.</note>
              <note xml:space="preserve" xml:id="note-0634-05" corresp="note-0634-05a" place="margin">982.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quam huc uſque ideam Syſtematis Planetarii dedi, Aſtro-<lb />nomicis nititur obſervationibus; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, de huc uſque dictis, nul-<lb />la lis eſt inter Aſtronomos, ſi excipiamus, quæ lineam ellipti-<lb />cam &amp; </s>
          <s xml:space="preserve">motum Telluris ſpectant.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quidam Planetarum orbitas non eſſe ellipticas, ſed illos, <lb />in motu, aliam ovalem deſcribere contendunt: </s>
          <s xml:space="preserve">ex obſerva-<lb />tionibus Tichonis Brahe deduxit Keplerus, lineas has eſſe el-<lb />lipticas; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">curvas alias à Planetis non poſſe deſcribi, in par-<lb />te ſequenti videbimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Qui Tellurem quieſcere contendunt, nullo Aſtronomico <lb />aut Phyſico nituntur argumento; </s>
          <s xml:space="preserve">id eſt, ex Phoenomenis <lb />non ratiocinantur: </s>
          <s xml:space="preserve">neglectâ Syſtematis ſimplicitate, &amp; </s>
          <s xml:space="preserve">in <lb />hoc motuum analogià, ſententiam ſuam obſervationibus <lb />non contrariari defendunt; </s>
          <s xml:space="preserve">in quo illos errare, in parte ſe-<lb />quenti videbimus.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT II.</head>
        <head rend="italics" xml:space="preserve">De motu apparenti.</head>
        <p>
          <s xml:space="preserve">QUi, lecto capite præcedenti, coelum intuebitur, illud ſe, <lb />quod ibi exponitur, ſyſtema contemplari vix credet; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">exactior motuum coeleſtium conſideratio dubium <lb />augebit. </s>
          <s xml:space="preserve">Nil mirum, in cœlis præter falſas apparentias vix <lb />
<ptr xml:id="note-0634-06a" corresp="note-0634-06" type="noteAnchor" />
quicquam obſervamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0634-06" corresp="note-0634-06a" place="margin">983.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0635" />
        <pb facs="0635a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0635a-01" />
          <label>0635a-01</label>
        </figure>
        <pb facs="0636" />
        <pb facs="0637" n="(115)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. II.</fw>
        <p>
          <s xml:space="preserve">Variis motibus agitatus ſpectator, qui ſe quieſcere cogitat, <lb />&amp; </s>
          <s xml:space="preserve">intuetur corpora, circa quorum diſtantiam &amp; </s>
          <s xml:space="preserve">magnitudi-<lb />nem falſa fert judicia, vulgaris eſt cœlorum contemplator. <lb /></s>
          <s xml:space="preserve">Per multa ſæcula verum Mundi Syſtema, cœlum etiam ex-<lb />actius obſervantes, latuit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Explicandum autem nobis eſt, quomodo omnia, quæ circa <lb />
<ptr xml:id="note-0637-01a" corresp="note-0637-01" type="noteAnchor" />
corpora cœleſtia obſervantur, reſpectu ſpectatoris in Tel-<lb />lure, locum habeant in Syſtemate expoſito; </s>
          <s xml:space="preserve">id eſt, ex ve-<lb />ris motibus apparentias deducemus. </s>
          <s xml:space="preserve">Quod fieri non poteſt, <lb />niſi quibuſdam generalibus præmiſſis, de motu apparenti in <lb />genere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0637-01" corresp="note-0637-01a" place="margin">984.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motum verum nullâ arte à nobis obſervari poſſe, extra o-<lb />mne dubium eſt; </s>
          <s xml:space="preserve">ſolus motus relativus ſub ſenſus cadit; </s>
          <s xml:space="preserve">de <lb />eo etiam tantùm agitur in capite præcedenti: </s>
          <s xml:space="preserve">Quis affirma. <lb /></s>
          <s xml:space="preserve">re aut negare cum ratione poterit, non motu communi o-<lb />mnia corpora nobis nota, per ſpatia immenſa transferri?</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Motus relativus ab apparenti diſtinguendus eſt; </s>
          <s xml:space="preserve">hic enim <lb />
<ptr xml:id="note-0637-02a" corresp="note-0637-02" type="noteAnchor" />
eſt mutâtio viſa in ſitu corporum, &amp; </s>
          <s xml:space="preserve">pendet à mutatione in <lb />picturâ in fundo oculi; </s>
          <s xml:space="preserve">nam objecta illam inter ſe relationem <lb />apparentem habent, quæ datur in oculo inter objectorum <lb />repræſentationes; </s>
          <s xml:space="preserve">videntur enim ut in oculo depinguntur<ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0637-03a" corresp="note-0637-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">mutatio in hac picturâ ex corporum motu, ferè ſemper <lb />differt cum mutatione relationis inter ipſa corpora; </s>
          <s xml:space="preserve">ut ex <lb />picturæ formatione ſequitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0637-02" corresp="note-0637-02a" place="margin">985.</note>
              <note xml:space="preserve" xml:id="note-0637-03" corresp="note-0637-03a" n="*" anchored="true" place="margin">716.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cœlum nibil eſt prœter ſpatium immenſum, quod videri <lb />
<ptr xml:id="note-0637-04a" corresp="note-0637-04" type="noteAnchor" />
non poteſt, &amp; </s>
          <s xml:space="preserve">nigrum apparêret <ptr type="noteAnchor" />, niſi continuò radii lumi-
<ptr xml:id="note-0637-05a" corresp="note-0637-05" type="noteAnchor" />
nis innumeri, à corporibus cœleſtibus manantes Atmoſphæ-<lb />ram penetrarent. </s>
          <s xml:space="preserve">Plerique per rectas lineas, à corporibus <lb />ad nos, perveniunt, multi tamen in Atmoſphærâ varias pa-<lb />tiuntur reflectiones &amp; </s>
          <s xml:space="preserve">totam Atmoſphæram illuminant; </s>
          <s xml:space="preserve">in-<lb />de de die, etiam abſque nubium reflectione, corpora illu-<lb />ſtrantur, ad quæ radii ſolares directè pervenire nequeunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0637-04" corresp="note-0637-04a" place="margin">986.</note>
              <note xml:space="preserve" xml:id="note-0637-05" corresp="note-0637-05a" n="*" anchored="true" place="margin">845.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii hi ſunt hæterogenei, &amp; </s>
          <s xml:space="preserve">quidem albi; </s>
          <s xml:space="preserve">nam corpora <lb />dantur hiſce radiis illuſtrata, quæ alba apparent; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hæc, per <lb />priſmata viſa, ad extremitates coloribus tinguntur; </s>
          <s xml:space="preserve">quod in <lb />colore homogeneo non obtinet <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">etiam circulus chartæ al-
<ptr xml:id="note-0637-06a" corresp="note-0637-06" type="noteAnchor" />
bæ, diametri ſemi pollicis, panno nigro ſuper impoſitus, ſi
</s>
          <pb facs="0638" n="(116)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
hiſce radiis illuminetur, per priſma oblongus apparet, &amp; </s>
          <s xml:space="preserve"><lb />iidem colores, qui in radiis ſolaribus obſervantur <ptr type="noteAnchor" />, eodem
<ptr xml:id="note-0638-01a" corresp="note-0638-01" type="noteAnchor" />
modo hìc videntur; </s>
          <s xml:space="preserve">quæ omnia minimè obtinerent, ſi aër, ut <lb />à plurimis ſtatuitur, foret liquidum cœruleum, id eſt, per <lb />quod ſoli radii cœrulei, ſaltem maximâ copiâ, tranſeunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0637-06" corresp="note-0637-06a" n="*" anchored="true" place="margin">874.</note>
              <note xml:space="preserve" xml:id="note-0638-01" corresp="note-0638-01a" n="*" anchored="true" place="margin">861.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum cœlum nigrum intuemur, radii albi memorati oculos <lb />
<ptr xml:id="note-0638-02a" corresp="note-0638-02" type="noteAnchor" />
intrant, unde color cœruleus cœlorum oritur. </s>
          <s xml:space="preserve">Quia adſueti <lb />ſumus colorem videre, ubi objectum datur coloratum, etiam <lb />ad objectum refertur color cœlorum; </s>
          <s xml:space="preserve">cùm autem hic ver-<lb />ſus omnes partes æqualiter obſervetur, concipimus ſuperfi-<lb />
<ptr xml:id="note-0638-03a" corresp="note-0638-03" type="noteAnchor" />
ciem cavam ſphœricam, in cujus centro ipſi poſiti ſumus; </s>
          <s xml:space="preserve">ſu-<lb />perficies hœc ut opaca, ideoque ultra omnia corpora nobis <lb />viſibilia remota, imaginatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0638-02" corresp="note-0638-02a" place="margin">987.</note>
              <note xml:space="preserve" xml:id="note-0638-03" corresp="note-0638-03a" place="margin">988.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando inter planum &amp; </s>
          <s xml:space="preserve">oculum datur Corpus, de cujus <lb />diſtantiâ judicium ferre non poſſumus, plano applicatum no-<lb />bis apparet corpus, quæcunque fuerit diſtantia inter hoc &amp; </s>
          <s xml:space="preserve"><lb />planum; </s>
          <s xml:space="preserve">nulla enim datur ratio, quare partes plani, quæ ad <lb />latera imaginis corporis in oculo depinguntur, non ad ean-<lb />dem diſtantiam cum corpore apparêrent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Inde etiam omnia corpora cœleſtia, (quorum minimè à <lb />
<ptr xml:id="note-0638-04a" corresp="note-0638-04" type="noteAnchor" />
nobis diſtans, Luna nempè, ita removetur, ut judicium de <lb />diſtantiâ non detur <ptr type="noteAnchor" />,) ad ſphœram imaginariam, memora-
<ptr xml:id="note-0638-05a" corresp="note-0638-05" type="noteAnchor" />
tam, referuntur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">omnia œque remota apparent; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in ſu-<lb />perficie ſphœrœ cavœ moveri videntur. </s>
          <s xml:space="preserve">Sic Luna inter ſtellas <lb />fixas concipitur, licet illius diſtantia vix rationem ſenſibilem <lb />habeat ad Saturni diſtantiam, quæ ipſa evaneſcit collata cum <lb />immenſâ ſtellarum fixarum remotione. </s>
          <s xml:space="preserve">Non mirum eſt igi-<lb />tur, ſi de magnitudine corporum cœleſtium &amp; </s>
          <s xml:space="preserve">cœlorum im-<lb />menſitate nil noſcat vulgus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0638-04" corresp="note-0638-04a" place="margin">989.</note>
              <note xml:space="preserve" xml:id="note-0638-05" corresp="note-0638-05a" n="*" anchored="true" place="margin">732.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Videmus ex dictis, quomodo ex dato motu corporis cu-<lb />juſcunque, &amp; </s>
          <s xml:space="preserve">noto motu Telluris, motus apparens determi-<lb />netur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sphæram diximus imaginari ultra ſtellas fixas, in cujus cen-<lb />tro datur ſpectator <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">orbita Telluris adeò eſt exigua re-
<ptr xml:id="note-0638-06a" corresp="note-0638-06" type="noteAnchor" />
ſpectu diametri hujus ſphæræ, ut ex tranſlato cum Tellure, <lb />ſpectatore, centrum ſphæræ ſenſibiliter non mutetur; </s>
          <s xml:space="preserve">Qua-<lb />re in omnibus ſuperficiei Tellur is punctis, &amp; </s>
          <s xml:space="preserve">in tempore quo-<lb />
<ptr xml:id="note-0638-07a" corresp="note-0638-07" type="noteAnchor" />
</s>
          <pb facs="0639" n="(117)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. III.</fw>
cunque, eandem Terricolœ imaginantur ſphæram, ad quam <lb />corpora cœleſtia referunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quam, in ſequentibus, nomina-<lb />bimus ſphœram ſtellarum fixarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0638-06" corresp="note-0638-06a" n="*" anchored="true" place="margin">988.</note>
              <note xml:space="preserve" xml:id="note-0638-07" corresp="note-0638-07a" place="margin">990.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hiſce poſitis, ſi per Tellurem, &amp; </s>
          <s xml:space="preserve">corpus, lineam concipia-<lb />
<ptr xml:id="note-0639-01a" corresp="note-0639-01" type="noteAnchor" />
mus, quœ ultra corpus continuata ſphœram memoratam ſecat, <lb />habemus punctum, ad quod corpus memoratum refertur, &amp; </s>
          <s xml:space="preserve"><lb />quod eſt locus apparens corporis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0639-01" corresp="note-0639-01a" place="margin">991.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum corpus, aut Tellus, aut ambo, moventur, agitatur <lb />hæc linea, &amp; </s>
          <s xml:space="preserve">motus apparens eſt linea, quam inter ſtellas <lb />
<ptr xml:id="note-0639-02a" corresp="note-0639-02" type="noteAnchor" />
fixas deſcribit extremitas lineœ memoratæ, tranſeuntis per <lb />Tellurem &amp; </s>
          <s xml:space="preserve">corpus, cujus motus apparens obſervatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0639-02" corresp="note-0639-02a" place="margin">992.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Idcirco eœdem apparentiœ ex tranſlatâ Tellure ſequuntur, <lb />
<ptr xml:id="note-0639-03a" corresp="note-0639-03" type="noteAnchor" />
quàm ex tranſlato corpore, &amp; </s>
          <s xml:space="preserve">eædem etiam ex motu amborum <lb />deduci poßunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0639-03" corresp="note-0639-03a" place="margin">993.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si autem Corpus &amp; </s>
          <s xml:space="preserve">Tellus ita moveantur, ut linea, quœ <lb />
<ptr xml:id="note-0639-04a" corresp="note-0639-04" type="noteAnchor" />
per bœc corpora tranſit, motu parallelo feratur, corpus in-<lb />ter ſtellas fixas quieſcere videbitur; </s>
          <s xml:space="preserve">quia ſpatium, in hoc <lb />caſu, ab extremitate lineæ inter ſtellas percurſum, non <lb />poteſt ſuperare ſpatium à Tellure percurſum; </s>
          <s xml:space="preserve">linea autem <lb />æqualis toti ſpatio, quod à Tellure poteſt percurri, ad diſtan-<lb />tiam ſtellarum fixarum remota, nobis ſenſibilis non eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0639-04" corresp="note-0639-04a" place="margin">994.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex motu Telluris circa axem etiam datur motus apparens, <lb />
<ptr xml:id="note-0639-05a" corresp="note-0639-05" type="noteAnchor" />
qui ſuo tempore, ex fundamentis in hoc capite poſitis, fa-<lb />cilè deducetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0639-05" corresp="note-0639-05a" place="margin">995.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motum apparentem à relativo differre, &amp; </s>
          <s xml:space="preserve">ex motu ſpe-<lb />ctatoris variari, navigantes quotidie experiuntur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT III.</head>
        <head rend="italics" xml:space="preserve">De Phœnomenis Solis ex motu Telluris in orbitâ.</head>
        <p>
          <s xml:space="preserve">SIt Sol in S; </s>
          <s xml:space="preserve">Tellus in orbitâ ſuâ in T; </s>
          <s xml:space="preserve">rs ſphæra ſtella-<lb />
<ptr xml:id="note-0639-06a" corresp="note-0639-06" type="noteAnchor" />
rum fixarum; </s>
          <s xml:space="preserve">locus apparens Solis eſt s <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Dum Tellus
<ptr xml:id="note-0639-07a" corresp="note-0639-07" type="noteAnchor" />
in orbit â transfertur à Tin t, Sol moveri videtur, &amp; </s>
          <s xml:space="preserve">percur-<lb />
<ptr xml:id="note-0639-08a" corresp="note-0639-08" type="noteAnchor" />
rere arcum s r <ptr type="noteAnchor" />, qui menſurat angulum r S s, æqualem
<ptr xml:id="note-0639-09a" corresp="note-0639-09" type="noteAnchor" />
angulo T S t; </s>
          <s xml:space="preserve">ita, ut celeritas motus apparentis Solis pen-<lb />deat, à celeritate motus angularis Telluris, reſpectu centri <lb />Solis; </s>
          <s xml:space="preserve">qui motus ex duplici cauſâ creſcit; </s>
          <s xml:space="preserve">ex imminutâ di-
</s>
          <pb facs="0640" n="(118)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſtantiâ à Sole, &amp; </s>
          <s xml:space="preserve">ex auctâ celeritate Telluris: </s>
          <s xml:space="preserve">quæ ambæ <lb />
<ptr xml:id="note-0640-01a" corresp="note-0640-01" type="noteAnchor" />
cauſæ ſemper concurrunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare motus apparentis Solis
<ptr xml:id="note-0640-02a" corresp="note-0640-02" type="noteAnchor" />
inœqualitas ſenſibilis eſt. </s>
          <s xml:space="preserve">In integr â Telluris revolutione, e-<lb />
<ptr xml:id="note-0640-03a" corresp="note-0640-03" type="noteAnchor" />
tiam integrum circulum Sol percurrere videtur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0639-06" corresp="note-0639-06a" place="margin"><hi rend="small caps">TAB. XXI</hi>. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0639-07" corresp="note-0639-07a" place="margin">996.</note>
              <note xml:space="preserve" xml:id="note-0639-08" corresp="note-0639-08a" n="*" anchored="true" place="margin">991.</note>
              <note xml:space="preserve" xml:id="note-0639-09" corresp="note-0639-09a" n="*" anchored="true" place="margin">992.</note>
              <note xml:space="preserve" xml:id="note-0640-01" corresp="note-0640-01a" n="*" anchored="true" place="margin">944.</note>
              <note xml:space="preserve" xml:id="note-0640-02" corresp="note-0640-02a" place="margin">797.</note>
              <note xml:space="preserve" xml:id="note-0640-03" corresp="note-0640-03a" place="margin">998.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Via hæc apparens Solis, Linea Ecliptica vocatur. </s>
          <s xml:space="preserve">Eſt ſe-<lb />
<ptr xml:id="note-0640-04a" corresp="note-0640-04" type="noteAnchor" />
ctio ſphæræ ſtellarum fixarum cum plano Eclipticæ, ad hanc <lb />ſphæram uſque continuato.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0640-04" corresp="note-0640-04a" place="margin">999.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dividitur hæc via in duodecim partes æquales, quæ ſin-<lb />gulæ continent 30. </s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve">; partes hæ vocantur Signa, &amp; </s>
          <s xml:space="preserve">no-<lb />minibus dantur; </s>
          <s xml:space="preserve">Aries ♈, Taurus ♉, Gemini II, Cancer ♋, <lb />Leo ♌, Virgo ♍, Libra ♎, Scorpius ♏, Sagittarius ♐, <lb />Capricornus <unclear reason="illegible" />, Aquarius ♒, Piſces <unclear reason="illegible" />. </s>
          <s xml:space="preserve">Unde hæ partes <lb />nomina mutuatæ ſint, ubi de ſtellis fixis acturi ſumus vide-<lb />bimus.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Diutius in percurrendis ſex ſignis primis bœret Sol, quàm <lb />
<ptr xml:id="note-0640-05a" corresp="note-0640-05" type="noteAnchor" />
in ſex poſterioribus, daturque differentia novem dierum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0640-05" corresp="note-0640-05a" place="margin">1000.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Licèt circulus nullum habeat principium aut finem, ubi <lb />
<ptr xml:id="note-0640-06a" corresp="note-0640-06" type="noteAnchor" />
tamen, in hoc, puncta varia determinanda ſunt, quoddam <lb />punctum pro principio habendum eſt; </s>
          <s xml:space="preserve">hoc, in lineâ Eclipti-<lb />câ, eſt primum punctum Arietis; </s>
          <s xml:space="preserve">quomodo determinetur, in <lb />ſequentibus videbimus. </s>
          <s xml:space="preserve">Non eſt ſixum inter ſtellas fixas; </s>
          <s xml:space="preserve">id-<lb />circo orbitæ Planetarum, quæ adeò parum mutantur, ut pro <lb />
<ptr xml:id="note-0640-07a" corresp="note-0640-07" type="noteAnchor" />
immutabilibus haberi poſſint <ptr type="noteAnchor" />, non eundem reſpectu bujus
<ptr xml:id="note-0640-08a" corresp="note-0640-08" type="noteAnchor" />
puncti ſitum ſervant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0640-06" corresp="note-0640-06a" place="margin">1001.</note>
              <note xml:space="preserve" xml:id="note-0640-07" corresp="note-0640-07a" place="margin">1002.</note>
              <note xml:space="preserve" xml:id="note-0640-08" corresp="note-0640-08a" n="*" anchored="true" place="margin">929.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Diſtantia Solis à primo puncto Arietis, in conſequentiâ, <lb />
<ptr xml:id="note-0640-09a" corresp="note-0640-09" type="noteAnchor" />
menſurata, dicitur Solis Longitudo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0640-09" corresp="note-0640-09a" place="margin">1003.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Longitudines cœterorum corporum cœleſtium, eodem modo in <lb />
<ptr xml:id="note-0640-10a" corresp="note-0640-10" type="noteAnchor" />
Eclipticâ menſurantur; </s>
          <s xml:space="preserve">Ad banc referuntur, ſi circulus ma-<lb />
<ptr xml:id="note-0640-11a" corresp="note-0640-11" type="noteAnchor" />
jor per corpus concipiatur perpendicularis ad Eclipticam; <lb /></s>
          <s xml:space="preserve">punctum enim, in quo hæc ab illo circulo ſecatur, determi-<lb />nat corporis longitudinem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0640-10" corresp="note-0640-10a" place="margin">1004.</note>
              <note xml:space="preserve" xml:id="note-0640-11" corresp="note-0640-11a" place="margin">1005.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Diſtantia corporis cœieſtis à lineâ Eclipticâ, vocatur il-<lb />
<ptr xml:id="note-0640-12a" corresp="note-0640-12" type="noteAnchor" />
lius Latitudo. </s>
          <s xml:space="preserve">Eſt arcus circuli majoris, ad Eclipticam per-<lb />pendicularis, inter corpus &amp; </s>
          <s xml:space="preserve">Eclipticam interceptus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0640-12" corresp="note-0640-12a" place="margin">1006.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0641" n="(119)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. IV.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p rend="italics">
          <s xml:space="preserve">Si in centro ſphæræ ſtellarum fixarum, ad planum Eclipti-<lb />
<ptr xml:id="note-0641-01a" corresp="note-0641-01" type="noteAnchor" />
cæ, concipiamus lineam perpendicularem, puncta, in quibus bæc <lb />memoratam ſphæram ſecant, vocantur Poli Eclipticæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0641-01" corresp="note-0641-01a" place="margin">1007.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p rend="italics">
          <s xml:space="preserve">Zodiacus eſt Zona, quæ concipitur in cœlis, quam in duas <lb />
<ptr xml:id="note-0641-02a" corresp="note-0641-02" type="noteAnchor" />
partes æqualès ſecat linea Ecliptica, &amp; </s>
          <s xml:space="preserve">quæ, ab utraque par-<lb />te terminatur circulo line æ Eclipticæ parallelo, &amp; </s>
          <s xml:space="preserve">ab hac octo <lb />gradibus diſtanti. </s>
          <s xml:space="preserve">Propter exiguam orbium Planetarum, ut <lb />&amp; </s>
          <s xml:space="preserve">Lunæ, inclinationem ad planum Eclipticæ, nunquam <lb />
<ptr xml:id="note-0641-03a" corresp="note-0641-03" type="noteAnchor" />
extra Zodiacum, corpora ulla ſyſtematis Planetarii apparent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0641-02" corresp="note-0641-02a" place="margin">1008.</note>
              <note xml:space="preserve" xml:id="note-0641-03" corresp="note-0641-03a" place="margin">1009.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p rend="italics">
          <s xml:space="preserve">Inter hæc, quæ eandem habent longitudinem dicuntur in <lb />
<ptr xml:id="note-0641-04a" corresp="note-0641-04" type="noteAnchor" />
conjunctione.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0641-04" corresp="note-0641-04a" place="margin">1010.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p>
          <s xml:space="preserve">In oppoſitione dicuntur, quorum longitudines differunt <lb />
<ptr xml:id="note-0641-05a" corresp="note-0641-05" type="noteAnchor" />
180. </s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0641-05" corresp="note-0641-05a" place="margin">1011.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IV.</head>
        <head rend="italics" xml:space="preserve">De Phænomenis Planetarum inferiorum, ex horum, <lb />&amp; Telluris, motibus in orbitis ſuis.</head>
        <p>
          <s xml:space="preserve">SIt S Sol; </s>
          <s xml:space="preserve">AVB v orbita Planetæ inferioris; </s>
          <s xml:space="preserve">Tellus in or-<lb />
<ptr xml:id="note-0641-06a" corresp="note-0641-06" type="noteAnchor" />
bitâ ſuâ T; </s>
          <s xml:space="preserve">a v b portio ſphæræ ſtellarum fixarum; </s>
          <s xml:space="preserve">Lo-<lb />cus apparens Solis eſt v <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0641-07a" corresp="note-0641-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0641-06" corresp="note-0641-06a" place="margin"><hi rend="small caps">TAB. XXI</hi>. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0641-07" corresp="note-0641-07a" n="*" anchored="true" place="margin">991.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ex Tellure, ad orbitam Planetæ, ducantur tangentes <lb />T A a, TB b, clarè patet, nunquam ad majorem diſtan-<lb />tiam, quàm v a aut v b à Sole, in motu apparenti, removeri <lb />Planetam; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hunc illum, in motu apparenti circa Tellurem, <lb />quaſi comitari.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Diſtantia apparens Planetæ à Sole, dicitur illius Elongatio. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0641-08a" corresp="note-0641-08" type="noteAnchor" />
v a aut v b eſt elongatio maxima: </s>
          <s xml:space="preserve">hæc ex duabus cauſis va-<lb />
<ptr xml:id="note-0641-09a" corresp="note-0641-09" type="noteAnchor" />
riat; </s>
          <s xml:space="preserve">quia nempè &amp; </s>
          <s xml:space="preserve">Tellus &amp; </s>
          <s xml:space="preserve">Planeta in lineis ellipticis re-<lb />volvuntur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0641-10a" corresp="note-0641-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0641-08" corresp="note-0641-08a" place="margin">1012.</note>
              <note xml:space="preserve" xml:id="note-0641-09" corresp="note-0641-09a" place="margin">1013.</note>
              <note xml:space="preserve" xml:id="note-0641-10" corresp="note-0641-10a" n="*" anchored="true" place="margin">929.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planeta, citiùs quàm Tellus, revolutionem peragit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò,
<ptr xml:id="note-0641-11a" corresp="note-0641-11" type="noteAnchor" />
in motu ſuo, inter Tellurem &amp; </s>
          <s xml:space="preserve">Solem tranſit, &amp; </s>
          <s xml:space="preserve">deinde ultra <lb />
<ptr xml:id="note-0641-12a" corresp="note-0641-12" type="noteAnchor" />
</s>
          <pb facs="0642" n="(120)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
Solem reſpectu Telluris movetur: </s>
          <s xml:space="preserve">ita, ut duobus modis cum <lb />Sole in conjunctione ſit, nunquam autem in oppoſitione.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0641-11" corresp="note-0641-11a" place="margin">1014.</note>
              <note xml:space="preserve" xml:id="note-0641-12" corresp="note-0641-12a" n="*" anchored="true" place="margin">948.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut ideam habeamus motus apparentis Planetæ, concipe-<lb />re debemus, cum Tellure moveri lineas TBb, TS v, TAa; <lb /></s>
          <s xml:space="preserve">ita ut puncta A, V, B, &amp; </s>
          <s xml:space="preserve">v, dum Tellus revolutionem pera-<lb />git, orbitam Planetæ circumrotentur; </s>
          <s xml:space="preserve">Planeta verò, qui <lb />celerius revolvitur, per hæc puncta ſucceſſivè iterum atque <lb />iterum tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dum ab V in Din orbitâ fertur, inter fixas ab v verſus d <lb />
<ptr xml:id="note-0642-01a" corresp="note-0642-01" type="noteAnchor" />
moveri videtur; </s>
          <s xml:space="preserve">in hoc caſu, motus apparens eſt in antece-<lb />dentiâ &amp; </s>
          <s xml:space="preserve">Planeta eſt retrogradus. </s>
          <s xml:space="preserve">In D ſtationarius dicitur; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0642-02a" corresp="note-0642-02" type="noteAnchor" />
quia per aliquod tempus, in eodem loco, inter ſtellas fixas ap-<lb />paret: </s>
          <s xml:space="preserve">hoc obtinet, ubi Planetæ orbita, in loco, in quo Pla-<lb />neta verſatur, ad orbitam Telluris, in loco in quo hæc da-<lb />tur, ita inclinatur, ut ductâ linea t d lineæ T D parallelâ, &amp; </s>
          <s xml:space="preserve"><lb />parum ab hac diſtanti, D d ſit ad T t, ut Planetæ celeritas, <lb />in orbitâ, ad Telluris celeritatem; </s>
          <s xml:space="preserve">hæ lineolæ eodem tem-<lb />pore percurruntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">linea, quæ per Tellurem &amp; </s>
          <s xml:space="preserve">Plane-
<ptr xml:id="note-0642-03a" corresp="note-0642-03" type="noteAnchor" />
tam ducitur, motu parallelo fertur, quo locus Planetæ ap-<lb />parens non mutatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0642-04a" corresp="note-0642-04" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0642-01" corresp="note-0642-01a" place="margin">1015.</note>
              <note xml:space="preserve" xml:id="note-0642-02" corresp="note-0642-02a" place="margin">1016.</note>
              <note xml:space="preserve" xml:id="note-0642-03" corresp="note-0642-03a" n="*" anchored="true" place="margin">53.</note>
              <note xml:space="preserve" xml:id="note-0642-04" corresp="note-0642-04a" n="*" anchored="true" place="margin">994.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inter d &amp; </s>
          <s xml:space="preserve">B magis ad orbitam Telluris inclinatur Planetæ <lb />orbita, quare extremitas lineæ tranſeuntis per Tellurem &amp; </s>
          <s xml:space="preserve"><lb />Planetam, licèt Planeta celerius Tellure moveatur, in con-<lb />
<ptr xml:id="note-0642-05a" corresp="note-0642-05" type="noteAnchor" />
ſequentiâ fertur; </s>
          <s xml:space="preserve">verſus quam partem etiam dirigitur motus <lb />apparens Planetæ<ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Cùm tamen motus apparens Solis mo-
<ptr xml:id="note-0642-06a" corresp="note-0642-06" type="noteAnchor" />
tum apparentem Planetæ ſuperet, elongatio augetur, quæ po-<lb />ſito Planetâ in B eſt maxima. </s>
          <s xml:space="preserve">Dum arcum B v Planeta per-<lb />currit, in conſequentiâ etiam eſt motus apparens, &amp; </s>
          <s xml:space="preserve">motum <lb />Solis apparentem ſuperat, ad quem accedit, &amp; </s>
          <s xml:space="preserve">transgredi-<lb />tur, ab hoc recedendo, donec pervenerit ad A. </s>
          <s xml:space="preserve">Inter A &amp; </s>
          <s xml:space="preserve"><lb />E motus in conſequentiâ continuatur; </s>
          <s xml:space="preserve">ſed Sol, cujus mo-<lb />tus apparens in hoc caſu velocior eſt, ut de arcu d B expli-<lb />catum, ad Planetam accedit, &amp; </s>
          <s xml:space="preserve">minuitur elongatio. </s>
          <s xml:space="preserve">In E, <lb />eodem modo ac in D, ſtationarius eſt Planeta, inter E &amp; </s>
          <s xml:space="preserve">V <lb />
<ptr xml:id="note-0642-07a" corresp="note-0642-07" type="noteAnchor" />
iterum retrogradus eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0642-05" corresp="note-0642-05a" place="margin">1017.</note>
              <note xml:space="preserve" xml:id="note-0642-06" corresp="note-0642-06a" n="*" anchored="true" place="margin">992.</note>
              <note xml:space="preserve" xml:id="note-0642-07" corresp="note-0642-07a" place="margin">1018.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planetæ orbita ad planum Eclipticæ inclinatur<ptr type="noteAnchor" />, idèo non
<ptr xml:id="note-0642-08a" corresp="note-0642-08" type="noteAnchor" />
in lineâ Eclipticâ moveri videtur, ſed nunc minus nunc ma-
</s>
          <pb facs="0643" n="(121)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. IV.</fw>
gis ab hac diſtat, &amp; </s>
          <s xml:space="preserve">in curvâ irregulari ferri videtur, quæ <lb />interdum Eclipticam ſecat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0642-08" corresp="note-0642-08a" place="margin">958. 959.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit NVN orbita Planetæ cujus nodi N, N; </s>
          <s xml:space="preserve">ſit S Sol; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0643-01a" corresp="note-0643-01" type="noteAnchor" />
T t Telluris orbita in plano Eclipticæ; </s>
          <s xml:space="preserve">Telius T; </s>
          <s xml:space="preserve">Planeta <lb />V. </s>
          <s xml:space="preserve">Si V A concipiatur, per Planetam ad planum Eclipticæ <lb />perpendicularis, angulus VTA, aut potius arcus, qui hunc <lb />menſurat, eſt latitudo Planetæ <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">vocatur hæc latitudo Geo-
<ptr xml:id="note-0643-02a" corresp="note-0643-02" type="noteAnchor" />
centrica, ut diſtinguatur à latitudine Planetæ ex Sole viſi, <lb />quæ Heliocentrica dicitur, &amp; </s>
          <s xml:space="preserve">eſt in hoc caſu angulus VSA; <lb /></s>
          <s xml:space="preserve">de illa hìc agitur, Phœnomena ex Tellure viſa examinamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0643-01" corresp="note-0643-01a" place="margin"><hi rend="small caps">TAB. XXI</hi>. <lb />fig 5.</note>
              <note xml:space="preserve" xml:id="note-0643-02" corresp="note-0643-02a" n="*" anchored="true" place="margin">1006.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando Planeta eſt in Nodo, in lineâ Eclipticâ apparet, <lb />
<ptr xml:id="note-0643-03a" corresp="note-0643-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">curva à Planetâ, motu apparenti in Zodiaco deſcripta, ſe-<lb />cat lineam Eclipticam; </s>
          <s xml:space="preserve">recedendo à Nodo augetur Planetæ <lb />
<ptr xml:id="note-0643-04a" corresp="note-0643-04" type="noteAnchor" />
latitudo, quæ etiam pro Telluris ſitu variatur; </s>
          <s xml:space="preserve">ſic manente <lb />Planetâ in V, major eſt latitudo ſi Tellus ſit in T, quàm ſi foret <lb />in t. </s>
          <s xml:space="preserve">Si, manente Tellure, Planetam ex V ad v tranſlatum <lb />concipiamus, ex duplici cauſâ angulus v TB minor erit an-<lb />gulo VTA, ex acceſſu Planetæ ad nodum, &amp; </s>
          <s xml:space="preserve">ex receſſu <lb />ſpectatoris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0643-03" corresp="note-0643-03a" place="margin">1019.</note>
              <note xml:space="preserve" xml:id="note-0643-04" corresp="note-0643-04a" place="margin">1020.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc conſideremus Tellurem &amp; </s>
          <s xml:space="preserve">Planetam continuò <lb />moveri, facilè concipiemus mutari omnibus momentis lati-<lb />tudinem ex utraque cauſâ, quæ interdum contrariè agunt, <lb />interdum, in augendâ aut minuendâ latitudine, conſpirant; <lb /></s>
          <s xml:space="preserve">unde neceſſariò oritur motus apparens in curvâ irregulari, <lb />ut ante dictum, quæ Eclipticam ſecat, quoties nodos trans-<lb />greditur Planeta, id eſt, bis in ſingulis hujus revolutioni-<lb />bus; </s>
          <s xml:space="preserve">curva etiam hæc, ab utraque parte, non ultra certos <lb />limites in Zodiaco ab Eclipticâ recedit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Teleſcopio etiam deteguntur Phoenomena notabilia Pla-<lb />netarum inferiorum, quæ ab horum opacitate pendent.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit S Sol; </s>
          <s xml:space="preserve">T Tellus; </s>
          <s xml:space="preserve">A, B, C, v, D, E, F, V, Planeta <lb />
<ptr xml:id="note-0643-05a" corresp="note-0643-05" type="noteAnchor" />
inferior, Venus ex gr.</s>
          <s xml:space="preserve">, in orbitâ. </s>
          <s xml:space="preserve">Hic mutuato à Sole lu-<lb />mine lucet, &amp; </s>
          <s xml:space="preserve">hæmiſphærium Soli obverſum tantum illumi-<lb />natur, hæmiſphærium alterum inviſibile eſt: </s>
          <s xml:space="preserve">Idcirco ſola <lb />pars hæmiſphærii illuminati, quæ Telluri obvertitur, ex hac <lb />videri poteſt; </s>
          <s xml:space="preserve">in V Planeta videri non poteſt, in v rotundus <lb />apparêret, niſi radii ſolares impedirent quo minus videatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0643-05" corresp="note-0643-05a" place="margin"><hi rend="small caps">TAB. XXI</hi>. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0644" n="122" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Ex v progrediendo, Planeta continuò decreſcit, in D ha. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0644-01a" corresp="note-0644-01" type="noteAnchor" />
bet figuram d, in e &amp; </s>
          <s xml:space="preserve">f delineatur, ut in E &amp; </s>
          <s xml:space="preserve">F apparet, <lb />ulteriuſque decreſcit, donec evaneſcat in V; </s>
          <s xml:space="preserve">deinde iterum <lb />creſcit ſucceſſivè mutando figuram, donec totum hæmiſphæ-<lb />rium illuminatum verſus Tellurem dirigatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0644-01" corresp="note-0644-01a" place="margin">1021.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando nodus datur in V, aut in viciniis, Planeta in ipſo <lb />
<ptr xml:id="note-0644-02a" corresp="note-0644-02" type="noteAnchor" />
diſco Solis, &amp; </s>
          <s xml:space="preserve">quaſi Soli applicatum, videtur, &amp; </s>
          <s xml:space="preserve">obſervatur ma-<lb />cula nigra, quæ ſuper Solis ſuper ficie movetur: </s>
          <s xml:space="preserve">in hoc caſu, <lb />propriè loquendo, Planetam non videmus, ſed ubi radios ſo-<lb />lares intercipiat decernimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0644-02" corresp="note-0644-02a" place="margin">1022.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quo minus à Tellure diſtat Planeta, eo major apparet <ptr type="noteAnchor" />,
<ptr xml:id="note-0644-03a" corresp="note-0644-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">magis lucidus; </s>
          <s xml:space="preserve">ſed dum ad Tellurem accedit, pars lucida <lb />
<ptr xml:id="note-0644-04a" corresp="note-0644-04" type="noteAnchor" />
viſibilis minuitur, ita ut ex unâ cauſâ creſcat lumen, ex a-<lb />liâ minuatur; </s>
          <s xml:space="preserve">daturque diſtantia, ad quam lux reflexa eſt <lb />maxima.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0644-03" corresp="note-0644-03a" place="margin">1023.</note>
              <note xml:space="preserve" xml:id="note-0644-04" corresp="note-0644-04a" n="*" anchored="true" place="margin">733.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT V.</head>
        <head rend="italics" xml:space="preserve">De Pbænomenis Planetarum ſuperiorum, ex horum <lb />&amp; Telluris motibus in orbitis ſuis.</head>
        <p>
          <s xml:space="preserve">IN multis, cum explicatis circa Planetas inferiores, coin-<lb />cidunt ſuperiorum motus apparentes, in multis differunt. <lb /></s>
          <s xml:space="preserve">Non ſemper hi Solem comitantur, ſed ſæpe in oppoſitione <lb />
<ptr xml:id="note-0644-05a" corresp="note-0644-05" type="noteAnchor" />
obſervantur; </s>
          <s xml:space="preserve">in motu tamen, ut de inferioribus dictum, <lb />non ſemper in conſequentiâ ferri videntur, ſed ſæpe ſtationa-<lb />
<ptr xml:id="note-0644-06a" corresp="note-0644-06" type="noteAnchor" />
rii, ſæpe retrogradi ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0644-05" corresp="note-0644-05a" place="margin">1024.</note>
              <note xml:space="preserve" xml:id="note-0644-06" corresp="note-0644-06a" place="margin">1025.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit M Planeta ſuperior, ex gr. </s>
          <s xml:space="preserve">Mars, in orbitâ; </s>
          <s xml:space="preserve">ATHB <lb />
<ptr xml:id="note-0644-07a" corresp="note-0644-07" type="noteAnchor" />
orbita Telluris. </s>
          <s xml:space="preserve">Tempus periodicum Telluris brevius eſt <lb />
<ptr xml:id="note-0644-08a" corresp="note-0644-08" type="noteAnchor" />
tempore periodico Martis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò inter hunc &amp; </s>
          <s xml:space="preserve">Solem in
<ptr xml:id="note-0644-09a" corresp="note-0644-09" type="noteAnchor" />
motu ſuo tranſit ellus, in quo caſu Planeta in F, inter ſtel-<lb />las fixas Soli oppoſitus, apparet. </s>
          <s xml:space="preserve">Per Mducantur lineæ BM; <lb /></s>
          <s xml:space="preserve">AM, orbitam Telluris tangentes, quæ continuatæ in G &amp; </s>
          <s xml:space="preserve">D <lb />in ſphærâ ſtellarum fixarum pertingunt. </s>
          <s xml:space="preserve">Concipiamus, <lb />dum Planeta in orbitâ transfertur, lineas has etiam moveri, <lb />ita ut puncta A &amp; </s>
          <s xml:space="preserve">B, in quibus lineæ per Planetam tranſeun-<lb />tes orbitam Telluris tangunt, in tempore periodico Pla-<lb />netæ revolutionem peragant. </s>
          <s xml:space="preserve">Cùm autem Tellus celerius
</s>
          <pb facs="0645" n="123" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. VI.</fw>
revolvatur, per puncta A &amp; </s>
          <s xml:space="preserve">B, in motu ſuo tranſit. </s>
          <s xml:space="preserve">In hoc <lb />motu ultra FD &amp; </s>
          <s xml:space="preserve">FG à loco Planetæ è Sole viſo non re-<lb />movetur locus apparens è Tellure. </s>
          <s xml:space="preserve">Sit in hujus orbitâ pun-<lb />ctum T tale, ut ductâ lineâ t m parallelâ lineæ TM, Tt ſit ad <lb />Mm, ut Telluris celeritas ad Planetæ celeritatem; </s>
          <s xml:space="preserve">in quo <lb />caſu hæ lineolæ eodem tempore percurruntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">interea
<ptr xml:id="note-0645-01a" corresp="note-0645-01" type="noteAnchor" />
quieſcere videtur Planeta <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ſtationarius dicitur. </s>
          <s xml:space="preserve">Eodem
<ptr xml:id="note-0645-02a" corresp="note-0645-02" type="noteAnchor" />
modo ſtationarius eſt, poſitâ Tellure in H. </s>
          <s xml:space="preserve">In motu Tellu-<lb />ris inter T &amp; </s>
          <s xml:space="preserve">H, Planeta ab E per F in antecedentiâ move-<lb />ri videtur &amp; </s>
          <s xml:space="preserve">retrogradus dicitur, dum reliquam orbitæ ſuæ <lb />partem percurrit Tellus, directus eſt Planeta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0644-07" corresp="note-0644-07a" place="margin">1026.</note>
              <note xml:space="preserve" xml:id="note-0644-08" corresp="note-0644-08a" place="margin">TAB. XXII. <lb />fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0644-09" corresp="note-0644-09a" n="*" anchored="true" place="margin">948.</note>
              <note xml:space="preserve" xml:id="note-0645-01" corresp="note-0645-01a" n="*" anchored="true" place="margin">53.</note>
              <note xml:space="preserve" xml:id="note-0645-02" corresp="note-0645-02a" n="*" anchored="true" place="margin">994.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Phænomena circa latitudinem ſimilia ſunt iis, quæ expli-<lb />
<ptr xml:id="note-0645-03a" corresp="note-0645-03" type="noteAnchor" />
cata ſunt reſpectu Planetarnm inferiorum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0645-03" corresp="note-0645-03a" place="margin">1027.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1018.</note>
        <p>
          <s xml:space="preserve">Fupiter &amp; </s>
          <s xml:space="preserve">Saturnus ad magnam diſtantiam Telluris orbi-<lb />
<ptr xml:id="note-0645-05a" corresp="note-0645-05" type="noteAnchor" />
tam cingunt, quare ferè tota illorum hæmiſphæria, quæ â <lb />Sole illuminantur, è Tellure viſibilia ſunt; </s>
          <s xml:space="preserve">ideô ſemper rotun-<lb />di apparent hi Planetæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0645-05" corresp="note-0645-05a" place="margin">1028.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quia minus diſtat Mars, paululum gibboſus apparet, in-<lb />
<ptr xml:id="note-0645-06a" corresp="note-0645-06" type="noteAnchor" />
ter conjunctionem &amp; </s>
          <s xml:space="preserve">oppoſitionem cum Sole.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0645-06" corresp="note-0645-06a" place="margin">1029.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VI.</head>
        <head rend="italics" xml:space="preserve">De Phænomenis Satellitum, ex motu horum in orbi-<lb />tis. Vbi de Eclipſibus Solis &amp; Lunæ.</head>
        <p>
          <s xml:space="preserve">SAtellites Fovis &amp; </s>
          <s xml:space="preserve">Saturni ſemper in motu primarios ſuos <lb />
<ptr xml:id="note-0645-07a" corresp="note-0645-07" type="noteAnchor" />
comitantur, &amp; </s>
          <s xml:space="preserve">nunquam ultra certos limites, qui ex ho-<lb />rum, à primariis, diſtantiis facilè determinantur, ab utra-<lb />que parte recedere videntur; </s>
          <s xml:space="preserve">alterniſque vicibus in antece-<lb />dentiâ &amp; </s>
          <s xml:space="preserve">in conſequentiâ feruntur. </s>
          <s xml:space="preserve">Aliquando omnes ad <lb />eandem partem primarii dantur, aliquando inter ipſos pri-<lb />marius obſervatur; </s>
          <s xml:space="preserve">omnes ſemper aut in eâdem lineâ rectâ <lb />
<ptr xml:id="note-0645-08a" corresp="note-0645-08" type="noteAnchor" />
diſponuntur, aut parum ab bac diſtant. </s>
          <s xml:space="preserve">Quæ omnia ex mo-<lb />tu circa primarios, in planis exiguos inter ſe, &amp; </s>
          <s xml:space="preserve">cum plano <lb />Eclipticæ, angulos efficientibus, facilè deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0645-07" corresp="note-0645-07a" place="margin">1030.</note>
              <note xml:space="preserve" xml:id="note-0645-08" corresp="note-0645-08a" place="margin">1031.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non omnes Saturni aut Jovis Satellites ſemper ſimul viſi-<lb />
<ptr xml:id="note-0645-09a" corresp="note-0645-09" type="noteAnchor" />
biles ſunt, aliquando à primario obteguntur, ſæpe in umbram <lb />primarii immerguntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0645-09" corresp="note-0645-09a" place="margin">1032.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0646" n="124" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio i.</hi></head>
        <p>
          <s xml:space="preserve">Talis in umbram immerſio dicitur Satellitis Eclipſis.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1033.</note>
        <p>
          <s xml:space="preserve">Sit S Sol; </s>
          <s xml:space="preserve">T t Telluris orbita, I Jupiter; </s>
          <s xml:space="preserve">M m orbita ſe-<lb />
<ptr xml:id="note-0646-02a" corresp="note-0646-02" type="noteAnchor" />
cundarii Jovialis. </s>
          <s xml:space="preserve">Dum ab M ad m movetur ſecundarius, E-<lb />clipſin patitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">à Sole non illuminatus inviſibilis eſt. </s>
          <s xml:space="preserve">Po-<lb />ſitâ Tellure verſus T, immerſio in umbram facile obſervatur, <lb />emerſio contra magis ſenſibilis eſt, poſitâ Tellure verſus t.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0646-02" corresp="note-0646-02a" place="margin">TAB XXII. <lb />fig. 2.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inter Saturni comites annulum dari diximus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">circa quem
<ptr xml:id="note-0646-03a" corresp="note-0646-03" type="noteAnchor" />
notandum, illum nunquam à ſpectatore in Tellure latiorem vi-<lb />
<ptr xml:id="note-0646-04a" corresp="note-0646-04" type="noteAnchor" />
deri, quam in fig. </s>
          <s xml:space="preserve">4. </s>
          <s xml:space="preserve">Tab. </s>
          <s xml:space="preserve">xx. </s>
          <s xml:space="preserve">repræſentatur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">aliquando in-<lb />viſibilem eſſe; </s>
          <s xml:space="preserve">quando nempe planum annuli continuatum <lb />per Tellurem tranſit; </s>
          <s xml:space="preserve">annuli enim craſſities ſenſibilis non <lb />eſt. </s>
          <s xml:space="preserve">Etiam non videtur annulus, quando hujus planum conti-<lb />nuatum, inter Solem &amp; </s>
          <s xml:space="preserve">Tellurem tranſit; </s>
          <s xml:space="preserve">tunc enim ſuper-<lb />ficies annuli illuminata à Tellure avertitur: </s>
          <s xml:space="preserve">in utroque caſu <lb />Saturnus rotundus apparet, in ultimo tamen, ex radiis ab an-<lb />nulc interceptis, faſcia nigra in Planetæ ſuperficie obſervatur, <lb />ſimilis illi, quæ ab umbrâ annuli pendet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0646-03" corresp="note-0646-03a" place="margin">1034.</note>
              <note xml:space="preserve" xml:id="note-0646-04" corresp="note-0646-04a" n="*" anchored="true" place="margin">963.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Telluris Satellitis, Lunæ nempe, Phoenomena noſtri re-<lb />ſpectu notabiliora ſunt, &amp; </s>
          <s xml:space="preserve">peculiariter explicanda.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sæpiſſimè Soli conjungitur, totieſque buic opponitur, <lb />
<ptr xml:id="note-0646-05a" corresp="note-0646-05" type="noteAnchor" />
non tamen in ſingulis revolutionibus Lunæ in orbitâ; </s>
          <s xml:space="preserve">nam <lb />dum Luna poſt revolutionem integram 27. </s>
          <s xml:space="preserve">dier. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">ite-<lb />rum redit ad locum inter ſtellas fixas, in quo cum Sole fuit <lb />conjuncta, Sol ex hoc loco receſſit, &amp; </s>
          <s xml:space="preserve">ab hoc circiter diſtat <lb />27. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">itaque conjunctiones vicinæ diſtant viginti novem
<ptr xml:id="note-0646-06a" corresp="note-0646-06" type="noteAnchor" />
diebus cum ſemiſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0646-05" corresp="note-0646-05a" place="margin">1035.</note>
              <note xml:space="preserve" xml:id="note-0646-06" corresp="note-0646-06a" place="margin">1036.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">960. 996. 998.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p>
          <s xml:space="preserve">Menſis Lunaris periodicus, eſt tempus revolutionis Lunæ <lb />
<ptr xml:id="note-0646-08a" corresp="note-0646-08" type="noteAnchor" />
in orbitâ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0646-08" corresp="note-0646-08a" place="margin">1037.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p>
          <s xml:space="preserve">Menſis Lunaris Synodicus, ſeu lunatio, eſt tempus, quod Lu-<lb />
<ptr xml:id="note-0646-09a" corresp="note-0646-09" type="noteAnchor" />
na impendit inter conjunctiones cum Sole proximas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0646-09" corresp="note-0646-09a" place="margin">1038.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inviſibilis eſt Luna in conjunctione cum Sole; </s>
          <s xml:space="preserve">quia hæ-<lb />
<ptr xml:id="note-0646-10a" corresp="note-0646-10" type="noteAnchor" />
miſphærium illuminatum à Tellure avertitur. </s>
          <s xml:space="preserve">Sit Tellus T; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0646-11a" corresp="note-0646-11" type="noteAnchor" />
Luna in N inter Solem &amp; </s>
          <s xml:space="preserve">Tellurem; </s>
          <s xml:space="preserve">hemiſphærium illumi-<lb />natum erit m l i, quod in Tellure videri non poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0646-10" corresp="note-0646-10a" place="margin">1039.</note>
              <note xml:space="preserve" xml:id="note-0646-11" corresp="note-0646-11a" place="margin">TAB. XXII. <lb />fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0647" />
        <pb facs="0647a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0647a-01" />
          <label>0647a-01</label>
        </figure>
        <pb facs="0648" />
        <pb facs="0649" n="125" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. VI.</fw>
        <p>
          <s xml:space="preserve">Dum Luna, in orbitâ, à conjunctione ad oppoſitionem, ſer-<lb />
<ptr xml:id="note-0649-01a" corresp="note-0649-01" type="noteAnchor" />
tur, pars illuminata, quæ ſemper verſus Solem dirigitur, <lb />continuò magis ac magis ſpectatoribus in Tellure viſibilis eſt; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in punctis A, B, C, ſucceſſivè figuras a, b, c, acquirit Luna. </s>
          <s xml:space="preserve"><lb />In P, in oppoſitione cum Sole, rotunda apparet; </s>
          <s xml:space="preserve">deinde per <lb />
<ptr xml:id="note-0649-02a" corresp="note-0649-02" type="noteAnchor" />
D, E, F, tranſeundo decreſcit, ut in d, e, f, repræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-01" corresp="note-0649-01a" place="margin">1040.</note>
              <note xml:space="preserve" xml:id="note-0649-02" corresp="note-0649-02a" place="margin">1041.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p>
          <s xml:space="preserve">Conjunctio Lunæ cum Sole vocatur Novilunium. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0649-03a" corresp="note-0649-03" type="noteAnchor" />
Poſt conjunctionem Luna quaſi renaſci videtur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-03" corresp="note-0649-03a" place="margin">1042.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p>
          <s xml:space="preserve">Oppoſitio Lunæ cum Sole vocatur Plenilunium; </s>
          <s xml:space="preserve">quia Luna <lb />
<ptr xml:id="note-0649-04a" corresp="note-0649-04" type="noteAnchor" />
tota lucida apparet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-04" corresp="note-0649-04a" place="margin">1043.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p rend="italics">
          <s xml:space="preserve">Nomine communi oppoſitio &amp; </s>
          <s xml:space="preserve">conjunctio Satellitis cum Sole <lb />
<ptr xml:id="note-0649-05a" corresp="note-0649-05" type="noteAnchor" />
vocantur Syzygiæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-05" corresp="note-0649-05a" place="margin">1044.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In A &amp; </s>
          <s xml:space="preserve">F pars Lunæ obſcura, radiis à Tellure reflexis, <lb />
<ptr xml:id="note-0649-06a" corresp="note-0649-06" type="noteAnchor" />
paululum illuminatur; </s>
          <s xml:space="preserve">ideò videtur à ſpectatore cui Sol viſi-<lb />bilis non eſt, id eſt, in primo caſu poſt occaſum Solis, in <lb />ſecundo ante hujus ortum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-06" corresp="note-0649-06a" place="margin">1045.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p rend="italics">
          <s xml:space="preserve">Quando Solis lumen à Lunâ intercipitur ita ut in totum, <lb />
<ptr xml:id="note-0649-07a" corresp="note-0649-07" type="noteAnchor" />
aut pro parte, reſpectu ſpectatoris cujuſcunque in Tellure, <lb />Sol obtegatur, Sol dicitur Eclipſin pati.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-07" corresp="note-0649-07a" place="margin">1046.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propriè loquendo, hæc eſt Eclipſis Telluris, in cujus ſu-<lb />perficiem cadit Lunæ umbra aut penumbra.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 8.</head>
        <p>
          <s xml:space="preserve">Lunæ Eclipſis eſt obſcuratio Lunæ ex umbrâ Telluris. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0649-08a" corresp="note-0649-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-08" corresp="note-0649-08a" place="margin">1047.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Nunquam Solis Eclipſis obſervatur, niſi quando Novilu-<lb />
<ptr xml:id="note-0649-09a" corresp="note-0649-09" type="noteAnchor" />
nium celebratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-09" corresp="note-0649-09a" place="margin">1048.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Nunquam Luna deliquium patitur, niſi in Plenilunio.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1049.</note>
        <p>
          <s xml:space="preserve">Non tamen in ſingulis Syzygiis Luminaria deficiunt; </s>
          <s xml:space="preserve">quia <lb />
<ptr xml:id="note-0649-11a" corresp="note-0649-11" type="noteAnchor" />
Luna non in Plano Eclipticæ movetur <ptr type="noteAnchor" />, in quo ſemper dan-
<ptr xml:id="note-0649-12a" corresp="note-0649-12" type="noteAnchor" />
tur Sol &amp; </s>
          <s xml:space="preserve">Tellus; </s>
          <s xml:space="preserve">quare, propter latitudinem Lunæ, hujus <lb />umbra, in Novilunio, ſæpe Tellurem non tangit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ipſa, <lb />in Plenilunio, ad latus umbræ Telluris tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-11" corresp="note-0649-11a" place="margin">1050.</note>
              <note xml:space="preserve" xml:id="note-0649-12" corresp="note-0649-12a" n="*" anchored="true" place="margin">969.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando autem Lunæ latitudo aut nulla aut exigua eſt, <lb />id eſt, quando in Nodo, aut propè bunc, verſatur Luna in <lb />
<ptr xml:id="note-0649-13a" corresp="note-0649-13" type="noteAnchor" />
</s>
          <pb facs="0650" n="126" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA.</fw>
Syzygiis, Eclipſis obſervatur; </s>
          <s xml:space="preserve">in hoc caſu in Eclipticâ, aut <lb />parum ab hac diſtans, apparet Luna; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">inde nomen ſuum <lb />habet hæc linea.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0649-13" corresp="note-0649-13a" place="margin">1051.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut quæ Lunæ Eclipſin ſpectant clariùs pateant, ſit Lunæ <lb />
<ptr xml:id="note-0650-01a" corresp="note-0650-01" type="noteAnchor" />
ſemita OO; </s>
          <s xml:space="preserve">planum Eclipticæ RR; </s>
          <s xml:space="preserve">in hoc ſemper datur <lb />centrum umbræ Telluris <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Nodus orbitæ Lunæ eſt N.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0650-01" corresp="note-0650-01a" place="margin">TAB. XXIII. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">940. 939.</note>
        <p>
          <s xml:space="preserve">Si centrum umbræ Telluris ſit in A, non obſcuratur Lu-<lb />na, quæ in F tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si minus à Nodo diſtet Luna in Plenilunio, ut in G, um-<lb />
<ptr xml:id="note-0650-03a" corresp="note-0650-03" type="noteAnchor" />
bra Telluris datur in B, &amp; </s>
          <s xml:space="preserve">Luna pro parte obſcuratur; </s>
          <s xml:space="preserve">hæc <lb />Eclipſis dicitur Partialis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0650-03" corresp="note-0650-03a" place="margin">1052.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si, poſitâ in D, Plenilunium celebretur, in totum <lb />
<ptr xml:id="note-0650-04a" corresp="note-0650-04" type="noteAnchor" />
tenebris obtegitur Luna in I; </s>
          <s xml:space="preserve">in L in umbram cadit, in H <lb />ex hac exit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">Eclipſis dicitur Totalis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0650-04" corresp="note-0650-04a" place="margin">1053.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Centralis vocatur Eclipſis, quando centrum Lunæ tranſit <lb />
<ptr xml:id="note-0650-05a" corresp="note-0650-05" type="noteAnchor" />
per centrum Vmbræ, quod in ipſo Nodo N tantùm obtinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0650-05" corresp="note-0650-05a" place="margin">1054.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">De Telluris umbrâ huc uſque locuti ſumus; </s>
          <s xml:space="preserve">quia, quan-<lb />do de Tellure loquimur, cum hac conjunctam etiam intelli-<lb />gimus Atmoſphæram, de qua alibi <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">de Atmoſpbæræ umbrâ
<ptr xml:id="note-0650-06a" corresp="note-0650-06" type="noteAnchor" />
propriè agitur in Eclipſibus Lunaribus; </s>
          <s xml:space="preserve">ipſius enim Tellu-<lb />
<ptr xml:id="note-0650-07a" corresp="note-0650-07" type="noteAnchor" />
ris umbra ad Lunam non pertingit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0650-06" corresp="note-0650-06a" place="margin">1055.</note>
              <note xml:space="preserve" xml:id="note-0650-07" corresp="note-0650-07a" n="*" anchored="true" place="margin">418.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit T Tellus, Atmoſphærâ FDGGDF circum. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0650-08a" corresp="note-0650-08" type="noteAnchor" />
data. </s>
          <s xml:space="preserve">Radii ſolares BD, BD, Atmoſphæram tangen-<lb />tes, rectâ progrediuntur, &amp; </s>
          <s xml:space="preserve">Atmoſphæræ umbram ter-<lb />minant, extra quam ſi Luna detur, immediatè à radiis So-<lb />laribus illuminatur, non verò eodem modo, inter BD &amp; </s>
          <s xml:space="preserve">BD, <lb />illuſtratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0650-08" corresp="note-0650-08a" place="margin">TAB. XXIV. <lb />fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Radii, qui obliquè Atmoſphæram intrant, refractionem pa-<lb />
<ptr xml:id="note-0650-09a" corresp="note-0650-09" type="noteAnchor" />
tiuntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">dum ad Tellurem accedunt, continuò in me-
<ptr xml:id="note-0650-10a" corresp="note-0650-10" type="noteAnchor" />
dium denſius atque denſius penetrant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideoque omnibus
<ptr xml:id="note-0650-11a" corresp="note-0650-11" type="noteAnchor" />
momentis inflectuntur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">per curvas moventur. </s>
          <s xml:space="preserve">Sic radii
<ptr xml:id="note-0650-12a" corresp="note-0650-12" type="noteAnchor" />
EF, EF, in curvis FG, FG, Tellurem tangentibus, <lb />Atmoſphæram penetrant. </s>
          <s xml:space="preserve">Omne lumen inter EF, EF, à <lb />Tellure intercipitur, &amp; </s>
          <s xml:space="preserve">Radii GA, GA, terminant Tel-<lb />luris umbram.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0650-09" corresp="note-0650-09a" place="margin">1056.</note>
              <note xml:space="preserve" xml:id="note-0650-10" corresp="note-0650-10a" n="*" anchored="true" place="margin">617.</note>
              <note xml:space="preserve" xml:id="note-0650-11" corresp="note-0650-11a" n="*" anchored="true" place="margin">424. 429.</note>
              <note xml:space="preserve" xml:id="note-0650-12" corresp="note-0650-12a" n="*" anchored="true" place="margin">617.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lumen autem inter EF &amp; </s>
          <s xml:space="preserve">BD, ab Atmoſphærâ refra-<lb />ctum, diſpergitur inter GA &amp; </s>
          <s xml:space="preserve">BD continuatam, &amp; </s>
          <s xml:space="preserve">ultra A,
</s>
          <pb facs="0651" n="127" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. VI.</fw>
mucronem umbræ Telluris, lumina ab omnibus partibus con-<lb />funduntur, ſed recedendo à Tellure continuò debiliora ſunt: <lb /></s>
          <s xml:space="preserve">ita ut Vmbra Atmoſphæræ non ſit umbra perfecta ſed lu-<lb />
<ptr xml:id="note-0651-01a" corresp="note-0651-01" type="noteAnchor" />
men debile, quo Luna in Eclipſi viſibilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0651-01" corresp="note-0651-01a" place="margin">1057.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Atmoſphæræ umbra eſt conica; </s>
          <s xml:space="preserve">quia Solis diameter At-<lb />
<ptr xml:id="note-0651-02a" corresp="note-0651-02" type="noteAnchor" />
moſphæræ diametrum, quæ vix à Telluris diametro differt, <lb />ſuperat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">conus hicce ad Martem non pertingit, ut ex <lb />obſervationibus immediatis conſtat: </s>
          <s xml:space="preserve">umbræ autem diame-<lb />ter, in loco, ubi ab orbitâ Lunæ ſecatur, à Telluris diame-<lb />tro vix quartâ parte ſuperatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0651-02" corresp="note-0651-02a" place="margin">1058.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simili ratiocinio, quo probavimus Lunam in Atmoſphæ-<lb />ræ umbram cadere, quando in plenilunio Luna in Nodo, <lb />aut propè hunc datur, probatur Lunæ umbram in Tellu-<lb />rem cadere in Novilunio, quando aut in Nodo aut prope <lb />
<ptr xml:id="note-0651-03a" corresp="note-0651-03" type="noteAnchor" />
Nodum Luna verſatur, ideòque in hoc caſu Solem Eclipſin <lb />pati; </s>
          <s xml:space="preserve">circa quam varia ſunt notanda.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0651-03" corresp="note-0651-03a" place="margin">1059.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Sol S; </s>
          <s xml:space="preserve">Luna T; </s>
          <s xml:space="preserve">cadat hujus umbra in planum quod-<lb />
<ptr xml:id="note-0651-04a" corresp="note-0651-04" type="noteAnchor" />
cunque in GH. </s>
          <s xml:space="preserve">Umbra hæc penumbrâ circumdatur; <lb /></s>
          <s xml:space="preserve">nam ultra L &amp; </s>
          <s xml:space="preserve">E, planum hoc ab integro Solis Hæ-<lb />miſphærio illuminatur; </s>
          <s xml:space="preserve">ab L accedendo ad H, &amp; </s>
          <s xml:space="preserve">ab E <lb />ad G lumen continuò minuitur, &amp; </s>
          <s xml:space="preserve">in viciniis G &amp; </s>
          <s xml:space="preserve">H, ra-<lb />dii, ab exiguâtantùm parte ſuperficiei Solis, ad planum <lb />perveniunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0651-04" corresp="note-0651-04a" place="margin">TAB. XXII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 9.</head>
        <p>
          <s xml:space="preserve">Lux hæc imminuta, qua, ab omni parte, umbra GH cir-<lb />
<ptr xml:id="note-0651-05a" corresp="note-0651-05" type="noteAnchor" />
cumdatur vocatur penumbra.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0651-05" corresp="note-0651-05a" place="margin">1060.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Simili penumbrâ Telluris umbra, in Eclipſi Lunari, cir-<lb />
<ptr xml:id="note-0651-06a" corresp="note-0651-06" type="noteAnchor" />
cumdatur, ſed hæc tantum in viciniis umbræ ſenſibilis eſt, &amp; </s>
          <s xml:space="preserve"><lb />ideo exiguam babet latitudinem; </s>
          <s xml:space="preserve">integra autem poteſt obſer-<lb />
<ptr xml:id="note-0651-07a" corresp="note-0651-07" type="noteAnchor" />
vari à ſpectatore, poſito in Plano, in quod umbra cadit, <lb />qui caſus in Eclipſi Solari extat. </s>
          <s xml:space="preserve">Spectator in I aut F ſe-<lb />midiametrum Solis tantùm videre poteſt, reliquum diametri <lb />à Lunâ obtegitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ab L progrediendo verſus H, Sol à Lu-<lb />nâ continuò magis ac magis obtegitur, donec in ipſâ umbrâ <lb />planè inviſibilis ſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0651-06" corresp="note-0651-06a" place="margin">1061.</note>
              <note xml:space="preserve" xml:id="note-0651-07" corresp="note-0651-07a" place="margin">1062.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur Solarem dari Eclipſin, licèt Lunæ um-<lb />
<ptr xml:id="note-0651-08a" corresp="note-0651-08" type="noteAnchor" />
bra Tellurem non tangat, ſi modo penumbra ad bujus ſuper-
</s>
          <pb facs="0652" n="128" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ficiem perveniat. </s>
          <s xml:space="preserve">Etiam non in omnibus locis in quibus Sol <lb />
<ptr xml:id="note-0652-01a" corresp="note-0652-01" type="noteAnchor" />
viſibilis eſt, Eclipſin obſervari; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in locis, in quibus obſer-<lb />
<ptr xml:id="note-0652-02a" corresp="note-0652-02" type="noteAnchor" />
vatur, diverſam eſſe, pro ut umbra, aut pars varia penum-<lb />bræ, per locum tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0651-08" corresp="note-0651-08a" place="margin">1063.</note>
              <note xml:space="preserve" xml:id="note-0652-01" corresp="note-0652-01a" place="margin">1064.</note>
              <note xml:space="preserve" xml:id="note-0652-02" corresp="note-0652-02a" place="margin">1065.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lunæ Eclipſis verô ubique eadem eſt, ubi Luna, durante E-<lb />
<ptr xml:id="note-0652-03a" corresp="note-0652-03" type="noteAnchor" />
clipſi, viſibilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0652-03" corresp="note-0652-03a" place="margin">1066.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando umbra ipſa Lunæ in Tellurem cadit, Totalis dici-<lb />
<ptr xml:id="note-0652-04a" corresp="note-0652-04" type="noteAnchor" />
tur Solis Eclipſis; </s>
          <s xml:space="preserve">ſi penumbra tantùm pertingat ad Tellu-<lb />rem, Partialis dicitur, illudque in genere conſiderando E-<lb />clipſin.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0652-04" corresp="note-0652-04a" place="margin">1067.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quantum autem ad loca peculiaria, Totalis dicitur, in il-<lb />
<ptr xml:id="note-0652-05a" corresp="note-0652-05" type="noteAnchor" />
lis locis in quibus umbra tranſit; </s>
          <s xml:space="preserve">Centralis in illis, in quibus <lb />centrum umbræ tranſit, id eſt, in quibus centrum Lunæ ob-<lb />tegit Solis centrum; </s>
          <s xml:space="preserve">tandem Partialis dicitur, ubi penum-<lb />bra tantùm tranſit, delineatur hæc in fig. </s>
          <s xml:space="preserve">6.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0652-05" corresp="note-0652-05a" place="margin">1068.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quo umbra GH latior eſt, eo in pluribus locis Eclipſis <lb />
<ptr xml:id="note-0652-06a" corresp="note-0652-06" type="noteAnchor" />
totalis eſt, &amp; </s>
          <s xml:space="preserve">diutius Sol in totum obſcuratur. </s>
          <s xml:space="preserve">Diverſa verò <lb />
<ptr xml:id="note-0652-07a" corresp="note-0652-07" type="noteAnchor" />
eſt hæc umbræ latitudo, pro variâ Lunæ à Tellure, &amp; </s>
          <s xml:space="preserve">hujus à <lb />Sole, diſtantiâ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0652-06" corresp="note-0652-06a" place="margin">1069.</note>
              <note xml:space="preserve" xml:id="note-0652-07" corresp="note-0652-07a" place="margin">TAB. XXII. <lb />fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si Lunæ Eclipſis detur, poſitâ Tellure in Peribelio, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0652-08a" corresp="note-0652-08" type="noteAnchor" />
Lunâ in Apogeo, id eſt, ad diſtantiam à Tellure maximam, <lb />umbra Lunæ ad Tellurem non pertingit, &amp; </s>
          <s xml:space="preserve">Luna integrum <lb />Solem non obtegit; </s>
          <s xml:space="preserve">Annularis talis dicitur Eclipſis, &amp; </s>
          <s xml:space="preserve">re-<lb />præſentatur in fig. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0652-08" corresp="note-0652-08a" place="margin">1070.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VII.</head>
        <head rend="italics" xml:space="preserve">De Pbænomenis ex motu Solis, Planetarum, &amp; Lunæ, <lb />circa axes.</head>
        <p>
          <s xml:space="preserve">Solis motus circa axem, ſenſibilis eſt ex maculis, quæ in <lb />
<ptr xml:id="note-0652-09a" corresp="note-0652-09" type="noteAnchor" />
Solis ſuperficie ſæpiſſimè obſervantur; </s>
          <s xml:space="preserve">hæ ſingulis diebus <lb />ſitum ſuum &amp; </s>
          <s xml:space="preserve">figuram mutari, &amp; </s>
          <s xml:space="preserve">nunc celerius nunc tardius <lb />ferri, videntur; </s>
          <s xml:space="preserve">quæ omnia ex motu ſuperficiei ſphæricæ <lb />facilè deducuntur: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">Sol, qui, ſi tali motu non agitaretur, <lb />ſemel tantùm in integro anno totam ſuperficiem Telluri ſuc-<lb />ceſſivè obverteret, nunc illam integram, in minori quàm <lb />unius menſis ſpatio, Terricolis videndam præbet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0652-09" corresp="note-0652-09a" place="margin">1071.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0653" />
        <pb facs="0653a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0653a-01" />
          <label>0653a-01</label>
        </figure>
        <pb facs="0654" />
        <pb facs="0655" n="(129)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. VII.</fw>
        <p>
          <s xml:space="preserve">Similia ſunt Phænomena ex rotatione Fovis, Martis, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0655-01a" corresp="note-0655-01" type="noteAnchor" />
Veneris, circa axes, qui motus, ex maculis in Planetarum <lb />ſuperficiebus, ſenſibiles ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-01" corresp="note-0655-01a" place="margin">1072.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum Tellus circa axem rotatur, ſpectator, qui transfertur, <lb />ſe quieſcere, omnia verò corpora coeleſtia moveri, imagi-<lb />natur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p rend="italics">
          <s xml:space="preserve">Puncta, in ſphærâ ſtellarum fixarum, in quibus axis Tel-<lb />
<ptr xml:id="note-0655-02a" corresp="note-0655-02" type="noteAnchor" />
luris, ab utraque parte continuatus, pertingit, vocantur <lb />Poli Mundi.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-02" corresp="note-0655-02a" place="margin">1073.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Motus apparens, ex motu Telluris circa axem, vocatur <lb />
<ptr xml:id="note-0655-03a" corresp="note-0655-03" type="noteAnchor" />
Motus diurnus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-03" corresp="note-0655-03a" place="margin">1074.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Concipitur Planum per centrum Telluris tranſiens, ad bu-<lb />
<ptr xml:id="note-0655-04a" corresp="note-0655-04" type="noteAnchor" />
jus axem perpendiculare, quaquaverſum continuatum, &amp; </s>
          <s xml:space="preserve">cir-<lb />culus, in quo ſphæram ſtellarum fixarum ſecat, vocatur Æ-<lb />quator coeleſtis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-04" corresp="note-0655-04a" place="margin">1075.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In motu Telluris circa Solem movetur Æquator, ſed cùm <lb />
<ptr xml:id="note-0655-05a" corresp="note-0655-05" type="noteAnchor" />
planum hujus circuli motu parallelo feratur, Æquator cœle-<lb />ſtis non mutatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-05" corresp="note-0655-05a" place="margin">1076.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">994.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p rend="italics">
          <s xml:space="preserve">Circuli, quorum plana per axem Telluris tranſeunt, vocan-<lb />
<ptr xml:id="note-0655-07a" corresp="note-0655-07" type="noteAnchor" />
tur Meridiani.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-07" corresp="note-0655-07a" place="margin">1077.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Omnes per polos Mundi tranſeunt, &amp; </s>
          <s xml:space="preserve">ad Æquatorem per-<lb />
<ptr xml:id="note-0655-08a" corresp="note-0655-08" type="noteAnchor" />
pendiculares ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-08" corresp="note-0655-08a" place="margin">1078.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p rend="italics">
          <s xml:space="preserve">Arcus Meridiani cujuſcunque, inter Æquatorem &amp; </s>
          <s xml:space="preserve">Sidus <lb />
<ptr xml:id="note-0655-09a" corresp="note-0655-09" type="noteAnchor" />
interceptus, vocatur Declinatio Sideris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-09" corresp="note-0655-09a" place="margin">1079.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit, in Tellure T, ſpectator, qui viſum dirigit per T A; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0655-10a" corresp="note-0655-10" type="noteAnchor" />
poſt aliquod tempus, ubi linea T A, ex motu Telluris, trans-<lb />lata erit in T a, ſi per eandem lineam viſum ſpectator diri-<lb />gat, corpus A tranſlatum apparebit per arcum a A; </s>
          <s xml:space="preserve">ubi <lb />verò linea ad priſtinum ſitum T A redierit, corpus inte-<lb />gram revolutionem peregiſſe videbitur. </s>
          <s xml:space="preserve">Si autem viſum per <lb />Telluris axem dirigat, quia hic quieſcit, corpus, quod in axe <lb />videtur, non tranſlatum apparebit; </s>
          <s xml:space="preserve">ideò in Polis Mundi mo-<lb />
<ptr xml:id="note-0655-11a" corresp="note-0655-11" type="noteAnchor" />
</s>
          <pb facs="0656" n="(130)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tus diurnus non obſervatur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Corpora autem in horum vi-
<ptr xml:id="note-0656-01a" corresp="note-0656-01" type="noteAnchor" />
ciniis, circa polos rotari clarum eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">corpus motu diurno <lb />circulum eo majorem deſcribere, circa polum immobilem, <lb />quo magis ab hoc diſtat. </s>
          <s xml:space="preserve">Ideò tota ſphæra ſtellarum fixa-<lb />
<ptr xml:id="note-0656-02a" corresp="note-0656-02" type="noteAnchor" />
rum, circa axem Telluris continuatum, revolvere videtur, <lb />in eo tempore, in quo Tellus revera circa axem rotatur. <lb /></s>
          <s xml:space="preserve">Motus ergo diurnus communis eſt omnibus corporibus cœ-<lb />leſtibus, niſi quatenus turbatur motibus antea memoratis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0655-10" corresp="note-0655-10a" place="margin"><hi rend="small caps">TAB. XXIII</hi>. <lb />fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0655-11" corresp="note-0655-11a" place="margin">1080.</note>
              <note xml:space="preserve" xml:id="note-0656-01" corresp="note-0656-01a" n="*" anchored="true" place="margin">1073.</note>
              <note xml:space="preserve" xml:id="note-0656-02" corresp="note-0656-02a" place="margin">1081.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Æquator ab utroque polo æqualiter diſtat, &amp; </s>
          <s xml:space="preserve">dividit cœlum <lb />in duo hæmiſphæria, quorum puncta media ſunt Poli, qui <lb />ergo à ſingulis punctis Æquatoris æqualiter diſtant; </s>
          <s xml:space="preserve">corpora <lb />
<ptr xml:id="note-0656-03a" corresp="note-0656-03" type="noteAnchor" />
idcirco cæleſtia, quæ ſunt in Æquatore, motu diurno ipſum <lb />Æquatorem deſcribere videntur, circulum omnium maximum, <lb />qui motu diurno deſcribi poteſt; </s>
          <s xml:space="preserve">reliqua corpora circulos <lb />
<ptr xml:id="note-0656-04a" corresp="note-0656-04" type="noteAnchor" />
Æquatori parallelos deſcribunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0656-03" corresp="note-0656-03a" place="margin">1082.</note>
              <note xml:space="preserve" xml:id="note-0656-04" corresp="note-0656-04a" place="margin">1083.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Axis Telluris ad planum Eclipticæ inclinatur, &amp; </s>
          <s xml:space="preserve">efficit <lb />angulum 66. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">31′. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">diſtant ideò Poli Mundi, à Polis E-
<ptr xml:id="note-0656-05a" corresp="note-0656-05" type="noteAnchor" />
clipticæ, gradibus 23. </s>
          <s xml:space="preserve">29′.</s>
          <s xml:space="preserve">; &amp; </s>
          <s xml:space="preserve">angulum 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29′. </s>
          <s xml:space="preserve">cum plano <lb />
<ptr xml:id="note-0656-06a" corresp="note-0656-06" type="noteAnchor" />
Eclipticæ format planum Æquatoris. </s>
          <s xml:space="preserve">Planum utrumque per <lb />Telluris centrum tranſit, cùm autem hoc pro centro ſphæ-<lb />ræ ſtellarum fixarum haberi poſſit <ptr type="noteAnchor" />, ſequitur Æquatorem
<ptr xml:id="note-0656-07a" corresp="note-0656-07" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">lineam Eclipticam eße circulos majores, qui ad ſe mutuo <lb />
<ptr xml:id="note-0656-08a" corresp="note-0656-08" type="noteAnchor" />
inclinantur, &amp; </s>
          <s xml:space="preserve">ſeſe mutuo ſecant, in duobus punctis oppoſitis, <lb />principio Ariëtis &amp; </s>
          <s xml:space="preserve">principio Libræ quæ puncta in viâ Solis <lb />hiſce interſectionibus determinantur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0656-05" corresp="note-0656-05a" place="margin">1084.</note>
              <note xml:space="preserve" xml:id="note-0656-06" corresp="note-0656-06a" n="*" anchored="true" place="margin">960.</note>
              <note xml:space="preserve" xml:id="note-0656-07" corresp="note-0656-07a" place="margin">1085.</note>
              <note xml:space="preserve" xml:id="note-0656-08" corresp="note-0656-08a" n="*" anchored="true" place="margin">988. 990.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1001.</note>
        <p>
          <s xml:space="preserve">Quando Sol eſt in illis punctis, motu diurno Æquatorem de-<lb />
<ptr xml:id="note-0656-10a" corresp="note-0656-10" type="noteAnchor" />
ſcribere videtur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">dum motu ſuo apparenti in Eclipticä
<ptr xml:id="note-0656-11a" corresp="note-0656-11" type="noteAnchor" />
transfertur, continuò magis ac magis ab Æquatore recedit, <lb />
<ptr xml:id="note-0656-12a" corresp="note-0656-12" type="noteAnchor" />
augeturque hujus declinatio, &amp; </s>
          <s xml:space="preserve">circulos de die in diem mino-<lb />res deſcribit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">donec ad diſtantiam maximam ab Æquatore
<ptr xml:id="note-0656-13a" corresp="note-0656-13" type="noteAnchor" />
pervenerit, quæ eſt 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29′. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">deinde iterum ad Æquato-
<ptr xml:id="note-0656-14a" corresp="note-0656-14" type="noteAnchor" />
rem accedit, hunc prætergreditur, etiam 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29′.</s>
          <s xml:space="preserve">, ad Po-<lb />
<ptr xml:id="note-0656-15a" corresp="note-0656-15" type="noteAnchor" />
lum oppoſitum accedens.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0656-10" corresp="note-0656-10a" place="margin">1086.</note>
              <note xml:space="preserve" xml:id="note-0656-11" corresp="note-0656-11a" place="margin">1087.</note>
              <note xml:space="preserve" xml:id="note-0656-12" corresp="note-0656-12a" n="*" anchored="true" place="margin">1082.</note>
              <note xml:space="preserve" xml:id="note-0656-13" corresp="note-0656-13a" n="*" anchored="true" place="margin">1083.</note>
              <note xml:space="preserve" xml:id="note-0656-14" corresp="note-0656-14a" place="margin">1088.</note>
              <note xml:space="preserve" xml:id="note-0656-15" corresp="note-0656-15a" n="*" anchored="true" place="margin">1084.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p>
          <s xml:space="preserve">Circuli, à Sole motu diurno deſcripti, ab Æquatore maximè <lb />
<ptr xml:id="note-0656-16a" corresp="note-0656-16" type="noteAnchor" />
diſtantes, id eſt 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29′.</s>
          <s xml:space="preserve">, vocantur Tropici.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0656-16" corresp="note-0656-16a" place="margin">1089.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unus tangit Lineam Eclipticam in primo gradu Cancri &amp;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0657" n="(131)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. VII.</fw>
dicitur Tropicus Cancri; </s>
          <s xml:space="preserve">alter, Tropicus Capricorni nomina-<lb />tus, per primum punctum ſigni Capricorni tranſit, ibique E-<lb />clipticam lineam tangit.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p>
          <s xml:space="preserve">Polus Mundi Tropico Cancri vicinus, vocatur Polus Ar-<lb />
<ptr xml:id="note-0657-01a" corresp="note-0657-01" type="noteAnchor" />
cticus, &amp; </s>
          <s xml:space="preserve">Septentrionalis; </s>
          <s xml:space="preserve">oppoſitus Antarcticus nuncupatur, <lb />etiam Auſtralis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0657-01" corresp="note-0657-01a" place="margin">1090.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 8.</head>
        <p>
          <s xml:space="preserve">Circuli, à Polis Eclipticæ motu diurno deſcripti, id eſt, <lb />
<ptr xml:id="note-0657-02a" corresp="note-0657-02" type="noteAnchor" />
à Polis Mundi 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29′. </s>
          <s xml:space="preserve">diſtantes, nominantur Circuli Po-<lb />lares.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0657-02" corresp="note-0657-02a" place="margin">1091.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circulus Polaris Arcticus dicitur, qui Polum Arcticum <lb />circumdat; </s>
          <s xml:space="preserve">à Polo Antarctico alter nomen ſuum mutuatur.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Supereſt Lunæ motus circa axem, cujus effectus eſt, quod <lb />
<ptr xml:id="note-0657-03a" corresp="note-0657-03" type="noteAnchor" />
eadem Lunæ facies in perpetuum Telluri obvertatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0657-03" corresp="note-0657-03a" place="margin">1092.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Luna in N, facies Telluri obverſa eſt m n i; </s>
          <s xml:space="preserve">ſi Luna <lb />
<ptr xml:id="note-0657-04a" corresp="note-0657-04" type="noteAnchor" />
circa axem non rotaretur, &amp; </s>
          <s xml:space="preserve">ſingula puncta per lineas pa-<lb />
<ptr xml:id="note-0657-05a" corresp="note-0657-05" type="noteAnchor" />
rallelas tranſlatæ forent, linea m i coincideret cum lineâ l n <lb />in ſitu Lunæ in B, &amp; </s>
          <s xml:space="preserve">hemiſphærium memoratum m n i <lb />daretur in l m n; </s>
          <s xml:space="preserve">ſed quia, dum Luna quartam partem or-<lb />bitæ deſcribit, etiam quartam partem revolutionis circa <lb />axem peragit, facies quæ daretur in l m n, nunc datur in <lb />m n i, id eſt iterum Telluri obverſa. </s>
          <s xml:space="preserve">Eodem modo proba-<lb />tur, hanc eandem faciem m n i, in ſitu Lunæ in P, ſpectato-<lb />ri in Tellure eſſe conſpicuam, &amp; </s>
          <s xml:space="preserve">in E etiam Telluri obver-<lb />ti: </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">in omnibus aliis punctis orbitæ Lunæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0657-04" corresp="note-0657-04a" place="margin"><hi rend="small caps">TAB. XXII</hi>.</note>
              <note xml:space="preserve" xml:id="note-0657-05" corresp="note-0657-05a" place="margin">fig. 3.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Axis Lunæ ad planum orbitæ non eſt perpendicularis, ſed <lb />
<ptr xml:id="note-0657-06a" corresp="note-0657-06" type="noteAnchor" />
paululum ad hoc inclinatur: </s>
          <s xml:space="preserve">axis in motu ſuo circa Tellu-<lb />rem paralleliſmum ſervat, ut de Planetis primariis dictum <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0657-07a" corresp="note-0657-07" type="noteAnchor" />
idcirco ſitum ſuum mutat reſpectu ſpectatoris in Tellure, <lb />cui nunc unus, deinde alter Lunæ Polus viſibilis eſt, unde <lb />hæc motu quodam libratorio agitata videtur. </s>
          <s xml:space="preserve">Alius etiam <lb />
<ptr xml:id="note-0657-08a" corresp="note-0657-08" type="noteAnchor" />
in Lunâ obſervatur motus libratorius; </s>
          <s xml:space="preserve">motus circa axem <lb />eſt æquabilis, &amp; </s>
          <s xml:space="preserve">in orbitâ celeritate inæquali fertur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">idcir-
<ptr xml:id="note-0657-09a" corresp="note-0657-09" type="noteAnchor" />
co verſante Lunâ in Perigeo, id eſt, ad diſtantiam minimam <lb />à Tellure ubi celerrimè in orbitâ movetur <ptr type="noteAnchor" />, pars ſuperficiei,
<ptr xml:id="note-0657-10a" corresp="note-0657-10" type="noteAnchor" />
quæ, ex motu in orbitâ, Telluri obvertitur, non tota ex mo-
</s>
          <pb facs="0658" n="(132)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tu circa axem avertitur; </s>
          <s xml:space="preserve">ideò pars ſuperficiei Lunæ, antea <lb />non viſa, ad latus detegitur; </s>
          <s xml:space="preserve">quæ, ubi Luna pervenit ad <lb />Apogeum, iterum inviſibilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0657-06" corresp="note-0657-06a" place="margin">1093.</note>
              <note xml:space="preserve" xml:id="note-0657-07" corresp="note-0657-07a" n="*" anchored="true" place="margin">952.</note>
              <note xml:space="preserve" xml:id="note-0657-08" corresp="note-0657-08a" place="margin">1094.</note>
              <note xml:space="preserve" xml:id="note-0657-09" corresp="note-0657-09a" n="*" anchored="true" place="margin">966.</note>
              <note xml:space="preserve" xml:id="note-0657-10" corresp="note-0657-10a" n="*" anchored="true" place="margin">966.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT VIII.</head>
        <head xml:space="preserve">De Phænomenis Telluris ſuperficiem, &amp; peculiares <lb />hujus partes, ſpectantibus.</head>
        <p>
          <s xml:space="preserve">PHænomena cœleſtia, huc uſque examinata, explicavi-<lb />mus, ſpectatorem conſiderando agitatum motibus, qui-<lb />bus Tellus reverâ agitatur. </s>
          <s xml:space="preserve">Illum nunc ſuperficiei Telluris <lb />impoſitum, &amp; </s>
          <s xml:space="preserve">per varias hujus partes translatum, conſidera-<lb />mus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Phænomenon primum hìc notandum, eſt ex interpoſit â <lb />
<ptr xml:id="note-0658-01a" corresp="note-0658-01" type="noteAnchor" />
Tellure, dimidium cælorum viſum fugere ſpectatoris, poſiti in <lb />illius ſuperficie.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0658-01" corresp="note-0658-01a" place="margin">1095.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 1.</head>
        <p>
          <s xml:space="preserve">Circulus in cælis, qui ſeparat partem viſibilem ab inviſibi-<lb />
<ptr xml:id="note-0658-02a" corresp="note-0658-02" type="noteAnchor" />
li, quando radii, inæqualitatibus in Telluris ſuperficie, non <lb />intercipiuntur, vocatur Horizon.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0658-02" corresp="note-0658-02a" place="margin">1096.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cùm altitudo, ad quam ſpectator ſupra Telluris ſuperfi-<lb />ciem poſſit elevari, admodum exigua ſit, relata ad Telluris <lb />ſemidiametrum, oculus ſpectatoris poteſt haberi pro poſito <lb />in ipſâ ſuperficie.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Sit Tellus T; </s>
          <s xml:space="preserve">ſpectator in S; </s>
          <s xml:space="preserve">P E p e ſphæra ſtellarum <lb />
<ptr xml:id="note-0658-03a" corresp="note-0658-03" type="noteAnchor" />
fixarum; </s>
          <s xml:space="preserve">ſi per S concipiatur planum H H Tellurem tan-<lb />
<ptr xml:id="note-0658-04a" corresp="note-0658-04" type="noteAnchor" />
gens, erit hoc Horizontis planum, cujus ſectio cum ſphæ-<lb />râ ſtellarum fixarum eſt Horizon. </s>
          <s xml:space="preserve">Per centrum Telluris <lb />concipitur planum h b, ad H H parallelum; </s>
          <s xml:space="preserve">diſtantia h H <lb />inſenſibilis eſt, propter immenſam ſtellarum fixarum diſtan-<lb />tiam; </s>
          <s xml:space="preserve">poteſt ideò hujus plani ſectio cum ſphærâ memo-<lb />ratâ pro Horizonte H H uſurpari <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0658-03" corresp="note-0658-03a" place="margin"><hi rend="small caps">TAB. XXIII</hi>.</note>
              <note xml:space="preserve" xml:id="note-0658-04" corresp="note-0658-04a" place="margin">fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">994.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Adſcenſus ſiderum ſupra Horizontem, vocatur horum Or-<lb />
<ptr xml:id="note-0658-06a" corresp="note-0658-06" type="noteAnchor" />
tus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0658-06" corresp="note-0658-06a" place="margin">1097.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 3.</head>
        <p rend="italics">
          <s xml:space="preserve">Deſcenſus infra horizontem dicitur ſiderum Occaſus.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1098.</note>
        <pb facs="0659" n="(133)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. VIII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 4.</head>
        <p>
          <s xml:space="preserve">Si per centrum Telluris &amp; </s>
          <s xml:space="preserve">ſpectatorem concipiamus li-<lb />
<ptr xml:id="note-0659-01a" corresp="note-0659-01" type="noteAnchor" />
neam, quæ neceſſario horizonti perpendicularis eſt, inter <lb />ſtellas fixas pertinget in puncto Z, quod vocatur Zenit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-01" corresp="note-0659-01a" place="margin">1099.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 5.</head>
        <p rend="italics">
          <s xml:space="preserve">Punctum, huic oppoſitum N vocatur Nadir.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1100.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 6.</head>
        <p rend="italics">
          <s xml:space="preserve">Sectio plani Meridiani, per ſpectatorem tranſeuntis, cum <lb />
<ptr xml:id="note-0659-03a" corresp="note-0659-03" type="noteAnchor" />
Horizonte, vocatur Linea Meridiana.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-03" corresp="note-0659-03a" place="margin">1101.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">A ſeptentrione ad auſtrum dirigitur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 7.</head>
        <p>
          <s xml:space="preserve">Pars cœlorum Orientalis dicitur illa, ad quam corpora ſu-<lb />
<ptr xml:id="note-0659-04a" corresp="note-0659-04" type="noteAnchor" />
pra horizontem adſcendere videmus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">punctum Orientis <lb />illud, in quo perpendicularis ad lineam Meridianam ver-<lb />ſus hanc partem per ſpectatorem ducta, ſphæram ſtellarum <lb />fixarum ſecat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-04" corresp="note-0659-04a" place="margin">1102.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 8.</head>
        <p>
          <s xml:space="preserve">Punctum huic oppoſitum vocatur punctum Occidentis; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0659-05a" corresp="note-0659-05" type="noteAnchor" />
pars Occidentalis cœlorum Orientali opponitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-05" corresp="note-0659-05a" place="margin">1103.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 9.</head>
        <p>
          <s xml:space="preserve">Amplitudo, eſt arcus Horizontis, inter punctum Orientis, <lb />
<ptr xml:id="note-0659-06a" corresp="note-0659-06" type="noteAnchor" />
aut Occidentis, &amp; </s>
          <s xml:space="preserve">punctum, in quo ſidus oritur aut occidit, in-<lb />terceptus. </s>
          <s xml:space="preserve">Prima dicitur ortiva, altera occidua: </s>
          <s xml:space="preserve">utraque eſt <lb />aut ſeptentrionâlis aut meridionalis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-06" corresp="note-0659-06a" place="margin">1104.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 10.</head>
        <p>
          <s xml:space="preserve">Altitudo ſideris ſupra horizontem, vocatur arcus circuli <lb />
<ptr xml:id="note-0659-07a" corresp="note-0659-07" type="noteAnchor" />
perpendicularis ad Horizontem, in cujus centro eſt ſpectator, <lb />horizonte &amp; </s>
          <s xml:space="preserve">ſidere terminatus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-07" corresp="note-0659-07a" place="margin">1105.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando agitur de corporibus remotis, altitudo ſenſibiliter <lb />non differt, ſive ſpectator detur in ſuperficie Telluris, ſive in <lb />hujus centro. </s>
          <s xml:space="preserve">Corpora minus diſtantia altiora apparent poſi-<lb />to ſpectatore in centro.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 11.</head>
        <p>
          <s xml:space="preserve">Differentia altitudinis ſideris, pro diverſo ſitu ſpectatoris, <lb />
<ptr xml:id="note-0659-08a" corresp="note-0659-08" type="noteAnchor" />
in centro, aut in ſuperficie Telluris, vocatur Side s Paralaxis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-08" corresp="note-0659-08a" place="margin">1106.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Solius Lunæ Paralaxis obſervationibus determinatur: </s>
          <s xml:space="preserve">re-<lb />
<ptr xml:id="note-0659-09a" corresp="note-0659-09" type="noteAnchor" />
liquorum corporum ſyſtematis Planetarii diſtantia nimia eſt,
</s>
          <pb facs="0660" n="(134)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ut cum ſemidiametro Telluris conferantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">Paralaxis pen-<lb />det à ratione, quam ſemidiameter Telluris ad diſtantiam Pla-<lb />netæ habet; </s>
          <s xml:space="preserve">idcirco ipſius Martis, in oppoſitione cum Sole, <lb />
<ptr xml:id="note-0660-01a" corresp="note-0660-01" type="noteAnchor" />
Paralaxis obſervationes ſubtilliſſimas effugit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0659-09" corresp="note-0659-09a" place="margin">1107.</note>
              <note xml:space="preserve" xml:id="note-0660-01" corresp="note-0660-01a" place="margin">1108.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ubi Parallaxis datur, adſcenſu corporis ſupra horizontem <lb />
<ptr xml:id="note-0660-02a" corresp="note-0660-02" type="noteAnchor" />
minuitur, &amp; </s>
          <s xml:space="preserve">in Zenit nulla eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0660-02" corresp="note-0660-02a" place="margin">1109.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Altitudo apparens ſiderum, mutatur etiam ex aliâ cauſâ, <lb />quæ reſpectu omnium corporum Cœleſtium indeſcrimina-<lb />tim locum habet. </s>
          <s xml:space="preserve">Ex Atmoſphæræ refractione radii infle-<lb />
<ptr xml:id="note-0660-03a" corresp="note-0660-03" type="noteAnchor" />
ctuntur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">Sidera altiora apparent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quo tamen altiora
<ptr xml:id="note-0660-04a" corresp="note-0660-04" type="noteAnchor" />
ſunt, eo minor eſt hæc inflectio <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quia radii minus obliquè
<ptr xml:id="note-0660-05a" corresp="note-0660-05" type="noteAnchor" />
<ptr xml:id="note-0660-06a" corresp="note-0660-06" type="noteAnchor" />
<ptr xml:id="note-0660-07a" corresp="note-0660-07" type="noteAnchor" />
in Atmoſphæræ ſuperficiem incidunt. </s>
          <s xml:space="preserve">In Zenit refractio <lb />
<ptr xml:id="note-0660-08a" corresp="note-0660-08" type="noteAnchor" />
nulla eſt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">etiam ad diſtantiam viginti, aut triginta, gra-
<ptr xml:id="note-0660-09a" corresp="note-0660-09" type="noteAnchor" />
duum à Zenit ſenſibilis non eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0660-03" corresp="note-0660-03a" place="margin">1110.</note>
              <note xml:space="preserve" xml:id="note-0660-04" corresp="note-0660-04a" place="margin">1111.</note>
              <note xml:space="preserve" xml:id="note-0660-05" corresp="note-0660-05a" n="*" anchored="true" place="margin">1056.</note>
              <note xml:space="preserve" xml:id="note-0660-06" corresp="note-0660-06a" n="*" anchored="true" place="margin">624.</note>
              <note xml:space="preserve" xml:id="note-0660-07" corresp="note-0660-07a" n="*" anchored="true" place="margin">639.</note>
              <note xml:space="preserve" xml:id="note-0660-08" corresp="note-0660-08a" place="margin">1112.</note>
              <note xml:space="preserve" xml:id="note-0660-09" corresp="note-0660-09a" n="*" anchored="true" place="margin">629.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cùm ex hac refractione Sidera eleventur, viſibilia ſunt <lb />
<ptr xml:id="note-0660-10a" corresp="note-0660-10" type="noteAnchor" />
antequam ad horizontem perveniant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0660-10" corresp="note-0660-10a" place="margin">1113.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc omnia generaliter Telluris ſuperficies ſpectant, hu-<lb />
<ptr xml:id="note-0660-11a" corresp="note-0660-11" type="noteAnchor" />
jus variæ partes nunc ſunt examinandæ: </s>
          <s xml:space="preserve">determinantur hæ, <lb />
<ptr xml:id="note-0660-12a" corresp="note-0660-12" type="noteAnchor" />
referendo ad Tellurem varios circulos, quos in cœlis antea <lb />conſideravimus; </s>
          <s xml:space="preserve">ſic in Tellure conſideramus Æquatorem, <lb />
<ptr xml:id="note-0660-13a" corresp="note-0660-13" type="noteAnchor" />
Meridianos, Tropicos, circulos Polares; </s>
          <s xml:space="preserve">quibus circulis eo-<lb />dem modo Telluris ſuperficies dividitur, ac, circulis in cœ-<lb />lis, ſphæra ſtellarum fixarum: </s>
          <s xml:space="preserve">Quare circuli hi ita ſibi mu-<lb />tuo reſpondent, ut ductâ lineâ ex centro Telluris ad circu-<lb />lum in cœlis, hæc per circulum in Tellure tranſeat. </s>
          <s xml:space="preserve">Si po-<lb />li fuerint P, p, Æquator erit E e, Tropici T T, t t, cir-<lb />culi polares A A, a a.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0660-11" corresp="note-0660-11a" place="margin"><hi rend="small caps">TAB. XXIV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0660-12" corresp="note-0660-12a" place="margin">fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0660-13" corresp="note-0660-13a" place="margin">1114.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 12.</head>
        <p>
          <s xml:space="preserve">Meridianus Loci dicitur ille, qui per locum ipſum tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1115.</note>
        <p>
          <s xml:space="preserve">Hujus planum ad Horizontem eſt perpendiculare; </s>
          <s xml:space="preserve">quia <lb />
<ptr xml:id="note-0660-15a" corresp="note-0660-15" type="noteAnchor" />
per centrum Telluris &amp; </s>
          <s xml:space="preserve">ſpectatorem tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0660-15" corresp="note-0660-15a" place="margin">1116.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Linea Meridiana in Loco quocunque ducta, eſt pars Meri-<lb />
<ptr xml:id="note-0660-16a" corresp="note-0660-16" type="noteAnchor" />
diani Loci <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0660-16" corresp="note-0660-16a" place="margin">1117.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1101.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 13.</head>
        <p>
          <s xml:space="preserve">Latitudo Loci eſt hujus diſtantia ab Æquatore, id eſt, <lb />
<ptr xml:id="note-0660-18a" corresp="note-0660-18" type="noteAnchor" />
arcus interceptus inter Locum &amp; </s>
          <s xml:space="preserve">Æquatorem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0660-18" corresp="note-0660-18a" place="margin">1118.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0661" n="(135)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. VIII.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 14.</head>
        <p>
          <s xml:space="preserve">Circuli paralleli ad Æquatorem, vocantur Circuli Latitu-<lb />
<ptr xml:id="note-0661-01a" corresp="note-0661-01" type="noteAnchor" />
dinis; </s>
          <s xml:space="preserve">ut B b.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0661-01" corresp="note-0661-01a" place="margin">1119.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Determinatâ Latitudine Loci, determinatur circulus Latitu-<lb />dinis, qui per Locum tranſit, ut autem ſitus variorum Locorum <lb />inter ſe determinentur, in ſingulis circulis Loca determinan-<lb />da ſunt, quod fit concipiendo Meridianum, per Locum quem-<lb />cunque notabilem tranſeuntem, qui, ſectione ſuâ, in ſingulis <lb />circulis Latitudinis, punctum determinat, à quo diſtantiæ <lb />Locorum menſurantur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 15.</head>
        <p>
          <s xml:space="preserve">Meridianus memoratus, ad arbitrium ſumtus, vocatur Pri-<lb />
<ptr xml:id="note-0661-02a" corresp="note-0661-02" type="noteAnchor" />
mus Meridianus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0661-02" corresp="note-0661-02a" place="margin">1120.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 16.</head>
        <p rend="italics">
          <s xml:space="preserve">Diſtantia loci à primo Meridiano, in circulo Latitudinis <lb />
<ptr xml:id="note-0661-03a" corresp="note-0661-03" type="noteAnchor" />
Loci menſurata, vocatur Loci Longitudo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0661-03" corresp="note-0661-03a" place="margin">1121.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Aſtronomi omnia referunt ad Meridianum Loci, in quo ob-<lb />
<ptr xml:id="note-0661-04a" corresp="note-0661-04" type="noteAnchor" />
ſervationes ſuas inſtituunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0661-04" corresp="note-0661-04a" place="margin">1122.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In explicandis Phænomenis, quæ varias Telluris ſuperfi-<lb />ciei partes ſpectant, conſiderabimus ſpectatorem à Polo ver-<lb />ſus Æquatorem incedentem; </s>
          <s xml:space="preserve">ſolumque motum diurnum pri-<lb />mò conſiderabimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quando ſpectator in ipſo Polo Telluris T, datur in S, <lb />
<ptr xml:id="note-0661-05a" corresp="note-0661-05" type="noteAnchor" />
cum Horizonte coincidit Æquator cœleſtis E e, &amp; </s>
          <s xml:space="preserve">Polus <lb />
<ptr xml:id="note-0661-06a" corresp="note-0661-06" type="noteAnchor" />
<ptr xml:id="note-0661-07a" corresp="note-0661-07" type="noteAnchor" />
Mundi P eſt in Zenit; </s>
          <s xml:space="preserve">in hoc caſu, quia Circuli ad Hori-<lb />zontem paralleli, etiam ad Æquatorem paralleli ſunt; </s>
          <s xml:space="preserve">omnia <lb />corpora cœleſtia motu parallelo ad Horizontem moveri vi-<lb />dentur <ptr type="noteAnchor" />, in circulis, qui repræſentantur per lineas A a, B b.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0661-08a" corresp="note-0661-08" type="noteAnchor" />
Stellæ fixæ in Hemiſphærio E P e nunquam occidunt, reli-<lb />quæ nunquam videntur Horizon in hoc ſitu dicitur paralle-<lb />
<ptr xml:id="note-0661-09a" corresp="note-0661-09" type="noteAnchor" />
lus, aut ſphæra parallela.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0661-05" corresp="note-0661-05a" place="margin">1123.</note>
              <note xml:space="preserve" xml:id="note-0661-06" corresp="note-0661-06a" place="margin"><hi rend="small caps">TAB. XXIII</hi>.</note>
              <note xml:space="preserve" xml:id="note-0661-07" corresp="note-0661-07a" place="margin">fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0661-08" corresp="note-0661-08a" n="*" anchored="true" place="margin">1083.</note>
              <note xml:space="preserve" xml:id="note-0661-09" corresp="note-0661-09a" place="margin">1124.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſpectator in Tellure T à polo recedat, &amp; </s>
          <s xml:space="preserve">detur in S, <lb />
<ptr xml:id="note-0661-10a" corresp="note-0661-10" type="noteAnchor" />
Horizon dicitur obliquus, aut ſphæra obliqua; </s>
          <s xml:space="preserve">axis P p tunc <lb />
<ptr xml:id="note-0661-11a" corresp="note-0661-11" type="noteAnchor" />
<ptr xml:id="note-0661-12a" corresp="note-0661-12" type="noteAnchor" />
inclinatur ad Horizontem h b, eo magis, quo ſpectator ma-<lb />gis à polo removetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0661-10" corresp="note-0661-10a" place="margin">1125.</note>
              <note xml:space="preserve" xml:id="note-0661-11" corresp="note-0661-11a" place="margin"><hi rend="small caps">TAB. XXIII</hi>.</note>
              <note xml:space="preserve" xml:id="note-0661-12" corresp="note-0661-12a" place="margin">fig. 4.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 17.</head>
        <p>
          <s xml:space="preserve">Angulus, quem axis Telluris cum Horizonte efficit, vocatur <lb />
<ptr xml:id="note-0661-13a" corresp="note-0661-13" type="noteAnchor" />
Altitudo Poli <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0661-13" corresp="note-0661-13a" place="margin">1126.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1105.</note>
        <pb facs="0662" n="(136)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Hæc Poli altitudo æqualis eſt latitudini. </s>
          <s xml:space="preserve">Altitudo Poli <lb />
<ptr xml:id="note-0662-01a" corresp="note-0662-01" type="noteAnchor" />
eſt angulus P T b, cujus menſura eſt arcus P b, latitudo <lb />menſuratur arcu, qui in Tellure reſpondet arcui Z E in cœ-<lb />lis <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Hic autem æqualis eſt arcui P b; </s>
          <s xml:space="preserve">utriuſque enim com-
<ptr xml:id="note-0662-02a" corresp="note-0662-02" type="noteAnchor" />
plementum, ad quadrantem circuli, eſt arcus Z P.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0662-01" corresp="note-0662-01a" place="margin">1127.</note>
              <note xml:space="preserve" xml:id="note-0662-02" corresp="note-0662-02a" n="*" anchored="true" place="margin">1118.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hoc ſitu ſpectatoris, quia Æquator ad Horizontem in-<lb />
<ptr xml:id="note-0662-03a" corresp="note-0662-03" type="noteAnchor" />
clinatur, omnia corpora cœleſtia in circulis ad Horizontem, <lb />inclinatis lineis A a, B b, repræſentatis, motu diurno ferun-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0662-03" corresp="note-0662-03a" place="margin">1128.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quædam corpora cœleſtia in ſingulis Telluris revolutionibus <lb />
<ptr xml:id="note-0662-04a" corresp="note-0662-04" type="noteAnchor" />
oriuntur &amp; </s>
          <s xml:space="preserve">occidunt, illa nempe, quæ dantur inter paralle-<lb />los ad Æquatorem B b &amp; </s>
          <s xml:space="preserve">h i; </s>
          <s xml:space="preserve">quia omnes paralleli, inter hos, <lb />Horizonte ſecantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0662-04" corresp="note-0662-04a" place="margin">1129.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Plana Æquatoris &amp; </s>
          <s xml:space="preserve">Horizontis per Telluris centrum tran-<lb />ſeunt; </s>
          <s xml:space="preserve">hi circuli ideo ſeſe mutuo ſecant in duas partes æqua-<lb />les, &amp; </s>
          <s xml:space="preserve">dimidium Æquatoris ſupra Horizontem datur: </s>
          <s xml:space="preserve">Idcirco <lb />corpora cœleſtia, quæ in Æquatore dantur, per ſemi revo-<lb />
<ptr xml:id="note-0662-05a" corresp="note-0662-05" type="noteAnchor" />
lutionem Telluris circa axem <ptr type="noteAnchor" />, ſupra Horizontem verſan-
<ptr xml:id="note-0662-06a" corresp="note-0662-06" type="noteAnchor" />
tur; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, propter æquabilitatem motus circa axem, per æ-<lb />quale tempus inviſibilia ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0662-05" corresp="note-0662-05a" place="margin">1130.</note>
              <note xml:space="preserve" xml:id="note-0662-06" corresp="note-0662-06a" n="*" anchored="true" place="margin">1082.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæc etiam in puncto Orientis oriuntur, &amp; </s>
          <s xml:space="preserve">in puncto Occi-<lb />
<ptr xml:id="note-0662-07a" corresp="note-0662-07" type="noteAnchor" />
dentis infra Horizontem cadunt; </s>
          <s xml:space="preserve">nam ſectio planorum Æ-<lb />quatoris, &amp; </s>
          <s xml:space="preserve">Horizontis, perpendicularis eſt ad planum per-<lb />pendiculare ad ambo illa plana; </s>
          <s xml:space="preserve">hoc autem planum eſt pla-<lb />num Meridiani loci <ptr type="noteAnchor" />, quare ſectio memorata ad lineam Me-
<ptr xml:id="note-0662-08a" corresp="note-0662-08" type="noteAnchor" />
ridianam, normalis eſt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideòque per puncta Orientis &amp; </s>
          <s xml:space="preserve">Oc-
<ptr xml:id="note-0662-09a" corresp="note-0662-09" type="noteAnchor" />
cidentis tranſit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0662-07" corresp="note-0662-07a" place="margin">1131.</note>
              <note xml:space="preserve" xml:id="note-0662-08" corresp="note-0662-08a" n="*" anchored="true" place="margin">1078. 1116.</note>
              <note xml:space="preserve" xml:id="note-0662-09" corresp="note-0662-09a" n="*" anchored="true" place="margin">1117.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1102. 1103.</note>
        <p>
          <s xml:space="preserve">Corpora inter Æquatorem &amp; </s>
          <s xml:space="preserve">parallelum B b, qui Horizon-<lb />
<ptr xml:id="note-0662-11a" corresp="note-0662-11" type="noteAnchor" />
tem tangit, ut in circulo A a, diutius ſupra Horizontem, <lb />quàm infra Horizontem verſantur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">differentia hæc eſt eo <lb />major, quo magis circulus ut A a, ad Polüm, qui ſupra <lb />Horizontem elevatur, accedit; </s>
          <s xml:space="preserve">Contra, ex acceſſu corporis <lb />
<ptr xml:id="note-0662-12a" corresp="note-0662-12" type="noteAnchor" />
ad Polum oppoſitum, minuitur mora ſupra Horizontem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0662-11" corresp="note-0662-11a" place="margin">1132.</note>
              <note xml:space="preserve" xml:id="note-0662-12" corresp="note-0662-12a" place="margin">1133.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inæqualitas hæc inter moram corporis ſupra Horizontem &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0662-13a" corresp="note-0662-13" type="noteAnchor" />
moram infra Horizontem, augetur, cum auctâ altitudine Poli, <lb />propter diminutionem anguli ab Æquatore &amp; </s>
          <s xml:space="preserve">ejus parallelis <lb />cum Horizonte formati.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0662-13" corresp="note-0662-13a" place="margin">1134.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0663" n="(137)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. VIII.</fw>
        <p>
          <s xml:space="preserve">Corpora, quorum diſtantia à Polo æqualis eſt hujus altitu-<lb />
<ptr xml:id="note-0663-01a" corresp="note-0663-01" type="noteAnchor" />
dini, nunquam occidunt, talis enim eſt diſtantia circuli B b, <lb />qui Horizontem tangit, &amp; </s>
          <s xml:space="preserve">cujus pars nulla infra Horizontem <lb />pervenit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-01" corresp="note-0663-01a" place="margin">1135.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Corpora, à Polo minus diſtantia, ne quidem ad Hori-<lb />zontem pertingunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Simili ratiocinio patet, Corpora, quorum diſtantia à Polo <lb />
<ptr xml:id="note-0663-02a" corresp="note-0663-02" type="noteAnchor" />
oppoſito, non ſuperat altitudinem Poli, nunquam ſupra Hori-<lb />zontem adſcendere, &amp; </s>
          <s xml:space="preserve">ſemper inviſibilia eſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-02" corresp="note-0663-02a" place="margin">1136.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Per Zenit Z tranſeunt corpora, quorum diſtantia E Z, <lb />
<ptr xml:id="note-0663-03a" corresp="note-0663-03" type="noteAnchor" />
ab Æquatore, æqualis eſt altitudini Poli; </s>
          <s xml:space="preserve">æqualis enim E Z <lb />eſt latitudini loci, cui æqualis Poli altitudo <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-03" corresp="note-0663-03a" place="margin">1137.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1126.</note>
        <p>
          <s xml:space="preserve">Quando ſpectator S à Polo quantum poteſt receſſit, ad <lb />
<ptr xml:id="note-0663-05a" corresp="note-0663-05" type="noteAnchor" />
Æquatorem pervenit, cujus puncta æqualiter ab utroque <lb />
<ptr xml:id="note-0663-06a" corresp="note-0663-06" type="noteAnchor" />
<ptr xml:id="note-0663-07a" corresp="note-0663-07" type="noteAnchor" />
Polo diſtant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Tunc axis P p in Horizonte datur, cum quo
<ptr xml:id="note-0663-08a" corresp="note-0663-08" type="noteAnchor" />
Æquator angulum rectum efficit <ptr type="noteAnchor" />, quare Horizon dicitur
<ptr xml:id="note-0663-09a" corresp="note-0663-09" type="noteAnchor" />
Rectus, aut ſphæra recta.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-05" corresp="note-0663-05a" place="margin">1138.</note>
              <note xml:space="preserve" xml:id="note-0663-06" corresp="note-0663-06a" place="margin"><hi rend="small caps">TAB. XXIII</hi>.</note>
              <note xml:space="preserve" xml:id="note-0663-07" corresp="note-0663-07a" place="margin">fig. 5.</note>
              <note xml:space="preserve" xml:id="note-0663-08" corresp="note-0663-08a" n="*" anchored="true" place="margin">1075. 1114.</note>
              <note xml:space="preserve" xml:id="note-0663-09" corresp="note-0663-09a" n="*" anchored="true" place="margin">1075. 1114.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Horizon in duas partes æquales ſecat omnes circulos pa-<lb />rallelos ad Æquatorem, qui per lineas A a, B b repræſen-<lb />tantur; </s>
          <s xml:space="preserve">ideò omnia corpora cœleſtia, ſingulis Telluris revo-<lb />
<ptr xml:id="note-0663-10a" corresp="note-0663-10" type="noteAnchor" />
lutionibus, oriuntur, &amp; </s>
          <s xml:space="preserve">occidunt, &amp; </s>
          <s xml:space="preserve">per tempora æqualia <lb />viſibilia ſunt &amp; </s>
          <s xml:space="preserve">latent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-10" corresp="note-0663-10a" place="margin">1139.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ipſe Æquator per Zenit tranſit; </s>
          <s xml:space="preserve">ideòque omnia corpora <lb />
<ptr xml:id="note-0663-11a" corresp="note-0663-11" type="noteAnchor" />
quæ in hoc dantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-11" corresp="note-0663-11a" place="margin">1140.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si, quæ de motu diurno explicavimus, ad corpora appli-<lb />centur, de quorum aliis motibus apparentibus antea actum, <lb />facilè determinantur phœnomena ex motibus conjunctis; <lb /></s>
          <s xml:space="preserve">quæ Solem ſpectant cæteris notabiliora ſunt, &amp; </s>
          <s xml:space="preserve">ideò peculia-<lb />riter explicanda.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 18.</head>
        <p rend="italics">
          <s xml:space="preserve">Dies Naturalis vocatur Tempus lapſum inter receſſum <lb />
<ptr xml:id="note-0663-12a" corresp="note-0663-12" type="noteAnchor" />
Solis à Meridiano loci, &amp; </s>
          <s xml:space="preserve">acceſſum ſequentem ad eundem Me-<lb />ridianum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-12" corresp="note-0663-12a" place="margin">1141.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dies hic differt à tempore revolutionis Telluris circa <lb />
<ptr xml:id="note-0663-13a" corresp="note-0663-13" type="noteAnchor" />
axem quæ tempora æqualia forent, ſi immobilis inter Stellas <lb />fixas apparêret Sol; </s>
          <s xml:space="preserve">ſed dum motu diurno, in tempore u-<lb />nius revolutionis Telluris circa Axem, Sol circumfertur ab
</s>
          <pb facs="0664" n="138" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
Oriente in Occidentem, id eſt, in antecedentiâ <ptr type="noteAnchor" />, motu
<ptr xml:id="note-0664-01a" corresp="note-0664-01" type="noteAnchor" />
contrario in Eclipticâ movetur <ptr type="noteAnchor" />, quo tardius ad Meridia-
<ptr xml:id="note-0664-02a" corresp="note-0664-02" type="noteAnchor" />
num pertingit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0663-13" corresp="note-0663-13a" place="margin">1142.</note>
              <note xml:space="preserve" xml:id="note-0664-01" corresp="note-0664-01a" n="*" anchored="true" place="margin">1080.</note>
              <note xml:space="preserve" xml:id="note-0664-02" corresp="note-0664-02a" n="*" anchored="true" place="margin">996.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cùm autem non ſingulis diebus Sol ſpatium æquale per-<lb />
<ptr xml:id="note-0664-03a" corresp="note-0664-03" type="noteAnchor" />
currat in Eclipticâ <ptr type="noteAnchor" />, non æqualiter ſinguli Dies Naturales
<ptr xml:id="note-0664-04a" corresp="note-0664-04" type="noteAnchor" />
excedunt revolutionem Telluris circa axem; </s>
          <s xml:space="preserve">ideoque Dies <lb />hi ſunt inæquales inter ſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0664-03" corresp="note-0664-03a" place="margin">1143.</note>
              <note xml:space="preserve" xml:id="note-0664-04" corresp="note-0664-04a" n="*" anchored="true" place="margin">997.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Etiam aliâ ex cauſâ dies naturales inæquales ſunt, nem-<lb />pe ex inclinatione Eclipticæ reſpectu Æquatoris; </s>
          <s xml:space="preserve">unde ſe-<lb />quitur inæqualiter, in variis punctis, ad Æquatorem viam So-<lb />lis annuam inclinari; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">licet æqualiter in Eclipticâ ſin-<lb />gulis diebus progrederetur Sol, non æqualiter dies natura-<lb />les Tempus revolutionis circa axem excederent; </s>
          <s xml:space="preserve">nam re-<lb />ſoluto motu Solis in duos motus <ptr type="noteAnchor" />, quorum unus parallelus
<ptr xml:id="note-0664-05a" corresp="note-0664-05" type="noteAnchor" />
eſt Æquatori, alter huic perpendicularis, ille ſolus conſide-<lb />randus erit in determinando exceſſu memorato, &amp; </s>
          <s xml:space="preserve">inæqua-<lb />lem eſſe ex diverſà inclinatione indicatâ clarum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0664-05" corresp="note-0664-05a" n="*" anchored="true" place="margin">191.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hæ duæ cauſæ inæqualitatis ſæpe concurrunt, ſæpe con-<lb />trariè agunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dies ſinguli naturales dividuntur in viginti quatuor par-<lb />
<ptr xml:id="note-0664-06a" corresp="note-0664-06" type="noteAnchor" />
tes æquales, quæ Horæ dicuntur. </s>
          <s xml:space="preserve">Singulæ Horæ dividun-<lb />tur in Minuta ſexaginta, &amp; </s>
          <s xml:space="preserve">ſingula Minuta in Minuta ſecun-<lb />da ſexaginta, &amp; </s>
          <s xml:space="preserve">ſic ulterius. </s>
          <s xml:space="preserve">Partes bas Temporis in va-<lb />riis diebus, variare, ex dictis <ptr type="noteAnchor" />, clarè patet; </s>
          <s xml:space="preserve">ad æqualita-
<ptr xml:id="note-0664-07a" corresp="note-0664-07" type="noteAnchor" />
tem ab Aſtronomis reducuntur, conſiderando numerum <lb />Horarum in integrâ Solis revolutione in Eclipticâ, &amp; </s>
          <s xml:space="preserve">totum <lb />Tempus in tot partes æquales dividendo, quot dantur Horæ; <lb /></s>
          <s xml:space="preserve">quarum viginti quatuor prouno die habentur. </s>
          <s xml:space="preserve">Tempus, cujus <lb />
<ptr xml:id="note-0664-08a" corresp="note-0664-08" type="noteAnchor" />
partes hac methodo ad æqualitatem reducuntur, vocatur Tem-<lb />pus medium; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ipſa reductio vocatur Temporis Æquatio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0664-06" corresp="note-0664-06a" place="margin">1144.</note>
              <note xml:space="preserve" xml:id="note-0664-07" corresp="note-0664-07a" n="*" anchored="true" place="margin">1143.</note>
              <note xml:space="preserve" xml:id="note-0664-08" corresp="note-0664-08a" place="margin">1145.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">De diebus &amp; </s>
          <s xml:space="preserve">horis Temporis medii ſemper agitur in deter-<lb />
<ptr xml:id="note-0664-09a" corresp="note-0664-09" type="noteAnchor" />
minandis periodis motuum cæleſtium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0664-09" corresp="note-0664-09a" place="margin">1146.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 19.</head>
        <p>
          <s xml:space="preserve">Dies Artificialis eſt mora Solis ſupra Horizontem.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1147.</note>
        <p>
          <s xml:space="preserve">De hoc ſemper agitur, quando de Die loquimur, hunc <lb />opponendo Nocti. </s>
          <s xml:space="preserve">In determinanda dierum artificialium <lb />
<ptr xml:id="note-0664-11a" corresp="note-0664-11" type="noteAnchor" />
longitudine ad Temporis æquationem non attendemus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0664-11" corresp="note-0664-11a" place="margin">1148.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0665" />
        <pb facs="0665a" />
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0665a-01" />
          <label>0665a-01</label>
        </figure>
        <pb facs="0666" />
        <pb facs="0667" n="139" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. VIII.</fw>
        <p rend="italics">
          <s xml:space="preserve">Ortum Solis ſemper præcedit, &amp; </s>
          <s xml:space="preserve">occaſum inſequitur, cre-<lb />
<ptr xml:id="note-0667-01a" corresp="note-0667-01" type="noteAnchor" />
puſculum; </s>
          <s xml:space="preserve">hoc nomine deſignamus lucem illam dubiam, quæ <lb />
<ptr xml:id="note-0667-02a" corresp="note-0667-02" type="noteAnchor" />
vulgo Aurora &amp; </s>
          <s xml:space="preserve">Veſper vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-01" corresp="note-0667-01a" place="margin">1149.</note>
              <note xml:space="preserve" xml:id="note-0667-02" corresp="note-0667-02a" place="margin">1150.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Oriuntur crepuſcula ex Atmoſphærâ, quæ radiis ſolari-<lb />
<ptr xml:id="note-0667-03a" corresp="note-0667-03" type="noteAnchor" />
bus illuſtratur, &amp; </s>
          <s xml:space="preserve">cujus particulæ lumen quaquaverſum re-<lb />flectunt; </s>
          <s xml:space="preserve">unde radii quidam ad nos perveniunt, licèt Sol octo-<lb />decim gradibus infra borizontem deprimatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-03" corresp="note-0667-03a" place="margin">1151.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſphærâ parallelâ, id eſt, pro omnibus, quæ ſub Æ-<lb />
<ptr xml:id="note-0667-04a" corresp="note-0667-04" type="noteAnchor" />
quatore vivunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">dies &amp; </s>
          <s xml:space="preserve">noctes per totum annum ſunt æqua-
<ptr xml:id="note-0667-05a" corresp="note-0667-05" type="noteAnchor" />
les inter ſe <ptr type="noteAnchor" />, nempe duodecim horarum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-04" corresp="note-0667-04a" place="margin">1152.</note>
              <note xml:space="preserve" xml:id="note-0667-05" corresp="note-0667-05a" n="*" anchored="true" place="margin">1138.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1139.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1144.</note>
        <p rend="italics">
          <s xml:space="preserve">In ſphærâ obliquâ dies majores aut minores ſunt, pro va-<lb />
<ptr xml:id="note-0667-08a" corresp="note-0667-08" type="noteAnchor" />
riâ diſtantiâ Solis ab Æquatore, verſus unum aut alterum <lb />Polum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">verſus quos ab Æquatore recedit 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-08" corresp="note-0667-08a" place="margin">1153.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1131. 1132.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1087. 1088.</note>
        <p rend="italics">
          <s xml:space="preserve">In ipſo Æquatore datur circiter 22. </s>
          <s xml:space="preserve">Martis, &amp; </s>
          <s xml:space="preserve">23. </s>
          <s xml:space="preserve">Se-<lb />
<ptr xml:id="note-0667-11a" corresp="note-0667-11" type="noteAnchor" />
ptembris, &amp; </s>
          <s xml:space="preserve">dies nocti æquatur <ptr type="noteAnchor" />, quod ubique terrarum ob-
<ptr xml:id="note-0667-12a" corresp="note-0667-12" type="noteAnchor" />
tinet, ſolis Polis exceptis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-11" corresp="note-0667-11a" place="margin">1154.</note>
              <note xml:space="preserve" xml:id="note-0667-12" corresp="note-0667-12a" n="*" anchored="true" place="margin">1194.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 20.</head>
        <note xml:space="preserve" place="margin">1155.</note>
        <p>
          <s xml:space="preserve">Puncta Eclipticæ, in quibus ab Æquatore ſecatur <ptr type="noteAnchor" />, vo-
<ptr xml:id="note-0667-14a" corresp="note-0667-14" type="noteAnchor" />
cantur Æquinoctialia. </s>
          <s xml:space="preserve">Quia in his punctis verſatur Sol ubi <lb />datur æqualitas memorata dierum &amp; </s>
          <s xml:space="preserve">noctium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-14" corresp="note-0667-14a" n="*" anchored="true" place="margin">1085.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 21.</head>
        <p>
          <s xml:space="preserve">Puncta Eclipticæ, in quibus Tropici circulum hunc tan-<lb />gunt <ptr type="noteAnchor" />, dicuntur Solſtitialia. </s>
          <s xml:space="preserve">Quia per aliquot dies, quan-
<ptr xml:id="note-0667-15a" corresp="note-0667-15" type="noteAnchor" />
do ad hæc accedit Sol, &amp; </s>
          <s xml:space="preserve">ultra tranſit, ſenſibiliter declina-<lb />tionem non mutat, &amp; </s>
          <s xml:space="preserve">ſenſibiliter dierum longitudo non va-<lb />riat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-15" corresp="note-0667-15a" n="*" anchored="true" place="margin">1089.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sub Polis, ſidentur incolæ, ſemel in anno Solem orien-<lb />
<ptr xml:id="note-0667-16a" corresp="note-0667-16" type="noteAnchor" />
tem &amp; </s>
          <s xml:space="preserve">occidentem obſervant, &amp; </s>
          <s xml:space="preserve">dies unicus cum unicâ nocte <lb />integrum annum obſolvunt. </s>
          <s xml:space="preserve">Supra horizontem verſatur Sol, <lb />dum dimidiam Eclipticæ partem percurrit <ptr type="noteAnchor" />, per reliquum
<ptr xml:id="note-0667-17a" corresp="note-0667-17" type="noteAnchor" />
Tempus ſub Horizonte latet. </s>
          <s xml:space="preserve">Dies tamen protrahitur ex <lb />
<ptr xml:id="note-0667-18a" corresp="note-0667-18" type="noteAnchor" />
refractione <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">crepuſcula ſunt admodum diuturna, durant
<ptr xml:id="note-0667-19a" corresp="note-0667-19" type="noteAnchor" />
enim quamdiu declinatio Solis verſus Polum latentem non <lb />ſuperat 18. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-16" corresp="note-0667-16a" place="margin">1156.</note>
              <note xml:space="preserve" xml:id="note-0667-17" corresp="note-0667-17a" n="*" anchored="true" place="margin">1085. 1123.</note>
              <note xml:space="preserve" xml:id="note-0667-18" corresp="note-0667-18a" place="margin">1157.</note>
              <note xml:space="preserve" xml:id="note-0667-19" corresp="note-0667-19a" n="*" anchored="true" place="margin">1113.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1151.</note>
        <p>
          <s xml:space="preserve">In Polo Arctico in ſex ſignis primis, ab Ariete ad Libram, <lb />
<ptr xml:id="note-0667-21a" corresp="note-0667-21" type="noteAnchor" />
Sol ſupra Horizontem verſatur; </s>
          <s xml:space="preserve">ideò in hoc Polo dies no-<lb />ctem ſuperat novem diebus naturalibus <ptr type="noteAnchor" />, præter diminutio-
<ptr xml:id="note-0667-22a" corresp="note-0667-22" type="noteAnchor" />
nem noctis ex refractione <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0667-21" corresp="note-0667-21a" place="margin">1158.</note>
              <note xml:space="preserve" xml:id="note-0667-22" corresp="note-0667-22a" n="*" anchored="true" place="margin">1000.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1157.</note>
        <pb facs="0668" n="140" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Hiſce generalibus, quæ ſpectant diverſos Horizontis ſi-<lb />tus, expoſitis, quædam magis peculiaria ſunt examinanda.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Dividitur tota Telluris ſuperficies in quinque Zonas. </s>
          <s xml:space="preserve">Pri-<lb />
<ptr xml:id="note-0668-01a" corresp="note-0668-01" type="noteAnchor" />
ma inter duos Tropicos TT, t t, continetur, vocatur Zona <lb />
<ptr xml:id="note-0668-02a" corresp="note-0668-02" type="noteAnchor" />
Torrida; </s>
          <s xml:space="preserve">duæ dantur Temperatæ, &amp; </s>
          <s xml:space="preserve">duæ Frigidæ. </s>
          <s xml:space="preserve">Tempe-<lb />
<ptr xml:id="note-0668-03a" corresp="note-0668-03" type="noteAnchor" />
<ptr xml:id="note-0668-04a" corresp="note-0668-04" type="noteAnchor" />
rata Septentrionalis, Tropico Cancri TT, &amp; </s>
          <s xml:space="preserve">Circulo Polari <lb />
<ptr xml:id="note-0668-05a" corresp="note-0668-05" type="noteAnchor" />
Arctico AA, terminatur: </s>
          <s xml:space="preserve">Zona Temperata Auſtralis inter <lb />Tropicum t t, &amp; </s>
          <s xml:space="preserve">Circulum Polarem a a, continetur. </s>
          <s xml:space="preserve">Fri-<lb />
<ptr xml:id="note-0668-06a" corresp="note-0668-06" type="noteAnchor" />
gidæ Zonæ circulis polaribus circumſcribuntur, &amp; </s>
          <s xml:space="preserve">Poli ba-<lb />rum centra occupant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0668-01" corresp="note-0668-01a" place="margin">1159.</note>
              <note xml:space="preserve" xml:id="note-0668-02" corresp="note-0668-02a" place="margin">1160.</note>
              <note xml:space="preserve" xml:id="note-0668-03" corresp="note-0668-03a" place="margin">TAB. XXIV.</note>
              <note xml:space="preserve" xml:id="note-0668-04" corresp="note-0668-04a" place="margin">fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0668-05" corresp="note-0668-05a" place="margin">1161.</note>
              <note xml:space="preserve" xml:id="note-0668-06" corresp="note-0668-06a" place="margin">1162.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Zonâ Torridâ bis in anno, in meridie, per Zenit tran-<lb />
<ptr xml:id="note-0668-07a" corresp="note-0668-07" type="noteAnchor" />
ſit Sol <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Nam elevatio Poli minor eſt 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0668-08a" corresp="note-0668-08" type="noteAnchor" />
<ptr xml:id="note-0668-09a" corresp="note-0668-09" type="noteAnchor" />
diſtantia Solis ab Æquatore, verſus Polum qui ſupra Horizon-<lb />tem datur, bis in anno æquatur altitudini Poli <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ex quâ
<ptr xml:id="note-0668-10a" corresp="note-0668-10" type="noteAnchor" />
eâdem ratione in ipſis Zonæ hujus limitibus, ſub Tropicis <lb />
<ptr xml:id="note-0668-11a" corresp="note-0668-11" type="noteAnchor" />
nempe, ſemel tantùm ad Zenit accedit Sol in integro anno <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0668-07" corresp="note-0668-07a" place="margin">1163.</note>
              <note xml:space="preserve" xml:id="note-0668-08" corresp="note-0668-08a" n="*" anchored="true" place="margin">1137.</note>
              <note xml:space="preserve" xml:id="note-0668-09" corresp="note-0668-09a" n="*" anchored="true" place="margin">1160. 1127.</note>
              <note xml:space="preserve" xml:id="note-0668-10" corresp="note-0668-10a" n="*" anchored="true" place="margin">1087. 1088.</note>
              <note xml:space="preserve" xml:id="note-0668-11" corresp="note-0668-11a" place="margin">1164.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1087. 1089.</note>
        <p>
          <s xml:space="preserve">In Zonis Temperatis &amp; </s>
          <s xml:space="preserve">Frigidis altitudo Poli minima ex-<lb />
<ptr xml:id="note-0668-13a" corresp="note-0668-13" type="noteAnchor" />
cedit maximam diſtantiam Solis ab Æquatore <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò nun-
<ptr xml:id="note-0668-14a" corresp="note-0668-14" type="noteAnchor" />
<ptr xml:id="note-0668-15a" corresp="note-0668-15" type="noteAnchor" />
quam in hiſce per Zenit tranſit Sol <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ad majorem tamen
<ptr xml:id="note-0668-16a" corresp="note-0668-16" type="noteAnchor" />
<ptr xml:id="note-0668-17a" corresp="note-0668-17" type="noteAnchor" />
altitudinem eodem die adſcendit Sol, quo minor eſt altitudo <lb />Poli; </s>
          <s xml:space="preserve">quia eo minor etiam eſt inclinatio circulorum motus <lb />diurni ad Horizontem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0668-13" corresp="note-0668-13a" place="margin">1165.</note>
              <note xml:space="preserve" xml:id="note-0668-14" corresp="note-0668-14a" n="*" anchored="true" place="margin">1087. 1161.</note>
              <note xml:space="preserve" xml:id="note-0668-15" corresp="note-0668-15a" place="margin">1162.</note>
              <note xml:space="preserve" xml:id="note-0668-16" corresp="note-0668-16a" place="margin">1166.</note>
              <note xml:space="preserve" xml:id="note-0668-17" corresp="note-0668-17a" n="*" anchored="true" place="margin">1137.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Zonâ Torridâ, &amp; </s>
          <s xml:space="preserve">Zonis Temperatis, ſingulis diebus na-<lb />
<ptr xml:id="note-0668-18a" corresp="note-0668-18" type="noteAnchor" />
turalibus oritur &amp; </s>
          <s xml:space="preserve">occidit Sol <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">nam diſtantia Solis â Polo
<ptr xml:id="note-0668-19a" corresp="note-0668-19" type="noteAnchor" />
ſemper ſuperat Poli altitudinem <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Inæquales tamen ubi-
<ptr xml:id="note-0668-20a" corresp="note-0668-20" type="noteAnchor" />
<ptr xml:id="note-0668-21a" corresp="note-0668-21" type="noteAnchor" />
que, ſolo Æquatore excepto <ptr type="noteAnchor" />, ſunt Dies artificiales inter
<ptr xml:id="note-0668-22a" corresp="note-0668-22" type="noteAnchor" />
ſe <ptr type="noteAnchor" />, quæ inæqualitas eo major eſt, quo minus â Zona Fri-
<ptr xml:id="note-0668-23a" corresp="note-0668-23" type="noteAnchor" />
<ptr xml:id="note-0668-24a" corresp="note-0668-24" type="noteAnchor" />
gida locus diſtat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0668-18" corresp="note-0668-18a" place="margin">1167.</note>
              <note xml:space="preserve" xml:id="note-0668-19" corresp="note-0668-19a" n="*" anchored="true" place="margin">1129. 1137.</note>
              <note xml:space="preserve" xml:id="note-0668-20" corresp="note-0668-20a" place="margin">1168.</note>
              <note xml:space="preserve" xml:id="note-0668-21" corresp="note-0668-21a" n="*" anchored="true" place="margin">1087. 1160.</note>
              <note xml:space="preserve" xml:id="note-0668-22" corresp="note-0668-22a" place="margin">1161.</note>
              <note xml:space="preserve" xml:id="note-0668-23" corresp="note-0668-23a" n="*" anchored="true" place="margin">1152.</note>
              <note xml:space="preserve" xml:id="note-0668-24" corresp="note-0668-24a" n="*" anchored="true" place="margin">1132.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1134.</note>
        <p>
          <s xml:space="preserve">In circulis autem Polaribus, in quibus Zonæ Temperatæ <lb />
<ptr xml:id="note-0668-26a" corresp="note-0668-26" type="noteAnchor" />
â Frigidis ſeparantur, altitudo Poli æqualis eſt diſtantiæ So-<lb />lis â Polo, quando datur in Tropico vicino <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideoque in
<ptr xml:id="note-0668-27a" corresp="note-0668-27" type="noteAnchor" />
hoc caſu, id eſt, ſemel in anno, integram Sol, in motu diur-<lb />no, peragit revolutionem, in qua infra Horizontem non <lb />deſcendit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0668-26" corresp="note-0668-26a" place="margin">1169.</note>
              <note xml:space="preserve" xml:id="note-0668-27" corresp="note-0668-27a" n="*" anchored="true" place="margin">1089. 1091.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vbique autem in Zonâ Frigidâ Altitudo Poli ſuperat di-<lb />
<ptr xml:id="note-0668-28a" corresp="note-0668-28" type="noteAnchor" />
ſtantiam minimam Solis à Polo <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">idcirco, per aliquot revo-
<ptr xml:id="note-0668-29a" corresp="note-0668-29" type="noteAnchor" />
lutiones Telluris, datur Sol ad diſtantiam à polo illâ alti-
</s>
          <pb facs="0669" n="141" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. VIII.</fw>
tudine Poli minorem, &amp; </s>
          <s xml:space="preserve">per totum hocce tempus non occi-<lb />dit, ne quidem ad Horizontem pertingit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ubi autem di-
<ptr xml:id="note-0669-01a" corresp="note-0669-01" type="noteAnchor" />
ſtantia à Polo, in receſſu Solis ab hoc, altitudinem Poli, <lb />aut loci latitudinem <ptr type="noteAnchor" />, ſuperat, ſingulis diebus naturalibus o-
<ptr xml:id="note-0669-02a" corresp="note-0669-02" type="noteAnchor" />
ritur &amp; </s>
          <s xml:space="preserve">occidit Sol <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">deinde infra Horizontem, motu ver-
<ptr xml:id="note-0669-03a" corresp="note-0669-03" type="noteAnchor" />
<ptr xml:id="note-0669-04a" corresp="note-0669-04" type="noteAnchor" />
ſus Polum oppoſitum, eodem modo moratur, ac de motu ſu-<lb />pra borizontem dictum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0668-28" corresp="note-0668-28a" place="margin">1170.</note>
              <note xml:space="preserve" xml:id="note-0668-29" corresp="note-0668-29a" n="*" anchored="true" place="margin">1089. 1162.</note>
              <note xml:space="preserve" xml:id="note-0669-01" corresp="note-0669-01a" n="*" anchored="true" place="margin">1135.</note>
              <note xml:space="preserve" xml:id="note-0669-02" corresp="note-0669-02a" n="*" anchored="true" place="margin">1127.</note>
              <note xml:space="preserve" xml:id="note-0669-03" corresp="note-0669-03a" place="margin">1171.</note>
              <note xml:space="preserve" xml:id="note-0669-04" corresp="note-0669-04a" n="*" anchored="true" place="margin">1129.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1136.</note>
        <p>
          <s xml:space="preserve">Tempora hæc, in quibus Sol integras revolutiones ſupra <lb />Horizontem &amp; </s>
          <s xml:space="preserve">infra Horizontem in motu diurno peragit, <lb />eo majora ſunt, id eſt, dies &amp; </s>
          <s xml:space="preserve">nox longiſſimæ, eo diutius du-<lb />
<ptr xml:id="note-0669-06a" corresp="note-0669-06" type="noteAnchor" />
rant, quo locus in Zonâ frigidâ minùs à Polo diſtat, donec <lb />tandem in ipſo Polo integrum annum abſorbeant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0669-06" corresp="note-0669-06a" place="margin">1172.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex eâdem cauſâ, obliquitate nempe Eclipticæ reſpectu <lb />Æquatoris, ex qua profluunt, quæ dierum inæqualitatem, <lb />in variis locis diverſam, ſpectant, deducimus etiam diverſi-<lb />tatem Tempeſtatum, quæ ſingulis annis ſibi mutuo ſucce-<lb />dunt; </s>
          <s xml:space="preserve">de his reſpectu Zonarum Frigidarum &amp; </s>
          <s xml:space="preserve">Temperata-<lb />rum primò, deinde reſpectu Zonæ Torridæ, agam.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Radii Solares calorem aëri communicant, non quidem <lb />dum directè à Sole procedunt, ſed cùm à corporibus, aut <lb />Telluris ſuperficie, irregulariter reflectuntur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Effectus
<ptr xml:id="note-0669-07a" corresp="note-0669-07" type="noteAnchor" />
hic eo major eſt, quo radii minùs obliquè in Telluris ſuperfi-<lb />ciem impingunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">quidem ex duplici cauſâ. </s>
          <s xml:space="preserve">1. </s>
          <s xml:space="preserve">Reſoluto <lb />motu luminis in duos <ptr type="noteAnchor" />, quorum unus ad ſuperficiem paral-
<ptr xml:id="note-0669-08a" corresp="note-0669-08" type="noteAnchor" />
lelus eſt, alter perpendicularis; </s>
          <s xml:space="preserve">hoc ſolo in corpora lumen <lb />agit, &amp; </s>
          <s xml:space="preserve">auctâ obliquitate minuitur. </s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">In eandem ſuperfi-<lb />ciei Telluris partem eo majori numero agunt radii, quo <lb />magis directè accedunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0669-07" corresp="note-0669-07a" n="*" anchored="true" place="margin">582.</note>
              <note xml:space="preserve" xml:id="note-0669-08" corresp="note-0669-08a" n="*" anchored="true" place="margin">192.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce deducimus cauſas caloris augeri, dum ex acceſſu <lb />
<ptr xml:id="note-0669-09a" corresp="note-0669-09" type="noteAnchor" />
Solis verſus Polum, qui ſupra Horizontem datur Dies <lb />creſcunt; </s>
          <s xml:space="preserve">quia de die in diem ad majorem altitudinem ad-<lb />ſcendit Sol; </s>
          <s xml:space="preserve">ita ut imminutæ obliquitati ſeſe jungat mora <lb />diuturnior Solis ſupra Horizontem, quæ ad augendum ca-<lb />lorem concurrit; </s>
          <s xml:space="preserve">etiam dum dies creſcunt noctes minuun-<lb />tur, &amp; </s>
          <s xml:space="preserve">per tempus brevius decreſcit calor de die acquiſi-<lb />tus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0669-09" corresp="note-0669-09a" place="margin">1173.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Zonis Septentrionalibus, ut ex hiſce ſequitur, cauſa
</s>
          <pb facs="0670" n="142" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
caloris eſt omnium maxima, cùm Sol Tropicum Cancri at-<lb />
<ptr xml:id="note-0670-01a" corresp="note-0670-01" type="noteAnchor" />
tingit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Non tamen, ubi cauſa caloris eſt maxima, ipſe ca-
<ptr xml:id="note-0670-02a" corresp="note-0670-02" type="noteAnchor" />
lor eſt maximus; </s>
          <s xml:space="preserve">nam hic augetur quamdiu calor, interdiu <lb />acquiſitus, non in totum de nocte tollitur; </s>
          <s xml:space="preserve">licèt enim quo-<lb />tidiana augmenta minuantur, quamdiu augmentum datur, <lb />creſcit calor. </s>
          <s xml:space="preserve">Sic etiam frigus maximè intenſum non eſt in <lb />
<ptr xml:id="note-0670-03a" corresp="note-0670-03" type="noteAnchor" />
die breviſſimâ, in qua radiorum ſolarium obliquitas eſt ma-<lb />xima, &amp; </s>
          <s xml:space="preserve">abſentia Solis maximè diuturna; </s>
          <s xml:space="preserve">ſed frigus creſcit, <lb />quamdiu diminutio caloris durat; </s>
          <s xml:space="preserve">circa quam idem ratio-<lb />cinium, quàm circa caloris augmentum, inſtitui poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0670-01" corresp="note-0670-01a" place="margin">1174.</note>
              <note xml:space="preserve" xml:id="note-0670-02" corresp="note-0670-02a" n="*" anchored="true" place="margin">1090.</note>
              <note xml:space="preserve" xml:id="note-0670-03" corresp="note-0670-03a" place="margin">1175.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Dividitur annus in quatuor tempeſtates; </s>
          <s xml:space="preserve">calidiſſima vo-<lb />
<ptr xml:id="note-0670-04a" corresp="note-0670-04" type="noteAnchor" />
catur Æſtas; </s>
          <s xml:space="preserve">maximè frigida Hyems; </s>
          <s xml:space="preserve">temperata quæ Hye-<lb />mem ſequitur Ver; </s>
          <s xml:space="preserve">Autumnus Æſtatem ab Hyeme ſeparat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0670-04" corresp="note-0670-04a" place="margin">1176.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In regionibus Septentrionalibus, in initio Veris, Sol in <lb />
<ptr xml:id="note-0670-05a" corresp="note-0670-05" type="noteAnchor" />
principio Arietis apparet: </s>
          <s xml:space="preserve">in initio Æſtatis Sol ad Tropi-<lb />cum cancri pertingit. </s>
          <s xml:space="preserve">Vbi Sol ad principium Libræ perve-<lb />nit incboatur Autumnus: </s>
          <s xml:space="preserve">Tropicnm Capricorni percurrit <lb />Sol motu diurno in initio Hyemis, quæ omnia ex explicatis <ptr type="noteAnchor" />
<ptr xml:id="note-0670-06a" corresp="note-0670-06" type="noteAnchor" />
facilè deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0670-05" corresp="note-0670-05a" place="margin">1177.</note>
              <note xml:space="preserve" xml:id="note-0670-06" corresp="note-0670-06a" n="*" anchored="true" place="margin">1174. 1175.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In regionibus auſtralibus Æſtas cum Hyeme memoratâ coin-<lb />
<ptr xml:id="note-0670-07a" corresp="note-0670-07" type="noteAnchor" />
cidit, ver cum Autumno, &amp; </s>
          <s xml:space="preserve">vice verſâ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0670-07" corresp="note-0670-07a" place="margin">1178.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cauſæ generales, à quibus diviſio memorata pendet, ſæ-<lb />pe turbantur cauſis peculiaria loca ſpectantibus; </s>
          <s xml:space="preserve">præcipuè <lb />in Zonâ Torridâ, de qua ſeparatim agendum diximus. </s>
          <s xml:space="preserve">In <lb />
<ptr xml:id="note-0670-08a" corresp="note-0670-08" type="noteAnchor" />
pleriſque hujus Zonæ locis duæ tantum obſervantur Tempe-<lb />ſtates, Æſtas &amp; </s>
          <s xml:space="preserve">Hyems, quæ ſiccitate &amp; </s>
          <s xml:space="preserve">humiditate potiſſi-<lb />mum diſtinguuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0670-08" corresp="note-0670-08a" place="margin">1179.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quando Sol ad Zenit alicujus loci accedit, pluviæ dantur <lb />
<ptr xml:id="note-0670-09a" corresp="note-0670-09" type="noteAnchor" />
ferè continuæ, unde Calor minuitur; </s>
          <s xml:space="preserve">quod tempus ad Hye-<lb />mem refertur. </s>
          <s xml:space="preserve">Recedente Sole, minuuntur pluviæ, calor <lb />
<ptr xml:id="note-0670-10a" corresp="note-0670-10" type="noteAnchor" />
augetur, &amp; </s>
          <s xml:space="preserve">tempus hoc ad Æſtatem refertur</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0670-09" corresp="note-0670-09a" place="margin">1180.</note>
              <note xml:space="preserve" xml:id="note-0670-10" corresp="note-0670-10a" place="margin">1181.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In medio Zonæ Torridæ duæ dantur Æſtates &amp; </s>
          <s xml:space="preserve">totidem <lb />
<ptr xml:id="note-0670-11a" corresp="note-0670-11" type="noteAnchor" />
Hyemes; </s>
          <s xml:space="preserve">quia bis ad Zenit accedit Sol <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0670-11" corresp="note-0670-11a" place="margin">1182.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1163.</note>
        <p>
          <s xml:space="preserve">Ad latera hujus Zonæ, licèt Sol bis ad Zenit accedat; <lb /></s>
          <s xml:space="preserve">cùm inter acceſlus breve tempus detur, ambo Hyemes con-<lb />funduntur; </s>
          <s xml:space="preserve">quare duæ tantum tempeſtates in integro anno <lb />obſervantur.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0671" n="143" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. IX.</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT IX.</head>
        <head xml:space="preserve">De Phænomenis ex motu Axeos Telluris.</head>
        <p>
          <s xml:space="preserve">TElluris Axem motu Parallelo transferri diximus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">non
<ptr xml:id="note-0671-01a" corresp="note-0671-01" type="noteAnchor" />
conſideravimus motum exiguum, quo reverâ agitatur, <lb />de quo nunc agendum nobis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0671-01" corresp="note-0671-01a" n="*" anchored="true" place="margin">952.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Axis Telluris, ſervatâ inclinatione 66. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">31. </s>
          <s xml:space="preserve">ad planum <lb />
<ptr xml:id="note-0671-02a" corresp="note-0671-02" type="noteAnchor" />
Eclipticæ, in antecedentiâ revolvitur, id eſt, ſucceſſivè ver-<lb />ſus omnes partes dirigitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hujus extremitates, Poli nem-<lb />
<ptr xml:id="note-0671-03a" corresp="note-0671-03" type="noteAnchor" />
pe Mundi, circa Polos Eclipticæ circulos deſcribunt ab O-<lb />riente verſus Occidentem. </s>
          <s xml:space="preserve">Hæc autem revolutio abſolvi-<lb />tur circiter tempore viginti quinque millium annorum, quæ <lb />periodus Annus Magnus vocatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0671-02" corresp="note-0671-02a" place="margin">1183.</note>
              <note xml:space="preserve" xml:id="note-0671-03" corresp="note-0671-03a" place="margin">1184.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cùm Tellus ab hujus incolis pro immobili habeatur, mo-<lb />tus hic ad corpora cœleſtia refertur, ut de aliis motibus di-<lb />ctum. </s>
          <s xml:space="preserve">Ideò dum Poli mundi in antecedentiâ, circa Polos <lb />Eclipticæ, moventur, &amp; </s>
          <s xml:space="preserve">ſucceſſivè per omnia puncta, 23. <lb /></s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29. </s>
          <s xml:space="preserve">diſtantia ab his Polis, tranſeunt, hæc ipſa puncta, aut <lb />potius Stellæ fixæ, quæ in his dantur, ſucceſſivè ad Polos <lb />Mundi accedunt, &amp; </s>
          <s xml:space="preserve">in conſequentiâ ferri videntur, &amp; </s>
          <s xml:space="preserve">de-<lb />ſcribere circulos, qui reverâ â Polis Mundi deſcribuntur, <lb />circa Polos Eclipticæ, qui, in centris poſiti, ſoli quieſcunt. </s>
          <s xml:space="preserve"><lb />Nam cum ſtellis memoratis &amp; </s>
          <s xml:space="preserve">reliquæ, quia omnes eundem <lb />ſitum erga ſe mutuo ſervant <ptr type="noteAnchor" />, etiam tranſlatæ apparent.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">923.</note>
        <p>
          <s xml:space="preserve">Idcirco integra ſphæra Stellarum fixarum circa Axem, per <lb />
<ptr xml:id="note-0671-05a" corresp="note-0671-05" type="noteAnchor" />
Polos Eclipticæ tranſeuntem, rotari in conſequentiâ videtur; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſingulæ Stellæ circulos Eclipticæ parallelos, motu appa-<lb />renti, deſcribunt; </s>
          <s xml:space="preserve">quo motu latitudo Stellarum non muta-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0671-05" corresp="note-0671-05a" place="margin">1185.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planum Æquatoris cum Axe Telluris angulum efficit re-<lb />ctum; </s>
          <s xml:space="preserve">ideò, motu memorato Axeos, rotatur ſectio hujus <lb />Plani cum Plano Eclipticæ; </s>
          <s xml:space="preserve">quare prima puncta Ariëtis &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0671-06a" corresp="note-0671-06" type="noteAnchor" />
Libræ <ptr type="noteAnchor" />, quæ ſemper opponuntur, in ſpatio circiter vigin-
<ptr xml:id="note-0671-07a" corresp="note-0671-07" type="noteAnchor" />
ti quinque millium annorum totam lineam Eclipticam in an-<lb />tecedentiâ percurrunt: </s>
          <s xml:space="preserve">pro immobilibus tamen habentur à <lb />Terræ incolis, qui ipſas ſtellas fixas in conſequentiâ tranſla-<lb />tas imaginantur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0671-06" corresp="note-0671-06a" place="margin">1186.</note>
              <note xml:space="preserve" xml:id="note-0671-07" corresp="note-0671-07a" n="*" anchored="true" place="margin">1085.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1185.</note>
        <pb facs="0672" n="144" />
        <fw type="head">PHYSICES ELEMENTA</fw>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT X.</head>
        <head xml:space="preserve">De Stellis fixis.</head>
        <p>
          <s xml:space="preserve">STellas fixas diximus eſſe corpora lucida, ita remota, ut <lb />horum diſtantiæ cum diſtantiis ullis, in Syſtemate Plane-<lb />tario, non conferri poſſint. </s>
          <s xml:space="preserve">Non enim ſubtiliſſimis obſerva-<lb />
<ptr xml:id="note-0672-01a" corresp="note-0672-01" type="noteAnchor" />
tionibus Aſtronomi potuêre Polos Mundi tranſlatos obſervare <lb />in motu Telluris annuo, licèt circulos orbitæ Telluris æqua-<lb />les in cœlis deſcribant <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0672-01" corresp="note-0672-01a" place="margin">1187.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">952.</note>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> I.</head>
        <p>
          <s xml:space="preserve">Tranſlatio hæc Poli vocatur Paralaxis annua.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1188.</note>
        <p>
          <s xml:space="preserve">Diſtantiam ſtellarum immenſam eſſe, etiam ex obſervatio-<lb />nibus ope teleſcopiorum deducitur. </s>
          <s xml:space="preserve">Si Stella fixa quæcun-<lb />
<ptr xml:id="note-0672-04a" corresp="note-0672-04" type="noteAnchor" />
que, ex maximê lucidis &amp; </s>
          <s xml:space="preserve">conſpicuis, conſpiciatur adhibito <lb />Teleſcopio, per quod diameter Solis diametro orbitæ annuæ <lb />æqualis apparêret, quaſi punctum lucidum, ſine ſenſibili ma-<lb />gnitudine, apparebit; </s>
          <s xml:space="preserve">minores enim omnes Stellæ per Te-<lb />leſcopia, quàm nudis oculis, apparent, nam ex ſola ſcintilla-<lb />tione magnitudinem ſenſibilem habere videntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0672-04" corresp="note-0672-04a" place="margin">1189.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Vt Stellæ diſtinguantur, referuntur ad varias figuras, quæ <lb />
<ptr xml:id="note-0672-05a" corresp="note-0672-05" type="noteAnchor" />
in cælis imaginantur, &amp; </s>
          <s xml:space="preserve">Aſteriſmi vocantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0672-05" corresp="note-0672-05a" place="margin">1190.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In Zodiaco duodecim Aſteriſmi concipiuntur, Zodiaci Signa <lb />
<ptr xml:id="note-0672-06a" corresp="note-0672-06" type="noteAnchor" />
dicti, nominantur ut animalia, aut res quas repræſentant: <lb /></s>
          <s xml:space="preserve">Ariës, Taurus, Gemini, Cancer, Leo, Virgo, Libra, <lb />Scorpius, Sagittarius, Capricornus, Aquarius, Piſces. </s>
          <s xml:space="preserve">Si-<lb />
<ptr xml:id="note-0672-07a" corresp="note-0672-07" type="noteAnchor" />
gna hæc nomina ſua dedêre, duodecim partibus Eclipticæ de <lb />quibus antea <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0672-06" corresp="note-0672-06a" place="margin">1191.</note>
              <note xml:space="preserve" xml:id="note-0672-07" corresp="note-0672-07a" place="margin">1192.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">999.</note>
        <p>
          <s xml:space="preserve">Tempore Hiparchi, ſectiones Eclipticæ &amp; </s>
          <s xml:space="preserve">Æquatoris ſitæ <lb />erant inter Aſteriſmos Piſcis &amp; </s>
          <s xml:space="preserve">Ariëtis, &amp; </s>
          <s xml:space="preserve">Virginis &amp; </s>
          <s xml:space="preserve">Li-<lb />bræ, &amp; </s>
          <s xml:space="preserve">Aſteriſmi nomina dedêre illis Eclipticæ partibus, quæ <lb />per ſingulos Aſteriſmos tranſibant: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">partes Eclipticæ, po-<lb />
<ptr xml:id="note-0672-09a" corresp="note-0672-09" type="noteAnchor" />
nendo initium Ariëtis, &amp; </s>
          <s xml:space="preserve">Libræ in interſectionibus Æqua-<lb />toris &amp; </s>
          <s xml:space="preserve">Eclipticæ, uti in illo tempore, nomina ſervarunt, <lb />licet hæ interſectiones tranſlatæ ſint <ptr type="noteAnchor" />, unde Sol in Tauro
<ptr xml:id="note-0672-10a" corresp="note-0672-10" type="noteAnchor" />
dicitur, quando inter Stellas Aſteriſmi Ariëtis movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0672-09" corresp="note-0672-09a" place="margin">1193.</note>
              <note xml:space="preserve" xml:id="note-0672-10" corresp="note-0672-10a" n="*" anchored="true" place="margin">1186.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Zodiacus partem Cœli Septentrionalem à Meridionali ſe-<lb />parat.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0673" n="145" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. X.</fw>
        <p rend="italics">
          <s xml:space="preserve">In Septentrionali dantur Aſteriſmi, Vrſa minor, Vrſa <lb />
<ptr xml:id="note-0673-01a" corresp="note-0673-01" type="noteAnchor" />
major, Draco, Cepheus, Canes Venatici, Bootes, Corona <lb />Septentrionalis, Hercules, Lyra, Cygnus, Lacerta, Caſio-<lb />pèja, Camelopardus, Perſeus, Andromeda, Triangulum, <lb />Triangulum minus, Muſca, Auriga, Pegaſus, Equuleus, <lb />Delphin, Vulpecula, Anſer, Sagitta, Aquila, Antinous, <lb />Scutum Sobieskianum, Serpentarius, Serpens, Mons Mæ-<lb />nalus, Coma Berenicis, Leo minor, Linx.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0673-01" corresp="note-0673-01a" place="margin">1194.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In parte Meridionali Cælorum Aſteriſmi, quorum multi à <lb />
<ptr xml:id="note-0673-02a" corresp="note-0673-02" type="noteAnchor" />
nobis videri non poſſunt <ptr type="noteAnchor" />, ſunt, Cetus, Eridanus, Lepus,
<ptr xml:id="note-0673-03a" corresp="note-0673-03" type="noteAnchor" />
Orion, Canis major, Monocerotes, Canis minor, Argo-navis, <lb />Hydra, Vraniæ Sextans, Crater, Corvus, Centaurus, Lupus, <lb />Ara, Corona Auſtralis, Piſcis Auſtrinus, Phænix, Grus, In-<lb />dus, Pavo, Apus, Triangulum Auſtrale, Crux, Muſca, Cha-<lb />mæleon, Quercus Carolinum, Piſcis volans, Toucan ſive <lb />Anſer Americanus, Hydrus, Xiphias ſive Dorado.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0673-02" corresp="note-0673-02a" place="margin">1195.</note>
              <note xml:space="preserve" xml:id="note-0673-03" corresp="note-0673-03a" n="*" anchored="true" place="margin">1131.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi> 2.</head>
        <p rend="italics">
          <s xml:space="preserve">Stellæ, quæ inter Aſteriſmos dantur, vocantur informes.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin">1196.</note>
        <p>
          <s xml:space="preserve">Non omnes Stellæ æquè lucidæ apparent, &amp; </s>
          <s xml:space="preserve">ab Aſtrono-<lb />
<ptr xml:id="note-0673-05a" corresp="note-0673-05" type="noteAnchor" />
mis ad ſex claßes referuntur, omnium maximè lucidæ di-<lb />cuntur Primæ Magnitudinis; </s>
          <s xml:space="preserve">aliæ Secundæ, Tertiæ, &amp;</s>
          <s xml:space="preserve">c. <lb /></s>
          <s xml:space="preserve">Magnitudinis, ad ſextam uſque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0673-05" corresp="note-0673-05a" place="margin">1197.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quædam, ne quidem ad hanc ultimam claſſem referuntur, <lb />
<ptr xml:id="note-0673-06a" corresp="note-0673-06" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">Nebuloſæ dicuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0673-06" corresp="note-0673-06a" place="margin">1198.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Cælis etiam obſervamus Zonam quandam, non ubi-<lb />
<ptr xml:id="note-0673-07a" corresp="note-0673-07" type="noteAnchor" />
que ejuſdem latitudinis, quæ totum Cœlum circumdat, <lb />&amp; </s>
          <s xml:space="preserve">in quibuſdam locis ſeparatur, ut dupla ſit. </s>
          <s xml:space="preserve">Propter co-<lb />lorem via Lactea vocatur. </s>
          <s xml:space="preserve">Obſervationibus, ope Teleſco-<lb />piorum conſtat, congeriem eſſe viam hanc Stellarum innume-<lb />
<ptr xml:id="note-0673-08a" corresp="note-0673-08" type="noteAnchor" />
rarum, quæ viſum oculi inermis fugiunt, aut quia cæteris <lb />Stellis minores ſunt, aut quia magis diſtant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0673-07" corresp="note-0673-07a" place="margin">1199.</note>
              <note xml:space="preserve" xml:id="note-0673-08" corresp="note-0673-08a" place="margin">1200.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Verſus Polum Antarcticum duæ Nubeculæ, huic viæ ſimi-<lb />
<ptr xml:id="note-0673-09a" corresp="note-0673-09" type="noteAnchor" />
les, dantur, quæ etiam ſunt congeries Stellarum minimarum, <lb />niſi per Teleſcopia Viſibilium. </s>
          <s xml:space="preserve">Præter Stellas, quæ in hiſce Nu-<lb />beculis, &amp; </s>
          <s xml:space="preserve">Viâ lacteâ, obſervantur, maximo numero per to-<lb />
<ptr xml:id="note-0673-10a" corresp="note-0673-10" type="noteAnchor" />
tum Cælum, adhibitis Teleſcopiis, minores Stellæ detegun-<lb />tur, quæ nudis oculis non apparent. </s>
          <s xml:space="preserve">Sæpiſſimè Stellarum
</s>
          <pb facs="0674" n="(146)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
congeries, innermi oculo, pro unicâ Stellâ habetur. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0674-01a" corresp="note-0674-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0673-09" corresp="note-0673-09a" place="margin">1201.</note>
              <note xml:space="preserve" xml:id="note-0673-10" corresp="note-0673-10a" place="margin">1202.</note>
              <note xml:space="preserve" xml:id="note-0674-01" corresp="note-0674-01a" place="margin">1203.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Inter Stellas, quædam per vices videntur, &amp; </s>
          <s xml:space="preserve">inviſibiles <lb />fiunt, regulareſque periodos obſervant; </s>
          <s xml:space="preserve">aliæ ſucceſſivè nunc <lb />magis lucidæ, nunc hebetiori lumine præditæ, &amp; </s>
          <s xml:space="preserve">Teleſco-<lb />piis tantùm viſibiles, apparent; </s>
          <s xml:space="preserve">idque ſtatis temporibus.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Non tamen ſingulis periodis æquè claræ ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Aliquando ſubitò Stellæ apparuere, lumine lucidiores ſu-<lb />
<ptr xml:id="note-0674-02a" corresp="note-0674-02" type="noteAnchor" />
perantes, quæ deinde, ſucceſſivè decreſcentes, brevi evanue-<lb />runt, &amp; </s>
          <s xml:space="preserve">adhucdum latent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0674-02" corresp="note-0674-02a" place="margin">1204.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Præter Stellas, etiam in Cælo obſervamus varias maculas al-<lb />
<ptr xml:id="note-0674-03a" corresp="note-0674-03" type="noteAnchor" />
bidiores &amp; </s>
          <s xml:space="preserve">quodammodo lucidas, quæ nudis oculis inviſibiles <lb />ſunt; </s>
          <s xml:space="preserve">horum enim lumen ad Stellas, quæ in ipſis dantur, re-<lb />fertur aut pro Stellis nebuloſis habentur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0674-03" corresp="note-0674-03a" place="margin">1205.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quid ſint hæ maculæ, determinari non poteſt, fortè ſunt <lb />congeries Stellarum, quæ cum Stellis Teleſcopicis illam ha-<lb />bent relationem, quàm quæ Viam lacteam formant, cum illis, <lb />quæ nudis oculis deteguntur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">LIBERI IV. Pars II.</head>
        <head xml:space="preserve">Motuum Cœleſtium Cauſæ Phyſicæ.</head>
        <head xml:space="preserve">CAPUT XI.</head>
        <head rend="italics" xml:space="preserve">De univerſali Gravitate.</head>
        <p>
          <s xml:space="preserve">Expoſitis corporum cœleſtium motibus, ut &amp; </s>
          <s xml:space="preserve">Phœno-<lb />menis inde oriundis, quibus legibus motus hi peragan-<lb />tur explicandum erit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Leges, juxta quas corporum motus deriguntur, antea ex-<lb />poſuimus <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si hiſce unicam adamus, totum patet artificium,
<ptr xml:id="note-0674-04a" corresp="note-0674-04" type="noteAnchor" />
quo ingens Machina, Syſtema Planetarium, regitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0674-04" corresp="note-0674-04a" n="*" anchored="true" place="margin">124. 125. 126.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lex, cæteris addenda, hæc eſt. </s>
          <s xml:space="preserve">Omnia corpora in ſe <lb />
<ptr xml:id="note-0674-05a" corresp="note-0674-05" type="noteAnchor" />
mutuo gravia ſunt: </s>
          <s xml:space="preserve">gravitas hæc materiæ quantitati pro-<lb />
<ptr xml:id="note-0674-06a" corresp="note-0674-06" type="noteAnchor" />
portionalis eſt: </s>
          <s xml:space="preserve">ad inæquales diſtantias eſt inverſè, ut qua-<lb />
<ptr xml:id="note-0674-07a" corresp="note-0674-07" type="noteAnchor" />
dratum diſtantiæ. </s>
          <s xml:space="preserve">Id eſt, omnia corpora ſeſe mutuo petunt, <lb />aut verſus ſeſe mutuo tendunt, vi, quæ ſingulis particulis
</s>
          <pb facs="0675" n="(147)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. IV. CAP XI.</fw>
materiæ in ſingulas particulas competit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vis, qua corpus <lb />in alia agit, formatur ex omnibus viribus conjunctis <lb />particularum, ex quibus corpus conſtat; </s>
          <s xml:space="preserve">ideò vis hæc <lb />creſcit in ratione, in qua materiæ quantitas augetur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">im-<lb />mutabilis eſt in ſingulis particulis; </s>
          <s xml:space="preserve">ad eandem diſtantiam <lb />ſemper eadem; </s>
          <s xml:space="preserve">auctâ autem diſtantiâ decreſcit vis, ut qua-<lb />dratum diſtantiæ augetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0674-05" corresp="note-0674-05a" place="margin">1206.</note>
              <note xml:space="preserve" xml:id="note-0674-06" corresp="note-0674-06a" place="margin">1207.</note>
              <note xml:space="preserve" xml:id="note-0674-07" corresp="note-0674-07a" place="margin">1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vim hanc gravitatem nominamus, conſiderando corpus, <lb />
<ptr xml:id="note-0675-01a" corresp="note-0675-01" type="noteAnchor" />
quod verſus aliud ſponte tendit; </s>
          <s xml:space="preserve">quia eo nomine vis hæc in <lb />Telluris viciniis datur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0675-02a" corresp="note-0675-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0675-01" corresp="note-0675-01a" place="margin">1209.</note>
              <note xml:space="preserve" xml:id="note-0675-02" corresp="note-0675-02a" n="*" anchored="true" place="margin">73.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Conſiderando autem corpus, verſus quod aliud tendit, vim <lb />
<ptr xml:id="note-0675-03a" corresp="note-0675-03" type="noteAnchor" />
hanc vocamus attractionem. </s>
          <s xml:space="preserve">His nominibus eundem effe-<lb />ctum, &amp; </s>
          <s xml:space="preserve">nil præter effectum deſignamus; </s>
          <s xml:space="preserve">nam, cum omnis <lb />gravitas ſit reciproca <ptr type="noteAnchor" />, corpora in ſe mutuo gravitare,
<ptr xml:id="note-0675-04a" corresp="note-0675-04" type="noteAnchor" />
idem ſignificat, quàm corpora ſeſe mutuo attrahere, aut <lb />ad ſe mutuo ſponte tendere.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0675-03" corresp="note-0675-03a" place="margin">1210.</note>
              <note xml:space="preserve" xml:id="note-0675-04" corresp="note-0675-04a" n="*" anchored="true" place="margin">126.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Effectum hunc pro lege Naturæ habemus <ptr type="noteAnchor" />, quia nunquam
<ptr xml:id="note-0675-05a" corresp="note-0675-05" type="noteAnchor" />
failit, &amp; </s>
          <s xml:space="preserve">hujus cauſa nobis eſt ignota, &amp; </s>
          <s xml:space="preserve">ex legibus notis <lb />minimè deduci poteſt, ut ſtatim dicetur. </s>
          <s xml:space="preserve">Nunc autem talem <lb />gravitatem reverâ dari, ex Phœnomenis probandum eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0675-05" corresp="note-0675-05a" n="*" anchored="true" place="margin">4</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Planetæ primarii ſinguli in orbitis ſuis retinentur viribus, <lb />quæ ad centrum Solis tendunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò datur vis, qua Plane-
<ptr xml:id="note-0675-06a" corresp="note-0675-06" type="noteAnchor" />
tæ Solem verſus feruntur, &amp; </s>
          <s xml:space="preserve">qua Sol reciprocè ad illos <lb />ſingulos tendit <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">id eſt, Sol in Planetas, &amp; </s>
          <s xml:space="preserve">hi in Solem
<ptr xml:id="note-0675-07a" corresp="note-0675-07" type="noteAnchor" />
gravitant. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0675-08a" corresp="note-0675-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0675-06" corresp="note-0675-06a" n="*" anchored="true" place="margin">944. 226.</note>
              <note xml:space="preserve" xml:id="note-0675-07" corresp="note-0675-07a" place="margin">1211.</note>
              <note xml:space="preserve" xml:id="note-0675-08" corresp="note-0675-08a" n="*" anchored="true" place="margin">126.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Eodem modo patet, ſecundarios Foviales in Fovem, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0675-09a" corresp="note-0675-09" type="noteAnchor" />
Fovem in ipſos; </s>
          <s xml:space="preserve">ut &amp; </s>
          <s xml:space="preserve">Saturni Satellites in primarium, &amp; </s>
          <s xml:space="preserve"><lb />hunc illos gravitare <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0675-10a" corresp="note-0675-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0675-09" corresp="note-0675-09a" place="margin">1212.</note>
              <note xml:space="preserve" xml:id="note-0675-10" corresp="note-0675-10a" n="*" anchored="true" place="margin">966. 226. 126.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Etiam Luna &amp; </s>
          <s xml:space="preserve">Tellus in ſe mutuo graves ſunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0675-11a" corresp="note-0675-11" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0675-11" corresp="note-0675-11a" place="margin">1213.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Secundarii omnes in Solem gravitatem habent. </s>
          <s xml:space="preserve">Omnes <lb />
<ptr xml:id="note-0675-12a" corresp="note-0675-12" type="noteAnchor" />
enim, motu regulari, circa Primarios ita feruntur, quaſi Pri-<lb />
<ptr xml:id="note-0675-13a" corresp="note-0675-13" type="noteAnchor" />
marii quieſeerent; </s>
          <s xml:space="preserve">unde liquet, illos motu communi cum <lb />Primariis ferri; </s>
          <s xml:space="preserve">id eſt, eandem vim, qua omnibus momen-<lb />tis ad Solem feruntur Primarii, in Secundarios agere, &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0675-14a" corresp="note-0675-14" type="noteAnchor" />
hos eâdem celeritate cum Primariis Solem verſus ferri. <lb /></s>
          <s xml:space="preserve">Ipſæ Secundariorum irregularitates, quæ adeo ſunt exiguæ, <lb />ut reſpectu ſolius Lunæ ſint ſenſibiles, confirmant hanc Se-
</s>
          <pb facs="0676" n="(148)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
cundariorum gravitatem in Solem; </s>
          <s xml:space="preserve">nam irregularitates omnes <lb />pendere à mutatâ gravitate Lunæ Solem verſus, pro variâ di-<lb />ſtantiâ, &amp; </s>
          <s xml:space="preserve">ex eo quod lineæ, per quas ad Solem tendunt Tellus <lb />&amp; </s>
          <s xml:space="preserve">Luna, non ſint omnino parallelæ, in ſequentibus videbimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0675-12" corresp="note-0675-12a" place="margin">1214.</note>
              <note xml:space="preserve" xml:id="note-0675-13" corresp="note-0675-13a" n="*" anchored="true" place="margin">966. 226. 126.</note>
              <note xml:space="preserve" xml:id="note-0675-14" corresp="note-0675-14a" place="margin">1215.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex gravitate Secundariorum in Solem, ſequitur Solem in <lb />
<ptr xml:id="note-0676-01a" corresp="note-0676-01" type="noteAnchor" />
illos gravitare <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0676-02a" corresp="note-0676-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0676-01" corresp="note-0676-01a" place="margin">1216.</note>
              <note xml:space="preserve" xml:id="note-0676-02" corresp="note-0676-02a" n="*" anchored="true" place="margin">126.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa gravitatem Primariorum inter ſe, obſervarunt A ſtro-<lb />nomi, Saturnum viam mutare ubi Jovi, Planetarum longè <lb />
<ptr xml:id="note-0676-03a" corresp="note-0676-03" type="noteAnchor" />
maximo, eſt proximus; </s>
          <s xml:space="preserve">ita ut Fovem &amp; </s>
          <s xml:space="preserve">Saturnum in ſe mu-<lb />tuo graves eſſe, immediatis obſervationibus conſtet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0676-03" corresp="note-0676-03a" place="margin">1217.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Saturnus etiam in hoc caſu, ut Flamſtedius obſervavit, tur-<lb />
<ptr xml:id="note-0676-04a" corresp="note-0676-04" type="noteAnchor" />
bat motum ſatellitum Fovis, hos paululum ad ſe trahens, <lb />quod probat, &amp; </s>
          <s xml:space="preserve">hos Secundarios in Saturnum &amp; </s>
          <s xml:space="preserve">hunc in i-<lb />pſos gravitare. </s>
          <s xml:space="preserve">Ex quibus omnibus <ptr type="noteAnchor" /> collatis ſequitur, ſe-
<ptr xml:id="note-0676-05a" corresp="note-0676-05" type="noteAnchor" />
ptemdecim, Syſtema Planetarium componentia, corpora in ſe <lb />mutuo gravitare, licèt de ſingulorum in ſingulà gravitate ob-<lb />ſervationes immediatas inſtituere non liceat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0676-06a" corresp="note-0676-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0676-04" corresp="note-0676-04a" place="margin">1218.</note>
              <note xml:space="preserve" xml:id="note-0676-05" corresp="note-0676-05a" n="*" anchored="true" place="margin">1211. 1212. 1213. 1214. 1216. 1217. 1218.</note>
              <note xml:space="preserve" xml:id="note-0676-06" corresp="note-0676-06a" n="*" anchored="true" place="margin">7</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Legis pars ſecunda eſt <ptr type="noteAnchor" />, gravitatem materiæ quantitati
<ptr xml:id="note-0676-07a" corresp="note-0676-07" type="noteAnchor" />
proportionalem eſſe, id eſt, ſingulis materiæ particulis com-<lb />petere in ſingulas, ideòque legem gravitatis univerſalem eſ-<lb />ſe, &amp; </s>
          <s xml:space="preserve">ſingula corpora in alia corpora omnia gravitare; <lb /></s>
          <s xml:space="preserve">quod ex Phœnomenis etiam deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0676-07" corresp="note-0676-07a" n="*" anchored="true" place="margin">1207.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires gravitatis ſunt ut effectus æqualibus temporibus e-<lb />
<ptr xml:id="note-0676-08a" corresp="note-0676-08" type="noteAnchor" />
diti, &amp; </s>
          <s xml:space="preserve">ſunt hi ut quantitates materiæ translatæ, ſi transla-<lb />tiones fuerint æquales; </s>
          <s xml:space="preserve">idcirco, cùm corpora inæqualia, ad <lb />eandem diſtantiam à corpore attrahente, æquè celeriter ex <lb />gravitate moveantur <ptr type="noteAnchor" />, vires gravitatis materiæ quantitatis
<ptr xml:id="note-0676-09a" corresp="note-0676-09" type="noteAnchor" />
proportionem ſequi, clarum eſt. </s>
          <s xml:space="preserve">Idem experimur in omni-<lb />bus corporibus in Telluris viciniis, quæ Tellurem verſus, <lb />
<ptr xml:id="note-0676-10a" corresp="note-0676-10" type="noteAnchor" />
materiæ quantitati proportionalem, gravitatem habent <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0676-11a" corresp="note-0676-11" type="noteAnchor" />
Mutua autem horum omnium corporum gravitas ſenſibilis <lb />non eſt; </s>
          <s xml:space="preserve">quia reſpectu gravitatis Tellurem verſus admodum <lb />eſt exigua, ideoque motum ex hac turbare non valet <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſal-
<ptr xml:id="note-0676-12a" corresp="note-0676-12" type="noteAnchor" />
tem ut ſenſibilis detur directionis mutatio.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0676-08" corresp="note-0676-08a" place="margin">1219.</note>
              <note xml:space="preserve" xml:id="note-0676-09" corresp="note-0676-09a" n="*" anchored="true" place="margin">1215.</note>
              <note xml:space="preserve" xml:id="note-0676-10" corresp="note-0676-10a" place="margin">1220.</note>
              <note xml:space="preserve" xml:id="note-0676-11" corresp="note-0676-11a" n="*" anchored="true" place="margin">79.</note>
              <note xml:space="preserve" xml:id="note-0676-12" corresp="note-0676-12a" n="*" anchored="true" place="margin">190.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Et aliâ methodo, ex Phœnomenis, hanc univerſalitatem <lb />gravitatis, ſingularum materiæ particulis in alias probari poſ-<lb />ſe, ſtatim dicemus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1222.</note>
        <pb facs="0677" n="(149)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. XI.</fw>
        <p>
          <s xml:space="preserve">Pars legis, quam examinamus, tertia eſt, gravitatem de-<lb />creſcere, quando diſtantia augetur, &amp; </s>
          <s xml:space="preserve">eſſe inverſè ut quadra-<lb />tum diſtantiæ; </s>
          <s xml:space="preserve">quod ex Phœnomenis quoque ſequitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Corpora, in quæ vis gravitatis agit pro quantitate mate-<lb />
<ptr xml:id="note-0677-01a" corresp="note-0677-01" type="noteAnchor" />
riæ, ut in Syſtemate noſtro, eâdem, ut diximus, celeritate <lb />feruntur, in circumſtantiis iiſdem; </s>
          <s xml:space="preserve">ita ut non interſit, <lb />utrum majora an minora ſint corpora, &amp; </s>
          <s xml:space="preserve">moveantur qua-<lb />ſi eſſent æqualia. </s>
          <s xml:space="preserve">In hoc autem caſu, ſi vis verſus pun-<lb />ctum decreſcat in ratione inverſa quadrati diſtantiæ ab hoc <lb />puncto, &amp; </s>
          <s xml:space="preserve">corpora ad varias ab hoc ipſo diſtantias revol-<lb />vantur &amp; </s>
          <s xml:space="preserve">in circulis retineantur hac vi, quadrata temporum <lb />periodicorum erunt inter ſe, ut diſtantiarum cubi <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quod
<ptr xml:id="note-0677-02a" corresp="note-0677-02" type="noteAnchor" />
æquè in lineis Ellipticis, ad quorum focos diriguntur vires, <lb />reſpectu diſtantiarum mediarum, obtinere, à Geometris de-<lb />monſtratur. </s>
          <s xml:space="preserve">Hicce autem caſus in corporibus circa Solem, <lb />Saturnum, &amp; </s>
          <s xml:space="preserve">Jovem <ptr type="noteAnchor" />, revolventibus exſtat, unde ſequitur,
<ptr xml:id="note-0677-03a" corresp="note-0677-03" type="noteAnchor" />
vim gravitatis, recedendo à centris horum corporum, decre-<lb />ſcere in ratione inverſà quadratorum diſtantiarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0677-01" corresp="note-0677-01a" place="margin">1221.</note>
              <note xml:space="preserve" xml:id="note-0677-02" corresp="note-0677-02a" n="*" anchored="true" place="margin">239.</note>
              <note xml:space="preserve" xml:id="note-0677-03" corresp="note-0677-03a" n="*" anchored="true" place="margin">974.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hoc ratiocinio, poſitâ gravitate materiæ quantitati pro-<lb />
<ptr xml:id="note-0677-04a" corresp="note-0677-04" type="noteAnchor" />
portionali, illam in ratione inverſâ quadrati diſtantiæ decre-<lb />ſcere demonſtramus. </s>
          <s xml:space="preserve">Ex eodem, poſitâ gravitatis diminu-<lb />tione juxta hanc rationem, ſequitur, gravitatem materiæ quan-<lb />titati proportionalem eſſe, ut facilè liquet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0677-04" corresp="note-0677-04a" place="margin">1222.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Probamus autem alio argumento, diminutionem gravitatis <lb />ſæpius memoratam rationem inverſam quadrati diſtantiæ ſe-<lb />qui; </s>
          <s xml:space="preserve">ita ut circa ambas, de quibus agimus, gravitatis leges, <lb />nullum dubium ſupereſſe poſſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Planetæ moventur in Orbibus quieſcentibus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in his
<ptr xml:id="note-0677-05a" corresp="note-0677-05" type="noteAnchor" />
retinentur viribus, quæ ad punctum excentricum dirigun-<lb />
<ptr xml:id="note-0677-06a" corresp="note-0677-06" type="noteAnchor" />
tur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Conſtat autem hæc non obtinere, niſi vis centralis
<ptr xml:id="note-0677-07a" corresp="note-0677-07" type="noteAnchor" />
decreſcat in ratione inverſâ quadrati diſtantiæ <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0677-08a" corresp="note-0677-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0677-05" corresp="note-0677-05a" place="margin">1223.</note>
              <note xml:space="preserve" xml:id="note-0677-06" corresp="note-0677-06a" n="*" anchored="true" place="margin">929.</note>
              <note xml:space="preserve" xml:id="note-0677-07" corresp="note-0677-07a" n="*" anchored="true" place="margin">931.</note>
              <note xml:space="preserve" xml:id="note-0677-08" corresp="note-0677-08a" n="*" anchored="true" place="margin">241. 243.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Gravitatem etiam recedendo â Telluris centro, juxta <lb />
<ptr xml:id="note-0677-09a" corresp="note-0677-09" type="noteAnchor" />
eandem legem decreſcere, ex ſimili ratiocinio ſequitur. <lb /></s>
          <s xml:space="preserve">Luna enim in orbitâ retinetur vi, quæ ad Telluris cen-<lb />trum, id eſt ad punctum excentricum, tendit <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">licèt li-
<ptr xml:id="note-0677-10a" corresp="note-0677-10" type="noteAnchor" />
nea Apſidum non feratur motu parallelo, agitatio hujus, ſi <lb />ſingulas conſideremus revolutiones, admodum eſt exigua, ut <lb />hic pro quieſcente haberi poſſit: </s>
          <s xml:space="preserve">ſi enim computatio ineatur
</s>
          <pb facs="0678" n="(150)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
de vi quæ retinet Lunam in orbe ita agitato, diminutionem <lb />vis gravitatis reſpectu Lunæ, parum admodum à ratione in-<lb />verſâ quadrati diſtantiæ, differe detegimus, differentiamque <lb />à Solis actione pendere in ſequentibus videbimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0677-09" corresp="note-0677-09a" place="margin">1242.</note>
              <note xml:space="preserve" xml:id="note-0677-10" corresp="note-0677-10a" n="*" anchored="true" place="margin">967. 966. 226.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Nullumque dubium circa hanc diminutionem ſupererit, <lb />ſi conſideremus, Lunam in orbitâ retineri ex ipſâ vi, qua <lb />
<ptr xml:id="note-0678-01a" corresp="note-0678-01" type="noteAnchor" />
corpora in Telluris viciniis Tellurem verſus feruntur, immi-<lb />nutâ, juxta legem diminutionis ſæpiſſimè memoratam. </s>
          <s xml:space="preserve">Di-<lb />ſtantia media Lunæ eſt 60 {1/2} ſemid. </s>
          <s xml:space="preserve">Telluris; </s>
          <s xml:space="preserve">diametrum an-<lb />tea vidimus continere perticas Rhenolandicas 3400669 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">un-
<ptr xml:id="note-0678-02a" corresp="note-0678-02" type="noteAnchor" />
de, ex noto tempore periodico, facilè detegimus in uno mi-<lb />nuto primo temporis, Lunam in orbitâ percurrere perticas <lb />Rhenolandicas 16425 {1/2}. </s>
          <s xml:space="preserve">Hic arcus non eſt centeſima pars <lb />unius gradus, &amp; </s>
          <s xml:space="preserve">pro ipſius ſubtenſâ uſurpari poteſt; </s>
          <s xml:space="preserve">eſt ideò <lb />orbitæ diameter ad hunc arcum, ut ipſe ad ſuum ſinum ver-<lb />ſum; </s>
          <s xml:space="preserve">qui detegitur pedum Rhenol. </s>
          <s xml:space="preserve">15, 736.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">eſt acceſſus <lb />mutuus Lunæ &amp; </s>
          <s xml:space="preserve">Telluris, ex horum corporum mutuâ actio-<lb />ne, in uno minuto primo temporis. </s>
          <s xml:space="preserve">Celeritas, qua corpus <lb />gravitate ad aliud accedit, pendet à vi qua ab hoc alio attra-<lb />hitur, cujus ſingulæ particulæ materiæ, illud attrahunt; </s>
          <s xml:space="preserve">ideò <lb />celeritates Lunæ &amp; </s>
          <s xml:space="preserve">Telluris, in mutuo acceſſu, ſunt inverſè ut <lb />quantitates materiæ in his; </s>
          <s xml:space="preserve">quod etiam ex æquali motus quanti-<lb />tate in ut utroque corpore deducitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Hac ergo proportione
<ptr xml:id="note-0678-03a" corresp="note-0678-03" type="noteAnchor" />
detegimus, quantum, ex memorato ſpatio 15, 736. </s>
          <s xml:space="preserve">pedum, à <lb />Lunâ percurratur; </s>
          <s xml:space="preserve">ut quantitas materiæ in utroque corpore <lb />ad quantitatem materiæ in Tellure, ita ſpatium in acceſſu <lb />ad ſe mutuo ab ambobus percurſum, ad viam à ſolâ Lunâ <lb />percurſam. </s>
          <s xml:space="preserve">Quantitates autem materiæ in Lunâ &amp; </s>
          <s xml:space="preserve">Tellu-<lb />re, ut in ſequentibus videbimus, ſunt inter ſe ut 1. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">39, 37.</s>
          <s xml:space="preserve">; <lb />&amp; </s>
          <s xml:space="preserve">eſt 40, 37. </s>
          <s xml:space="preserve">ad 39, 37.</s>
          <s xml:space="preserve">, ut 15, 736. </s>
          <s xml:space="preserve">ad 15, 344 ſpatium à <lb />Lunâ percurſum; </s>
          <s xml:space="preserve">quod ergo à corpore quocunque, in ſpa-<lb />tio unius minuti primi, gravitate verſus Tellurem, ad di-<lb />ſtantiam Lunæ percurreretur. </s>
          <s xml:space="preserve">Creſcente hac vi, in ratione <lb />inverſà quadrati diſtantiæ à centro, ſpatium eodem tempore <lb />percurſum ad diſtantiam ſemidiametri Telluris, id eſt in hu-<lb />jus ſuperficie, erit 60 {1/2} x 60 {1/2} x 15, 344, ſcil. </s>
          <s xml:space="preserve">56158 pedum; <lb /></s>
          <s xml:space="preserve">ſed quia in omni motu æquabiliter accelerato, ut hic, <lb />(nam conſideramus vim ad diſtantiam ſuperficiei Telluris à
</s>
          <pb facs="0679" n="(151)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XI.</fw>
centro) quadrata temporum ſunt, ut ſpatia cadendo percur-<lb />ſa <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">dividendo hunc numerum per 60 x 60 id eſt, 3600,
<ptr xml:id="note-0679-01a" corresp="note-0679-01" type="noteAnchor" />
habemus ſpatium, in Telluris viciniis, in uno minuto ſecundo <lb />à corpore percurſum, ex vi qua Luna in orbitâ retinetur, <lb />quod detegitur 15, 6. </s>
          <s xml:space="preserve">pedum Rhenolandicorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0678-01" corresp="note-0678-01a" place="margin">1225.</note>
              <note xml:space="preserve" xml:id="note-0678-02" corresp="note-0678-02a" n="*" anchored="true" place="margin">976.</note>
              <note xml:space="preserve" xml:id="note-0678-03" corresp="note-0678-03a" n="*" anchored="true" place="margin">126. 65.</note>
              <note xml:space="preserve" xml:id="note-0679-01" corresp="note-0679-01a" n="*" anchored="true" place="margin">136.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si nunc examinemus gravitatem, quam quotidie experi-<lb />mur in omnibus corporibus, in Telluris viciniis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ex de-
<ptr xml:id="note-0679-02a" corresp="note-0679-02" type="noteAnchor" />
monſtratis circa pendulorum motum <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">experimentis
<ptr xml:id="note-0679-03a" corresp="note-0679-03" type="noteAnchor" />
circa pendula inſtitutis, conſtat, corpus cadendo etiam percur-<lb />rere in uno minuto ſecundo pedes Rhenolandicos 15, 6. </s>
          <s xml:space="preserve">ideo-<lb />que cadere ex vi, quæ Lunam in orbitâ retinet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0679-02" corresp="note-0679-02a" n="*" anchored="true" place="margin">72.</note>
              <note xml:space="preserve" xml:id="note-0679-03" corresp="note-0679-03a" n="*" anchored="true" place="margin">157. 158.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hac computatione negleximus conſiderationem actionis <lb />Solis, quia hæc exigua eſt, &amp; </s>
          <s xml:space="preserve">alternatim nunc auget, nunc <lb />minuit Lunæ gravitatem verſus Tellurem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Conſideravimus centra corporum in examine legis dimi-<lb />nutionis gravitatis, licèt gravitas ſingulas corporum particu-<lb />las ſpectet; </s>
          <s xml:space="preserve">quia mathematicâ demonſtratione conſtat, actio-<lb />
<ptr xml:id="note-0679-04a" corresp="note-0679-04" type="noteAnchor" />
nem corporis ſphærici, in quo ubique partes à centro æquè <lb />diſtantes ſunt homogeneæ, conſtantis ex particulis verſus <lb />quas gravitas datur, quæ decreſcit recedendo à ſingulis, in <lb />ratione inverſâ quadrati diſtantiæ, dirigi ad corporis cen-<lb />trum, &amp; </s>
          <s xml:space="preserve">recedendo ab hoc minui in eâdem ratione inverſâ <lb />quadrati diſtantiæ: </s>
          <s xml:space="preserve">ita ut tale corpus agat, quaſi omnis mate-<lb />ria ex qua conſtat, coacta foret in ipſo centro. </s>
          <s xml:space="preserve">Unde ſequen-<lb />tes deducimus concluſiones.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0679-04" corresp="note-0679-04a" place="margin">1226.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">In ſuperficiebus corporum, in quibus materia homogenea <lb />
<ptr xml:id="note-0679-05a" corresp="note-0679-05" type="noteAnchor" />
eſt ad diſtantias æquales à centro, gravitatem eſſe directè ut <lb />materiæ quantitatem, &amp; </s>
          <s xml:space="preserve">inverſe ut quadratum diametri <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0679-06a" corresp="note-0679-06" type="noteAnchor" />
nam in his corporibus diſtantiæ à centro ſunt ut diametri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0679-05" corresp="note-0679-05a" place="margin">1227.</note>
              <note xml:space="preserve" xml:id="note-0679-06" corresp="note-0679-06a" n="*" anchored="true" place="margin">1207. 1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſuperficiebus corporum ſphæricorum, homogeneorum, æ-<lb />
<ptr xml:id="note-0679-07a" corresp="note-0679-07" type="noteAnchor" />
qualium, gravitates eſſe ut corporum denſitates; </s>
          <s xml:space="preserve">nam diſtan-<lb />tiæ à centro ſunt æquales, in quo caſu gravitatis vires ſunt <lb />ut quantitates materiæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ, in corporibus æqualibus, ſunt
<ptr xml:id="note-0679-08a" corresp="note-0679-08" type="noteAnchor" />
ut denſitates <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0679-09a" corresp="note-0679-09" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0679-07" corresp="note-0679-07a" place="margin">1228.</note>
              <note xml:space="preserve" xml:id="note-0679-08" corresp="note-0679-08a" n="*" anchored="true" place="margin">1207.</note>
              <note xml:space="preserve" xml:id="note-0679-09" corresp="note-0679-09a" n="*" anchored="true" place="margin">288. 79.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſuperficiebus corporum ſphæricorum, inæqualium, ho-<lb />
<ptr xml:id="note-0679-10a" corresp="note-0679-10" type="noteAnchor" />
mogeneornm, æquè denſorum, gravitates ſunt inverſè, ut qua-<lb />drata diametrorum <ptr type="noteAnchor" />, quia in harum ratione ſunt diſtantiæ à
<ptr xml:id="note-0679-11a" corresp="note-0679-11" type="noteAnchor" />
</s>
          <pb facs="0680" n="(152)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
centris: </s>
          <s xml:space="preserve">ſunt etiam gravitates directè ut diametrorum cubi <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0680-01a" corresp="note-0680-01" type="noteAnchor" />
nam in hac ratione ſunt materiæ quantitates in ſphæris: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />ratio compoſita ex directà cuborum diametrorum, &amp; </s>
          <s xml:space="preserve">inver-<lb />ſâ harum quadratorum, eſt directa ipſarum Diametrorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0679-10" corresp="note-0679-10a" place="margin">1229.</note>
              <note xml:space="preserve" xml:id="note-0679-11" corresp="note-0679-11a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0680-01" corresp="note-0680-01a" n="*" anchored="true" place="margin">1207.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ideò, ſi &amp; </s>
          <s xml:space="preserve">denſitates &amp; </s>
          <s xml:space="preserve">diametri differant, gravitates in <lb />
<ptr xml:id="note-0680-02a" corresp="note-0680-02" type="noteAnchor" />
ſuperficiebus erunt in ratione compoſitâ denſitatum <ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">Dia-
<ptr xml:id="note-0680-03a" corresp="note-0680-03" type="noteAnchor" />
metrorum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Idcirco diviſâ gravitate in ſuperficie, per dia-
<ptr xml:id="note-0680-04a" corresp="note-0680-04" type="noteAnchor" />
metrum, detegitur denſitas; </s>
          <s xml:space="preserve">quæ ergo ſequitur rationem di-<lb />
<ptr xml:id="note-0680-05a" corresp="note-0680-05" type="noteAnchor" />
rectam gravitatis in ſuperficie &amp; </s>
          <s xml:space="preserve">inverſam diametri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0680-02" corresp="note-0680-02a" place="margin">1230.</note>
              <note xml:space="preserve" xml:id="note-0680-03" corresp="note-0680-03a" n="*" anchored="true" place="margin">1228.</note>
              <note xml:space="preserve" xml:id="note-0680-04" corresp="note-0680-04a" n="*" anchored="true" place="margin">1229.</note>
              <note xml:space="preserve" xml:id="note-0680-05" corresp="note-0680-05a" place="margin">1231.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In ſphærâ homogeneâ, cavâ, ubique ejuſdem craſſitiei cor-<lb />
<ptr xml:id="note-0680-06a" corresp="note-0680-06" type="noteAnchor" />
pus ubicunque poſitum nullam gravitatem habet, gravitati-<lb />bus oppoſitis ſeſe mutuo exactè deſtruentibus: </s>
          <s xml:space="preserve">Unde ſequi-<lb />tur, in ſphærâ homogeneâ, corpus accedendo ad centrum, <lb />
<ptr xml:id="note-0680-07a" corresp="note-0680-07" type="noteAnchor" />
verſus centrum gravitare ex ſolâ actione ſphæræ, cujus ſemi-<lb />diameter eſt diſtantia corporis à centro, quæ gravitas de-<lb />creſcit, accedendo ad centrum, in ratione diſtantiæ à cen-<lb />tro <ptr type="noteAnchor" />, nam omnis materia, quæ ad majorem à centro diſtan-
<ptr xml:id="note-0680-08a" corresp="note-0680-08" type="noteAnchor" />
tiam datur, ſphæram cavam format, in qua actiones in cor-<lb />pus ſeſe mutuo deſtruunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0680-09a" corresp="note-0680-09" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0680-06" corresp="note-0680-06a" place="margin">1232.</note>
              <note xml:space="preserve" xml:id="note-0680-07" corresp="note-0680-07a" place="margin">1233.</note>
              <note xml:space="preserve" xml:id="note-0680-08" corresp="note-0680-08a" n="*" anchored="true" place="margin">1229.</note>
              <note xml:space="preserve" xml:id="note-0680-09" corresp="note-0680-09a" n="*" anchored="true" place="margin">1232.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Gravitatem huc uſque, explicatam pro lege naturæ eſſe <lb />habendam diximus, quia hujus cauſa nos latet, &amp; </s>
          <s xml:space="preserve">quia mi-<lb />nimè pendet ab ullâ lege nobis notâ; </s>
          <s xml:space="preserve">quod clarè patebit, ſi <lb />ad ſequentia attendamus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Gravitatem requirere præſentiam corporis attrahentis; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0680-10a" corresp="note-0680-10" type="noteAnchor" />
ſic Satellites, ex gr. </s>
          <s xml:space="preserve">Jovis, in Jovem gravitant, ubicunque <lb />hic detur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0680-10" corresp="note-0680-10a" place="margin">1234.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1212.</note>
        <p rend="italics">
          <s xml:space="preserve">Manente diſtantia, celeritatem, qua corpora ex gravitate <lb />
<ptr xml:id="note-0680-12a" corresp="note-0680-12" type="noteAnchor" />
feruntur, pendêre à quantitate materiæ in corpore attrahen-<lb />
<ptr xml:id="note-0680-13a" corresp="note-0680-13" type="noteAnchor" />
te <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Et celeritatem non variari, quæcunque fuerit maſſa cor-
<ptr xml:id="note-0680-14a" corresp="note-0680-14" type="noteAnchor" />
poris gravitantis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0680-15a" corresp="note-0680-15" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0680-12" corresp="note-0680-12a" place="margin">1235.</note>
              <note xml:space="preserve" xml:id="note-0680-13" corresp="note-0680-13a" n="*" anchored="true" place="margin">1207.</note>
              <note xml:space="preserve" xml:id="note-0680-14" corresp="note-0680-14a" place="margin">1236.</note>
              <note xml:space="preserve" xml:id="note-0680-15" corresp="note-0680-15a" n="*" anchored="true" place="margin">1207.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ulterius, ſi gravitas pendeat à lege motus notâ, ad impa-<lb />
<ptr xml:id="note-0680-16a" corresp="note-0680-16" type="noteAnchor" />
ctum corporis extranei referri debere, &amp; </s>
          <s xml:space="preserve">quia gravitas eſt <lb />continua, impactum etiam continuum requiri.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0680-16" corresp="note-0680-16a" place="margin">1237.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si talis materia continuò in corpora impingens detur, ne-<lb />ceſſario eſt fluida, &amp; </s>
          <s xml:space="preserve">quidem ſubtiliſſima, quæ penetrat cor-<lb />pora quæcunque; </s>
          <s xml:space="preserve">corpora enim in aliis utcunque incluſa <lb />gravia ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0681" n="(153)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. XI.</fw>
        <p>
          <s xml:space="preserve">Videat nunc Mathematicus, an fluidum adeo ſubtile, ut <lb />corporum omnium poros liberrimè permeèt, &amp; </s>
          <s xml:space="preserve">adeò ra-<lb />rum, ut motui corporum ſenſibiliter non obſtet, (in loco <lb />enim aëre vacuo penduli motus diutiſſimè continuatur) cor-<lb />pora ingentia tantâ cum vi ad ſe mutuo poſſit propellere? <lb /></s>
          <s xml:space="preserve">Explicet quomodo hæc actio creſcat in ratione maſſæ corpo-<lb />ris verſus quod aliud fertur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Tandem, quod omnium
<ptr xml:id="note-0681-01a" corresp="note-0681-01" type="noteAnchor" />
mihi difficillimum videtur, dicat, quomodo omnia corpo-<lb />ra, in quocunque ſitu, eâdem manente diſtantiâ, &amp; </s>
          <s xml:space="preserve">cor-<lb />pore verſus quod gravitas datur, eadem velocitate feran-<lb />tur <ptr type="noteAnchor" />, id eſt, quomodo liquidum, quod niſi in ſuperfi-
<ptr xml:id="note-0681-02a" corresp="note-0681-02" type="noteAnchor" />
cies, ſive ipſorum corporum, ſive illarum internarum par-<lb />ticularum, ad quas acceſſus ex interpoſitis particulis non im-<lb />peditur, actionem ſuam exerere non poteſt, communicet <lb />corporibus motus quantitatem, quæ in omnibus corporibus <lb />exactiſſimè ſequatur proportionem quantitatis materiæ in his, <lb />quod in gravitate ubique obtineri, hoc capite probavimus, <lb />&amp; </s>
          <s xml:space="preserve">quod directo experimento demonſtravimus reſpectu gra-<lb />vitatis in Telluris viciniis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0681-03a" corresp="note-0681-03" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0681-01" corresp="note-0681-01a" n="*" anchored="true" place="margin">1235.</note>
              <note xml:space="preserve" xml:id="note-0681-02" corresp="note-0681-02a" n="*" anchored="true" place="margin">1236.</note>
              <note xml:space="preserve" xml:id="note-0681-03" corresp="note-0681-03a" n="*" anchored="true" place="margin">77.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non tamen negamus, ab ullo impactu pendere gravita-<lb />
<ptr xml:id="note-0681-04a" corresp="note-0681-04" type="noteAnchor" />
tem, ſed illam non ſequi ex ullo impactu, juxta leges nobis <lb />notas, clare patêre contendimus, gravitatiſque cauſam nos <lb />omnino latêre fatemur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0681-04" corresp="note-0681-04a" place="margin">1238.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XII.</head>
        <head rend="italics" xml:space="preserve">De Materiâ Cœleſti; ubi Vacuum dari probatur.</head>
        <p>
          <s xml:space="preserve">EXpoſitis legibus, quibus totum Syſtema Planetarium regi-<lb />tur, varia præmittenda erunt, antequam ad ipſius Syſte-<lb />matis explicationem Phyſicam accedamus. </s>
          <s xml:space="preserve">De Materiâ cœ <lb />leſti, id eſt de medio, in quibus corpora Syſtema compo-<lb />nentia moventur, ante omnia quædam dicenda ſunt, quod <lb />paucis fieri poſſet, ſi inter omnes conſtaret Philoſophos, in <lb />rebus inane dari.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Probavimus antea vacuum poſſibile eſſe <ptr type="noteAnchor" />, nunc illud re-
<ptr xml:id="note-0681-05a" corresp="note-0681-05" type="noteAnchor" />
verâ dari demonſtrandum nobis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0681-05" corresp="note-0681-05a" n="*" anchored="true" place="margin">13.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex ſolâ motus conſideratione, vacuum dari deducitur, quod <lb />
<ptr xml:id="note-0681-06a" corresp="note-0681-06" type="noteAnchor" />
</s>
          <pb facs="0682" n="(154)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tritum &amp; </s>
          <s xml:space="preserve">vulgare admodum eſt argumentum, cujus vis ut pa-<lb />teat, conſiderandum, non quidem omnes motus ſine vacuo <lb />impoſſibiles eſſe, ſed pleroſque illorum, qui quotidie obſer-<lb />vantur, quod longiori diſcuſſione pleniſſimè poſſe evinci, per-<lb />ſuaſum habeo; </s>
          <s xml:space="preserve">ſed ſequenti conſideratione ita clarè patêre <lb />mihi videtur, ut plura addere inutile foret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0681-06" corresp="note-0681-06a" place="margin">1239.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non mutabilem figuram habent particulæ omnium minimæ; <lb /></s>
          <s xml:space="preserve">nam conſtat particula, cujus figura mutatur, ex particulis <lb />minoribus, quæ inter ſe moventur, &amp; </s>
          <s xml:space="preserve">ideò, ſi figuram mu-<lb />tabilem habet, non eſt ex particulis omnium minimis.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si autem figura harum particularum ſit immutabilis, &amp; </s>
          <s xml:space="preserve"><lb />corpus inter has poſſit moveri, ſine tali ſeparatione particula-<lb />rum, quæ interſtitium vacuum relinquit, pendebit hoc à fi-<lb />gurâ particularum, &amp; </s>
          <s xml:space="preserve">à relatione, quam habent inter ſe, quod <lb />Mathematicus non negabit: </s>
          <s xml:space="preserve">idcirco ſi hiſce ſervatis (figurâ &amp; </s>
          <s xml:space="preserve"><lb />relatione) augeantur particulæ, &amp; </s>
          <s xml:space="preserve">in hoc caſu corpora ſine <lb />vacuo moveri poterunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Videat nunc quis, auctis particulis minimis, ut magnitu-<lb />dine pedem cubicum æquent, quæcunque fuerit harum fi-<lb />gura, &amp; </s>
          <s xml:space="preserve">cum cæteris particulis relatio, quas, in eadem ra-<lb />tione, cum primis auctas ponimus, utrum corpora magnitu-<lb />dinis cujuſcunque, inter has particulas poſſint ferri per rectas <lb />lineas, &amp; </s>
          <s xml:space="preserve">per curvas quaſcunque, nunquam ſeparatis parti-<lb />culis, ut ſpatia vacua inter has dentur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Particulas ſubtiliſſimas conceptu non aſſequimur, &amp; </s>
          <s xml:space="preserve">ideò <lb />ſæpè his tribuimus proprietates, quæ ex harum figurâ non ſe-<lb />quuntur, qui corriguntur errores, ſi particulas auctas ima-<lb />ginemur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Etiam argumento, ex reſiſtentiâ deducto, vacuum dari <lb />
<ptr xml:id="note-0682-01a" corresp="note-0682-01" type="noteAnchor" />
probamus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0682-01" corresp="note-0682-01a" place="margin">1240.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Materiam inertem eſſe diximus <ptr type="noteAnchor" />, circa vocem quidam
<ptr xml:id="note-0682-02a" corresp="note-0682-02" type="noteAnchor" />
contendunt, rem ipſam nemo negat; </s>
          <s xml:space="preserve">Ex hac ſequitur, non <lb />poſſe per fluidum corpus moveri, quin patiatur reſiſtentiam <ptr type="noteAnchor" />,
<ptr xml:id="note-0682-03a" corresp="note-0682-03" type="noteAnchor" />
ideoque retardationem <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Reſiſtentia ex materiæ inertiâ,
<ptr xml:id="note-0682-04a" corresp="note-0682-04" type="noteAnchor" />
quam hic ſolam conſideramus, pendet à materiæ quantitate <lb />ex loco removendæ, quæ eadem eſt, ſive partes fluidi ſint <lb />majores, ſive minores, ſi corporis celeritas maneat: </s>
          <s xml:space="preserve">unde ſe-
</s>
          <pb facs="0683" n="(155)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XII.</fw>
quitur, in determinandis, quæ reſiſtentiam ſpectant, ad ſub-<lb />tilitatem fluidi non eſſe attendendum, quamdiu hoc poros <lb />corporum permeare non poteſt; </s>
          <s xml:space="preserve">ſi enim ad illam pervenia-<lb />mus partium tenuitatem, ut fluidum pro parte per corpus <lb />penetret, corpori minori copiâ reſiſtet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0682-02" corresp="note-0682-02a" n="*" anchored="true" place="margin">12.</note>
              <note xml:space="preserve" xml:id="note-0682-03" corresp="note-0682-03a" n="*" anchored="true" place="margin">319.</note>
              <note xml:space="preserve" xml:id="note-0682-04" corresp="note-0682-04a" n="*" anchored="true" place="margin">330.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus nunc Globum quemcunque, per medium e-<lb />juſdem denſitatis cum globo, tranſlatum, &amp; </s>
          <s xml:space="preserve">cui per corpo-<lb />ris poros tranſitus non patet; </s>
          <s xml:space="preserve">omnibus momentis retarda-<lb />tur, ita ut ejus velocitas tandem ad dimidium reducatur; <lb /></s>
          <s xml:space="preserve">quod fieri, mathematicâ demonſtratione conſtat, antequam <lb />corpus bis diametri longitudinem percurrat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut propoſitionem hanc ad motum in fluido ſubtiliſſimo, <lb />omnium corporum poros liberrimè penetranti, &amp; </s>
          <s xml:space="preserve">omnia re-<lb />plente, applicare poſſimus, concipiendum eſt, corpus ſphæ-<lb />ricum, ſine poris, quod dari poſſe, intimè jungendo par-<lb />ticulas materiæ, nemo inficias ibit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Talis corporis reſiſtentiam, in fluido quocunque, à magni-<lb />tudine partium fluidi non pendere, &amp; </s>
          <s xml:space="preserve">eandem eſſe, ſive fluidi <lb />partes ſint æquales, ſive utcunque inæquales inter ſe, patet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si omnia ſint materiâ plena, niſi per fluidum, ejuſdem <lb />denſitatis cum hoc corpore, poterit hoc moveri; </s>
          <s xml:space="preserve">nam in-<lb />currit in omnem materiam, quæ datur in locis, per quæ tran-<lb />ſit, &amp; </s>
          <s xml:space="preserve">in his materia ſine interſtitiis, ut in corpore, datur; </s>
          <s xml:space="preserve">id-<lb />circo amittet dimidium velocitatis, antequam duarum dia-<lb />metrorum ſuarum longitudinem percurrat.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Augeatur corpus manente materiæ quantitate, &amp; </s>
          <s xml:space="preserve">ſervato <lb />hoc homogeneo; </s>
          <s xml:space="preserve">id eſt, dentur pori in corpore, per quos <lb />materiæ partes ſubſtiliſſimæ liberrimè tranſeant, &amp; </s>
          <s xml:space="preserve">ſint hi <lb />pori æqualiter per totum corpus diſperſi. </s>
          <s xml:space="preserve">Si corpus ſic mu-<lb />tatum moveatur, non in totam ſuperficiem incurrit fluidum <lb />ſubtiliſſimum de quo agimus, ſed tantùm in partes ſuperfi-<lb />ciei, quæ poros interjacent, quæ partes ſimul ſumtæ, quia <lb />corpus homogeneum ponimus, valent ſuperficiem corporis in <lb />conſtitutione primâ, ſine poris; </s>
          <s xml:space="preserve">Aucto enim corpore, ſuperfi-<lb />cies non fuit mutata, ſed tantùm dilatata, interjectis poris: <lb /></s>
          <s xml:space="preserve">ita ut corpus in utroque caſu eandem patiatur reſiſtentiam, <lb />ex impactu in ſuperficiem; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">reſiſtentia in corpore dilatato
</s>
          <pb facs="0684" n="156" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
major eſt ex incurſu fluidi in particulas internas corporis: <lb /></s>
          <s xml:space="preserve">quare corpus hoc citius dimidium ſui motus in ſecundo, quàm <lb />in primo caſu, amittet; </s>
          <s xml:space="preserve">id eſt, antequam duas diametros pri-<lb />mæ magnitudinis percurrat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò majorem motus quanti-<lb />tatem amittit, dum per duas diametros ſecundæ magnitudi-<lb />nis tranfertur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hoc autem experientiæ adverſatur; </s>
          <s xml:space="preserve">nam globus homo-<lb />geneus, aureus, plumbeus, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">quantitatem motus multò <lb />minorem in aquâ &amp; </s>
          <s xml:space="preserve">aëre amittit; </s>
          <s xml:space="preserve">unde ſequitur hypoteſin, <lb />omnia materiâ repleri, falſam eſſe. </s>
          <s xml:space="preserve">Vacuum ergo datur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vacuum dari etiam cum Phænomenis circa gravitatem con-<lb />
<ptr xml:id="note-0684-01a" corresp="note-0684-01" type="noteAnchor" />
gruit, ex quibus ſequitur, hanc materiæ quantitati propor-<lb />tionalem eſſe. </s>
          <s xml:space="preserve">Si omnia materiâ replentur, gravitas verſus <lb />omnes partes æqualis datur, &amp; </s>
          <s xml:space="preserve">vires quæ verſus partes oppo-<lb />ſitas diriguntur, ſeſe mutuo deſtruunt, &amp; </s>
          <s xml:space="preserve">nulla ſenſibilis <lb />gravitas obſervari poteſt, quod experientiæ adverſatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0684-01" corresp="note-0684-01a" place="margin">1241.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hiſce præmiſſis ad Materiam coeleſtem tranſeundum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">A motu Materiæ coeleſtis, ſi quædam detur, non pen-<lb />dent corporum coeleſtium motus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quo corruit illorum ſen-
<ptr xml:id="note-0684-02a" corresp="note-0684-02" type="noteAnchor" />
tentia, qui motu communi cum materiâ, quæ Syſtema Plane-<lb />
<ptr xml:id="note-0684-03a" corresp="note-0684-03" type="noteAnchor" />
tarium replet, corpora cæleſtia tranſlata contendunt. </s>
          <s xml:space="preserve">Quæ <lb />etiam motu Cometarum evertitur ſententia; </s>
          <s xml:space="preserve">ſi medium in <lb />Syſtemate daretur, quod in motu ſuo Planetas ſecum fert, <lb />&amp; </s>
          <s xml:space="preserve">etiam ſecum traheret Cometas, ſaltem ſenſibiliter hos in <lb />motu turbaret, dum ferè directè ad Solem accedunt, aut ab <lb />hoc recedunt, aut in antecedentia moventur, id eſt, motu <lb />contrario motui talis materiæ; </s>
          <s xml:space="preserve">qui motus cùm non turbari, &amp; </s>
          <s xml:space="preserve"><lb />ſequi viam quæ à gravitate pendet, obſerventur, clarum eſt, <lb />Materiam coeleſtem, ſi detur &amp; </s>
          <s xml:space="preserve">movetur, ſenſibilem in corpo-<lb />ra Syſtematis Planetariinon exerere actionem; </s>
          <s xml:space="preserve">quod etiam ex <lb />parvâ hujus reſiſtentiâ deducitur; </s>
          <s xml:space="preserve">nam, ex collatis antiquiſ-<lb />ſimis cum recentioribus obſervationibus ſenſibiliter in moti-<lb />bus non retardatos Planetas conſtat. </s>
          <s xml:space="preserve">Reſiſtentia tamen in <lb />aëre ſenſibilis eſt, quare denſitas medii in quo Planetæ mo-<lb />verentur ferè in immenſum minor eſt, idcirco, niſi tali me-<lb />
<ptr xml:id="note-0684-04a" corresp="note-0684-04" type="noteAnchor" />
dio ſubtiliſſimo, non repletur Syſtema Planetarium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0684-02" corresp="note-0684-02a" place="margin">1242.</note>
              <note xml:space="preserve" xml:id="note-0684-03" corresp="note-0684-03a" n="*" anchored="true" place="margin">1238</note>
              <note xml:space="preserve" xml:id="note-0684-04" corresp="note-0684-04a" place="margin">1243.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Materiæ verò quantitatem, quantumvis exiguam, per totum
</s>
          <pb facs="0685" n="157" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XIII.</fw>
Syſtema poſſe diſpergi, relictis interſtitiis minimis, ex ma-<lb />teriæ diviſibilitate, deducitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0685-01a" corresp="note-0685-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0685-01" corresp="note-0685-01a" n="*" anchored="true" place="margin">26.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIII.</head>
        <head xml:space="preserve">De Motu Telluris.</head>
        <p>
          <s xml:space="preserve">PRæter in Capite præcedenti diſcuſſam quæſtionem, &amp; </s>
          <s xml:space="preserve">a-<lb />lia datur examinanda, antequam ad totius Syſtematis ex-<lb />plicationem accedamus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ut nullum dubium ſuperſit circa Syſtema, in primo capite <lb />hujus libri explicatum, probandus nobis hìc eſt Telluris mo-<lb />tus, de quo non mirum ſi plures dubitaverint; </s>
          <s xml:space="preserve">nullis enim, <lb />niſi à ſpectatoribus in Tellure inſtitutis, obſervationibus, <lb />motus coeleſtes à nobis determinari queunt, &amp; </s>
          <s xml:space="preserve">eadem Phoe-<lb />nomena apparent, ſive corpora ipſa transferantur, ſive ſpecta-<lb />tor moveatur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ita ut immediatis obſervationibus non conſtet,
<ptr xml:id="note-0685-02a" corresp="note-0685-02" type="noteAnchor" />
utrum motus Telluris ad corpora coeleſtia non referri debeat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0685-02" corresp="note-0685-02a" n="*" anchored="true" place="margin">993.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Tellurem circa Solem circumferri, ex motuum analogiâ <lb />
<ptr xml:id="note-0685-03a" corresp="note-0685-03" type="noteAnchor" />
deducitur, &amp; </s>
          <s xml:space="preserve">ex examine legum naturæ demonſtratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0685-03" corresp="note-0685-03a" place="margin">1244.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quod motuum analogiam ſpectat, notandum, circa Jo-<lb />vem &amp; </s>
          <s xml:space="preserve">Saturnum rotari Satellites corpore centrali minores; <lb /></s>
          <s xml:space="preserve">Circa Tellurem Luna, Tellure minor, revolvitur; </s>
          <s xml:space="preserve">Tandem <lb />circa Solem girantur corpora minora Mercurius, Venus, <lb />Mars, Jupiter, &amp; </s>
          <s xml:space="preserve">Saturnus; </s>
          <s xml:space="preserve">Si cum his Telius rotetur, ubique <lb />in Syſtemate noſtro corpora minora circa majora moventur; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0685-04a" corresp="note-0685-04" type="noteAnchor" />
in hac autem regulâ exceptio dabitur reſpectu Solis, ſi ingens <lb />hoc corpus, in motu, minimam Telluris maſſam <ptr type="noteAnchor" /> cingat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0685-04" corresp="note-0685-04a" place="margin">1245.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">975.</note>
        <p>
          <s xml:space="preserve">Circa Solem, Jovem, &amp; </s>
          <s xml:space="preserve">Saturnum, circa quos ſingulos <lb />plurima corpora revolvuntur, lentius moventur, quæ magis à <lb />corpore centrali diſtant, &amp; </s>
          <s xml:space="preserve">quidem juxta hanc regulam, qua-<lb />
<ptr xml:id="note-0685-06a" corresp="note-0685-06" type="noteAnchor" />
drata temporum periodicorum ſequi rationem cuborum di-<lb />ſtantiarum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ regula applicari poteſt Telluri, ſi hæc
<ptr xml:id="note-0685-07a" corresp="note-0685-07" type="noteAnchor" />
cum cæteris Planetis circa Solem circumferatur, ut patet, <lb />ſi illius tempus periodicum, (tempus nempe in quo Sol in-<lb />tegram revolutionem peragere videtur,) ut &amp; </s>
          <s xml:space="preserve">diſtantia à <lb />Sole, cum cæterorum Planetarum diſtantiis &amp; </s>
          <s xml:space="preserve">temporibus <lb />periodicis, conferantur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0685-06" corresp="note-0685-06a" place="margin">1246.</note>
              <note xml:space="preserve" xml:id="note-0685-07" corresp="note-0685-07a" n="*" anchored="true" place="margin">974.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vnicam autem patitur exceptionem regula hæc, ſi, Sole
</s>
          <pb facs="0686" n="158" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
translato, Tellus quieſcat. </s>
          <s xml:space="preserve">In hoc caſu Mercurius, Venus, <lb />Mars, Jupiter, &amp; </s>
          <s xml:space="preserve">Saturnus, huic regulæ in motibus ſubji-<lb />ciuntur, ut &amp; </s>
          <s xml:space="preserve">quinque Satellites Saturni, &amp; </s>
          <s xml:space="preserve">quatuor Jovia-<lb />les Planetæ ſola Luna cum Sole, circa Tellurem, propor-<lb />tionem omnino diverſam ſervant, &amp; </s>
          <s xml:space="preserve">non modo celeritas So-<lb />lis major eſt, quàm quæ ex hac regulà requiritur, ſed &amp; </s>
          <s xml:space="preserve">ve-<lb />locitate ad minimum vicies &amp; </s>
          <s xml:space="preserve">ſexies Lunam vincit, licèt ad <lb />diſtantiam maximam, reſpectu Lunæ diſtantiæ, à Tellure re-<lb />moveatur: </s>
          <s xml:space="preserve">ita ut &amp; </s>
          <s xml:space="preserve">hoc reſpectu motuum coeleſtium analo-<lb />gia turbetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hiſce argumentis alia addam, quibus, motum Telluris <lb />ſequelam eſſe neceſſariam Legum naturæ, ex Phoenomenis <lb />deductarum, clarè patebit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Omnia corpora in ſe mutuo gravia ſunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideòque Sol
<ptr xml:id="note-0686-01a" corresp="note-0686-01" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">Tellus; </s>
          <s xml:space="preserve">ſed motus, quo hæc duo corpora verſus ſe mutuo <lb />
<ptr xml:id="note-0686-02a" corresp="note-0686-02" type="noteAnchor" />
feruntur, ex directis obſervationibus deducitur. </s>
          <s xml:space="preserve">Quodcun-<lb />que horum corporum circa aliud moveatur, deſcribit areas, <lb />lineis ad centrum hujus ductis, temporibus proportionales, <lb />quod ex obſervationibus Aſtronomicis conſtat; </s>
          <s xml:space="preserve">idcirco in <lb />curvâ retinetur corpus motum, per vim, quæ ad aliûs cen-<lb />trum dirigitur <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Cùm autem actioni ſemper æqualis ſit re-
<ptr xml:id="note-0686-03a" corresp="note-0686-03" type="noteAnchor" />
actio <ptr type="noteAnchor" />, niſi Natur æ leges, quæ ubique conſtanter locum ba-
<ptr xml:id="note-0686-04a" corresp="note-0686-04" type="noteAnchor" />
bent, in totum evertantur, duo hæc corpora motibus æqua-<lb />libus ſeſe mutuo petunt, id eſt celeritatibus, quæ ſunt inver-<lb />ſè ut horum maſſæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod etiam ex lege gravitatis imme-
<ptr xml:id="note-0686-05a" corresp="note-0686-05" type="noteAnchor" />
diatè deducitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0686-06a" corresp="note-0686-06" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0686-01" corresp="note-0686-01a" place="margin">1247.</note>
              <note xml:space="preserve" xml:id="note-0686-02" corresp="note-0686-02a" n="*" anchored="true" place="margin">1206.</note>
              <note xml:space="preserve" xml:id="note-0686-03" corresp="note-0686-03a" n="*" anchored="true" place="margin">226.</note>
              <note xml:space="preserve" xml:id="note-0686-04" corresp="note-0686-04a" n="*" anchored="true" place="margin">126.</note>
              <note xml:space="preserve" xml:id="note-0686-05" corresp="note-0686-05a" n="*" anchored="true" place="margin">65.</note>
              <note xml:space="preserve" xml:id="note-0686-06" corresp="note-0686-06a" n="*" anchored="true" place="margin">1235.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Materiæ quantitas in Tellure ferè nulla eſt reſpectu quanti-<lb />tatis materiæ in Sole, ut in Capite ſequenti videbimus; </s>
          <s xml:space="preserve">quare <lb />hic lentiſſimè movetur, dum celerrimè ad hunc accedit Tellus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Unde ſequitur Tellurem circaSolem circumferri, ne in <lb />hunc motu illo violentiſſimo cadat, quo in orbitâ retinetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Motus hic idem Telluris ex iiſdem principiis &amp; </s>
          <s xml:space="preserve">aliâ <lb />methodo deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Duo corpora, quæ vi quacunque ad ſe mutuo feruntur, <lb />tandem concurrent, aut continuo magis à ſe mutuo rece-<lb />dent, niſi utrumque ita moveatur, ut vim centrifugam ha-<lb />beat æqualem illi, qua verſus aliud fertur; </s>
          <s xml:space="preserve">cùm verò corpora
</s>
          <pb facs="0687" n="159" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XIII.</fw>
quæ in ſe mutuo gravitant, viribus æqualibus, ſeſe mutuo pe-<lb />
<ptr xml:id="note-0687-01a" corresp="note-0687-01" type="noteAnchor" />
tant <ptr type="noteAnchor" />, aut quod idem eſt <ptr type="noteAnchor" />, celeritatibus, quæ ſunt inverſè
<ptr xml:id="note-0687-02a" corresp="note-0687-02" type="noteAnchor" />
ut quantitates materiæ <ptr type="noteAnchor" />, non poterunt corpora hæc in
<ptr xml:id="note-0687-03a" corresp="note-0687-03" type="noteAnchor" />
motu circum ſe mutuo perſeverare, niſi ambo ita moveantur, <lb />
<ptr xml:id="note-0687-04a" corresp="note-0687-04" type="noteAnchor" />
ut vires centrifugas æquales habeant, quod, niſi ambo cir-<lb />ca commune ſuum gravitatis centrum, æqualibus tempori-<lb />bus, rotentur, non obtinet; </s>
          <s xml:space="preserve">id eſt, ſi propoſitio hæc ad <lb />Solem &amp; </s>
          <s xml:space="preserve">Tellurem applicetur, niſi circa punctum, cujus diſtan-<lb />tia à centro Solis eſt ad ipſius diſtantiam à centro Telluris, <lb />ut quantitas materiæ in Tellure ad materiæ quantitatem in <lb />
<ptr xml:id="note-0687-05a" corresp="note-0687-05" type="noteAnchor" />
Sole, ambo moveantur <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">quod punctum ergo parum admo-
dum à centro Solis diſtat. </s>
          <s xml:space="preserve">Cùm autem, quodcunque ho-<lb />rum corporum moveatur, in motu circa aliud perſeveret, <lb />ſequitur ambo motibus memoratis ſubjici, Solemque exiguo <lb />motu agitari, dum Tellus orbem maximum deſcribit. </s>
          <s xml:space="preserve">Ex <lb />quibus ſequitur, motum Telluris ab illo negari non poſſe, <lb />qui ex legibus motus, ex Phoenomenis deductis, ratiocina-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0687-01" corresp="note-0687-01a" n="*" anchored="true" place="margin">126.</note>
              <note xml:space="preserve" xml:id="note-0687-02" corresp="note-0687-02a" n="*" anchored="true" place="margin">65.</note>
              <note xml:space="preserve" xml:id="note-0687-03" corresp="note-0687-03a" place="margin">1248.</note>
              <note xml:space="preserve" xml:id="note-0687-04" corresp="note-0687-04a" n="*" anchored="true" place="margin">1235.</note>
              <note xml:space="preserve" xml:id="note-0687-05" corresp="note-0687-05a" n="*" anchored="true" place="margin">234. 235.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Probato motu Telluris annuo, &amp; </s>
          <s xml:space="preserve">relatâ Tellure inter Pla-<lb />netas, exigua tantùm difficultas ſupereſt reſpectu motus cir-<lb />ca axem; </s>
          <s xml:space="preserve">nemo enim qui de illo non dubitat, hunc negat; <lb /></s>
          <s xml:space="preserve">multi, conceſſo motu circa axem, Telluris annuum motum <lb />
<ptr xml:id="note-0687-06a" corresp="note-0687-06" type="noteAnchor" />
negant; </s>
          <s xml:space="preserve">ſatis ergo erit in tranſitu notare, omnes Planetas, <lb />circa quos reſpectu hujus motus obſervationes inſtituere li-<lb />cet, circa axes rotari; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">motum ſimilem Telluri competere, <lb />uniformem motum diurnum in corporibus, ad diſtantias quaſ-<lb />cunque, ſatis indicare. </s>
          <s xml:space="preserve">Quibus addendum, celeritatem <lb />Stellarum fixarum, in minori quàm viginti quatuor horarum <lb />ſpatio, revolutionem integram peragentium, vix magis pro-<lb />babilem eſſe, quàm à nobis concipi poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0687-06" corresp="note-0687-06a" place="margin">1249.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Etiam motus hic omnium corporum coeleſtium Naturæ <lb />legibus adverſatur; </s>
          <s xml:space="preserve">nam, ſi hæc rotentur, circulos, quo-<lb />
<ptr xml:id="note-0687-07a" corresp="note-0687-07" type="noteAnchor" />
rum centrum Tellus occupat, motu æquabili, ſingulis die-<lb />bus, percurrunt; </s>
          <s xml:space="preserve">id eſt, deſcribunt areas lineis ad centrum <lb />Telluris ductis temporibus proportionales; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in orbitis reti-<lb />nentur viribus, quæ ad centrum Telluris diriguntur <ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0687-08a" corresp="note-0687-08" type="noteAnchor" />
quibus, proprer omnis actionis reciprocationem <ptr type="noteAnchor" />, Tellus
<ptr xml:id="note-0687-09a" corresp="note-0687-09" type="noteAnchor" />
</s>
          <pb facs="0688" n="160" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
etiam continuò verſus illa corpora trahitur; </s>
          <s xml:space="preserve">ita ut violentiſ-<lb />ſimo motu neceſſario agitari debeat; </s>
          <s xml:space="preserve">unde patet motum diur-<lb />num non ad ipſa corpora coeleſtia referri debere, ſed ad <lb />Tellurem circa axem rotantem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0687-07" corresp="note-0687-07a" place="margin">1250.</note>
              <note xml:space="preserve" xml:id="note-0687-08" corresp="note-0687-08a" n="*" anchored="true" place="margin">226.</note>
              <note xml:space="preserve" xml:id="note-0687-09" corresp="note-0687-09a" n="*" anchored="true" place="margin">126.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Objiciunt, qui Tellurem quieſcere contendunt, corpora <lb />
<ptr xml:id="note-0688-01a" corresp="note-0688-01" type="noteAnchor" />
in Telluris ſuperficie, ex vi centrifugâ, juxta tangentem ad <lb />circulùm, Æquatori parallelum, debere à Tellure recede-<lb />re <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Reſpondemus, corpora eodem motu cum ſuperficie
<ptr xml:id="note-0688-02a" corresp="note-0688-02" type="noteAnchor" />
Telluris, in locis in quibus antur, transferri, &amp; </s>
          <s xml:space="preserve">ideò reſpe-<lb />ctu punctorum ſuperficiei conari recedere per lineas ad axem <lb />perpendiculares <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">etiam corpora gravitate ad centrum Tel-
<ptr xml:id="note-0688-03a" corresp="note-0688-03" type="noteAnchor" />
luris tendere <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò, motu ex hiſce ambobus compoſi-
<ptr xml:id="note-0688-04a" corresp="note-0688-04" type="noteAnchor" />
to, corpus continuò, aut moveri aut moveri conari <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſed
<ptr xml:id="note-0688-05a" corresp="note-0688-05" type="noteAnchor" />
quia primus motus reſpectu ſecundi eſt admodum exiguus, <lb />parum tantùm à directione verſus centrum detorquetur gra-<lb />ve, &amp; </s>
          <s xml:space="preserve">paululum gravitas minuitur, eo magis, quo locus ma-<lb />gis à polo diſtat; </s>
          <s xml:space="preserve">Quod experientiæ congruit; </s>
          <s xml:space="preserve">in ſequenti-<lb />bus etiam videbimus, ubi de Telluris figurà agemus, directio-<lb />nem memoratam gravium, ubique dirigi perpendiculariter ad <lb />Telluris ſuperſiciem. </s>
          <s xml:space="preserve">Corpus, quod in altum projicitur, <lb />non modo motu quo projicitur gaudet, ſed etiam fertur mo-<lb />tu impreſſo illi, qui hoc projicit, aut machinæ, ex qua pro-<lb />pellitur, id eſt, motu communi cum ſuperficie Telluris fertur; <lb /></s>
          <s xml:space="preserve">ideòque in eâdem lineêa, cum ſuperficie Telluris tranſlatâ <lb />movetur, in qua tranſlatum foret ſi Tellus quieſceret.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0688-01" corresp="note-0688-01a" place="margin">1251.</note>
              <note xml:space="preserve" xml:id="note-0688-02" corresp="note-0688-02a" n="*" anchored="true" place="margin">217.</note>
              <note xml:space="preserve" xml:id="note-0688-03" corresp="note-0688-03a" n="*" anchored="true" place="margin">223.</note>
              <note xml:space="preserve" xml:id="note-0688-04" corresp="note-0688-04a" n="*" anchored="true" place="margin">1226.</note>
              <note xml:space="preserve" xml:id="note-0688-05" corresp="note-0688-05a" n="*" anchored="true" place="margin">190. 198.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIV.</head>
        <head xml:space="preserve">De Denſitate Planetarum.</head>
        <p>
          <s xml:space="preserve">SUpereſt, antequam ad Syſtematis explicationem Phyſicam <lb />tranſeamus, ut quantitates materiæ in quibuſdam corpo-<lb />ribus, &amp; </s>
          <s xml:space="preserve">horum denſitates, determinemus; </s>
          <s xml:space="preserve">quibus notis ef-<lb />fectus legum, quibus hæc corpora reguntur, facilius pate-<lb />bunt.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Quantitates materiæ, in variis corporibus, ſunt inter ſe, ut <lb />gravitates ad eandem diſtantiam ab hiſce corporius <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ
<ptr xml:id="note-0688-06a" corresp="note-0688-06" type="noteAnchor" />
gravitates ſunt inter ſe inverſè, ut quadrata temporum perio-
</s>
          <pb facs="0689" n="161" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XI.</fw>
dicorum corporum revolventium, circa varia illa corpora, ad <lb />eandem illam diſtantiam <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Multiplicando quantitates, quæ
<ptr xml:id="note-0689-01a" corresp="note-0689-01" type="noteAnchor" />
ſunt in hac ratione, per eandem quantitatem, cubum nempe <lb />hujus diſtantiæ, non mutatur ratio harum quantitatum; </s>
          <s xml:space="preserve">quæ <lb />ergo ſunt inter ſe, ut quotientes diviſionum cubi memorati, <lb />per quadrata temporum periodicorum memoratorum; </s>
          <s xml:space="preserve">ſed <lb />detegitur quotiens talis diviſionis, pro corpore quocunque, <lb />dividendo cubum alterius diſtantiæ cujuſcunque, per quadra-<lb />tum temporis periodici corporis ad hanc diſtantiam revol-<lb />ventis: </s>
          <s xml:space="preserve">quotientes enim tales ſunt æquales inter ſe, pro omni-<lb />bus corporibus, circa idem, ad diſtantias quaſcunque revol-<lb />ventibus; </s>
          <s xml:space="preserve">ut ſequitur ex æqualitate rationis inter cubos di-<lb />ſtantiarum, &amp; </s>
          <s xml:space="preserve">quadrata temporum periodicorum ad has <lb />diſtantias <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ex qubius deducimus, quantitates materiæ in
<ptr xml:id="note-0689-02a" corresp="note-0689-02" type="noteAnchor" />
corporibus quibuſcunque, in Syſtemate noſtro, eſſe inter ſe <lb />
<ptr xml:id="note-0689-03a" corresp="note-0689-03" type="noteAnchor" />
directè, ut cubos diſtantiarum ad quas, circa hæc, corpora a-<lb />lia revolvuntur, &amp; </s>
          <s xml:space="preserve">inverſè ut quadrata temporum periodi-<lb />corum horum corporum revolventium.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0688-06" corresp="note-0688-06a" n="*" anchored="true" place="margin">1207.</note>
              <note xml:space="preserve" xml:id="note-0689-01" corresp="note-0689-01a" n="*" anchored="true" place="margin">236.</note>
              <note xml:space="preserve" xml:id="note-0689-02" corresp="note-0689-02a" place="margin">1252.</note>
              <note xml:space="preserve" xml:id="note-0689-03" corresp="note-0689-03a" n="*" anchored="true" place="margin">974.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Demonſtrantur hæc, ſeponendo agitationem corporis cen-<lb />tralis, cujus materiæ quantitas quæritur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propter Solis magnitudinem, reſpectu Veneris ex. </s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve">, <lb />quem ex Planetis ſolum conſideramus, vix ex hujus actione <lb />agitatur ille <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">Venus poteſt conſiderari quaſi motus cir-
<ptr xml:id="note-0689-04a" corresp="note-0689-04" type="noteAnchor" />
ca corpus quieſcens.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0689-04" corresp="note-0689-04a" n="*" anchored="true" place="margin">1235.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Satellites Jovis &amp; </s>
          <s xml:space="preserve">Saturni, motu quidem communi cum <lb />primariis feruntur, ſed circa ipſos, quaſi circa corpora qui-<lb />eſcentia, propter primariorum magnitudinem, transferuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Luna autem ſatis ſenſibiliter in Tellurem agit, &amp; </s>
          <s xml:space="preserve">hanc a-<lb />gitat; </s>
          <s xml:space="preserve">quare antequam, ope regulæ memoratæ <ptr type="noteAnchor" />, cum motu
<ptr xml:id="note-0689-05a" corresp="note-0689-05" type="noteAnchor" />
Lunæ computationem inire poſſimus, de conferendâ materiæ <lb />quantitate in Tellure, cum materiæ quantitatibus in Sole, <lb />Jove, &amp; </s>
          <s xml:space="preserve">Saturno, determinanda eſt diſtantia, ad quam Lu-<lb />
<ptr xml:id="note-0689-06a" corresp="note-0689-06" type="noteAnchor" />
na, circa Tellurem quieſcentem, id eſt actione Lunæ non <lb />tranſlatam, revolvi poßet, in eodem tempore periodico, in <lb />quo revolutionem ſuam reverâ peragit, Hìc etiam non at-<lb />tendimus ad motum communem Telluri &amp; </s>
          <s xml:space="preserve">Lunæ, quo circa <lb />Solem ambo feruntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0689-05" corresp="note-0689-05a" n="*" anchored="true" place="margin">1252.</note>
              <note xml:space="preserve" xml:id="note-0689-06" corresp="note-0689-06a" place="margin">1253.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0690" n="162" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Luna in motu ſuo circa Tellurem perſeverat; </s>
          <s xml:space="preserve">ideò Tel-<lb />lus &amp; </s>
          <s xml:space="preserve">illa circa commune gravitatis centrum rotantur: </s>
          <s xml:space="preserve">ut <lb />
<ptr xml:id="note-0690-01a" corresp="note-0690-01" type="noteAnchor" />
ex demonſtratis circa Tellurem &amp; </s>
          <s xml:space="preserve">Solem <ptr type="noteAnchor" /> ſequitur, &amp; </s>
          <s xml:space="preserve">Lu-
na, vi qua verſus Tellurem tendit, revolvitur in orbitâ, <lb />cujus ſemi-diameter eſt diſtantia Lunæ à memorato commu-<lb />ni centro gravitatis Lunæ &amp; </s>
          <s xml:space="preserve">Telluris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0690-01" corresp="note-0690-01a" n="*" anchored="true" place="margin">1248.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit L hæc Lunæ diſtantia à communi centro gravitatis; <lb /></s>
          <s xml:space="preserve">T diſtantia Telluris ab eodem centro; </s>
          <s xml:space="preserve">L + T eſt ergo di-<lb />ſtantia Lunæ à Tellure, &amp; </s>
          <s xml:space="preserve">eſt 60 {1/2} ſemidiam. </s>
          <s xml:space="preserve">Telluris; </s>
          <s xml:space="preserve">me-<lb />diam enim diſtantiam hìc conſideramus; </s>
          <s xml:space="preserve">Sit D diſtantia <lb />quam quærimus, ad quam, circa Tellurem quieſcentem, <lb />gravitate ſuâ verſus Tellurem, poſſet moveri Luna, in tem-<lb />pore, in quo revera ad diſtantiam L, circa commune gra-<lb />vitatis centrum rotatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Propter hanc temporum periodicorum æqualitatem, vis, <lb />qua Luna ad diſtantiam D poſſet in orbitâ retineri, eſt ad vim, <lb />qua ad diſtantiam L, in orbe ſuo retinetur, ut D ad L <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">232.</note>
        <p>
          <s xml:space="preserve">Sed vis, qua Luna ad Tellurem tenderet, &amp; </s>
          <s xml:space="preserve">in orbitâ <lb />retineretur ad diſtantiam D, eſt ad vim, qua nunc in orbitâ <lb />retinetur cûm â Tellure diſtat L + T, ut, L + T<hi rend="superscript">9</hi> ad <lb />
<ptr xml:id="note-0690-03a" corresp="note-0690-03" type="noteAnchor" />
Dq <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Ergo
D, L :</s>
          <s xml:space="preserve">: <hi rend="overline">L + T<hi rend="superscript">q</hi></hi>, D<hi rend="superscript">q</hi> <lb />Ideoque D<hi rend="superscript">c</hi> = L x <hi rend="overline">L + T</hi><hi rend="superscript">q</hi> &amp; </s>
          <s xml:space="preserve">D<hi rend="superscript">c</hi> x <hi rend="overline">L + T</hi> = L x <lb /><hi rend="overline">L + T</hi><hi rend="superscript">c</hi>: </s>
          <s xml:space="preserve">unde ſequentem deducimus proportionem <lb />Idcirco L + T, D : </s>
          <s xml:space="preserve">: </s>
          <s xml:space="preserve">L + T, ad primam ex dualbus <lb />mediis proportionalibus inter l + T &amp; </s>
          <s xml:space="preserve">L.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0690-03" corresp="note-0690-03a" n="*" anchored="true" place="margin">1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">L + T eſt ad L, ut quantitas materiæ, in Tellure &amp; </s>
          <s xml:space="preserve"><lb />Lunâ conjunctim, ad quantitatem materiæ in Tellure ſolâ *: <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0690-04a" corresp="note-0690-04" type="noteAnchor" />
quæ quantitates materiæ, ut in ſequentibus videbimus, ſunt <lb />inter ſe, ut 40, 37. </s>
          <s xml:space="preserve">ad 39, 37.</s>
          <s xml:space="preserve">, &amp; </s>
          <s xml:space="preserve">prima duarum mediarum <lb />proportionalium, inter hos numeros, eſt 40, 035.</s>
          <s xml:space="preserve">; ergo 40, 37. <lb /></s>
          <s xml:space="preserve">eſt ad 40, 035.</s>
          <s xml:space="preserve">, ut 60 {1/2} ad diſtantiam quæſitam, quæ dete-<lb />gitur 60 ſemidiametrorum Telluris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0690-04" corresp="note-0690-04a" n="*" anchored="true" place="margin">234. 235.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa hanc operationem notandum eſt, diſtantiam D, non <lb />detegi, niſi detur ratio inter maſlam Lunæ &amp; </s>
          <s xml:space="preserve">Telluris, quæ
</s>
          <pb facs="0691" n="163" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. VI. CAP. XIV.</fw>
determinari non poteſt, niſi detur ratio inter denſitatem So-<lb />lis &amp; </s>
          <s xml:space="preserve">Telluris, ad quam detegendam, ut diſtantia D nota ſit, <lb />neceſſe eſt. </s>
          <s xml:space="preserve">Quare primo tentando detegitur D, &amp; </s>
          <s xml:space="preserve">approxi-<lb />mando exactè determinatur. </s>
          <s xml:space="preserve">Hanc autem eſſe 60 ſemi-<lb />diam. </s>
          <s xml:space="preserve">Telluris, conſtat; </s>
          <s xml:space="preserve">quia hac poſitâ detegitur, inter quan-<lb />titates materiæ Telluris &amp; </s>
          <s xml:space="preserve">Lunæ, ratio, quæ datur inter <lb />39, 37. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">I, ut in ſequentibus videbimus; </s>
          <s xml:space="preserve">qua adhibitâ pro-<lb />portione detegitur, ut vidimus, hæc ipſa diſtantia 60. </s>
          <s xml:space="preserve">ſemi-<lb />diametrorum.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Hiſce præmiſſis ipſam aggredimur computationem.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Diſtantia Veneris à centro Solis eſt 723. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tempus pe-<lb />riodicum 5393. </s>
          <s xml:space="preserve">horarum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0691-01a" corresp="note-0691-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0691-01" corresp="note-0691-01a" n="*" anchored="true" place="margin">959.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quartus Satelles Jovis diſtat à centro Jovis partibus 12, 507. <lb /></s>
          <s xml:space="preserve">quarum Venus à Sole diſtat 723.</s>
          <s xml:space="preserve">: hujus Satellitis tempus pe-<lb />riodicum eſt 402 horarum 5′. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">971.</note>
        <p>
          <s xml:space="preserve">Quartus Satelles Saturni diſtat à centro Saturni, partibus <lb />iiſdem 9,292.</s>
          <s xml:space="preserve">; &amp; </s>
          <s xml:space="preserve">tempus periodicum eſt 382 horarum 41′ *</s>
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">972.</note>
        <p>
          <s xml:space="preserve">Tandem diſtantia Lunæ 60. </s>
          <s xml:space="preserve">ſemidiam. </s>
          <s xml:space="preserve">Telluris à cen-<lb />tro hujus, eſt partium memoratarum 2,909. </s>
          <s xml:space="preserve">tempus periodi-<lb />cum medium 655. </s>
          <s xml:space="preserve">hor. </s>
          <s xml:space="preserve">43′.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Diviſis ſingulis cubis harum diſtantiarum, reſpectivè per <lb />
<ptr xml:id="note-0691-04a" corresp="note-0691-04" type="noteAnchor" />
ſuorum temporum periodicorum quadrata, dantur in quo-<lb />tientibus numeri, qui ſunt inter ſe, ut materiæ quantitates <lb />in dictis corporibus centralibus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">qui quotientes ſunt inter
<ptr xml:id="note-0691-05a" corresp="note-0691-05" type="noteAnchor" />
ſe ut numeri ſequentes,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0691-04" corresp="note-0691-04a" place="margin">1254.</note>
              <note xml:space="preserve" xml:id="note-0691-05" corresp="note-0691-05a" n="*" anchored="true" place="margin">1252.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin"> <lb />Quantitates # in Sole; # in Jove; # in Saturno; # in Tellure; <lb /># materiæ # 10000. # 9,248. # 4,223. # 0,0044. <lb /></note>
        <note xml:space="preserve" place="margin">1255.</note>
        <p>
          <s xml:space="preserve">Exobſervationibus aſtronomicis datur etiam proportio dia-<lb />metrorum horum corporum.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin"> <lb />Diametri # Solis ; # Jovis ; # Saturni; # Telluris. <lb /># 10000. # 1077. # 889. # 104. <lb /></note>
        <note xml:space="preserve" place="margin">1256.</note>
        <p>
          <s xml:space="preserve">Si quantitates materiæ memoratæ per diametrorum qua-<lb />
<ptr xml:id="note-0691-10a" corresp="note-0691-10" type="noteAnchor" />
drata dividantur, quotientes erunt inter ſe, ut pondera in ſu-<lb />perficiebus dictorum corporum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſunt autem quotientes hi
<ptr xml:id="note-0691-11a" corresp="note-0691-11" type="noteAnchor" />
ut numeri ſequentes.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0691-10" corresp="note-0691-10a" place="margin">1257.</note>
              <note xml:space="preserve" xml:id="note-0691-11" corresp="note-0691-11a" n="*" anchored="true" place="margin">1227.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin"> <lb />Gravitates # Solis; # Jovis: # Saturni; # Telluris <lb />in ſuperficiebus, # 10000. # 797,15. # 534,337. # 407,832. <lb /></note>
        <note xml:space="preserve" place="margin">1258.</note>
        <pb facs="0692" n="164" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Dividendo hos numeros per diametros, habemus propor-<lb />
<ptr xml:id="note-0692-01a" corresp="note-0692-01" type="noteAnchor" />
tionem denſitatum eorundem horum corporum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0692-01" corresp="note-0692-01a" place="margin">1259.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1231.</note>
        <p>
          <s xml:space="preserve">quotientes, hiſce diviſionibus detecti, ſequentium nume-<lb />rorum relationem habent.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" place="margin"> <lb />Deſitates # Solis; # Jovis; # Saturni; # Telluris. <lb /># 10000 # 7404. # 6011. # 39214. <lb /></note>
        <note xml:space="preserve" place="margin">1260.</note>
        <p>
          <s xml:space="preserve">Lunæ denſitatem in capite ultimo determinabimus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Minimè probabile eſt, corpora memorata quatuor homo-<lb />genea eſſe; </s>
          <s xml:space="preserve">circa Tellurem videbimus, in capite ſequenti 17.</s>
          <s xml:space="preserve">, <lb />illam verſus centrum denſiorem eſſe, quàm verſus ſuperſiciem; <lb /></s>
          <s xml:space="preserve">unde ſequitur denſitates non exactè determinari poſſe, qua-<lb />re tantùm determinantur denſitates mediæ, id eſt, quas cor-<lb />
<ptr xml:id="note-0692-05a" corresp="note-0692-05" type="noteAnchor" />
pora haberent, ſi ſervatâ materiæ quantitate &amp; </s>
          <s xml:space="preserve">magnitudi-<lb />ne reſpectu ſingulorum, corpora forent homogenea.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0692-05" corresp="note-0692-05a" place="margin">1261.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Proportio memorata <ptr type="noteAnchor" />, inter denſitates reſpectu omnium cor-
<ptr xml:id="note-0692-06a" corresp="note-0692-06" type="noteAnchor" />
rum, &amp; </s>
          <s xml:space="preserve">computationes reliquæ reſpectu Solis, Jovis, &amp; </s>
          <s xml:space="preserve">Sa-<lb />
<ptr xml:id="note-0692-07a" corresp="note-0692-07" type="noteAnchor" />
turni, ſenſibili errore expertes ſunt; </s>
          <s xml:space="preserve">quantum ad Tellurem, <lb />in his error fortè datur, corrigendus ex obſervationibus in <lb />tempore inſtituendis: </s>
          <s xml:space="preserve">Ponimus enim diſtantiam Lunæ, 60. <lb /></s>
          <s xml:space="preserve">ſemi-diam.</s>
          <s xml:space="preserve">, eſſe partium 2,909. </s>
          <s xml:space="preserve">quarum Venus à Sole diſtat <lb />723, id eſt, quarum Tellus à Sole diſtat, 1000 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ Lunæ
<ptr xml:id="note-0692-08a" corresp="note-0692-08" type="noteAnchor" />
diſtantia detegitur, ponendo Solis Paralaxin horizontalem 10″, <lb />quæ tamen pro verâ abſolutê haberi non poteſt, licèt ex obſer-<lb />vationibus exactiſſimis, de Martis Telluri maximè vicini Paral-<lb />laxi huc uſque inſtitutis, deducatur, ſed quæ nimium eſt <lb />exigua, ut circa obſervationes nulla erroris ſuſpicio ſuperſit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0692-06" corresp="note-0692-06a" place="margin">1262.</note>
              <note xml:space="preserve" xml:id="note-0692-07" corresp="note-0692-07a" n="*" anchored="true" place="margin">1260.</note>
              <note xml:space="preserve" xml:id="note-0692-08" corresp="note-0692-08a" n="*" anchored="true" place="margin">959. 960.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1108.</note>
        <p>
          <s xml:space="preserve">Errorem tamen ex malè determinatâ ratione, inter ſemi-<lb />diametrum Telluris &amp; </s>
          <s xml:space="preserve">hujus â Sole diſtantiam, non mutare <lb />determinatam Telluris denſitatem, ex ipſis computationi-<lb />bus circa hanc inſtitutis, deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Ex hiſce enim ſequitur, denſitates corporum eſſe inter ſe, in <lb />ratione compoſitâ ex directâ cuborum diſtantiarum corprum <lb />quæ circumferentur, &amp; </s>
          <s xml:space="preserve">inverſâ quadratorum temporum pe-<lb />riodicorum horum ipſorum corporum revolventium *: </s>
          <s xml:space="preserve">Ut <lb />
<ptr xml:id="note-0692-10a" corresp="note-0692-10" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">inverſâ cuborum diametrorum corporum centralium, <lb />quorum denſitates quæruntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ratio ex his compoſita, eſt
<ptr xml:id="note-0692-11a" corresp="note-0692-11" type="noteAnchor" />
compoſita ex ratione directâ ſractionis, cujus numerator eſt
</s>
          <pb facs="0693" n="165" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XV.</fw>
cubus diſtantiæ corporis revoluti, &amp; </s>
          <s xml:space="preserve">denominator cubus <lb />diametri corporis centralis, &amp; </s>
          <s xml:space="preserve">ratione inverſâ quadrati <lb />temporis periodici corporis circumacti. </s>
          <s xml:space="preserve">Fractio autem ta-<lb />lis datur, ſi nota ſit ratio inter diametrum corporis centra-<lb />lis &amp; </s>
          <s xml:space="preserve">diſtantiam corporis revoltventis ab hoc centro, licèt hæc <lb />diſtantia cum nullâ aliâ poſſit conferri; </s>
          <s xml:space="preserve">ratio autem hæ re-<lb />ſpectu Telluris &amp; </s>
          <s xml:space="preserve">Lunæ, æque ac reſpectu cæterorum cor-<lb />porum datur, quare &amp; </s>
          <s xml:space="preserve">Telluris denſitatis ratio ad reliquo-<lb />rum corporum denſitates exactè detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0692-10" corresp="note-0692-10a" n="*" anchored="true" place="margin">1254.</note>
              <note xml:space="preserve" xml:id="note-0692-11" corresp="note-0692-11a" n="*" anchored="true" place="margin">1257. 1259.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XV.</head>
        <head xml:space="preserve">Totius Syſtematis Planetarii explicatio Phyſica.</head>
        <p>
          <s xml:space="preserve">IN parte primâ hujus libri, motus corporum in Syſtemate <lb />
<ptr xml:id="note-0693-01a" corresp="note-0693-01" type="noteAnchor" />
Planetario expoſuimus, quomodo hi, ex legibus Naturæ <ptr type="noteAnchor" />,
<ptr xml:id="note-0693-02a" corresp="note-0693-02" type="noteAnchor" />
ſequantur explicandum eſt; </s>
          <s xml:space="preserve">id eſt, quomodo, corporibus <lb />
<ptr xml:id="note-0693-03a" corresp="note-0693-03" type="noteAnchor" />
his ſemel motis, in motibus quos obſervamus perſeverent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0693-01" corresp="note-0693-01a" n="*" anchored="true" place="margin">124. 125. 126.</note>
              <note xml:space="preserve" xml:id="note-0693-02" corresp="note-0693-02a" place="margin">1206. 1207.</note>
              <note xml:space="preserve" xml:id="note-0693-03" corresp="note-0693-03a" place="margin">1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus Solem &amp; </s>
          <s xml:space="preserve">Mercurium, ſi ſibi permittantur ad <lb />
<ptr xml:id="note-0693-04a" corresp="note-0693-04" type="noteAnchor" />
ſe mutuo accedent <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Si autem projiciantur poterunt, cir-
<ptr xml:id="note-0693-05a" corresp="note-0693-05" type="noteAnchor" />
ca commune gravitatis centrum, æqualibus temporibus, re-<lb />volvi, &amp; </s>
          <s xml:space="preserve">Ellipticas lineas immobiles deſcribere <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in
<ptr xml:id="note-0693-06a" corresp="note-0693-06" type="noteAnchor" />
illo motu perſeverare: </s>
          <s xml:space="preserve">conſtat enim mathematicâ demon-<lb />
<ptr xml:id="note-0693-07a" corresp="note-0693-07" type="noteAnchor" />
ſtratione, in hoc caſu, corpora circa commune centrum gra-<lb />vitatis deſcribere Ellipſes ſimiles illi, quam unum circa alte-<lb />rum quieſcens, iiſdem viribus, poſſet deſcribere: </s>
          <s xml:space="preserve">centrum <lb />hoc, propter magnitudinem Solis <ptr type="noteAnchor" />, vix ab ipſo Solis cen-
<ptr xml:id="note-0693-08a" corresp="note-0693-08" type="noteAnchor" />
tro idſtat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0693-04" corresp="note-0693-04a" place="margin">1263.</note>
              <note xml:space="preserve" xml:id="note-0693-05" corresp="note-0693-05a" n="*" anchored="true" place="margin">1206.</note>
              <note xml:space="preserve" xml:id="note-0693-06" corresp="note-0693-06a" n="*" anchored="true" place="margin">1248. 1208.</note>
              <note xml:space="preserve" xml:id="note-0693-07" corresp="note-0693-07a" place="margin">241.</note>
              <note xml:space="preserve" xml:id="note-0693-08" corresp="note-0693-08a" n="*" anchored="true" place="margin">235.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus ulterius, ad majorem à Sole diſtantiam, <lb />Venerem projici, turbabit hic paululum Mercurii mo-<lb />tum, qui etiam, actione ſuâ in Venerem, hunc paulu-<lb />lum à viâ deflectet, &amp; </s>
          <s xml:space="preserve">ambo Solem,, nunc verſus eandem <lb />partem, nunc ad partes diverſas, trahent; </s>
          <s xml:space="preserve">ſed omnes has <lb />irregularitates inſenſibiles eſſe videbimus, ſi Solis magnitudi-<lb />nem conſideremus; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò hæc tria corpora tendere ad <lb />punctum in viciniis Solis inter hæc corpora; </s>
          <s xml:space="preserve">quod ergo pa-<lb />rum admodum diſtat à communi centro gravitatis omnium.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Si ſucceſſivé Tellus, Mars, &amp; </s>
          <s xml:space="preserve">reliqui Planetæ, ad diſtan-
</s>
          <pb facs="0694" n="(166)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tias diverſas â Sole, projiciantur, idem ratiocinium locum <lb />habebit. </s>
          <s xml:space="preserve">Unde ſequitur omnes Planetas revolvi circa, <lb />
<ptr xml:id="note-0694-01a" corresp="note-0694-01" type="noteAnchor" />
omnium corporum Syſtema componentium, commune centrum <lb />gravitatis, quod parum à Sole diſtat, &amp; </s>
          <s xml:space="preserve">Planetas ſeſe mu-<lb />tuo ſenſibiliter in motibus non turbare; </s>
          <s xml:space="preserve">unde ſinguli lineas <lb />
<ptr xml:id="note-0694-02a" corresp="note-0694-02" type="noteAnchor" />
deſcribunt, quas circa Solem deſcriberent, ſi quiſque ſolus <lb />cum Sole in Syſtemate Planetario exiſteret; </s>
          <s xml:space="preserve">id eſt, Ellipſes <lb />immobiles: </s>
          <s xml:space="preserve">nam has ex vi gravitatis deſcribi conſtat <ptr type="noteAnchor" />, nul-
<ptr xml:id="note-0694-03a" corresp="note-0694-03" type="noteAnchor" />
laſque alias lineas excentricas immobiles, ex vi centraliad di-<lb />ſtantias æquales æqualiter agenti, deſcribi poſſe mathematicè <lb />evincitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0694-01" corresp="note-0694-01a" place="margin">1264.</note>
              <note xml:space="preserve" xml:id="note-0694-02" corresp="note-0694-02a" place="margin">1265.</note>
              <note xml:space="preserve" xml:id="note-0694-03" corresp="note-0694-03a" n="*" anchored="true" place="margin">1208. 241.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Clarius etiam patebit, omnes Planetas ad punctum in vici-<lb />niis Solis tendere, ſi conſideremus quantitatem materiæ in <lb />Sole, millies &amp; </s>
          <s xml:space="preserve">magis, materiæ quantitatem in Jove, Planeta-<lb />rum longè maximo, ſuperare <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0694-04a" corresp="note-0694-04" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0694-04" corresp="note-0694-04a" n="*" anchored="true" place="margin">1255.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum Planetæ omnes revolvuntur, licèt parum tantùm agi-<lb />
<ptr xml:id="note-0694-05a" corresp="note-0694-05" type="noteAnchor" />
tent Solem, hunc tamen agitant, &amp; </s>
          <s xml:space="preserve">diverſè trahunt, pro vario <lb />illorum ſitu inter ſe, unde motus exiguus in Sole oritur, qui <lb />ſemper pendet à motu jam acquiſito, &amp; </s>
          <s xml:space="preserve">mutatione in hoc ex <lb />actione memoratâ, quæ omnibus momentis mutatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0694-05" corresp="note-0694-05a" place="margin">1266.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hujus verò Solis agitationis effectus eſt, Planetas ſeſe mu-<lb />
<ptr xml:id="note-0694-06a" corresp="note-0694-06" type="noteAnchor" />
tuo minus, in motibus Ellipticis circa Solem turbare, quàm <lb />ſi Sol in medio Syſtematis quieſceret. </s>
          <s xml:space="preserve">Jupiter, ex. </s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve">, ſi <lb />æqualiter à Mercurio &amp; </s>
          <s xml:space="preserve">Sole diſter, æquali celeritate ad ſe <lb />trahet hæc duo corpora <ptr type="noteAnchor" />, unde ſitus reſpectu Solis minus
<ptr xml:id="note-0694-07a" corresp="note-0694-07" type="noteAnchor" />
turbatur, quàm ſi Sol hoc motu non agitaretur, &amp; </s>
          <s xml:space="preserve">Mercurius <lb />ſolus ad Jovem tenderet: </s>
          <s xml:space="preserve">pro variis Mercurii &amp; </s>
          <s xml:space="preserve">Solis à Jo-<lb />ve diſtantiis, unus aut alter magis attrahitur, &amp; </s>
          <s xml:space="preserve">ſemper in ſi-<lb />tu reſpectivo minor mutatio datur, dum ambo verſus ean-<lb />dem partem feruntur, quàm ſi, Sole quieſcente, Mercurius <lb />ſolus verſus Jovem moveretur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0694-06" corresp="note-0694-06a" place="margin">1267.</note>
              <note xml:space="preserve" xml:id="note-0694-07" corresp="note-0694-07a" n="*" anchored="true" place="margin">1235.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ratiocinium hoc ad omnes Planetarum magis à Sole diſtan-<lb />tium actiones, in minus diſtantes, applicari poteſt. </s>
          <s xml:space="preserve">Quod atti-<lb />net horum actionem in illos, pro vario ſitu ad Solem trahunt <lb />Planetam, aut hunc à Sole ſeparant, &amp; </s>
          <s xml:space="preserve">integram conſiderando <lb />revolutionem reſpectivam, id eſt, motum à conjunctione ad <lb />conjunctionem ſequentem, turbatio minor eſt, quam ſi Sol <lb />immobilis ſtaret.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0695" n="(167)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. XV.</fw>
        <p>
          <s xml:space="preserve">Magnitudo Solis, cum cæteris corporibus Syſtematis noſtri <lb />
<ptr xml:id="note-0695-01a" corresp="note-0695-01" type="noteAnchor" />
collati, in cauſâ eſt, ut ex ante demonſtratis patet, parum <lb />Planetas ſeſe mutuo turbare, cùm tamen non infinita ſit hæc <lb />magnitudo, non in totum actiones mutuæ contemnendæ <lb />ſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0695-01" corresp="note-0695-01a" place="margin">1268.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diximus obſervationibus Aſtronomicis conſtare, Jovem <lb />viam Saturni mutare ubi huic eſt proximus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare hæc
<ptr xml:id="note-0695-02a" corresp="note-0695-02" type="noteAnchor" />
turbatio præ cæteris ſenſibilis ſit, ex lege gravitatis dedu-<lb />citur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0695-02" corresp="note-0695-02a" n="*" anchored="true" place="margin">1217.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Actiones Jovis in Saturnum, quando huic eſt proximus, <lb />
<ptr xml:id="note-0695-03a" corresp="note-0695-03" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">Solis in eundem Planetam, qua hic in orbitâ retinetur, <lb />ſunt inter ſe directè ut quantitates materiæ in Jove &amp; </s>
          <s xml:space="preserve">Sole <ptr type="noteAnchor" />
<ptr xml:id="note-0695-04a" corresp="note-0695-04" type="noteAnchor" />
nempe ut 9,248. </s>
          <s xml:space="preserve">ad 10000. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">inverſè ut quadrata diſ-
<ptr xml:id="note-0695-05a" corresp="note-0695-05" type="noteAnchor" />
tantiarum Jovis &amp; </s>
          <s xml:space="preserve">Solis à Saturno, id eſt directè ut 81. </s>
          <s xml:space="preserve">ad <lb />16.</s>
          <s xml:space="preserve">; nam diſtantiæ, Saturni &amp; </s>
          <s xml:space="preserve">Jovis à Sole, ſunt ferè ut 9. </s>
          <s xml:space="preserve">ad <lb />
<ptr xml:id="note-0695-06a" corresp="note-0695-06" type="noteAnchor" />
5.</s>
          <s xml:space="preserve">; quare, ubi Jupiter Saturno eſt proximus, diſtantiæ hujus à <lb />Jove &amp; </s>
          <s xml:space="preserve">Sole ſunt ut 4. </s>
          <s xml:space="preserve">ad 9. </s>
          <s xml:space="preserve">Ratio compoſita ex memora-<lb />tis duabus eſt 749. </s>
          <s xml:space="preserve">ad 160000.</s>
          <s xml:space="preserve">, aut 1. </s>
          <s xml:space="preserve">ad 214.</s>
          <s xml:space="preserve">; hæc Jovis <lb />actio cum Saturni gravitate in Solem conſpirat, &amp; </s>
          <s xml:space="preserve">ideò banc <lb />parte {1/214} auget: </s>
          <s xml:space="preserve">unde non mirum turbationem ſenſibilem <lb />eſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0695-03" corresp="note-0695-03a" place="margin">1269.</note>
              <note xml:space="preserve" xml:id="note-0695-04" corresp="note-0695-04a" n="*" anchored="true" place="margin">1207.</note>
              <note xml:space="preserve" xml:id="note-0695-05" corresp="note-0695-05a" n="*" anchored="true" place="margin">1255.</note>
              <note xml:space="preserve" xml:id="note-0695-06" corresp="note-0695-06a" place="margin">1270.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non conſideramus hìc vim, qua Jupiter Solem trahit, nam <lb />hac orbita Saturni non mutatur, &amp; </s>
          <s xml:space="preserve">explicandum erat, quare <lb />Saturnum â viâ deflexum obſervent Aſtronomi; </s>
          <s xml:space="preserve">actione ta-<lb />men Jovis in Solem, magis ad Saturnum trahitur Sol, &amp; </s>
          <s xml:space="preserve">ſi-<lb />tus reſpectivus horum corporum magis turbatur, quàm obſer-<lb />vationibus Aſtronomicis detegitur. </s>
          <s xml:space="preserve">Vis qua Jupiter in ſitu <lb />memorato trahit Solem, &amp; </s>
          <s xml:space="preserve">qua ideò hic verſus Saturnum <lb />trahitur, eſt ad vim qua Jupiter Saturnum trahit, ut 16. </s>
          <s xml:space="preserve">ad <lb />25. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, id eſt ut 479. </s>
          <s xml:space="preserve">ad 749, qui numerus exprimit vim,
<ptr xml:id="note-0695-07a" corresp="note-0695-07" type="noteAnchor" />
qua Saturnus ad Jovem tendit, quando gravitas Saturni in <lb />Solem exprimitur per 160000. </s>
          <s xml:space="preserve">Si colligamus in unam ſum-<lb />mam vires Jovis, quibus Saturnum &amp; </s>
          <s xml:space="preserve">Solem trahit; </s>
          <s xml:space="preserve">erit vis, <lb />qua, ex interpoſito Jove, hæc corpora ad ſe mutuo ten-<lb />dunt, ad gravitatem Saturni in Solem, ut 1228, ad 160000.</s>
          <s xml:space="preserve">; <lb />ſed gravitas hæc eſt ad gravitatem Solis in Saturnum, ut <lb />
<ptr xml:id="note-0695-08a" corresp="note-0695-08" type="noteAnchor" />
160000. </s>
          <s xml:space="preserve">ad 67, 5 <ptr type="noteAnchor" />, quare acceſſus mutuus Solis &amp; </s>
          <s xml:space="preserve">Saturni,
<ptr xml:id="note-0695-09a" corresp="note-0695-09" type="noteAnchor" />
</s>
          <pb facs="0696" n="(168)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
eſt ad augmentum bujus acceſſus ex actione Jovis interpoſiti, ut <lb />160067. </s>
          <s xml:space="preserve">ad 1228. </s>
          <s xml:space="preserve">aut ut 130.</s>
          <s xml:space="preserve">, ad 1. </s>
          <s xml:space="preserve">Hæc notabilis eſt, &amp; </s>
          <s xml:space="preserve">om-<lb />nium longè maxima, turbatio in motu Planetæ primarii <lb />cujuscunque, hæc etiam in unico tantum caſu obtinet; </s>
          <s xml:space="preserve">nam, <lb />recedente Jove à Saturno, brevi inſenſibilis eſt turbatio motus <lb />Saturni.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0695-07" corresp="note-0695-07a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0695-08" corresp="note-0695-08a" n="*" anchored="true" place="margin">1207. 1255.</note>
              <note xml:space="preserve" xml:id="note-0695-09" corresp="note-0695-09a" place="margin">1271.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In eodem ſitu Jovis, Saturno proximi, hujus vis licèt in <lb />hoc caſu ſit omnium maxima, non æquè ſenſibilis eſt, ad <lb />viam Jovis circa Solem mutandam. </s>
          <s xml:space="preserve">Actio Saturni ad Jovem <lb />trahendum, eſtad hujus actionem, qua Solem trahit, ut 81. <lb /></s>
          <s xml:space="preserve">ad 16 <ptr type="noteAnchor" />, celerius ergo illum trahit, &amp; </s>
          <s xml:space="preserve">cûm verſus eandem
<ptr xml:id="note-0696-01a" corresp="note-0696-01" type="noteAnchor" />
partem trahantur, differentia harum virium eſt vis, cum qua ex <lb />Saturni actione, Jupiter &amp; </s>
          <s xml:space="preserve">Sol à ſe mutuo ſeparantur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ
<ptr xml:id="note-0696-02a" corresp="note-0696-02" type="noteAnchor" />
ideo eſt ad gravitatem Solis in Saturnum, ut 65. </s>
          <s xml:space="preserve">ad 16. </s>
          <s xml:space="preserve">Hæc <lb />autem Solis gravitas in Saturnum eſt ad gravitatem Jovis in <lb />Solem, ut 4,223. </s>
          <s xml:space="preserve">ad 10000. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">ut 25. </s>
          <s xml:space="preserve">ad 81. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, id eſt ut
<ptr xml:id="note-0696-03a" corresp="note-0696-03" type="noteAnchor" />
<ptr xml:id="note-0696-04a" corresp="note-0696-04" type="noteAnchor" />
106. </s>
          <s xml:space="preserve">ad 810000, aut ut 16. </s>
          <s xml:space="preserve">ad 122756; </s>
          <s xml:space="preserve">eſt idcirco vis tur-<lb />bans Saturni ad Jovis gravitatem in Solem, ut 65. </s>
          <s xml:space="preserve">ad 122756, <lb />aut ut 1. </s>
          <s xml:space="preserve">ad 1888.</s>
          <s xml:space="preserve">; ita ex actione maximâ Saturni, partetan-<lb />
<ptr xml:id="note-0696-05a" corresp="note-0696-05" type="noteAnchor" />
tùm {1/1888}, minuitur gravitas Jovis in Solem, quæ turbatio <lb />inſenſibilis eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0696-01" corresp="note-0696-01a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0696-02" corresp="note-0696-02a" n="*" anchored="true" place="margin">175.</note>
              <note xml:space="preserve" xml:id="note-0696-03" corresp="note-0696-03a" n="*" anchored="true" place="margin">1207. 1255.</note>
              <note xml:space="preserve" xml:id="note-0696-04" corresp="note-0696-04a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0696-05" corresp="note-0696-05a" place="margin">1272.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Reliquæ Planetarum mutuæ perturbationes ſunt multò mi-<lb />nores, ut patebit determinando illam, quæ omnium harum <lb />maxima eſt, Jovis in Martem, quæ computatione ſimili præ-<lb />cedenti detegitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Diſtantiæ Jovis à Marte &amp; </s>
          <s xml:space="preserve">Sole, quando Mars inter hunc <lb />&amp; </s>
          <s xml:space="preserve">Jovem in eâdem lineâ datur, ſunt circiter ut 7. </s>
          <s xml:space="preserve">ad 10. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0696-06a" corresp="note-0696-06" type="noteAnchor" />
quare vires, cum quibus Jupiter hæc corpora trahit, ſunt <lb />ut 100. </s>
          <s xml:space="preserve">ad 49. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, quarum virium differentia eſt ad gravitatem
<ptr xml:id="note-0696-07a" corresp="note-0696-07" type="noteAnchor" />
Solis in Jovem, ut 51. </s>
          <s xml:space="preserve">ad 49.</s>
          <s xml:space="preserve">. Gravitas hæc Solis in Jovem, <lb />eſt ad gravitatem Martis in Solem, ut 9,248. </s>
          <s xml:space="preserve">ad 1000. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0696-08a" corresp="note-0696-08" type="noteAnchor" />
ut 9. </s>
          <s xml:space="preserve">ad 100 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt ut 83. </s>
          <s xml:space="preserve">ad 1000000.</s>
          <s xml:space="preserve">; aut ut 49. </s>
          <s xml:space="preserve">ad
<ptr xml:id="note-0696-09a" corresp="note-0696-09" type="noteAnchor" />
590443.</s>
          <s xml:space="preserve">; &amp; </s>
          <s xml:space="preserve">vis perturbans Jovis ad gravitatem Martis in So-<lb />lem, ut 51. </s>
          <s xml:space="preserve">ad 590443; </s>
          <s xml:space="preserve">aut ut 1. </s>
          <s xml:space="preserve">ad 11577: </s>
          <s xml:space="preserve">Quare Mar-<lb />
<ptr xml:id="note-0696-10a" corresp="note-0696-10" type="noteAnchor" />
tis gravitas in Solem, parte tantùm {1/11577}, actione Jovis illi <lb />proximi minuitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0696-06" corresp="note-0696-06a" n="*" anchored="true" place="margin">961. 962.</note>
              <note xml:space="preserve" xml:id="note-0696-07" corresp="note-0696-07a" n="*" anchored="true" place="margin">1280.</note>
              <note xml:space="preserve" xml:id="note-0696-08" corresp="note-0696-08a" n="*" anchored="true" place="margin">1207. 1255.</note>
              <note xml:space="preserve" xml:id="note-0696-09" corresp="note-0696-09a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0696-10" corresp="note-0696-10a" place="margin">1273.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quantumvis perturbationes hæ, ex actione Planetarum <lb />
<ptr xml:id="note-0696-11a" corresp="note-0696-11" type="noteAnchor" />
</s>
          <pb facs="0697" n="(169)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XV.</fw>
in ſe mutuo ſint exiguæ, &amp; </s>
          <s xml:space="preserve">licèt, quæ in ſitu Planetarum di-<lb />verſo locum habent, quodammodo ſeſe mutuo compenſent, <lb />hiſce tamen paululum mutatur proportio, in qua decreſcit <lb />vis, quæ Planetas in orbitis retinet, ita ut non exactè minua-<lb />tur in ratione inverlâ quadrati diſtantiæ, idcirco licèt ſenſibi-<lb />liter quieſcant orbitæ, poſt multas revolutiones ſitus barum or-<lb />bitarum paululum mutatus obſervatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0697-01a" corresp="note-0697-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0696-11" corresp="note-0696-11a" place="margin">1274.</note>
              <note xml:space="preserve" xml:id="note-0697-01" corresp="note-0697-01a" n="*" anchored="true" place="margin">243. 929.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce omnibus ſequitur Planetas in principio, ad diſ-<lb />
<ptr xml:id="note-0697-02a" corresp="note-0697-02" type="noteAnchor" />
tantias ad quas à Sole moventur, ſemel projectos, in moti-<lb />bus, legibus ante expoſitis, perſeverare; </s>
          <s xml:space="preserve">excentricitatemque <lb />orbitarum pendere à celeritate, &amp; </s>
          <s xml:space="preserve">directione primæ projec-<lb />tionis. </s>
          <s xml:space="preserve">Motus autem hi diutiſſimè conſervari poſſunt, prop-<lb />ter materiæ coeleſtis exiguam reſiſtentiam.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0697-02" corresp="note-0697-02a" place="margin">1275.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Patet etiam, quare lineis ad centrum Solis ductis deſcribant <lb />areas temporibus proportionales; </s>
          <s xml:space="preserve">quia nempe cæteræ gravi-<lb />tates in Syſtemate exiguæ ſunt, reſpectu gravitatis verſus So-<lb />lem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideòque hac ſolâ in orbitis retinentur Planetæ, un-
<ptr xml:id="note-0697-03a" corresp="note-0697-03" type="noteAnchor" />
de hæc arearum proportio ſequitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Motus etiam in li-
<ptr xml:id="note-0697-04a" corresp="note-0697-04" type="noteAnchor" />
neis Ellipticis lentiſſimè tranſlatis, ex lege gravitatis ſequitur; <lb /></s>
          <s xml:space="preserve">hæ enim immobiles eſſent, ſi in Solem tantùm graves eſſent <lb />Planetæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ex actione autem mutuâ Planetarum lenta orbium
<ptr xml:id="note-0697-05a" corresp="note-0697-05" type="noteAnchor" />
agitatio deducitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Quod autem ſpectat proportionem,
<ptr xml:id="note-0697-06a" corresp="note-0697-06" type="noteAnchor" />
quæ inter cubos diſtantiarum &amp; </s>
          <s xml:space="preserve">temporum periodicorum <lb />quadrata obſervatur, ſequitur hæc quoque ex gravitatis le-<lb />ge <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ita ut ſi hiſce addamus, quæ de deflectione Saturni dixi-
<ptr xml:id="note-0697-07a" corresp="note-0697-07" type="noteAnchor" />
mus <ptr type="noteAnchor" />, nihil explicandum ſuperſit, circa motum Planetarum
<ptr xml:id="note-0697-08a" corresp="note-0697-08" type="noteAnchor" />
primariorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0697-03" corresp="note-0697-03a" n="*" anchored="true" place="margin">1265.</note>
              <note xml:space="preserve" xml:id="note-0697-04" corresp="note-0697-04a" n="*" anchored="true" place="margin">225.</note>
              <note xml:space="preserve" xml:id="note-0697-05" corresp="note-0697-05a" n="*" anchored="true" place="margin">241. 1208.</note>
              <note xml:space="preserve" xml:id="note-0697-06" corresp="note-0697-06a" n="*" anchored="true" place="margin">1274.</note>
              <note xml:space="preserve" xml:id="note-0697-07" corresp="note-0697-07a" n="*" anchored="true" place="margin">239. 1208.</note>
              <note xml:space="preserve" xml:id="note-0697-08" corresp="note-0697-08a" n="*" anchored="true" place="margin">1217. 1270.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Cometarum motus à lege Gravitatis pendere, etiam ex ob-<lb />
<ptr xml:id="note-0697-09a" corresp="note-0697-09" type="noteAnchor" />
ſervationibus deducitur; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">horum reſpectu, ut circa Pla-<lb />netas dictum, Solis gravitas prævalet, &amp; </s>
          <s xml:space="preserve">hac gravitate à <lb />viâ rectâ deflectuntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">viæ autem curvaturam ab hac eâ-
<ptr xml:id="note-0697-10a" corresp="note-0697-10" type="noteAnchor" />
dem gravitate etiam pendere ex eo ſequitur, quod corpus <lb />ex hac gravitate deſcribat aut Ellipſin, aut Parabolam aut Hy-<lb />perbolam <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quales lineas deſcripſiſſe hos Cometas conſtat,
<ptr xml:id="note-0697-11a" corresp="note-0697-11" type="noteAnchor" />
quorum Trajectoriæ fuere determinatæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0697-09" corresp="note-0697-09a" place="margin">1276.</note>
              <note xml:space="preserve" xml:id="note-0697-10" corresp="note-0697-10a" n="*" anchored="true" place="margin">980. 226.</note>
              <note xml:space="preserve" xml:id="note-0697-11" corresp="note-0697-11a" n="*" anchored="true" place="margin">241. 1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Satellites Jovis &amp; </s>
          <s xml:space="preserve">Saturni circa primarios iiſdem legibus <lb />
<ptr xml:id="note-0697-12a" corresp="note-0697-12" type="noteAnchor" />
moventur, quibus primarii circa Solem rotantur <ptr type="noteAnchor" />, quare mo-
<ptr xml:id="note-0697-13a" corresp="note-0697-13" type="noteAnchor" />
</s>
          <pb facs="0698" n="(170)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tuum horum explicatio <ptr type="noteAnchor" /> ad illos etiam referri poteſt, nam
<ptr xml:id="note-0698-01a" corresp="note-0698-01" type="noteAnchor" />
in tribus hiſce caſibus, circa Solem, Jovem &amp; </s>
          <s xml:space="preserve">Saturnum, <lb />dantur corpora minora, ad varias diſtantias, circa corpus <lb />multò majus revolventia.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0697-12" corresp="note-0697-12a" place="margin">1277.</note>
              <note xml:space="preserve" xml:id="note-0697-13" corresp="note-0697-13a" n="*" anchored="true" place="margin">944. 966. 974.</note>
              <note xml:space="preserve" xml:id="note-0698-01" corresp="note-0698-01a" n="*" anchored="true" place="margin">1275.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Dum ſecundarii circa primarium rotantur, omnes motu <lb />
<ptr xml:id="note-0698-02a" corresp="note-0698-02" type="noteAnchor" />
communi moveri poſſe, clarum eſt, quo non turbantur mo-<lb />tus reſpectivi, quibus inter ſe agitantur, quia diverſis impreſ-<lb />ſionibus corpus eodem tempore ferri poteſt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Motus pri-
<ptr xml:id="note-0698-03a" corresp="note-0698-03" type="noteAnchor" />
mario cum ſatellitibus ſuis communis, eſt motus primarii circa <lb />Solem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0698-02" corresp="note-0698-02a" place="margin">1278.</note>
              <note xml:space="preserve" xml:id="note-0698-03" corresp="note-0698-03a" n="*" anchored="true" place="margin">125.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Turbantur tamen ſecundariorum motus ex Solis actione, ver-<lb />
<ptr xml:id="note-0698-04a" corresp="note-0698-04" type="noteAnchor" />
ſus quem pro vario ſitu nunc primario celerius, nunc tardius <lb />feruntur, plerumque etiam per directiones diverſas in cen-<lb />tro Solis concurrentes; </s>
          <s xml:space="preserve">hæ irregularites, quæ exiguæ ſunt, <lb />in ſatellitibus Saturni &amp; </s>
          <s xml:space="preserve">Jovis obſervari non poſſunt, licètre-<lb />verâ ſimiles ſint illis, quæ in motu Lunæ obſervantur; </s>
          <s xml:space="preserve">mini-<lb />ma hujus deviatio nobis admodum eſt ſenſibilis; </s>
          <s xml:space="preserve">exactiſſimè <lb />autem Lunæ irregularitates ex Theoriâ gravitatis ſequi, in ca-<lb />pite ſequenti patebit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0698-04" corresp="note-0698-04a" place="margin">1279.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVI.</head>
        <head rend="italics" xml:space="preserve">Motus Lunæ Explicatio Phyſica.</head>
        <p>
          <s xml:space="preserve">LUnam &amp; </s>
          <s xml:space="preserve">Tellurem ſemel projectas, circa commune gravi-<lb />
<ptr xml:id="note-0698-05a" corresp="note-0698-05" type="noteAnchor" />
tatis centrum in motu perſeverare poſſe conſtat <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Si im-
<ptr xml:id="note-0698-06a" corresp="note-0698-06" type="noteAnchor" />
preſſione communi quacunque ferantur, per lineas rectas pa-<lb />rallelas inter ſe, ut de ſatellitibus Jovis &amp; </s>
          <s xml:space="preserve">Saturni dictum <ptr type="noteAnchor" />,
<ptr xml:id="note-0698-07a" corresp="note-0698-07" type="noteAnchor" />
motus hic non turbabit motum circa centrum commune gra-<lb />vitatis, quod ſolum directionem hanc ſequetur; </s>
          <s xml:space="preserve">quia reſ-<lb />pectu amborum corporum quieſcit. </s>
          <s xml:space="preserve">Corpora verò motu com-<lb />poſito, ex hac impreſſione &amp; </s>
          <s xml:space="preserve">motu circa commune gravitatis <lb />centrum feruntur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt circa hoc tranſlatum girantur, ut
<ptr xml:id="note-0698-08a" corresp="note-0698-08" type="noteAnchor" />
circa idem quieſcens ante hujus motum. </s>
          <s xml:space="preserve">Si omnibus mo-<lb />mentis novæ impreſſiones, communes ambobus corporibus, <lb />in hæc agant, poterit omnibus momentis mutari via centri <lb />gravitatis, quæ mutatio ſimilis erit illi, quam ſubirent cor-<lb />pora ipſa, ſi motu reſpectivo carêrent.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0698-05" corresp="note-0698-05a" place="margin">1280.</note>
              <note xml:space="preserve" xml:id="note-0698-06" corresp="note-0698-06a" n="*" anchored="true" place="margin">1263.</note>
              <note xml:space="preserve" xml:id="note-0698-07" corresp="note-0698-07a" n="*" anchored="true" place="margin">1278.</note>
              <note xml:space="preserve" xml:id="note-0698-08" corresp="note-0698-08a" n="*" anchored="true" place="margin">190.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0699" n="(171)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. XVI.</fw>
        <p>
          <s xml:space="preserve">Exhiſce deducimus, ſi, dum Luna &amp; </s>
          <s xml:space="preserve">Tellus circa commu-<lb />ne centrum gravitatis in gyrum moventur, ambæ proji-<lb />ciantur, viam centri gravitatis ex actione Solis, in utrum-<lb />que corpus agenti, illam eſſe, quam corpus, eodem modo <lb />projectum, circa Solem deſcribere poſſet.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Unde ſequitur Lunam motum Telluris turbare, &amp; </s>
          <s xml:space="preserve">cen-<lb />
<ptr xml:id="note-0699-01a" corresp="note-0699-01" type="noteAnchor" />
trum commune gravitatis borum corporum de ſcribere orbitam, <lb />circa Solem, quam buc uſque à Tellure ipſâ deſcriptam dixi-<lb />mus; </s>
          <s xml:space="preserve">quia ad actionem Lunæ huc uſque non attendimus; <lb /></s>
          <s xml:space="preserve">Tellus autem deſcribit curvam irregularem. </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0699-02a" corresp="note-0699-02" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0699-01" corresp="note-0699-01a" place="margin">1281.</note>
              <note xml:space="preserve" xml:id="note-0699-02" corresp="note-0699-02a" place="margin">1282.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſito Sole in S; </s>
          <s xml:space="preserve">ſit, in F, centrum commune gravita-<lb />
<ptr xml:id="note-0699-03a" corresp="note-0699-03" type="noteAnchor" />
tis Lunæ Q &amp; </s>
          <s xml:space="preserve">Telluris M, in Plenilunio: </s>
          <s xml:space="preserve">poſt integram Lu-<lb />
<ptr xml:id="note-0699-04a" corresp="note-0699-04" type="noteAnchor" />
<ptr xml:id="note-0699-05a" corresp="note-0699-05" type="noteAnchor" />
nationem, id eſt iterum in Plenilunio, ſit hocce centrum in <lb />A; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſit FDA orbita, quam Telluris vocamus, &amp; </s>
          <s xml:space="preserve">in qua <lb />memoratum centrum gravitatis reverâ movetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0699-03" corresp="note-0699-03a" place="margin">1283.</note>
              <note xml:space="preserve" xml:id="note-0699-04" corresp="note-0699-04a" place="margin">TAB. XXIV.</note>
              <note xml:space="preserve" xml:id="note-0699-05" corresp="note-0699-05a" place="margin">fig. 4.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Lunatio hæc diviſa in quatuor partes æquales; </s>
          <s xml:space="preserve">poſt <lb />primam centrum gravitatis erit in E, Luna in P, Tellus in <lb />L; </s>
          <s xml:space="preserve">lapsâ ſecundâ temporis parte, in Novilunio, centrum <lb />gravitatis erit in D, Luna in R, Tellus in I; </s>
          <s xml:space="preserve">in quadraturâ <lb />ſequenti, centrum gravitatis erit in B, Luna in O, Tellus <lb />in H; </s>
          <s xml:space="preserve">tandem in Plenilunio poſito centro gravitatis in A, <lb />Luna erit in N, Tellus in G: </s>
          <s xml:space="preserve">quæ omnia ſequuntur ex re-<lb />volutione Telluris &amp; </s>
          <s xml:space="preserve">Lunæ circa commune centrum gravi-<lb />tatis, dum hoc in orbitâ circa Solem movetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Videmus ergo Tellurem moveri in curvâ MLIHG, quæ <lb />in ſingulis Lunationibus bis inflectitur, quæ curva etiam in <lb />ſe non redit, quia inflectiones, in variis revolutionibus circa <lb />Solem, non coincidunt; </s>
          <s xml:space="preserve">quia duodecim Lunationes cum <lb />tertiâ parte circiter ſingulis annis abſolvuntur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Irregularitas hæc motus Telluris, quæ ex legibus Naturæ <lb />
<ptr xml:id="note-0699-06a" corresp="note-0699-06" type="noteAnchor" />
deducitur, nimium eſt exigua, ut in obſervationibus Aſtro-<lb />nomicis ſenſibilis ſit; </s>
          <s xml:space="preserve">quare ſine errore ponimus, centrum ip-<lb />ſum Telluris orbitam FDA percurrere; </s>
          <s xml:space="preserve">nam MF, aut <lb />DI, diſtantia maxima Telluris ab hac orbitâ, eſt circiter <lb />pars quadrageſima diſtantiæ MR, quæ ipſa non eſt trecen-<lb />teſima pars diſtantiæ FS.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0699-06" corresp="note-0699-06a" place="margin">1284.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Etiam, in explicandis quæ Lunam ſpectant, negligimus con-<lb />
<ptr xml:id="note-0699-07a" corresp="note-0699-07" type="noteAnchor" />
</s>
          <pb facs="0700" n="(172)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſiderationem motus Telluris, circa ſæpius memoratum cen-<lb />trum gravitatis; </s>
          <s xml:space="preserve">ſed ponimus banc revolvere ad diſtantiam <lb />à centro Telluris 60. </s>
          <s xml:space="preserve">ſemid.</s>
          <s xml:space="preserve">; quia, ut antea demonſtravi-<lb />mus <ptr type="noteAnchor" />, ad hanc diſtantiam, in ſuo tempore periodico, re-
<ptr xml:id="note-0700-01a" corresp="note-0700-01" type="noteAnchor" />
volvere poſſet circa Tellurem quieſcentem, aut tranſlatam <lb />in orbitâ, in qua ex Lunæ actione non turbatur Tel-<lb />lus. </s>
          <s xml:space="preserve">Multo facilius hac methodo Lunæ irregularitates de-<lb />teguntur, quæ eædem ſunt, ut facile patet, ſive Luna circa <lb />commune centrum gravitatis Lunæ &amp; </s>
          <s xml:space="preserve">Telluris, ſive circa ip-<lb />ſum Telluris centrum rotetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0699-07" corresp="note-0699-07a" place="margin">1285.</note>
              <note xml:space="preserve" xml:id="note-0700-01" corresp="note-0700-01a" n="*" anchored="true" place="margin">1253.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit Sol S; </s>
          <s xml:space="preserve">Tellus in T; </s>
          <s xml:space="preserve">Lunæ orbita AL Bl; </s>
          <s xml:space="preserve">Tandem <lb />
<ptr xml:id="note-0700-02a" corresp="note-0700-02" type="noteAnchor" />
detur Luna in A in quadraturâ; </s>
          <s xml:space="preserve">per AS verſus Solem ten-<lb />
<ptr xml:id="note-0700-03a" corresp="note-0700-03" type="noteAnchor" />
<ptr xml:id="note-0700-04a" corresp="note-0700-04" type="noteAnchor" />
dit, eodem modo, &amp; </s>
          <s xml:space="preserve">eâdem cum vi, qua Tellus, verſus <lb />S per TS fertur; </s>
          <s xml:space="preserve">quia diſtantiæ AS &amp; </s>
          <s xml:space="preserve">TS ſunt æquales: <lb /></s>
          <s xml:space="preserve">repræſentetur vis hæc per TS aut AS poterit vis, qua Lu-<lb />na conatur deſcendere per AS, reſolvi in duas, formato <lb />parallelogrammo ADST; </s>
          <s xml:space="preserve">ita ut Luna conetur moveri per <lb />AD &amp; </s>
          <s xml:space="preserve">AT, viribus, quæ hiſce lineis repræſentantur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0700-02" corresp="note-0700-02a" place="margin">1286.</note>
              <note xml:space="preserve" xml:id="note-0700-03" corresp="note-0700-03a" place="margin">TAB. XXV.</note>
              <note xml:space="preserve" xml:id="note-0700-04" corresp="note-0700-04a" place="margin">fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">192.</note>
        <p>
          <s xml:space="preserve">Vi per AD agenti, Luna eâdem cum celeritate, &amp; </s>
          <s xml:space="preserve">ver-<lb />ſus eandem partem cum Tellure fertur; </s>
          <s xml:space="preserve">propter lineas paral-<lb />lelas &amp; </s>
          <s xml:space="preserve">æquales TS &amp; </s>
          <s xml:space="preserve">AD; </s>
          <s xml:space="preserve">quare ex hoc motu relatioin-<lb />ter Lunam &amp; </s>
          <s xml:space="preserve">Tellurem non mutatur; </s>
          <s xml:space="preserve">vis autem per AT <lb />cum gravitate Lunæ in Tellurem conſpirat, &amp; </s>
          <s xml:space="preserve">augetur gra-<lb />
<ptr xml:id="note-0700-06a" corresp="note-0700-06" type="noteAnchor" />
vitas hæc ex actione Solis, quando Luna in quadraturis da-<lb />tur: </s>
          <s xml:space="preserve">eſtque augmentum ad Telluris gravitatem in Solem, ut <lb />AT, Lunæ diſtantia à Tellure, ad TS, Telluris diſtantiam <lb />à Sole.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0700-06" corresp="note-0700-06a" place="margin">1287.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Manente TS, Telluris diſtantiâ à Sole, creſcit &amp; </s>
          <s xml:space="preserve">minui-<lb />
<ptr xml:id="note-0700-07a" corresp="note-0700-07" type="noteAnchor" />
tur augmentum memoratum gravitatis in ratione lineæ AT, <lb />diſtantiæ Lunæ à Tellure.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0700-07" corresp="note-0700-07a" place="margin">1288.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Manente autem hac Lunæ diſtantiâ à Tellure AT, ſi au-<lb />geatur TS minor erit AT reſpectu AS; </s>
          <s xml:space="preserve">ideo licèt non mu-<lb />taretur vis, qua Tellus &amp; </s>
          <s xml:space="preserve">Luna verſus Solem cadunt, aug-<lb />mentum minus erit, &amp; </s>
          <s xml:space="preserve">eo minus, quo major eſt TS, id eſt, <lb />erit inverſè ut TS; </s>
          <s xml:space="preserve">vis autem gravitatis non manet, quando <lb />TS augetur, ſed minuitur; </s>
          <s xml:space="preserve">quare &amp; </s>
          <s xml:space="preserve">eo reſpectu minuitur <lb />augmentum memoratum, &amp; </s>
          <s xml:space="preserve">quidem in eâdem ratione cum
</s>
          <pb facs="0701" />
          <s xml:space="preserve">
<pb facs="0701a" />
<ptr xml:id="fig-0701a-01a" corresp="fig-0701a-01" type="figureAnchor" />
<pb facs="0702" />
<pb facs="0703" n="(173)" /><fw type="head">MATHEMATICA LIB. IV. CAP. XVI.</fw>
hac vi gravitatis; </s>
          <s xml:space="preserve">ideòque in ratione inverſa # ; </s>
          <s xml:space="preserve">quadrati diſ-<lb />tantiæ TS <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi hæc diminutio cum ſtatim memoratâ con-
<ptr xml:id="note-0703-01a" corresp="note-0703-01" type="noteAnchor" />
jungatur, videmus augmentum, de quo agimus, ſequi ratio-<lb />
<ptr xml:id="note-0703-02a" corresp="note-0703-02" type="noteAnchor" />
nem inverſam cubi diſtantiæ Telluris à Sole.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <figure xml:id="fig-0701a-01" corresp="fig-0701a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0701a-01" />
                <label>0701a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0703-01" corresp="note-0703-01a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0703-02" corresp="note-0703-02a" place="margin">1289.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Manente Telluris à Sole diſtantiá, Lunæ gravitas in Tel-<lb />
<ptr xml:id="note-0703-03a" corresp="note-0703-03" type="noteAnchor" />
lurem lentius in Quadraturis decreſcit, quàm pro ratione <lb />inverſâ Quadrati diſtantiæ à Telluris centro; </s>
          <s xml:space="preserve">nam ſi aug-<lb />mentum, in hoc caſu, ſequeretur inverſam hanc rationem <lb />quadrati diſtantiæ, quam ſequitur gravitas ex Telluris actione <ptr type="noteAnchor" />,
<ptr xml:id="note-0703-04a" corresp="note-0703-04" type="noteAnchor" />
non turbaretur hæc ratio; </s>
          <s xml:space="preserve">augmentum verò creſcit, dum gra-<lb />vitas ipſa minuitur; </s>
          <s xml:space="preserve">quare augmentum, quando diſtantia au-<lb />getur, ſemper majus eſt quàm requiritur, ideòque diminutio <lb />minor.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0703-03" corresp="note-0703-03a" place="margin">1290.</note>
              <note xml:space="preserve" xml:id="note-0703-04" corresp="note-0703-04a" n="*" anchored="true" place="margin">1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Augmentum hoc determinatur in mediis Lunæ à Tellure <lb />
<ptr xml:id="note-0703-05a" corresp="note-0703-05" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">hujus à Sole diſtantiis: </s>
          <s xml:space="preserve">ſint AT &amp; </s>
          <s xml:space="preserve">TS hæ diſtantiæ <lb />mediæ; </s>
          <s xml:space="preserve">eſt augmentum quæſitum ad gravitatem Telluris in <lb />Solem ut AT ad TS <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eſt etiam hæc gravitas Telluris in
<ptr xml:id="note-0703-06a" corresp="note-0703-06" type="noteAnchor" />
Solem ad gravitatem Lunæ in Tellurem, (quia corpora hæc <lb />hiſce gravitatibus in orbitis retinentur) directè ut TS ad <lb />TA, &amp; </s>
          <s xml:space="preserve">inverſè ut quadrata temporum periodicorum Tellu-<lb />ris circa Solem &amp; </s>
          <s xml:space="preserve">Lunæ circa Tellurem <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">eſt idcirco aug-
<ptr xml:id="note-0703-07a" corresp="note-0703-07" type="noteAnchor" />
mentum quæſitum ad gravitatem Lunæ in Tellurem, in ra-<lb />tione compoſitâ, ex hiſce rationibus; </s>
          <s xml:space="preserve">id eſt, in ratione me-<lb />moratâ inverſâ temporum periodicorum Telluris &amp; </s>
          <s xml:space="preserve">Lunæ, <lb />cæteris rationibus ſeſe mutuo deſtruentibus. </s>
          <s xml:space="preserve">Tempora hæc <lb />dantur &amp; </s>
          <s xml:space="preserve">ſunt inverſè horum quadrata ut 1. </s>
          <s xml:space="preserve">ad 178,73.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0703-05" corresp="note-0703-05a" place="margin">1291.</note>
              <note xml:space="preserve" xml:id="note-0703-06" corresp="note-0703-06a" n="*" anchored="true" place="margin">1287.</note>
              <note xml:space="preserve" xml:id="note-0703-07" corresp="note-0703-07a" n="*" anchored="true" place="margin">237. 1236.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit nunc Luna in L, in quo ſitu Sol Lunam &amp; </s>
          <s xml:space="preserve">Tellurem, <lb />
<ptr xml:id="note-0703-08a" corresp="note-0703-08" type="noteAnchor" />
per eandem lineam, ad ſe trahit, ſed non æqualiter; </s>
          <s xml:space="preserve">Lunam <lb />
<ptr xml:id="note-0703-09a" corresp="note-0703-09" type="noteAnchor" />
<ptr xml:id="note-0703-10a" corresp="note-0703-10" type="noteAnchor" />
majori cum vi, quia minus ab illo diſtat: </s>
          <s xml:space="preserve">differentia harum <lb />virium eſt vis, qua Luna à Tellure retrahitur, &amp; </s>
          <s xml:space="preserve">qua gravi-<lb />tas Lunæ in Tellurem minuitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0703-08" corresp="note-0703-08a" place="margin">1292.</note>
              <note xml:space="preserve" xml:id="note-0703-09" corresp="note-0703-09a" place="margin">TAB. XXV.</note>
              <note xml:space="preserve" xml:id="note-0703-10" corresp="note-0703-10a" place="margin">fig. 1.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vires, quibus Luna in L, &amp; </s>
          <s xml:space="preserve">Tellus in T, verſus Solem <lb />tendunt, ſunt inter ſe ut quadrata linearum ST &amp; </s>
          <s xml:space="preserve">SL <ptr type="noteAnchor" />,
<ptr xml:id="note-0703-11a" corresp="note-0703-11" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">differentia virium, id eſt vis turbans, ad vim qua Tellus <lb />verſus Solem deſcendit, ut differentia horum quadratorum ad <lb />quadratum lineæ LS, id eſt, quam proximè, ut dupla <lb />LT ad LS aut TS; </s>
          <s xml:space="preserve">nam hæ lineæ parum admodum inter
</s>
          <pb facs="0704" n="(174)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſe differunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">differentia quadratorum, quorum radices pa-<lb />
<ptr xml:id="note-0704-01a" corresp="note-0704-01" type="noteAnchor" />
rum inter ſe differunt, eſt ſervatâ proportione dupla illius, <lb />quæ inter radices datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0703-11" corresp="note-0703-11a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0704-01" corresp="note-0704-01a" place="margin">1293.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ergo TS, ut antea, repræſentet vim, qua Tellus ver-<lb />ſus Solem deſcendit, L l repræſentabit vim turbantem &amp; </s>
          <s xml:space="preserve"><lb />gravitatem minuentem, dum in quadraturis vis turbans per <lb />AT repræſentatur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1286.</note>
        <p>
          <s xml:space="preserve">Detur Luna in l; </s>
          <s xml:space="preserve">iterum cum Tellure, per eandem li-<lb />
<ptr xml:id="note-0704-03a" corresp="note-0704-03" type="noteAnchor" />
neam, à Sole attrahitur; </s>
          <s xml:space="preserve">ſed quia Tellus minus diſtat, cele-<lb />rius hæc verſus Solem movetur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ita ut deturvis, quæ Tel-
<ptr xml:id="note-0704-04a" corresp="note-0704-04" type="noteAnchor" />
lurem à Lunâ ſeparat, differentia nempe virium Lunam &amp; </s>
          <s xml:space="preserve"><lb />Tellurem trahentium; </s>
          <s xml:space="preserve">quæ vis cum gravitate Lunæ in Tel-<lb />lurem contrariè agit, &amp; </s>
          <s xml:space="preserve">hanc minuit; </s>
          <s xml:space="preserve">eodem modo ac ex <lb />majori gravitate Lunæ in Solem, poſitâ illâ in L, demon-<lb />ſtratum fuit. </s>
          <s xml:space="preserve">In L l etiam vis ſeparans à vi ſeparante in L vix <lb />differt; </s>
          <s xml:space="preserve">hæc enim ut vidimus proportionalis eſt differentiæ <lb />quadratorum linearum TS &amp; </s>
          <s xml:space="preserve">LS, &amp; </s>
          <s xml:space="preserve">illa, ut ſimili demon-<lb />ſtratione evincitur, differentiæ quadratorum linearum l S <lb />&amp; </s>
          <s xml:space="preserve">TS; </s>
          <s xml:space="preserve">quæ differentiæ, propter exiguam L l reſpectu TS, <lb />vixinter ſe differunt; </s>
          <s xml:space="preserve">ita ut vis, quæ minuit gravitatem Lunæ <lb />in l etiam repræſentetur per L l.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0704-03" corresp="note-0704-03a" place="margin">1294.</note>
              <note xml:space="preserve" xml:id="note-0704-04" corresp="note-0704-04a" n="*" anchored="true" place="margin">1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Major tamen paululum eſt vis perturbans in conjunctione in <lb />
<ptr xml:id="note-0704-05a" corresp="note-0704-05" type="noteAnchor" />
L, quam in oppoſitione in l; </s>
          <s xml:space="preserve">nam poſitis differentiis æqua-<lb />libus inter radices, quadrata ſervata proportione, eo magis <lb />differunt, quo minora ſunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſic ſervatâ proportione magis <lb />differunt vires in L &amp; </s>
          <s xml:space="preserve">T quam in T &amp; </s>
          <s xml:space="preserve">l, quæ etiam mi-<lb />nores ſunt <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0704-05" corresp="note-0704-05a" place="margin">1295.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1208.</note>
        <p>
          <s xml:space="preserve">Concludimus exhis, vim quæ in Syzygiis gravitatem Lunæ <lb />
<ptr xml:id="note-0704-07a" corresp="note-0704-07" type="noteAnchor" />
minuit, duplam eſſe illius, quæ banc auget in quadraturis; <lb /></s>
          <s xml:space="preserve">nempe ut L l ad AT. </s>
          <s xml:space="preserve">Quare in Syzygiis, Lunæ gravitas <lb />ex actione Solis minuitur parte, quæ eſt adtotam gravitatem, <lb />ut 1. </s>
          <s xml:space="preserve">ad 89, 36; </s>
          <s xml:space="preserve">nam in quadraturis augmentum gravitatis <lb />eſt ad ipſam, ut I. </s>
          <s xml:space="preserve">ad 178,73. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0704-07" corresp="note-0704-07a" place="margin">1296.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1291.</note>
        <p>
          <s xml:space="preserve">In Syzygiis vis perturbans ſequitur eandem proportionem <lb />
<ptr xml:id="note-0704-09a" corresp="note-0704-09" type="noteAnchor" />
cum ſemiſſe hujus, id eſt cum vi perturbante in quadratu-<lb />ris <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eſt ergo directè ut diſtantia Lunæ à Tellure <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in-
<ptr xml:id="note-0704-10a" corresp="note-0704-10" type="noteAnchor" />
<ptr xml:id="note-0704-11a" corresp="note-0704-11" type="noteAnchor" />
verſè ut cubus diſtantiæ Telluris à Sole <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0704-09" corresp="note-0704-09a" place="margin">1297.</note>
              <note xml:space="preserve" xml:id="note-0704-10" corresp="note-0704-10a" n="*" anchored="true" place="margin">1296.</note>
              <note xml:space="preserve" xml:id="note-0704-11" corresp="note-0704-11a" n="*" anchored="true" place="margin">1288.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1289.</note>
        <pb facs="0705" n="(175)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. XVI.</fw>
        <p>
          <s xml:space="preserve">In Syzygiis gravitas Lunæ in Tellurem, in receſſu illius <lb />
<ptr xml:id="note-0705-01a" corresp="note-0705-01" type="noteAnchor" />
ab bujus centro, magis minuitur, quam juxta rationem in-<lb />verſam quadrati diſtantiæ, ab hoc centro; </s>
          <s xml:space="preserve">in hac enim ra-<lb />tione minueretur, ſi vis ablatitia perturbans eandem ſeque-<lb />retur rationem; </s>
          <s xml:space="preserve">cùm autem hæc contra creſcat, quando diſ-<lb />tantia augetur <ptr type="noteAnchor" /> ſemper diminutio major eſt, quam juxta hanc
<ptr xml:id="note-0705-02a" corresp="note-0705-02" type="noteAnchor" />
rationem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0705-01" corresp="note-0705-01a" place="margin">1298.</note>
              <note xml:space="preserve" xml:id="note-0705-02" corresp="note-0705-02a" n="*" anchored="true" place="margin">129@.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Tandem ſit Luna in F, loco quocunque intermedio inter <lb />
<ptr xml:id="note-0705-03a" corresp="note-0705-03" type="noteAnchor" />
Quadraturam &amp; </s>
          <s xml:space="preserve">Syzygiam, verſus Solem trahitur per FS, <lb />
<ptr xml:id="note-0705-04a" corresp="note-0705-04" type="noteAnchor" />
à quo cùm minus diſtet, quàm Tellus T, majori cum vi <lb />
<ptr xml:id="note-0705-05a" corresp="note-0705-05" type="noteAnchor" />
quàm Tellus trahitur: </s>
          <s xml:space="preserve">Sit vis, quâ Luna ad Solem tendit, <lb />ad vim, quâ Tellus ad eundem fertur, ut FM ad TS, <lb />quæ etiam in præcedentibus, eandem Telluris gravitatem <lb />deſignat. </s>
          <s xml:space="preserve">Formetur Parallelogrammum FHMI, cujus dia-<lb />gonalis ſit FM, &amp; </s>
          <s xml:space="preserve">cujus latus FH ſit parallelum, &amp; </s>
          <s xml:space="preserve">æqua-<lb />le, lineæ TS. </s>
          <s xml:space="preserve">Motus Lunæ verſus Solem reſolvitur in <lb />duos, unum per FH, alterum per FI; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">hæ lineæ de-<lb />ſignant vires quibus Luna per ipſas moveri conatur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Mo-
<ptr xml:id="note-0705-06a" corresp="note-0705-06" type="noteAnchor" />
tus per FH communis eſt Lunæ &amp; </s>
          <s xml:space="preserve">Telluri, quæ, æquali <lb />vi per lineam huic parallelam, etiam ad Solem tendit; </s>
          <s xml:space="preserve">ita ut, <lb />hoc motu Lunæ, hujus ſitus reſpectu Telluris non mute-<lb />tur, &amp; </s>
          <s xml:space="preserve">vis perturbans ſit ſolus motus per FI.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0705-03" corresp="note-0705-03a" place="margin">1299.</note>
              <note xml:space="preserve" xml:id="note-0705-04" corresp="note-0705-04a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0705-05" corresp="note-0705-05a" place="margin">fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0705-06" corresp="note-0705-06a" n="*" anchored="true" place="margin">192.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propter immenſam Solis diſtantiam, pars MS lineæ MF <lb />exigua eſt reſpectu totius, &amp; </s>
          <s xml:space="preserve">angulus FST, ubi maximus <lb />eſt, ut AST, vix ſextam unius gradus partem ſuperat; </s>
          <s xml:space="preserve">un-<lb />de ſequitur, lineas MI &amp; </s>
          <s xml:space="preserve">SN admodum eſſe vicinas, punc-<lb />taque I &amp; </s>
          <s xml:space="preserve">N vix diſtare, &amp; </s>
          <s xml:space="preserve">ſine errore ſenſibili poſſe con-<lb />fundi; </s>
          <s xml:space="preserve">qui tamen error, quantumvis ſit contemnendus, in <lb />conſideratione integræ revolutionis, compenſatur errore <lb />contrario, poſitâ Lunâ in E. </s>
          <s xml:space="preserve">Vis ergo perturbans deſignatur <lb />per FN.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Notandum, quando lineæ ES ſola pars EF conſideratur, <lb />
<ptr xml:id="note-0705-07a" corresp="note-0705-07" type="noteAnchor" />
hane pro parallelâh aberi lineæ L l, propter exiguum angu-<lb />lum, quem hæ lineæ efficiunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0705-07" corresp="note-0705-07a" place="margin">1300.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex puncto N ducatur perpendiculum NQ ad lineam <lb />
<ptr xml:id="note-0705-08a" corresp="note-0705-08" type="noteAnchor" />
FT, continuatam ſi neceſſe fuerit, per quam Luna in Tel-<lb />lurem gravitat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">conſtruatur parallelogrammum FPNQ rec-
</s>
          <pb facs="0706" n="(176)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
tangulum; </s>
          <s xml:space="preserve">concipiamus vim per FN reſolutam in duas, per <lb />FQ &amp; </s>
          <s xml:space="preserve">FP agentes, &amp; </s>
          <s xml:space="preserve">hiſce lineis repræſentatas <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Vi, per
<ptr xml:id="note-0706-01a" corresp="note-0706-01" type="noteAnchor" />
FQ, vis gravitatis minuitur, in caſu hujus figuræ, augetur <lb />quando punctum Q inter F &amp; </s>
          <s xml:space="preserve">T cadit; </s>
          <s xml:space="preserve">vi autem per FP <lb />Luna in orbitâ trahitur verſus Syzygiam vicinam L, &amp; </s>
          <s xml:space="preserve">ac-<lb />celeratur aut retardatur Lunæ motus, pro ut vis hæc cum <lb />motu Lunæ conſpirat, aut contrariè agit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0705-08" corresp="note-0705-08a" place="margin">1301.</note>
              <note xml:space="preserve" xml:id="note-0706-01" corresp="note-0706-01a" n="*" anchored="true" place="margin">192.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In viciniis Syzygiæ minuitur Lunæ gravitas, &amp; </s>
          <s xml:space="preserve">linea FQ, <lb />quæ diminutionis hujus proportionem ſequitur, minuitur <lb />recedendo à Syzygiâ donec evaneſcat, ad diſtantiam ab hac <lb />54. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">44′.</s>
          <s xml:space="preserve">; ad majorem Lunæ à Syzygiâ diſtantiam Q inter <lb />F &amp; </s>
          <s xml:space="preserve">T cadit, &amp; </s>
          <s xml:space="preserve">ex Solis actione gravitas Lunæ in Tellurem <lb />augetur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vis per FP in Syzygiâ L nulla eſt, recedendo ab hac au-<lb />getur ad octantem uſque, punctum medium inter Syzygiam &amp; </s>
          <s xml:space="preserve"><lb />Quadraturam, minuitur iterum donec in B etiam nulla ſit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Inter B &amp; </s>
          <s xml:space="preserve">l aut l &amp; </s>
          <s xml:space="preserve">A, motus perturbantes eodem mo-<lb />
<ptr xml:id="note-0706-02a" corresp="note-0706-02" type="noteAnchor" />
do determinantur, ac in parte oppoſitâ inferiori ALB or-<lb />bitæ ; </s>
          <s xml:space="preserve">in E &amp; </s>
          <s xml:space="preserve">F æqualis eſt gravitatis diminutio, &amp; </s>
          <s xml:space="preserve">in illo <lb />ſitu æquali vi in orbitâ verſus Syzygiam l trahitur, quâ <lb />in F verſus Syzygiam L pellitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0706-02" corresp="note-0706-02a" place="margin">1302.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur, in motu Lunæ à Syzygiâ ad Quadra-<lb />
<ptr xml:id="note-0706-03a" corresp="note-0706-03" type="noteAnchor" />
turam, inter L &amp; </s>
          <s xml:space="preserve">B ut &amp; </s>
          <s xml:space="preserve">l &amp; </s>
          <s xml:space="preserve">A, gravitatem Lunæ in <lb />Tellurem continuò augeri &amp; </s>
          <s xml:space="preserve">Lunam in motu continuò retarda-<lb />ri. </s>
          <s xml:space="preserve">In motu autem à Quadratur â ad Syzygiam, inter B &amp; </s>
          <s xml:space="preserve"><lb />
<ptr xml:id="note-0706-04a" corresp="note-0706-04" type="noteAnchor" />
l ut &amp; </s>
          <s xml:space="preserve">A &amp; </s>
          <s xml:space="preserve">L, minuitur omnibus momentis Lunæ gravitas, <lb />&amp; </s>
          <s xml:space="preserve">bujus motus in orbitâ acceleratur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0706-03" corresp="note-0706-03a" place="margin">1303.</note>
              <note xml:space="preserve" xml:id="note-0706-04" corresp="note-0706-04a" place="margin">1304.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Determinantur vires à quibus eſfectus hi pendent, conferen-<lb />do has cum vi notâ, quâ gravitas in Quadraturis augetur <ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0706-05a" corresp="note-0706-05" type="noteAnchor" />
quæ per Lunæ diſtantiam à centro Telluris repræſentatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0706-05" corresp="note-0706-05a" n="*" anchored="true" place="margin">1291.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lineæ MI, HF, ST, ex conſtructione ſunt æquales; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0706-06a" corresp="note-0706-06" type="noteAnchor" />
ideò, cùm puncta I &amp; </s>
          <s xml:space="preserve">N confundantur, MN valet ST, &amp; </s>
          <s xml:space="preserve"><lb />MS æqualis eſt NT. </s>
          <s xml:space="preserve">Lineæ MF &amp; </s>
          <s xml:space="preserve">ST repræſentant vires, <lb />quibus Luna in F &amp; </s>
          <s xml:space="preserve">Tellus in T verſus Solem S feruntur; <lb /></s>
          <s xml:space="preserve">ſunt ergo ut quadratum lineæ TS ad quadratum lineæ FS <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0706-07a" corresp="note-0706-07" type="noteAnchor" />
quare, cùm FG ſit differentia harum linearum, differunt <lb />inter ſe FM &amp; </s>
          <s xml:space="preserve">TS duplâ GF <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">addendo GF li-
<ptr xml:id="note-0706-08a" corresp="note-0706-08" type="noteAnchor" />
</s>
          <pb facs="0707" n="(177)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XVI.</fw>
neæ FM, differentia inter GM &amp; </s>
          <s xml:space="preserve">TS, id eſt MS, <lb />erit tripla lineæ FG; </s>
          <s xml:space="preserve">quantum ergo etiam valet NT: <lb /></s>
          <s xml:space="preserve">FE autem eſt dupla FG <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò NT ad FE ut tria ad duo.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0706-06" corresp="note-0706-06a" place="margin">1305.</note>
              <note xml:space="preserve" xml:id="note-0706-07" corresp="note-0706-07a" n="*" anchored="true" place="margin">1208.</note>
              <note xml:space="preserve" xml:id="note-0706-08" corresp="note-0706-08a" n="*" anchored="true" place="margin">1293.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1300.</note>
        <p>
          <s xml:space="preserve">Continuetur FT, ſi neceſſè fuerit, &amp; </s>
          <s xml:space="preserve">ad hanc, ex E, <lb />ducatur perpendicularis EV; </s>
          <s xml:space="preserve">triangula EVF, &amp; </s>
          <s xml:space="preserve">NQT, <lb />rectangula, erunt ſimilia, propter angulos alternos VFE <lb />
<ptr xml:id="note-0707-02a" corresp="note-0707-02" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">QTN <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">Idcirco NT ad FE, id eſt, tria ad duo,
ut NQ, æqualis FP, ad EV; </s>
          <s xml:space="preserve">quæ ergo proportionalis <lb />eſt duabus tertiis partibus vis, quæ exprimitur per FP; </s>
          <s xml:space="preserve">ſed <lb />EV eſt ſinus anguli ETV ad centrum, dupli anguli <lb />EFV ad circumferentiam, æqualis angulo FTL, di-<lb />ſtantiæ Lunæ à Syzygiâ. </s>
          <s xml:space="preserve">Idcirco, ut radius, TA, aut <lb />
<ptr xml:id="note-0707-03a" corresp="note-0707-03" type="noteAnchor" />
TE, ad ſeſqui-ſinum duplæ diſtantiæ Lunæ à Syzygiâ, <lb />nempe FP, ita augmentum gravitatis in quadraturis, <lb />quod radio TA deſignatur, ad vim, quæ motum Lunæ in <lb />orbitâ accelerat aut retardat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0707-02" corresp="note-0707-02a" n="*" anchored="true" place="margin">1300.</note>
              <note xml:space="preserve" xml:id="note-0707-03" corresp="note-0707-03a" place="margin">1306.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Computatio diminutionis gravitatis, &amp;</s>
          <s xml:space="preserve">, in minori diſtantiâ <lb />à Quadraturis, hujus augmenti, exiiſdem principiis deducitur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Repræſentatur hæc diminutio lineâ FQ, quæ valet QT, <lb />minus radio; </s>
          <s xml:space="preserve">ſed ex conſideratione triangulorum ſtatim me-<lb />moratorum ſeſqui VF, valet QT; </s>
          <s xml:space="preserve">ideò ſeſqui VT plus <lb />dimidio radio deſignat diminutionem gravitatis quæſitam; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />radius eſt ad ſummam aut differentiam ſeſqui co-ſinus duplæ <lb />
<ptr xml:id="note-0707-04a" corresp="note-0707-04" type="noteAnchor" />
diſtantiæ Lunæ à Syzygiâ &amp; </s>
          <s xml:space="preserve">dimidii radii, ut augmentum <lb />gravitatis in Quadraturis ad diminutionem, aut augmentum, <lb />gravitatis in ſitu Lunæ de quo computatio initur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0707-04" corresp="note-0707-04a" place="margin">1307.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Differentiâ co-ſinus à dimidio radio utimur, quando an-<lb />gulus, cujus eſt co-ſinus, angulum rectum ſuperat; </s>
          <s xml:space="preserve">quia in <lb />hoc caſu utimur co-ſinu complementi anguli ad duos angu-<lb />los rectos; </s>
          <s xml:space="preserve">quando in hoc eodem caſu ſeſqui co-ſinus, quo <lb />utimur, ſemi-radium ſuperat, quantitas detecta eſt addititia, <lb />id eſt, gravitatem auget, quod ubique inter Quadraturam &amp; </s>
          <s xml:space="preserve"><lb />35. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">16′. </s>
          <s xml:space="preserve">ab hac obtinet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Vires hæ, quæcunque fuerint orbitæ Lunaris figura, exactè <lb />
<ptr xml:id="note-0707-05a" corresp="note-0707-05" type="noteAnchor" />
determinantur; </s>
          <s xml:space="preserve">nam conferuntur cum augmento gravitatis <lb />in Quadraturis, poſitâ Lunâ in Quadraturâ ad eandem diſtan-<lb />tiam à Tellure, ad quam reverâ datur in loco de quo agitur;</s>
          <s xml:space="preserve">
</s>
          <pb facs="0708" n="(178)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
augmentum vero hoc in omni Caſu detegitur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0707-05" corresp="note-0707-05a" place="margin">1308.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1291. 1288.</note>
        <p>
          <s xml:space="preserve">Licèt extra ſcopum hujus operis ſit, computum, motus Lunæ <lb />
<ptr xml:id="note-0708-02a" corresp="note-0708-02" type="noteAnchor" />
tradere, neceſſè duxi breviter exponere, quâ methodo vires, <lb />quibus Luna regitur, detegantur; </s>
          <s xml:space="preserve">quia eo facilius effectum <lb />generalem virium concipimus, quo exactius ipſas novimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0708-02" corresp="note-0708-02a" place="margin">1289.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut nunc motum Lunæ examinemus, ſingulatim hujus va-<lb />riæ irregularitates perpendendæ ſunt, quod ut ſine confuſio-<lb />ne fiat, varias removemus irregularitates &amp; </s>
          <s xml:space="preserve">concipimus Lu-<lb />nam, in circulo motam circa Tellurem, in quâ curvâ reti-<lb />neri poſſe ex gravitate conſtat <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ex actione Solis turba-
<ptr xml:id="note-0708-03a" corresp="note-0708-03" type="noteAnchor" />
tur hic motus, &amp; </s>
          <s xml:space="preserve">orbita magis convexa eſt in Quadraturis <lb />quàm in Syzygiis. </s>
          <s xml:space="preserve">Curvæ, à corpore vi centrali deſcriptæ, <lb />convexitas eo major eſt, quo vis centralis majori cum vi cor-<lb />pus omnibus momentis ex viâ detorquet; </s>
          <s xml:space="preserve">etiam eo major <lb />eſt, quo corpus lentius movetur, quia vis centralis diutius a-<lb />gens majorem edit effectum in inflectendâ corporis viâ. </s>
          <s xml:space="preserve">Ex <lb />cauſis contrariis minuitur convexitas curvæ. </s>
          <s xml:space="preserve">Ambæ con-<lb />currunt in augendâ orbitæ convexitate in Quadraturis <ptr type="noteAnchor" />, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0708-04a" corresp="note-0708-04" type="noteAnchor" />
hac minuendà in Syzygiis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0708-03" corresp="note-0708-03a" n="*" anchored="true" place="margin">241. 1208. <lb />1309.</note>
              <note xml:space="preserve" xml:id="note-0708-04" corresp="note-0708-04a" n="*" anchored="true" place="margin">1303.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1304.</note>
        <p>
          <s xml:space="preserve">Ex his ſequitur circularem orbitæ Lunaris figuram in ova-<lb />lem mutari, cujus major axis per Quadraturas tranſit; </s>
          <s xml:space="preserve">ut <lb />partes magis convexæ in Quadraturis dentur. </s>
          <s xml:space="preserve">Quare Luna <lb />
<ptr xml:id="note-0708-06a" corresp="note-0708-06" type="noteAnchor" />
minus à Tellure in Syzygiis, magis in Quadraturis diſtat; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve"><lb />non mirum Lunam ad Tellurem accedere, dum gravitas <lb />hujus minuitur; </s>
          <s xml:space="preserve">quia acceſſus non eſt effectus immediatus <lb />hujus diminutionis, ſed inflectionis orbitæ verſus Quadraturas.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0708-06" corresp="note-0708-06a" place="margin">1310.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Motus Lunæ, ſublatâ Solis actione, non eſt in circulo, ſed <lb />in Ellipſi, cujus focorum alter cum Telluris centro coincidit <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0708-07a" corresp="note-0708-07" type="noteAnchor" />
nam orbita Lunæ eſt excentrica &amp; </s>
          <s xml:space="preserve">vi gravitatis in hac retinetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0708-07" corresp="note-0708-07a" n="*" anchored="true" place="margin">967. 241. <lb />1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Demonſtrata ergo non exactè ad motum Lunæ applicari <lb />poſſunt; </s>
          <s xml:space="preserve">cùm autem vires, quæ deviationes explicatas gene-<lb />rant, in Lunam reverâ agant, Ellipſis, quam Luna ſub-<lb />lato Sole deſcriberet, mutatur, &amp;</s>
          <s xml:space="preserve">, cæteris paribus, propo-<lb />
<ptr xml:id="note-0708-08a" corresp="note-0708-08" type="noteAnchor" />
ſitiones n. </s>
          <s xml:space="preserve">1309. </s>
          <s xml:space="preserve">1310. </s>
          <s xml:space="preserve">ad Lunæ motum applicari poſſunt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0708-08" corresp="note-0708-08a" place="margin">1311.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Quadraturis &amp; </s>
          <s xml:space="preserve">Syzygiis, vis perturbans, cum vi gra-<lb />
<ptr xml:id="note-0708-09a" corresp="note-0708-09" type="noteAnchor" />
vitatis verſus Tellurem, in eâdem lineâ agit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideòque vis
<ptr xml:id="note-0708-10a" corresp="note-0708-10" type="noteAnchor" />
quæ continuò in Lunam agit, &amp; </s>
          <s xml:space="preserve">hanc in orbitâ retinet, ad cen-<lb />
<ptr xml:id="note-0708-11a" corresp="note-0708-11" type="noteAnchor" />
</s>
          <pb facs="0709" n="(179)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. VI. CAP. XVI.</fw>
trum Telluris dirigitur, &amp; </s>
          <s xml:space="preserve">Luna deſcribit areas, lineis ad <lb />hoc centrum ductis, temporibus proportionales <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0708-09" corresp="note-0708-09a" place="margin">1312.</note>
              <note xml:space="preserve" xml:id="note-0708-10" corresp="note-0708-10a" n="*" anchored="true" place="margin">1286. 1292.</note>
              <note xml:space="preserve" xml:id="note-0708-11" corresp="note-0708-11a" place="margin">1294.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">225.</note>
        <p>
          <s xml:space="preserve">In aliis orbitæ punctis, ut F, præter vim, quæ in Lineâ <lb />
<ptr xml:id="note-0709-02a" corresp="note-0709-02" type="noteAnchor" />
FT agit, datur &amp; </s>
          <s xml:space="preserve">alia, cujus directio ad FT eſt perpendi-<lb />
<ptr xml:id="note-0709-03a" corresp="note-0709-03" type="noteAnchor" />
<ptr xml:id="note-0709-04a" corresp="note-0709-04" type="noteAnchor" />
cularis <ptr type="noteAnchor" />, quæ hìc per FP repræſentatur: </s>
          <s xml:space="preserve">directio vis ex
<ptr xml:id="note-0709-05a" corresp="note-0709-05" type="noteAnchor" />
ambabus compoſita dirigitur paululum ad latus lineæ FT, <lb />&amp; </s>
          <s xml:space="preserve">non tendit ad Telluris centrum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare areæ lineis ad cen-
<ptr xml:id="note-0709-06a" corresp="note-0709-06" type="noteAnchor" />
trum Telluris ductis non ſunt exactè temporibus proportiona-<lb />les <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In octantibus FP eſt omnium maxima; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">vis, quæ
<ptr xml:id="note-0709-07a" corresp="note-0709-07" type="noteAnchor" />
per hanc lineam repræſentatur, eſt ad gravitatem Lunæ ver-<lb />ſus Tellurem, in hoc puncto, in mediis Lunæ &amp; </s>
          <s xml:space="preserve">Solis di-<lb />
<ptr xml:id="note-0709-08a" corresp="note-0709-08" type="noteAnchor" />
ſtantiis, ut 1. </s>
          <s xml:space="preserve">ad 119,49. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare directio vis compoſitæ, ex
actionibus Solis &amp; </s>
          <s xml:space="preserve">Telluris in Lunam, cum lineâ FT effi-<lb />cit angulum circiter ſemi gradus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0709-02" corresp="note-0709-02a" place="margin">1313.</note>
              <note xml:space="preserve" xml:id="note-0709-03" corresp="note-0709-03a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0709-04" corresp="note-0709-04a" place="margin">fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0709-05" corresp="note-0709-05a" n="*" anchored="true" place="margin">1301.</note>
              <note xml:space="preserve" xml:id="note-0709-06" corresp="note-0709-06a" n="*" anchored="true" place="margin">190.</note>
              <note xml:space="preserve" xml:id="note-0709-07" corresp="note-0709-07a" n="*" anchored="true" place="margin">226.</note>
              <note xml:space="preserve" xml:id="note-0709-08" corresp="note-0709-08a" n="*" anchored="true" place="margin">1306. 1307.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Variis irregularitatibus aliis ſubjicitur motus Lunæ, ita ut, <lb />curvam omnino irregularem deſcribat; </s>
          <s xml:space="preserve">quam ut computa-<lb />tionibus, quantum fieri poteſt exactiſſimis, ſubjiciant, ad El-<lb />
<ptr xml:id="note-0709-09a" corresp="note-0709-09" type="noteAnchor" />
lipſin reducunt Aſtronomi, quam variis motibus agitatam, <lb />etiam mutabilem, concipiunt, ne Luna banc deſerat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0709-09" corresp="note-0709-09a" place="margin">1314.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Circa vires centrales notavimus, corpus non deſcribere <lb />Ellipſin, ſi vis centralis, qua in orbitâ retinetur, in aliâ ra-<lb />tione decreſcat, quam in ratione inverſâ quadrati diſtantiæ; <lb /></s>
          <s xml:space="preserve">curvam tamen ſæpe poſſe reduci ad Ellipſin mobilem <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">cir-
<ptr xml:id="note-0709-10a" corresp="note-0709-10" type="noteAnchor" />
ca quod notandum Ellipſin, in hoc motu, circa focum rotari, <lb />
<ptr xml:id="note-0709-11a" corresp="note-0709-11" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">motum Ellipſeos dirigi ver ſus eandem partem, cummotu cor-<lb />poris in bac, quando vis centralis celerius decreſcit quàm <lb />pro ratione inverſâ quadrati diſtantiæ. </s>
          <s xml:space="preserve">Si autem vis cen-<lb />
<ptr xml:id="note-0709-12a" corresp="note-0709-12" type="noteAnchor" />
tralis tardius decreſcat in receſſu à centro, Ellipſis in con-<lb />trariam partem fertur; </s>
          <s xml:space="preserve">ut hæc Mathematicâ demonſtratio-<lb />ne conſtant.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0709-10" corresp="note-0709-10a" n="*" anchored="true" place="margin">243.</note>
              <note xml:space="preserve" xml:id="note-0709-11" corresp="note-0709-11a" place="margin">1315.</note>
              <note xml:space="preserve" xml:id="note-0709-12" corresp="note-0709-12a" place="margin">1316.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex hiſce ſequitur, Lunæ orbitam ad Ellipticam referri non <lb />poſſe, niſi quatuor motibus ſingulis revolutionibus hanc agi-<lb />tatam concipiamus; </s>
          <s xml:space="preserve">id eſt, niſi linea A pſidum, quæ per cen-<lb />trum Telluris tranſit, bis progrediatur, &amp; </s>
          <s xml:space="preserve">bis regrediatur.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Progrediuntur Apſides Lunâ in Syzygiis verſante <ptr type="noteAnchor" /> aut po-
<ptr xml:id="note-0709-13a" corresp="note-0709-13" type="noteAnchor" />
tius in motu Lunæ, inter puncta a Syzygiis 54. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">44′. </s>
          <s xml:space="preserve">dif-<lb />
<ptr xml:id="note-0709-14a" corresp="note-0709-14" type="noteAnchor" />
<ptr xml:id="note-0709-15a" corresp="note-0709-15" type="noteAnchor" />
tantia <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">In Quadraturis, &amp; </s>
          <s xml:space="preserve">inter puncta ab his diſtantia 35.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0709-16a" corresp="note-0709-16" type="noteAnchor" />
</s>
          <pb facs="0710" n="(180)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
gr. </s>
          <s xml:space="preserve">16′, Apſides regrediuntur, id eſt in antecedentiâ moventur <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0709-13" corresp="note-0709-13a" place="margin">1317.</note>
              <note xml:space="preserve" xml:id="note-0709-14" corresp="note-0709-14a" n="*" anchored="true" place="margin">1315. 1298.</note>
              <note xml:space="preserve" xml:id="note-0709-15" corresp="note-0709-15a" n="*" anchored="true" place="margin">1307.</note>
              <note xml:space="preserve" xml:id="note-0709-16" corresp="note-0709-16a" place="margin">1318.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1316. 1290. <lb />1307.</note>
        <p>
          <s xml:space="preserve">Vires à quibus progreſſus &amp; </s>
          <s xml:space="preserve">regreſſus Apſidum pendent <lb />
<ptr xml:id="note-0710-02a" corresp="note-0710-02" type="noteAnchor" />
ſunt vires motum Lunæ turbantes, antea explicatæ ; </s>
          <s xml:space="preserve">ideo, <lb />cùm vis turbans in Syzygiis, ſit dupla vis turbantis in Qua-<lb />draturis <ptr type="noteAnchor" />, progreſſus, integrâ conſideratâ Lunæ revolutione,
<ptr xml:id="note-0710-03a" corresp="note-0710-03" type="noteAnchor" />
regreſſum ſuperat, cæteris paribus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0710-02" corresp="note-0710-02a" place="margin">1319.</note>
              <note xml:space="preserve" xml:id="note-0710-03" corresp="note-0710-03a" n="*" anchored="true" place="margin">1296.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In circulo, cujus centrum in centro virium datur, diminu-<lb />tio vis, in receſſu à centro, nullum edit effectum; </s>
          <s xml:space="preserve">quia in <lb />hac lineâ non à centro recedit corpus; </s>
          <s xml:space="preserve">Idcirco effectus di-<lb />minutionis hujus eſt eo major, quo à tali circulo magis diſ-<lb />fert curva, quam corpus deſcribit.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">In orbitâ Ellipticâ, cujus Focorum alter cum virium cen-<lb />tro coincidit, curvatura in Apſidibus omnium maximè à tali <lb />
<ptr xml:id="note-0710-04a" corresp="note-0710-04" type="noteAnchor" />
circulo differt, &amp; </s>
          <s xml:space="preserve">effectus diminutionis vis in receſſu à vi-<lb />rium centro, eſt omniùm maximus. </s>
          <s xml:space="preserve">Si orbita hæc parum fue-<lb />
<ptr xml:id="note-0710-05a" corresp="note-0710-05" type="noteAnchor" />
rit excentrica, in extremitatibus axeos minoris parum ad-<lb />modum à circulo memorato differt Ellipſis, &amp; </s>
          <s xml:space="preserve">diminutionis <lb />effectus eſt omnium minimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0710-04" corresp="note-0710-04a" place="margin">1320.</note>
              <note xml:space="preserve" xml:id="note-0710-05" corresp="note-0710-05a" place="margin">1321.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Progreſſus, &amp; </s>
          <s xml:space="preserve">regreſſus, Apſidum pendent à proportio-<lb />
<ptr xml:id="note-0710-06a" corresp="note-0710-06" type="noteAnchor" />
ne, juxta quam decreſcit vis gravitatis recedendo à Tel-<lb />luris centro <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">eſt ideò effectus diminutionis vis centralis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0710-06" corresp="note-0710-06a" place="margin">1322.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1315. 1316.</note>
        <p>
          <s xml:space="preserve">Varias ſubit mutationes explicatus Apſidum motus; </s>
          <s xml:space="preserve">om-<lb />
<ptr xml:id="note-0710-08a" corresp="note-0710-08" type="noteAnchor" />
nium celerrimè progrediuntur Apſides, in Lunæ revolutione, <lb />
<ptr xml:id="note-0710-09a" corresp="note-0710-09" type="noteAnchor" />
poſitâ Apſidum lineâ in bis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in boc ipſo caſu omnium lentiſ-
<ptr xml:id="note-0710-10a" corresp="note-0710-10" type="noteAnchor" />
<ptr xml:id="note-0710-11a" corresp="note-0710-11" type="noteAnchor" />
ſimè, in eâdem revolutione remeant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quia, propter exiguam
<ptr xml:id="note-0710-12a" corresp="note-0710-12" type="noteAnchor" />
Lunæ excentricitatem, parum, ab extremitatibus axeos mi-<lb />
<ptr xml:id="note-0710-13a" corresp="note-0710-13" type="noteAnchor" />
noris orbitæ diſtant Quadraturæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0710-08" corresp="note-0710-08a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0710-09" corresp="note-0710-09a" place="margin">fig. 2.</note>
              <note xml:space="preserve" xml:id="note-0710-10" corresp="note-0710-10a" place="margin">1323.</note>
              <note xml:space="preserve" xml:id="note-0710-11" corresp="note-0710-11a" n="*" anchored="true" place="margin">1317. 1322.</note>
              <note xml:space="preserve" xml:id="note-0710-12" corresp="note-0710-12a" place="margin">1320.</note>
              <note xml:space="preserve" xml:id="note-0710-13" corresp="note-0710-13a" n="*" anchored="true" place="margin">1318. 1322. <lb />1321.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Poſitâ lineâ Apſiaum in Quadraturis, omnium minimè in <lb />
<ptr xml:id="note-0710-14a" corresp="note-0710-14" type="noteAnchor" />
Syzygiis in conſequentiâ feruntur Apſides <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">celerrimè au-
<ptr xml:id="note-0710-15a" corresp="note-0710-15" type="noteAnchor" />
<ptr xml:id="note-0710-16a" corresp="note-0710-16" type="noteAnchor" />
tem redeunt in Quadraturis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, in boc caſu, in integrâ
<ptr xml:id="note-0710-17a" corresp="note-0710-17" type="noteAnchor" />
Lunæ revolutione, regreſſus progreſſum ſuperat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0710-14" corresp="note-0710-14a" place="margin">1324.</note>
              <note xml:space="preserve" xml:id="note-0710-15" corresp="note-0710-15a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0710-16" corresp="note-0710-16a" place="margin">fig. 3.</note>
              <note xml:space="preserve" xml:id="note-0710-17" corresp="note-0710-17a" n="*" anchored="true" place="margin">1317. 1322.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">1321.</note>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1318. 1322.</note>
        <p>
          <s xml:space="preserve">Dum Tellus in orbitâ transfertur, linea Apſidum ſucceſ-<lb />
<ptr xml:id="note-0710-20a" corresp="note-0710-20" type="noteAnchor" />
ſivè omnes acquirit ſitus reſpectu Solis; </s>
          <s xml:space="preserve">quare plurimis re-<lb />
<ptr xml:id="note-0710-21a" corresp="note-0710-21" type="noteAnchor" />
volutionibus Lunæ ſimul conſideratis progrediuntur Apſides <ptr type="noteAnchor" />,
<ptr xml:id="note-0710-22a" corresp="note-0710-22" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">ex obſervationibus conſtat, in ſpatio circiter octo anno-<lb />rum lineam Apſidum integram peragere revolutionem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0710-20" corresp="note-0710-20a" place="margin">1320.</note>
              <note xml:space="preserve" xml:id="note-0710-21" corresp="note-0710-21a" place="margin">1325.</note>
              <note xml:space="preserve" xml:id="note-0710-22" corresp="note-0710-22a" n="*" anchored="true" place="margin">1319.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Orbitæ excentricitatem etiam inconſtantem eſſe diximus.</s>
          <s xml:space="preserve" />
        </p>
        <pb facs="0711" n="(181)" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. XVI.</fw>
        <p>
          <s xml:space="preserve">Augetur corporis excentricitas, ſi vis centralis, continuâ <lb />
<ptr xml:id="note-0711-01a" corresp="note-0711-01" type="noteAnchor" />
diminutione, celerius quàm ante decreſcat, dum corpus ab <lb />Apſide imâ ad Apſidem ſummam transfertur; </s>
          <s xml:space="preserve">tunc enim, om-<lb />nibus momentis, minus trahitur, quam ſi vis non decreſceret; <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò magis recedit. </s>
          <s xml:space="preserve">Augetur etiam eâdem orbitæ excentri-<lb />citas, in eodem caſu, in motu ab Apſide ſummâ adimam, quia <lb />in hoc caſu, acceſſu ad centrum, celerius creſcit vis, quo ma-<lb />gis verſus centrum deſcendit corpus; </s>
          <s xml:space="preserve">ita ut in utroque caſu <lb />differentia inter maximam &amp; </s>
          <s xml:space="preserve">minimam diſtantiam à centro vi-<lb />rium, major fiat, ideòque excentricitas augeatur. </s>
          <s xml:space="preserve">Simili ratio-<lb />
<ptr xml:id="note-0711-02a" corresp="note-0711-02" type="noteAnchor" />
cinio patet excentricitatem minui, quando vis centralis auge-<lb />tur, in motu corporis ab Abſide imâ ad ſummam, &amp; </s>
          <s xml:space="preserve">quando <lb />hæc minuitur in motu ab Apſide ſummâ ad imam, id eſt <lb />quando lentius decreſcit, quàm ante, inreceſſu à centro.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0711-01" corresp="note-0711-01a" place="margin">1326.</note>
              <note xml:space="preserve" xml:id="note-0711-02" corresp="note-0711-02a" place="margin">1327.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hiſce ad motum Lunæ applicatis, patet: </s>
          <s xml:space="preserve">Orbitæ excentrici-<lb />
<ptr xml:id="note-0711-03a" corresp="note-0711-03" type="noteAnchor" />
tatem, ſingulis revolutionibus, varias ſubire mutationes. </s>
          <s xml:space="preserve">Eſ-<lb />
<ptr xml:id="note-0711-04a" corresp="note-0711-04" type="noteAnchor" />
ſeomnium maximam, poſitâ lineâ Apſidum in Syzygiis; </s>
          <s xml:space="preserve">quia, vi-<lb />ribus in Apſidibus collatis, celerius decreſcunt quàm pro ra-<lb />tione inverſâ quadrati diſtantiæ <ptr type="noteAnchor" />, unde augmentum hoc ſe-
<ptr xml:id="note-0711-05a" corresp="note-0711-05" type="noteAnchor" />
quitur <ptr type="noteAnchor" />, quod in hoc ſitu prævalet <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Orbitam verò omnium
<ptr xml:id="note-0711-06a" corresp="note-0711-06" type="noteAnchor" />
minimè eſſe excentricam, verſante lineâ Apſidum in Quadra-<lb />
<ptr xml:id="note-0711-07a" corresp="note-0711-07" type="noteAnchor" />
turis, prævalente diminutione excentricitatis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0711-03" corresp="note-0711-03a" place="margin">1328.</note>
              <note xml:space="preserve" xml:id="note-0711-04" corresp="note-0711-04a" place="margin">1329.</note>
              <note xml:space="preserve" xml:id="note-0711-05" corresp="note-0711-05a" n="*" anchored="true" place="margin">1298.</note>
              <note xml:space="preserve" xml:id="note-0711-06" corresp="note-0711-06a" n="*" anchored="true" place="margin">1326.</note>
              <note xml:space="preserve" xml:id="note-0711-07" corresp="note-0711-07a" n="*" anchored="true" place="margin">1320.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1290. 1327.</note>
        <p>
          <s xml:space="preserve">Lunam diximus moveri in plano ad Eclipticæ planum in-<lb />
<ptr xml:id="note-0711-09a" corresp="note-0711-09" type="noteAnchor" />
clinatum; </s>
          <s xml:space="preserve">lineam Nodorum rotari in antecedentiâ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in-
<ptr xml:id="note-0711-10a" corresp="note-0711-10" type="noteAnchor" />
conſtantem eſſe Orbitæ inclinationem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">effectus hi ex actio-
<ptr xml:id="note-0711-11a" corresp="note-0711-11" type="noteAnchor" />
ne Solis in Lunam etiam deducuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0711-09" corresp="note-0711-09a" place="margin">1321.</note>
              <note xml:space="preserve" xml:id="note-0711-10" corresp="note-0711-10a" n="*" anchored="true" place="margin">970.</note>
              <note xml:space="preserve" xml:id="note-0711-11" corresp="note-0711-11a" n="*" anchored="true" place="margin">969.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Propter exiguam orbitæ Lunaris inclinationem, vires quas <lb />huc uſque in plano Eclipticæ agentes non attendendo ad or-<lb />bitæ inclinationem conſideravimus, ſine ſenſibili errore, ad <lb />orbitæ planum, referuntur, &amp; </s>
          <s xml:space="preserve">Luna, in hoc, motibus ante <lb />explicatis ſubjicitur: </s>
          <s xml:space="preserve">Sed datur vis, quæ Lunam ex plano or-<lb />
<ptr xml:id="note-0711-12a" corresp="note-0711-12" type="noteAnchor" />
bitæ removet; </s>
          <s xml:space="preserve">ita ut hoc planum agitatum concipere debea-<lb />mus, ne Luna orbitam deſerat <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0711-12" corresp="note-0711-12a" place="margin">1330.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1314.</note>
        <p>
          <s xml:space="preserve">Sit Luna in F; </s>
          <s xml:space="preserve">attendendo ad illa, quæ de actione Solis <lb />
<ptr xml:id="note-0711-14a" corresp="note-0711-14" type="noteAnchor" />
ſuperius dicta ſunt <ptr type="noteAnchor" />, liquet planum parallelogrammi FHMI
<ptr xml:id="note-0711-15a" corresp="note-0711-15" type="noteAnchor" />
<ptr xml:id="note-0711-16a" corresp="note-0711-16" type="noteAnchor" />
per lineam TS tranſire, quæ centra Solis &amp; </s>
          <s xml:space="preserve">Telluris jungit; <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0711-17a" corresp="note-0711-17" type="noteAnchor" />
ideòque in plano Eclipticæ datur; </s>
          <s xml:space="preserve">ita ut punctum N, ad <lb />quod dirigitur vis FN turbans ex actione Solis, in hoc pla-<lb />no detur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0711-14" corresp="note-0711-14a" place="margin">1331.</note>
              <note xml:space="preserve" xml:id="note-0711-15" corresp="note-0711-15a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0711-16" corresp="note-0711-16a" place="margin">fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0711-17" corresp="note-0711-17a" n="*" anchored="true" place="margin">1299.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0712" n="(182)" />
        <fw type="head">PHYSICES ELEMENTA</fw>
        <p>
          <s xml:space="preserve">Repræſentetur hæc eâdem vis per FI; </s>
          <s xml:space="preserve">in F ad orbitæ pla-<lb />
<ptr xml:id="note-0712-01a" corresp="note-0712-01" type="noteAnchor" />
num detur perpendicularis FR &amp; </s>
          <s xml:space="preserve">concipiatur parallelogram-<lb />
<ptr xml:id="note-0712-02a" corresp="note-0712-02" type="noteAnchor" />
<ptr xml:id="note-0712-03a" corresp="note-0712-03" type="noteAnchor" />
mum FRI i, cujus latus F i in plano orbitæ detur, &amp; </s>
          <s xml:space="preserve">cujus <lb />diagonalis ſit FI; </s>
          <s xml:space="preserve">vis turbans per F I reſolvitur in duas, per <lb />FR &amp; </s>
          <s xml:space="preserve">F i, quas hæ lineæ repræſentant <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">quarum hæc in
<ptr xml:id="note-0712-04a" corresp="note-0712-04" type="noteAnchor" />
plano orbitæ agit: </s>
          <s xml:space="preserve">ita ut ad hanc debeamus referre, quæ ſpec-<lb />tant vim turbantem, de qua in n. </s>
          <s xml:space="preserve">1299. </s>
          <s xml:space="preserve">egimus; </s>
          <s xml:space="preserve">lineæ enim F i <lb />&amp; </s>
          <s xml:space="preserve">FI vix differunt, &amp; </s>
          <s xml:space="preserve">planum parallelogrammi FRI i ad pla-<lb />num orbitæ Lunaris eſt perpendiculare.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0712-01" corresp="note-0712-01a" place="margin">1332.</note>
              <note xml:space="preserve" xml:id="note-0712-02" corresp="note-0712-02a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0712-03" corresp="note-0712-03a" place="margin">fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0712-04" corresp="note-0712-04a" n="*" anchored="true" place="margin">192.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Determinanda eſt linea FR, quæ repræſentat vim, quæ ad <lb />
<ptr xml:id="note-0712-05a" corresp="note-0712-05" type="noteAnchor" />
planum orbitæ perpendiculariter agit, &amp; </s>
          <s xml:space="preserve">Lunam ex hoc plano <lb />removet; </s>
          <s xml:space="preserve">relatio autem lineæ FR aut I i ad radium ET, eſt <lb />ratio vis turbantis, de qua hìc agitur, ad augmentum gravita-<lb />tis in Quadraturis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0712-05" corresp="note-0712-05a" place="margin">1333.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1286.</note>
        <p>
          <s xml:space="preserve">In caſu hujus figuræ in quâ linea Nodorum N n in Quadra-<lb />
<ptr xml:id="note-0712-07a" corresp="note-0712-07" type="noteAnchor" />
turis verſatur, detegitur FR; </s>
          <s xml:space="preserve">quia IT (quæ eſt NT fig. </s>
          <s xml:space="preserve">I.) <lb /></s>
          <s xml:space="preserve">datur <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">quia IT ad I i aut FR, ut radius ad ſinum in-
<ptr xml:id="note-0712-08a" corresp="note-0712-08" type="noteAnchor" />
clinationis crbitæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0712-07" corresp="note-0712-07a" place="margin">1334.</note>
              <note xml:space="preserve" xml:id="note-0712-08" corresp="note-0712-08a" n="*" anchored="true" place="margin">1305.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sed in omni caſu determinanda eſt vis, quæ Lunam ex pla-<lb />
<ptr xml:id="note-0712-09a" corresp="note-0712-09" type="noteAnchor" />
no pellit; </s>
          <s xml:space="preserve">ponamus ideò lineam Nodorum tranſlatam ad ſitum <lb />M m, quo, cæteris manentibus, mutatur I i. </s>
          <s xml:space="preserve">Ad m M con-<lb />tinuatam, ſi neceſſe fuerit, dentur perpendiculares i X &amp; </s>
          <s xml:space="preserve"><lb />IX, quæ angulum efficiunt æqualem inclinationi plani orbitæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0712-09" corresp="note-0712-09a" place="margin">1335.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ratio inter ET &amp; </s>
          <s xml:space="preserve">I i, id eſt ratio inter augmentum gravi-<lb />
<ptr xml:id="note-0712-10a" corresp="note-0712-10" type="noteAnchor" />
tatis in Quadraturis &amp; </s>
          <s xml:space="preserve">vim, quam quærimus, quæ Lunam ex <lb />orbitâ removet, eſt compoſita exrationibus lineæ ET ad TI, <lb />lineæ TI ad IX, &amp; </s>
          <s xml:space="preserve">tandem lineæ IX ad I i. </s>
          <s xml:space="preserve">Prima eſt ra-<lb />tio inter radium &amp; </s>
          <s xml:space="preserve">ter ſinum diſtantiæ Lunæ à Quadraturâ <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0712-11a" corresp="note-0712-11" type="noteAnchor" />
ſecunda eſt ratio radii ad ſinum anguli ITX, id eſt diſtantiæ <lb />Nodi à Syzygiâ; </s>
          <s xml:space="preserve">tertia tandem eſt ratio radii ad ſinum incli-<lb />nationis orbitæ: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ratio ex his compoſita, eſt ratio cubi radii <lb />ad ter productum ſinu m diſtantiarum Lunæ à Quadratur â, &amp; </s>
          <s xml:space="preserve"><lb />Nodi à Syzygiâ, ut &amp; </s>
          <s xml:space="preserve">inclinationis plani. </s>
          <s xml:space="preserve">Ad hanc vim etiam <lb />reſerendus n. </s>
          <s xml:space="preserve">1308.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0712-10" corresp="note-0712-10a" place="margin">1336.</note>
              <note xml:space="preserve" xml:id="note-0712-11" corresp="note-0712-11a" n="*" anchored="true" place="margin">1305.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis hæc in Quadraturis nulla eſt, quia punctum I cum <lb />
<ptr xml:id="note-0712-12a" corresp="note-0712-12" type="noteAnchor" />
puncto T, centro Telluris, coincidit, &amp; </s>
          <s xml:space="preserve">evaneſcit linea I i, li-<lb />neis FI &amp; </s>
          <s xml:space="preserve">F i concurrentibus, in plano orbitæ; </s>
          <s xml:space="preserve">quod etiam ex
</s>
          <pb facs="0713" n="(183)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XVI.</fw>
computatione memoratâ <ptr type="noteAnchor" /> ſequitur; </s>
          <s xml:space="preserve">evaneſcente ſinu diſtantiæ
<ptr xml:id="note-0713-01a" corresp="note-0713-01" type="noteAnchor" />
Lunæ à Quadraturâ; </s>
          <s xml:space="preserve">ideoque toto producto, quod per ſinum <lb />hunc multiplicatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0712-12" corresp="note-0712-12a" place="margin">1337.</note>
              <note xml:space="preserve" xml:id="note-0713-01" corresp="note-0713-01a" n="*" anchored="true" place="margin">1136.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Evaneſcit idem hoc productum, &amp; </s>
          <s xml:space="preserve">cum hoc vis, quam <lb />
<ptr xml:id="note-0713-02a" corresp="note-0713-02" type="noteAnchor" />
repræſentat, evaneſcente ſinu diſtantiæ Nodi à Syzygiâ, id <lb />
<ptr xml:id="note-0713-03a" corresp="note-0713-03" type="noteAnchor" />
<ptr xml:id="note-0713-04a" corresp="note-0713-04" type="noteAnchor" />
eſt, poſitâ lineâ Nodorum in Syzygiis; </s>
          <s xml:space="preserve">etiam hoc ex eo de-<lb />ducitur, quod linea Nodorum N n continuata per Solem tran-<lb />ſit; </s>
          <s xml:space="preserve">quare Sol in ipſo plano orbitæ datur; </s>
          <s xml:space="preserve">ideoque Lunam, <lb />niſi in hoc plano trahere non poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0713-02" corresp="note-0713-02a" place="margin">1338.</note>
              <note xml:space="preserve" xml:id="note-0713-03" corresp="note-0713-03a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0713-04" corresp="note-0713-04a" place="margin">Fig. 5.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Vis etiam, quam examinamus, augetur in acceſſu Lunæ ad <lb />
<ptr xml:id="note-0713-05a" corresp="note-0713-05" type="noteAnchor" />
Syzygiam, &amp; </s>
          <s xml:space="preserve">in receſſu Nodi ab hac. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /></s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0713-05" corresp="note-0713-05a" place="margin">1339.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1336.</note>
        <p>
          <s xml:space="preserve">Sit P p planum Eclipticæ; </s>
          <s xml:space="preserve">PA orbita Lunæ; </s>
          <s xml:space="preserve">ubi Lu-<lb />
<ptr xml:id="note-0713-07a" corresp="note-0713-07" type="noteAnchor" />
na ad A pervenit, id eſt paululum à Nodo receſſit, ex plano <lb />
<ptr xml:id="note-0713-08a" corresp="note-0713-08" type="noteAnchor" />
<ptr xml:id="note-0713-09a" corresp="note-0713-09" type="noteAnchor" />
orbitæ removetur, &amp; </s>
          <s xml:space="preserve">in ſecundo momento non per AB, con-<lb />tinuationem orbitæ PA, ſed per A b fertur; </s>
          <s xml:space="preserve">quia per B b ad <lb />planum Eclipticæ accedit; </s>
          <s xml:space="preserve">itaque movetur, quaſi ex Nodo ma-<lb />gis diſtante p procederet. </s>
          <s xml:space="preserve">Unde patet Nodos regredi, dum <lb />
<ptr xml:id="note-0713-10a" corresp="note-0713-10" type="noteAnchor" />
Luna in orbitâ movetur, quamdiu à Nodo recedit: </s>
          <s xml:space="preserve">etiam re-<lb />meant Nodi in acceſſu Lunæ ad Nodum oppoſitum; </s>
          <s xml:space="preserve">quia cùm <lb />Luna continuò ex orbitâ verſus planum Eclipticæ pellatur, <lb />continuò ad punctum minus diſtans dirigitur, &amp; </s>
          <s xml:space="preserve">citius ad No-<lb />dum pervenit, quàm ſi tali motu non agitata eâdem celeritate <lb />in motu continuaſſet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0713-07" corresp="note-0713-07a" place="margin">1340.</note>
              <note xml:space="preserve" xml:id="note-0713-08" corresp="note-0713-08a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0713-09" corresp="note-0713-09a" place="margin">Fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0713-10" corresp="note-0713-10a" place="margin">1341.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Integram conſiderando Lunæ revolutionem, cæteris pari-<lb />
<ptr xml:id="note-0713-11a" corresp="note-0713-11" type="noteAnchor" />
bus, celerrimè in antecedentiâ moventur Nodi, verſante <lb />Lunâ in Syzygiis <ptr type="noteAnchor" />, deinde lentius atque lentius, donec
<ptr xml:id="note-0713-12a" corresp="note-0713-12" type="noteAnchor" />
quieſcant, verſante Lunâ in Quadraturis <ptr type="noteAnchor" />,</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0713-11" corresp="note-0713-11a" place="margin">1342.</note>
              <note xml:space="preserve" xml:id="note-0713-12" corresp="note-0713-12a" n="*" anchored="true" place="margin">1339.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1337.</note>
        <p>
          <s xml:space="preserve">Dum Tellus circa Solem rotatur, etiam non attendendo ad <lb />motum ſtatim memoratum Nodorum, linea Nodorum ſuc-<lb />
<ptr xml:id="note-0713-14a" corresp="note-0713-14" type="noteAnchor" />
ceſſivè omnes ſitus poſſibiles acquirit reſpectu Solis; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">, ſin-<lb />gulis annis, bis per Syzygias, bis per Quadratur as tran-<lb />ſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0713-14" corresp="note-0713-14a" place="margin">1343.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Si nunc plurimas conſideremus Lunæ revolutiones, Nodi in <lb />
<ptr xml:id="note-0713-15a" corresp="note-0713-15" type="noteAnchor" />
integrâ revolutione celerrimè remeant, verſantibus No-<lb />dis in Quadraturis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">dein lentius, donec quieſcant, poſitâ
<ptr xml:id="note-0713-16a" corresp="note-0713-16" type="noteAnchor" />
lineâ Nodorum in Syzygiis <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0713-15" corresp="note-0713-15a" place="margin">1344.</note>
              <note xml:space="preserve" xml:id="note-0713-16" corresp="note-0713-16a" n="*" anchored="true" place="margin">1339.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1338.</note>
        <p>
          <s xml:space="preserve">Hac eadem vi, qua Nodi moventur, mutatur etiam orbitæ <lb />
<ptr xml:id="note-0713-18a" corresp="note-0713-18" type="noteAnchor" />
</s>
          <pb facs="0714" n="184" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
inclinatio; </s>
          <s xml:space="preserve">augetur in receſſu Lunæ à Nodo; </s>
          <s xml:space="preserve">minuitur in <lb />acceſſu ad Nodum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0713-18" corresp="note-0713-18a" place="margin">1345.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Angulus enim bp L, minor eſt angulo APL, &amp; </s>
          <s xml:space="preserve">eâdem <lb />
<ptr xml:id="note-0714-01a" corresp="note-0714-01" type="noteAnchor" />
de causâ continuo minuitur, &amp; </s>
          <s xml:space="preserve">inclinatio major fit; </s>
          <s xml:space="preserve">ubi autem <lb />
<ptr xml:id="note-0714-02a" corresp="note-0714-02" type="noteAnchor" />
<ptr xml:id="note-0714-03a" corresp="note-0714-03" type="noteAnchor" />
Luna ad maximam diſtantiam à plano Eclipticæ pervenit, &amp; </s>
          <s xml:space="preserve"><lb />ad Nodum oppoſitum accedit, continuò directio motus Lunæ <lb />verſus planum Eclipticæ inflectitur, &amp; </s>
          <s xml:space="preserve">minus ad hoc inclina-<lb />tur, quàm ſi in orbitâ motum continuaret: </s>
          <s xml:space="preserve">ſit Npn planum <lb />Eclipticæ; </s>
          <s xml:space="preserve">curva Nn orbita Lunæ; </s>
          <s xml:space="preserve">vi qua Luna continuo <lb />ex hac removetur, mutatur Lunæ via, &amp; </s>
          <s xml:space="preserve">percurrit curvam Np, <lb />quæ magis ad Npn in N inclinatur, quàm in p; </s>
          <s xml:space="preserve">ita ut pla-<lb />ni orbitæ inclinationem bis mutatam concipere debeamus <ptr type="noteAnchor" />, dum
<ptr xml:id="note-0714-04a" corresp="note-0714-04" type="noteAnchor" />
à Nodo ad Nodum movetur Luna: </s>
          <s xml:space="preserve">ideòque quater in ſingulis <lb />
<ptr xml:id="note-0714-05a" corresp="note-0714-05" type="noteAnchor" />
Lunæ revolutionibus, bis minuitur, bis iterum augetur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0714-01" corresp="note-0714-01a" place="margin">1346.</note>
              <note xml:space="preserve" xml:id="note-0714-02" corresp="note-0714-02a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0714-03" corresp="note-0714-03a" place="margin">fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0714-04" corresp="note-0714-04a" n="*" anchored="true" place="margin">1314.</note>
              <note xml:space="preserve" xml:id="note-0714-05" corresp="note-0714-05a" place="margin">1347.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Poſitis Nodis N, n, in Quadraturis, vires quæ in unicâ re-<lb />
<ptr xml:id="note-0714-06a" corresp="note-0714-06" type="noteAnchor" />
volutione augent inclinationem, &amp; </s>
          <s xml:space="preserve">hanc minuunt, ſunt æqua-<lb />
<ptr xml:id="note-0714-07a" corresp="note-0714-07" type="noteAnchor" />
<ptr xml:id="note-0714-08a" corresp="note-0714-08" type="noteAnchor" />
les inter ſe; </s>
          <s xml:space="preserve">nam propter æqualem diſtantiam utriuſque Nodi <lb />à Syzygiis, vires inclinationem mutantes in ND &amp; </s>
          <s xml:space="preserve">nE ſunt <lb />æquales viribus, in punctis reſpondentibus, in D n &amp; </s>
          <s xml:space="preserve">EN<ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0714-09a" corresp="note-0714-09" type="noteAnchor" />
illis inclinatio augetur, his minuitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">diminutio anguli inclina-
<ptr xml:id="note-0714-10a" corresp="note-0714-10" type="noteAnchor" />
tionis ex primis ſecundarum actione inſtauratur, &amp; </s>
          <s xml:space="preserve">hic non <lb />mutatur. </s>
          <s xml:space="preserve">In motu memorato <ptr type="noteAnchor" /> lineæ Nodorum reſpectu Solis,
<ptr xml:id="note-0714-11a" corresp="note-0714-11" type="noteAnchor" />
qui à ſitu parallelo lineæ hujus pender, Nodus N ad Syzygiam <lb />E fertur. </s>
          <s xml:space="preserve">Ubi ex gr. </s>
          <s xml:space="preserve">linea Nodorum pervenit ad ſitum Mm, <lb />Luna in receſſu à Nodis tranſit per Quadraturas N, n, in <lb />quibus vis, quæ inclinationem mutat nulla eſt <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">in quo-
<ptr xml:id="note-0714-12a" corresp="note-0714-12" type="noteAnchor" />
rum viciniis omnium eſt minima <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">in acceſſu autem ad Nodos
<ptr xml:id="note-0714-13a" corresp="note-0714-13" type="noteAnchor" />
ubique Luna à Quadraturis diſtat, &amp; </s>
          <s xml:space="preserve">vis major in hanc agit <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0714-14a" corresp="note-0714-14" type="noteAnchor" />
ideòque integram conſiderando revolutionem, augmentum <lb />
<ptr xml:id="note-0714-15a" corresp="note-0714-15" type="noteAnchor" />
anguli inclinationis ſuperat hujus diminutionem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">id eſt au-
<ptr xml:id="note-0714-16a" corresp="note-0714-16" type="noteAnchor" />
getur ille angulus aut quod idem eſt minuitur inclinatio; </s>
          <s xml:space="preserve">quod <lb />ubique obtinet in motu Nodorum à Quadraturis ad Syzygias.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0714-06" corresp="note-0714-06a" place="margin">1348.</note>
              <note xml:space="preserve" xml:id="note-0714-07" corresp="note-0714-07a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0714-08" corresp="note-0714-08a" place="margin">fig. 4.</note>
              <note xml:space="preserve" xml:id="note-0714-09" corresp="note-0714-09a" n="*" anchored="true" place="margin">1336.</note>
              <note xml:space="preserve" xml:id="note-0714-10" corresp="note-0714-10a" n="*" anchored="true" place="margin">1345.</note>
              <note xml:space="preserve" xml:id="note-0714-11" corresp="note-0714-11a" n="*" anchored="true" place="margin">1343.</note>
              <note xml:space="preserve" xml:id="note-0714-12" corresp="note-0714-12a" n="*" anchored="true" place="margin">1337.</note>
              <note xml:space="preserve" xml:id="note-0714-13" corresp="note-0714-13a" n="*" anchored="true" place="margin">1336.</note>
              <note xml:space="preserve" xml:id="note-0714-14" corresp="note-0714-14a" n="*" anchored="true" place="margin">1336.</note>
              <note xml:space="preserve" xml:id="note-0714-15" corresp="note-0714-15a" place="margin">1349.</note>
              <note xml:space="preserve" xml:id="note-0714-16" corresp="note-0714-16a" n="*" anchored="true" place="margin">1345.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vbi ad Syzygias pervenêre Nodi, inclinatio plani orbi-<lb />
<ptr xml:id="note-0714-17a" corresp="note-0714-17" type="noteAnchor" />
tæ eſt omnium minima; </s>
          <s xml:space="preserve">nam in motu Nodorum à Syzygiis ad <lb />
<ptr xml:id="note-0714-18a" corresp="note-0714-18" type="noteAnchor" />
Quadraturas, magis ac magis continuò inclinatur orbitæ pla-<lb />num; </s>
          <s xml:space="preserve">in hoc enim caſu in acceſſu ad Nodum per Quadratu-<lb />ras tranſit Luna, in receſſu ab his diſtat à Quadraturis, &amp; </s>
          <s xml:space="preserve">in in-
</s>
          <pb facs="0715" n="185" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XVII.</fw>
tegrâ Lunæ revolutione, vis, quæ inclinationem auget, ſupe-<lb />
<ptr xml:id="note-0715-01a" corresp="note-0715-01" type="noteAnchor" />
ratillam, quæ hanc minuit<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">idcirco augetur inclinatio; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eſt
<ptr xml:id="note-0715-02a" corresp="note-0715-02" type="noteAnchor" />
omnium maxima verſantibus Nodis in Quadr aturis, ubi rer-<lb />minatur diminutio anguli à Plano orbitæ cum plano Eclipticæ <lb />formati <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0714-17" corresp="note-0714-17a" place="margin">1350.</note>
              <note xml:space="preserve" xml:id="note-0714-18" corresp="note-0714-18a" place="margin">1351.</note>
              <note xml:space="preserve" xml:id="note-0715-01" corresp="note-0715-01a" n="*" anchored="true" place="margin">1337. 1345.</note>
              <note xml:space="preserve" xml:id="note-0715-02" corresp="note-0715-02a" place="margin">1352.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1349.</note>
        <p rend="italics">
          <s xml:space="preserve">Omnes, quos explicavimus, errores in motu Lunæ paululum <lb />
<ptr xml:id="note-0715-04a" corresp="note-0715-04" type="noteAnchor" />
majores ſunt in conjunctione quàm in oppoſitione<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0715-04" corresp="note-0715-04a" place="margin">1353.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1295.</note>
        <p>
          <s xml:space="preserve">Determinantur vires omnes perturbantes, detegendo ha-<lb />
<ptr xml:id="note-0715-06a" corresp="note-0715-06" type="noteAnchor" />
rum relationem cum augmento gravitatis in Quadraturis <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0715-07a" corresp="note-0715-07" type="noteAnchor" />
quare omnes easdem mutationes ſubeunt cum hoc augmento, <lb />
<ptr xml:id="note-0715-08a" corresp="note-0715-08" type="noteAnchor" />
id eſt, ſunt inversè, ut cubus diſtantiæ Solis à Tellure <ptr type="noteAnchor" />, qua
<ptr xml:id="note-0715-09a" corresp="note-0715-09" type="noteAnchor" />
manente, ſunt ut diſtantia Lunæ à Tellure <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Omnes vires
<ptr xml:id="note-0715-10a" corresp="note-0715-10" type="noteAnchor" />
perturbantes ſimul conſiderando prævalet gravitatis diminu-<lb />
<ptr xml:id="note-0715-11a" corresp="note-0715-11" type="noteAnchor" />
tio <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quod ex progreſſu Apſidum <ptr type="noteAnchor" />immediaté ſequitur; </s>
          <s xml:space="preserve">nam
<ptr xml:id="note-0715-12a" corresp="note-0715-12" type="noteAnchor" />
ex hoc patet, plurimis ſimul conſideratis revolutionibus, effe-<lb />
<ptr xml:id="note-0715-13a" corresp="note-0715-13" type="noteAnchor" />
ctum diminutionis gravitatis ſuperare effectum augmenti <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0715-14a" corresp="note-0715-14" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0715-06" corresp="note-0715-06a" place="margin">1354.</note>
              <note xml:space="preserve" xml:id="note-0715-07" corresp="note-0715-07a" n="*" anchored="true" place="margin">1306. 1307.</note>
              <note xml:space="preserve" xml:id="note-0715-08" corresp="note-0715-08a" place="margin">1336.</note>
              <note xml:space="preserve" xml:id="note-0715-09" corresp="note-0715-09a" n="*" anchored="true" place="margin">1289.</note>
              <note xml:space="preserve" xml:id="note-0715-10" corresp="note-0715-10a" n="*" anchored="true" place="margin">1288.</note>
              <note xml:space="preserve" xml:id="note-0715-11" corresp="note-0715-11a" place="margin">1355.</note>
              <note xml:space="preserve" xml:id="note-0715-12" corresp="note-0715-12a" n="*" anchored="true" place="margin">1296.</note>
              <note xml:space="preserve" xml:id="note-0715-13" corresp="note-0715-13a" n="*" anchored="true" place="margin">970. 1325.</note>
              <note xml:space="preserve" xml:id="note-0715-14" corresp="note-0715-14a" n="*" anchored="true" place="margin">1317. 1318.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ergo motu Lunæ generaliter conſiderato, minuitur gra-<lb />
<ptr xml:id="note-0715-15a" corresp="note-0715-15" type="noteAnchor" />
vitas Lunæ in Tellurem acceſſu Solis <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideòque, cùm mi-
<ptr xml:id="note-0715-16a" corresp="note-0715-16" type="noteAnchor" />
nus à Tellure trahatur, ab hac magis recedit, quàm recederet, <lb />ſi talis gravitatis diminutio non daretur; </s>
          <s xml:space="preserve">augetur ergo in hoc <lb />caſu Lunæ diſtantia, etiam tempus periodicum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tempus
<ptr xml:id="note-0715-17a" corresp="note-0715-17" type="noteAnchor" />
hoc maximum eſt, ut &amp; </s>
          <s xml:space="preserve">diſtantia Lunæ, cæteris paribus, <lb />
<ptr xml:id="note-0715-18a" corresp="note-0715-18" type="noteAnchor" />
maxima, verſante Tellure in Perihelio <ptr type="noteAnchor" />, quia omnium mi-
<ptr xml:id="note-0715-19a" corresp="note-0715-19" type="noteAnchor" />
nime à Sole diſtat.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0715-15" corresp="note-0715-15a" place="margin">1356.</note>
              <note xml:space="preserve" xml:id="note-0715-16" corresp="note-0715-16a" n="*" anchored="true" place="margin">1355. 1354.</note>
              <note xml:space="preserve" xml:id="note-0715-17" corresp="note-0715-17a" place="margin">1357.</note>
              <note xml:space="preserve" xml:id="note-0715-18" corresp="note-0715-18a" n="*" anchored="true" place="margin">224.</note>
              <note xml:space="preserve" xml:id="note-0715-19" corresp="note-0715-19a" n="*" anchored="true" place="margin">1354.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVII.</head>
        <head rend="italics" xml:space="preserve">De Planetarum Figuris.</head>
        <p>
          <s xml:space="preserve">Si ad Planetarum figuras attendamus, talibus illos præditos <lb />detegimus, quæ ex ipſis, quibus ſyſtema regitur, legibus <lb />ſequitur; </s>
          <s xml:space="preserve">quod ordini mirabili, quem ubique obſervamus, ad-<lb />modum congruum eſt, nullas in Planetas agere vires ad hos <lb />deſtruendos; </s>
          <s xml:space="preserve">id eſt illam eſſe Planetæ, ſive primarii, ſive ſe-<lb />
<ptr xml:id="note-0715-20a" corresp="note-0715-20" type="noteAnchor" />
cundarii, figuram, quam acquireret, ſi totus ex materiâ flui-<lb />dâ conſtaret; </s>
          <s xml:space="preserve">quod Phœnomenis congruit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0715-20" corresp="note-0715-20a" place="margin">1358.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unde ſequitur Planetas omnes primarios, &amp; </s>
          <s xml:space="preserve">ſecundarios, <lb />
<ptr xml:id="note-0715-21a" corresp="note-0715-21" type="noteAnchor" />
eſſe ſphæricos; </s>
          <s xml:space="preserve">conſtant enim ex materiâ cujus particulæ in <lb />ſe mutuo graves ſunt <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ex qua mutuâ attractione figura
<ptr xml:id="note-0715-22a" corresp="note-0715-22" type="noteAnchor" />
</s>
          <pb facs="0716" n="186" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſphærica generatur, codem modo ac gutta fit ſphærica ex aliâ <lb />partium attractione <ptr type="noteAnchor" /></s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0715-21" corresp="note-0715-21a" place="margin">1359.</note>
              <note xml:space="preserve" xml:id="note-0715-22" corresp="note-0715-22a" n="*" anchored="true" place="margin">1206. 1207.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">34.</note>
        <p>
          <s xml:space="preserve">Figura hæc ſphærica Planetarum ex motu circa Solem, <lb />
<ptr xml:id="note-0716-02a" corresp="note-0716-02" type="noteAnchor" />
aut ſecundariorum circa primarios, non mutatur; </s>
          <s xml:space="preserve">quia ſingu-<lb />læ particulæ eodem motu feruntur: </s>
          <s xml:space="preserve">motu autem circa axem <lb />mntationem figura ſubit, eo majorem, quo motus hic cele-<lb />rior eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0716-02" corresp="note-0716-02a" place="margin">1360.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit PP axis Planetæ; </s>
          <s xml:space="preserve">Ee diameter Æquatoris, ad axem <lb />
<ptr xml:id="note-0716-03a" corresp="note-0716-03" type="noteAnchor" />
perpendicularis; </s>
          <s xml:space="preserve">detur canalis PCE fluido repletus; </s>
          <s xml:space="preserve">pon-<lb />
<ptr xml:id="note-0716-04a" corresp="note-0716-04" type="noteAnchor" />
dere ſuo fluidum hoc verſus C in utroque crure deſcendit, <lb />
<ptr xml:id="note-0716-05a" corresp="note-0716-05" type="noteAnchor" />
&amp; </s>
          <s xml:space="preserve">non quieſcit, niſi preſſio in utroque crure æqualis ſit. <lb /></s>
          <s xml:space="preserve">Si Planeta quieſcat, altitudo fluidi in utroque crure æqua-<lb />lis eſt <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ſi vero Planeta circa axem Pp rotetur, vi centri-
<ptr xml:id="note-0716-06a" corresp="note-0716-06" type="noteAnchor" />
fugâ omne liquidum in crure CE à centrò conatur rece-<lb />dere <ptr type="noteAnchor" />, quæ vis cum vi gravitatis contrariè agit <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò-
<ptr xml:id="note-0716-07a" corresp="note-0716-07" type="noteAnchor" />
<ptr xml:id="note-0716-08a" corresp="note-0716-08" type="noteAnchor" />
que gravitatem minuit; </s>
          <s xml:space="preserve">ita ut æquilibrium non detur, <lb />niſi CE ſuperet CP. </s>
          <s xml:space="preserve">Tollamus nunc canalem, preſſio latera-<lb />lis fluidi, ex quo Planeta conſtat, non mutat gravitatem ver-<lb />ſus C, neque differentiam inter altitudines columnarum CE, <lb />CP<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">altior idcirco ubique eſt Planeta in Æquatore, quam in
<ptr xml:id="note-0716-09a" corresp="note-0716-09" type="noteAnchor" />
Polis, &amp; </s>
          <s xml:space="preserve">acquirit ex motu circa axem, figuram ſphæroidis <lb />depreſſi in Polis; </s>
          <s xml:space="preserve">elevatio enim continuò minuitur, acce-<lb />dendo ad Polum; </s>
          <s xml:space="preserve">quia vis centrifuga minuitur, propter immi-<lb />nutam diſtantiam ab Axe <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0716-10a" corresp="note-0716-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0716-03" corresp="note-0716-03a" place="margin">1361.</note>
              <note xml:space="preserve" xml:id="note-0716-04" corresp="note-0716-04a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0716-05" corresp="note-0716-05a" place="margin">fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0716-06" corresp="note-0716-06a" n="*" anchored="true" place="margin">1359.</note>
              <note xml:space="preserve" xml:id="note-0716-07" corresp="note-0716-07a" n="*" anchored="true" place="margin">217.</note>
              <note xml:space="preserve" xml:id="note-0716-08" corresp="note-0716-08a" n="*" anchored="true" place="margin">223.</note>
              <note xml:space="preserve" xml:id="note-0716-09" corresp="note-0716-09a" n="*" anchored="true" place="margin">280. 1362.</note>
              <note xml:space="preserve" xml:id="note-0716-10" corresp="note-0716-10a" place="margin">232</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si demonſtrata cum Phœnomenis conſerantur, patebit <lb />quare omnia corpora ſint Sphærica in ſyſtemate noſtro <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">hanc
<ptr xml:id="note-0716-11a" corresp="note-0716-11" type="noteAnchor" />
tamen figuram non eſſe exactam, &amp; </s>
          <s xml:space="preserve">motibus circa axes paulu-<lb />lum mutari <ptr type="noteAnchor" />, licèt in pleriſque hoc obſervari non poſſit, ex
<ptr xml:id="note-0716-12a" corresp="note-0716-12" type="noteAnchor" />
obſervationibus Jovis &amp; </s>
          <s xml:space="preserve">Telluris poterit deduci. </s>
          <s xml:space="preserve">Fovis axem <lb />
<ptr xml:id="note-0716-13a" corresp="note-0716-13" type="noteAnchor" />
breviorem eſſe diametro Æquatoris obſervarunt Aſtrono-<lb />mi; </s>
          <s xml:space="preserve">hic licet omnium Planetarum ſit maximus, omnium ce-<lb />lerrimè circa axem rotatur <ptr type="noteAnchor" />, ideòque differentia hæc obſerva-
<ptr xml:id="note-0716-14a" corresp="note-0716-14" type="noteAnchor" />
ri poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0716-11" corresp="note-0716-11a" n="*" anchored="true" place="margin">924.</note>
              <note xml:space="preserve" xml:id="note-0716-12" corresp="note-0716-12a" n="*" anchored="true" place="margin">1362.</note>
              <note xml:space="preserve" xml:id="note-0716-13" corresp="note-0716-13a" place="margin">1363.</note>
              <note xml:space="preserve" xml:id="note-0716-14" corresp="note-0716-14a" place="margin">962.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Elevatio Telluris, in Æquatore, à nobis determi-<lb />
<ptr xml:id="note-0716-15a" corresp="note-0716-15" type="noteAnchor" />
natur, quamvis fortè aliorum Planetarum incolis, ſi dentur, <lb />non magis eſt ſenſibilis, quam nobis elevationes in Marte &amp; </s>
          <s xml:space="preserve"><lb />Venere, quas non percipimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0716-15" corresp="note-0716-15a" place="margin">1364.</note>
            </div>
          </body>
        </floatingText>
        <pb facs="0717" n="187" />
        <fw type="head">MATHEMATICA LIB. IV. CAP. XVII.</fw>
        <p>
          <s xml:space="preserve">Ponamus Tellurem fluidam, memoratam ſphæroidem ac-<lb />
<ptr xml:id="note-0717-01a" corresp="note-0717-01" type="noteAnchor" />
quiret figuram <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ſi cohæreant partes verſus centrum, non co
<ptr xml:id="note-0717-02a" corresp="note-0717-02" type="noteAnchor" />
ſitus aliarum mutari poteſt, neque mutabitur, ſi in quibus-<lb />dam locis partes ad ſuperſiciem uſque cohæreant inter ſe; </s>
          <s xml:space="preserve">ita <lb />ut Maris ſuperficies neceſſario acquirat ſphæroidem figuram <lb />ad Polos depreſſam. </s>
          <s xml:space="preserve">Cùm verò, parum tantùm, ubique lit-<lb />tora ſupra Maris ſuperficiem, eleventur, continentem eandem <lb />ſequi figuram extra dubium eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0717-01" corresp="note-0717-01a" place="margin">1365.</note>
              <note xml:space="preserve" xml:id="note-0717-02" corresp="note-0717-02a" n="*" anchored="true" place="margin">1362.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut nunc hanc menſuremus elevationem, id eſt quantum <lb />diameter Æquatoris, ſuperet Axem, ad motum Telluris cir-<lb />ca hunc in ſpatio 23 ho. </s>
          <s xml:space="preserve">56′. </s>
          <s xml:space="preserve">4″. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> attendendum eſt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſequen-
<ptr xml:id="note-0717-03a" corresp="note-0717-03" type="noteAnchor" />
ti methodo, poſitâ Tellure homogeneâ computatio inſtitui-<lb />tur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0717-03" corresp="note-0717-03a" n="*" anchored="true" place="margin">960.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Telluris periſeria eſt pedum Rhenolandicorum 128202185.</s>
          <s xml:space="preserve">; <lb />
<ptr xml:id="note-0717-04a" corresp="note-0717-04" type="noteAnchor" />
ideò in uno minuto ſecundo temporis, punctum Æquatoris per-<lb />currit pedes 1488.</s>
          <s xml:space="preserve">; cujus arcus ſinus verſus eſt pedum o, 054, <lb />ſpatium quod in tali tempore ex vi centriſugâ à corpore per-<lb />curri poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0717-04" corresp="note-0717-04a" place="margin">1366.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Gravitate corpus, in uno minuto ſecundo, ut antea jam <lb />vidimus, cadendo percurrit pedes 15, 607; </s>
          <s xml:space="preserve">Sed hæc experi-<lb />menta inſtituta ſuere ad diſtantiam 48. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">ab Æquatore E e, <lb />
<ptr xml:id="note-0717-05a" corresp="note-0717-05" type="noteAnchor" />
<ptr xml:id="note-0717-06a" corresp="note-0717-06" type="noteAnchor" />
in pnncto A; </s>
          <s xml:space="preserve">vis centriſuga in E eſt ad vim centriſugam <lb />in A, ut CE, aut CA, nam parum admodum differunt hæ <lb />lineæ, ad AB; </s>
          <s xml:space="preserve">ſit vis hæ centrifuga Ab; </s>
          <s xml:space="preserve">ductâ perpen-<lb />diculari ba ad CA continuatam, relolvatur vis per A b, in <lb />duas per A a &amp; </s>
          <s xml:space="preserve">ab<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">illâ ſolâ minuitur gravitas, &amp; </s>
          <s xml:space="preserve">eſt Ab
<ptr xml:id="note-0717-07a" corresp="note-0717-07" type="noteAnchor" />
ad vim illam minuentem, ut CA ad AB; </s>
          <s xml:space="preserve">propter ſimilia trian-<lb />gula rectangula, Aba, &amp; </s>
          <s xml:space="preserve">ABC, habentia in A angulos <lb />oppoſitos ad verticem æquales; </s>
          <s xml:space="preserve">eſt ideò vis centrifuga in Æ <lb />quatore, qua corpus in minuto ſecundo percurrit O, 054; </s>
          <s xml:space="preserve">ad <lb />vim, gravitatem minuentem in A, in ratione duplicatâ <lb />radii AC ad AB, co-ſinum latitudinis AE, 48. </s>
          <s xml:space="preserve">gr.</s>
          <s xml:space="preserve">; ita ut ex <lb />hac vi minuente corpus in uno minuto ſecundo percurrat O, 0243.</s>
          <s xml:space="preserve">; <lb />quare, ſi Tellus quieſceret cadendo non percurreret pedes 15, 607.</s>
          <s xml:space="preserve">, <lb />ſed pedes 15, 632; </s>
          <s xml:space="preserve">qua gravitate corpus ſub Polis cadit, quia <lb />puncta hæc non moventur. </s>
          <s xml:space="preserve">Ad Æquatorem vi centrifugâ per-<lb />currit corpus O, 054. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">tantum cadit, in eodem tempore ab
</s>
          <pb facs="0718" n="188" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
altitudine pedum 15, 578.</s>
          <s xml:space="preserve">; unde patet gravitatem ſub Polis eſſe <lb />ad gravitatem ſub Æquatore, ut 289 ad 288.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0717-05" corresp="note-0717-05a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0717-06" corresp="note-0717-06a" place="margin">fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0717-07" corresp="note-0717-07a" n="*" anchored="true" place="margin">192.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si ſig. </s>
          <s xml:space="preserve">7. </s>
          <s xml:space="preserve">figuram Telluris repræſentat, pondus columnæ <lb />liquidi CE erit ad pondus columnæ liquidi CA, quieſcente <lb />Tellure, ut 289 ad 288; </s>
          <s xml:space="preserve">aliter enim, motâ Tellure, æqui-<lb />librium non dabitur; </s>
          <s xml:space="preserve">quia pars {1/259} columnæ CE vi centrifu-<lb />gâ ſuſtinetur; </s>
          <s xml:space="preserve">decreſcit enim vis centrifuga accedendo ad cen-<lb />trum in ratione diſtantiæ<ptr type="noteAnchor" />, in qua etiam ratione decreſcitgra-
<ptr xml:id="note-0718-01a" corresp="note-0718-01" type="noteAnchor" />
vitas <ptr type="noteAnchor" />, ita ut in ſingulis columnæ punctis eadem pars ponde-
<ptr xml:id="note-0718-02a" corresp="note-0718-02" type="noteAnchor" />
ris ſuſtineatur, quàm verſus ſuperſiciem.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0718-01" corresp="note-0718-01a" n="*" anchored="true" place="margin">232.</note>
              <note xml:space="preserve" xml:id="note-0718-02" corresp="note-0718-02a" n="*" anchored="true" place="margin">1233.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex his deducimus altitudinem CP, ad Polum, eſſe ad alti-<lb />
<ptr xml:id="note-0718-03a" corresp="note-0718-03" type="noteAnchor" />
tudinem EC, ad Æquatorem, ut 229 ad 230; </s>
          <s xml:space="preserve">poſitâ enim <lb />hac ratione inter Axem &amp; </s>
          <s xml:space="preserve">Æquatoris diametrum, ſide gravita-<lb />tibus in locis P &amp; </s>
          <s xml:space="preserve">E, Tellare quieſcente. </s>
          <s xml:space="preserve">computatio inea-<lb />tur, deteguntur eſſe inter ſe, ut 1121, 71. </s>
          <s xml:space="preserve">ad 1120, 71.</s>
          <s xml:space="preserve">; quæ ra-<lb />tio ubique obtinet in punctis reſpondentibus, id eſt quæ diſtant <lb />à centro ut CP ad PE; </s>
          <s xml:space="preserve">quia in utroque crure decreſcit gra-<lb />vitas in ratione diſtantiæ à centro <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Pondus habetur multi-
<ptr xml:id="note-0718-04a" corresp="note-0718-04" type="noteAnchor" />
plicando materiæ quantitatem per gravitatem; </s>
          <s xml:space="preserve">nam in utriuſque <lb />ratione creſcit pondus: </s>
          <s xml:space="preserve">multiplicando 1121, 71. </s>
          <s xml:space="preserve">per 229, &amp; </s>
          <s xml:space="preserve"><lb />1120. </s>
          <s xml:space="preserve">71 per 230. </s>
          <s xml:space="preserve">producta ſunt inter ſe, ut 288. </s>
          <s xml:space="preserve">ad 289.</s>
          <s xml:space="preserve">; <lb />quæ eſt ratio ponderum ante detecta. </s>
          <s xml:space="preserve">Diameter media Tellu-<lb />ris eſt 3400669 perticarum <ptr type="noteAnchor" />, ideò axis PP eſt 3393261, &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0718-05a" corresp="note-0718-05" type="noteAnchor" />
diameter Æquatoris Ee 3408078. </s>
          <s xml:space="preserve">perticarum, quæ Axem <lb />ſuperat perticis 14817, parte nempe {1/230}, &amp; </s>
          <s xml:space="preserve">Æquator magis <lb />
<ptr xml:id="note-0718-06a" corresp="note-0718-06" type="noteAnchor" />
elevatur perticis 7408, 5.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0718-03" corresp="note-0718-03a" place="margin">1367.</note>
              <note xml:space="preserve" xml:id="note-0718-04" corresp="note-0718-04a" n="*" anchored="true" place="margin">1233.</note>
              <note xml:space="preserve" xml:id="note-0718-05" corresp="note-0718-05a" n="*" anchored="true" place="margin">976.</note>
              <note xml:space="preserve" xml:id="note-0718-06" corresp="note-0718-06a" place="margin">1368.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hac computatione, ut monuimus, Tellurem homogeneam <lb />
<ptr xml:id="note-0718-07a" corresp="note-0718-07" type="noteAnchor" />
habuimus; </s>
          <s xml:space="preserve">ſi autem magis denſa ſit ad centrum, materia quæ adji-<lb />citur poterit haberi pro corpore ſeparato, à cujus centro pun-<lb />cta P &amp; </s>
          <s xml:space="preserve">E inæqualiter diſtant, &amp; </s>
          <s xml:space="preserve">in quod ideò diverſam <lb />gravitatem habent corpora in P &amp; </s>
          <s xml:space="preserve">E<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">diſſerentia eo ma-
<ptr xml:id="note-0718-08a" corresp="note-0718-08" type="noteAnchor" />
jor erit, quo hæ diſtantiæ magis differunt: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">etiam erit eo <lb />major reſpectu totius gravitatis, quo materiæ quantitas adje-<lb />cta, aut quod idem eſt, denſitas verſus centrum major eſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0718-07" corresp="note-0718-07a" place="margin">1369.</note>
              <note xml:space="preserve" xml:id="note-0718-08" corresp="note-0718-08a" place="margin">1266</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Magis inter ſe differre vires gravitatis in Polis &amp; </s>
          <s xml:space="preserve">Æquarore, <lb />quàmparte {1/289}, collatis experimentis ad varias Æquatoris diſtan-<lb />tias, ope pendulorum inſtitutis, conſtat, quibus vires gravitatis
</s>
          <pb facs="0719" n="189" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XVII.</fw>
interſe conferri poſſe vidimus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">differentia quæ revera datur
<ptr xml:id="note-0719-01a" corresp="note-0719-01" type="noteAnchor" />
fere dupla eſt illius, quæ computatione detegitur; </s>
          <s xml:space="preserve">unde ſe-<lb />quitur elevationem Æquatoris fere duplam eſſe illius, quam <lb />
<ptr xml:id="note-0719-02a" corresp="note-0719-02" type="noteAnchor" />
determinavimus 7408, 5. </s>
          <s xml:space="preserve">perticarum <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0719-01" corresp="note-0719-01a" n="*" anchored="true" place="margin">164. 165.</note>
              <note xml:space="preserve" xml:id="note-0719-02" corresp="note-0719-02a" place="margin">1370.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1368.</note>
        <p>
          <s xml:space="preserve">Si nunc ad ſphæroidem figuram Telluris attendamus, vide-<lb />mus gravia non directe tendere ad centrum Telluris, niſi <lb />
<ptr xml:id="note-0719-04a" corresp="note-0719-04" type="noteAnchor" />
in Polis &amp; </s>
          <s xml:space="preserve">Æquatore, ſed ubique perpendiculariter ad ſu-<lb />perficiem Sphæroidis; </s>
          <s xml:space="preserve">nam liquidum non quieſcit, niſi ſupre-<lb />ma ſuperficies cum directione gravium angulum rectum ſor-<lb />met <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſphæroidis figura formatur à fluidi quieſcentis ſuper-
<ptr xml:id="note-0719-05a" corresp="note-0719-05" type="noteAnchor" />
ficie. </s>
          <s xml:space="preserve">Hanc eandem gravium directionem etiam directè dedu-<lb />
<ptr xml:id="note-0719-06a" corresp="note-0719-06" type="noteAnchor" />
cimus ex vi centriſugâ. </s>
          <s xml:space="preserve">Corpus in A gravitate tendit ad C, <lb />
<ptr xml:id="note-0719-07a" corresp="note-0719-07" type="noteAnchor" />
<ptr xml:id="note-0719-08a" corresp="note-0719-08" type="noteAnchor" />
vi centrifugâ fertur per Ab; </s>
          <s xml:space="preserve">vis hæc in puncto A eſt ad <lb />gravitatem per AC.</s>
          <s xml:space="preserve">, ut I. </s>
          <s xml:space="preserve">ad 430, 8.</s>
          <s xml:space="preserve">: formato parallelogrammo <lb />lateribus AC &amp; </s>
          <s xml:space="preserve">Ab, poſitis his inter ſe, ut 430, 8.</s>
          <s xml:space="preserve">, ad I.</s>
          <s xml:space="preserve">, dia-<lb />gonalis deſignabit directionem gravium <ptr type="noteAnchor" />, formantem exiguum
<ptr xml:id="note-0719-09a" corresp="note-0719-09" type="noteAnchor" />
angulum cum lineâ AC. </s>
          <s xml:space="preserve">Vis per Ab creſcit acceſlu ad Æqua-<lb />torem, quo angulus hic augetur, ſed minuitur, propter au-<lb />ctum angulum CAb; </s>
          <s xml:space="preserve">ita ut in Æquatore, ubi vis centriſuga <lb />eſt maxima, directio gravium cum EC coincidat: </s>
          <s xml:space="preserve">in Polo co-<lb />incidit cum PC; </s>
          <s xml:space="preserve">quia vis centriſuga nulla datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0719-04" corresp="note-0719-04a" place="margin">1371.</note>
              <note xml:space="preserve" xml:id="note-0719-05" corresp="note-0719-05a" n="*" anchored="true" place="margin">272.</note>
              <note xml:space="preserve" xml:id="note-0719-06" corresp="note-0719-06a" place="margin">1372.</note>
              <note xml:space="preserve" xml:id="note-0719-07" corresp="note-0719-07a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0719-08" corresp="note-0719-08a" place="margin">fig. 7.</note>
              <note xml:space="preserve" xml:id="note-0719-09" corresp="note-0719-09a" n="*" anchored="true" place="margin">190.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In hac figurâ ſphæroidis determinatur latitudo loci angu-<lb />
<ptr xml:id="note-0719-10a" corresp="note-0719-10" type="noteAnchor" />
lo, ut ACE, quem cum Æquatore efficit linea, ex loco ad <lb />centrum ducta. </s>
          <s xml:space="preserve">Diviſo toto arcu PAE, hac methodo, in <lb />partes nonaginta, id eſt in gradus, facile patet accedendo ad <lb />
<ptr xml:id="note-0719-11a" corresp="note-0719-11" type="noteAnchor" />
Polum, gradus inſuperficie augeri; </s>
          <s xml:space="preserve">ſed hæc adeò exigua eſt <lb />differentia, ut, in menſurandis gradibus non admodum diſtanti-<lb />bus, detegi non poſſit; </s>
          <s xml:space="preserve">quia error ex fabricâ, &amp; </s>
          <s xml:space="preserve">uſu inſtrumento-<lb />rum, differentiam hanc ſuperat. </s>
          <s xml:space="preserve">Inde differunt paululum <lb />inter ſe gradus menſurati ad auſtrum &amp; </s>
          <s xml:space="preserve">boream Galliæ, ut &amp; </s>
          <s xml:space="preserve"><lb />in Angliâ, &amp; </s>
          <s xml:space="preserve">medius eſt omnium minimus; </s>
          <s xml:space="preserve">quare ex menſu-<lb />
<ptr xml:id="note-0719-12a" corresp="note-0719-12" type="noteAnchor" />
ris his de Telluris figurânil concludi poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0719-10" corresp="note-0719-10a" place="margin">1373.</note>
              <note xml:space="preserve" xml:id="note-0719-11" corresp="note-0719-11a" place="margin">1374.</note>
              <note xml:space="preserve" xml:id="note-0719-12" corresp="note-0719-12a" place="margin">1375.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XVIII.</head>
        <head rend="italics" xml:space="preserve">Motus Axeos Telluris Explicatio Phyſica.</head>
        <p>
          <s xml:space="preserve">Lunæ Nodos regredi, id eſt in antecedentiâ moveri <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">or-
<ptr xml:id="note-0719-13a" corresp="note-0719-13" type="noteAnchor" />
bitæ inclinationem mutationibus eſſe obnoxiam <ptr type="noteAnchor" />, demon-
<ptr xml:id="note-0719-14a" corresp="note-0719-14" type="noteAnchor" />
</s>
          <pb facs="0720" n="190" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſtravimus; </s>
          <s xml:space="preserve">concipiamus varias dari Lunas, ad eandem di-<lb />ſtantiam, æqualibus temporibus, circa Tellurem revolventes, <lb />in plano ad planum Eclipticæ inclinato; </s>
          <s xml:space="preserve">ſingulas iiſdem moti-<lb />bus agitari clarum eſt: </s>
          <s xml:space="preserve">concipiamus numerum Lunarum auge-<lb />ri, ita ut ſeſe mutuo tangant, &amp; </s>
          <s xml:space="preserve">annulum, cujus partes cohæ-<lb />rent, forment; </s>
          <s xml:space="preserve">dum annuli pars una trahitur, ut inclinationem <lb />augeat, pars altera motu contrario agitatur, ad inclinationem <lb />minuendam <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">Vis major in hoc caſu prævalet, id eſt, in mo-
<ptr xml:id="note-0720-01a" corresp="note-0720-01" type="noteAnchor" />
tu lineæ Nodorum à Quadraturis ad Syzygias annuli incli-<lb />
<ptr xml:id="note-0720-02a" corresp="note-0720-02" type="noteAnchor" />
natio minuitur in ſingulis hujus revolutionibus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eſt
<ptr xml:id="note-0720-03a" corresp="note-0720-03" type="noteAnchor" />
omnium minima, verſante lineâ Nodorum in Syzygiis <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Con-
<ptr xml:id="note-0720-04a" corresp="note-0720-04" type="noteAnchor" />
tra, augetur inclinatio dum linea Nodorum ex Syzygiis ad <lb />Quadraturas transfertur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">eſt omnium maxima, poſitâ
<ptr xml:id="note-0720-05a" corresp="note-0720-05" type="noteAnchor" />
lineâ Nodorum in his<ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Linea Nodorum continuò in ante-
<ptr xml:id="note-0720-06a" corresp="note-0720-06" type="noteAnchor" />
cedentiâ transfertur, niſi in Syzygiis ubi quieſcit<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0720-07a" corresp="note-0720-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0719-13" corresp="note-0719-13a" n="*" anchored="true" place="margin">1341.</note>
              <note xml:space="preserve" xml:id="note-0719-14" corresp="note-0719-14a" n="*" anchored="true" place="margin">1347.</note>
              <note xml:space="preserve" xml:id="note-0720-01" corresp="note-0720-01a" place="margin">1376.</note>
              <note xml:space="preserve" xml:id="note-0720-02" corresp="note-0720-02a" place="margin">1345.</note>
              <note xml:space="preserve" xml:id="note-0720-03" corresp="note-0720-03a" place="margin">1377.</note>
              <note xml:space="preserve" xml:id="note-0720-04" corresp="note-0720-04a" place="margin">1349.</note>
              <note xml:space="preserve" xml:id="note-0720-05" corresp="note-0720-05a" place="margin">1378.</note>
              <note xml:space="preserve" xml:id="note-0720-06" corresp="note-0720-06a" place="margin">1351.</note>
              <note xml:space="preserve" xml:id="note-0720-07" corresp="note-0720-07a" place="margin">1352. 1341 1344.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si quantitas materiæ in annulo minuatur, non mutantur <lb />
<ptr xml:id="note-0720-08a" corresp="note-0720-08" type="noteAnchor" />
hujus motus; </s>
          <s xml:space="preserve">quia à gravitate pendent, quæ æqualiter in ſin-<lb />gulas materiæ particulas agit <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0720-08" corresp="note-0720-08a" place="margin">1379.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1207.</note>
        <p>
          <s xml:space="preserve">Si annuli diameter minuatur, in ratione hujus diminutio-<lb />nis minuuntur motus <ptr type="noteAnchor" />, ſed nullus in totum evaneſcit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">iiſ-
<ptr xml:id="note-0720-10a" corresp="note-0720-10" type="noteAnchor" />
dem motibus agitatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0720-10" corresp="note-0720-10a" n="*" anchored="true" place="margin">1354.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Concipiamus nunc Tellurem ſphæricam; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in plano Æ-<lb />
<ptr xml:id="note-0720-11a" corresp="note-0720-11" type="noteAnchor" />
quatoris, cum plano Eclipticæ efficiente angulum 23. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">29′.</s>
          <s xml:space="preserve">, <lb />annulum dari, in eodem tempore cum Tellure revolventem; <lb /></s>
          <s xml:space="preserve">minuatur hic ut Tellurem tangat, &amp; </s>
          <s xml:space="preserve">cum hac cohæreat; </s>
          <s xml:space="preserve">hiſce <lb />annulis motus memorati non tolluntur; </s>
          <s xml:space="preserve">nam cùm Tellus nul-<lb />lâ vi in determinato ſitu retineatur, cedit impreſſionibus annuli, <lb />cujus agitationes tamen minuuntur, ex auctâ materiâ moven-<lb />dâ, dum vis motrix eadem manet.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0720-11" corresp="note-0720-11a" place="margin">1381.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Caſus hic revera extat, nam Telluris figura eſt ſphærica, an-<lb />nulo in Æquatore circumdata, quo Tellus ad Æquatorem ma-<lb />gis elevatur <ptr type="noteAnchor" />, cujus annuli linea Nodorum eſt ſectio planorum
<ptr xml:id="note-0720-12a" corresp="note-0720-12" type="noteAnchor" />
Æquatoris &amp; </s>
          <s xml:space="preserve">Eclipticæ. </s>
          <s xml:space="preserve">Unde ſequentes deducimus conclu-<lb />ſiones.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0720-12" corresp="note-0720-12a" n="*" anchored="true" place="margin">1370.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Æquinoctiis inclinatio Æquatoris eſt omnium minima <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0720-13a" corresp="note-0720-13" type="noteAnchor" />
ideòque Axeos inclinatio omnium maxima; </s>
          <s xml:space="preserve">nam cum plano <lb />
<ptr xml:id="note-0720-14a" corresp="note-0720-14" type="noteAnchor" />
Æquatoris angulum rectum efficit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Augetur inclinatio Æ-
<ptr xml:id="note-0720-15a" corresp="note-0720-15" type="noteAnchor" />
</s>
          <pb facs="0721" n="191" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XIX.</fw>
quatoris, id eſt minuitur Axeos inclinatio, donec Sol in <lb />
<ptr xml:id="note-0721-01a" corresp="note-0721-01" type="noteAnchor" />
Solticiis detur, ubi hæc eſt omnium minima, illa omnium <lb />
<ptr xml:id="note-0721-02a" corresp="note-0721-02" type="noteAnchor" />
maxima <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Idcirco bis in anno minuitnr Telluris Axeos in-
<ptr xml:id="note-0721-03a" corresp="note-0721-03" type="noteAnchor" />
clinatio, bis inſtauratur. </s>
          <s xml:space="preserve">Et Sectio plani Æquatoris cum <lb />
<ptr xml:id="note-0721-04a" corresp="note-0721-04" type="noteAnchor" />
plano Æclipticæ, quæ in Æquinoctiis quieſcit, per reli-<lb />quum tempus in antecedentiâ movetur<ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0720-13" corresp="note-0720-13a" place="margin">1382.</note>
              <note xml:space="preserve" xml:id="note-0720-14" corresp="note-0720-14a" place="margin">1377.</note>
              <note xml:space="preserve" xml:id="note-0720-15" corresp="note-0720-15a" n="*" anchored="true" place="margin">1075.</note>
              <note xml:space="preserve" xml:id="note-0721-01" corresp="note-0721-01a" place="margin">1383.</note>
              <note xml:space="preserve" xml:id="note-0721-02" corresp="note-0721-02a" n="*" anchored="true" place="margin">1377.</note>
              <note xml:space="preserve" xml:id="note-0721-03" corresp="note-0721-03a" place="margin">1384.</note>
              <note xml:space="preserve" xml:id="note-0721-04" corresp="note-0721-04a" place="margin">1385.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1378.</note>
        <p>
          <s xml:space="preserve">Ad planum orbitæ Lunaris etiam inclinatur planum Æqua-<lb />
<ptr xml:id="note-0721-06a" corresp="note-0721-06" type="noteAnchor" />
toris; </s>
          <s xml:space="preserve">nam exiguum angulum illud cum Plano Eclipticæ eſſi-<lb />cit <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ideò eodem modo in annulum agit Luna, quàm Sol; </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0721-07a" corresp="note-0721-07" type="noteAnchor" />
licèt illa minor ſit, quia Sole multo minus diſtat, in annulum <lb />majorem exerit actionem. </s>
          <s xml:space="preserve">Quare etiam ex actione Lunæ, bis <lb />
<ptr xml:id="note-0721-08a" corresp="note-0721-08" type="noteAnchor" />
in ſingulis hujus revolutionibus mutatur, &amp; </s>
          <s xml:space="preserve">bis inſtauratur, <lb />Axeos Telluris inclinatio ad Planum orbitæ Lunæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò-
<ptr xml:id="note-0721-09a" corresp="note-0721-09" type="noteAnchor" />
que ad planum Eclipticæ: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">in antecedentiâ fertur Sectio <lb />Plani Æquatoris cum plano orbitæ <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ex quo motu tranſla-
<ptr xml:id="note-0721-10a" corresp="note-0721-10" type="noteAnchor" />
tio ſectionis illius plani cum plano Eclipticæ neceſſario ſe-<lb />quitur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0721-06" corresp="note-0721-06a" place="margin">1386.</note>
              <note xml:space="preserve" xml:id="note-0721-07" corresp="note-0721-07a" n="*" anchored="true" place="margin">969.</note>
              <note xml:space="preserve" xml:id="note-0721-08" corresp="note-0721-08a" place="margin">1387.</note>
              <note xml:space="preserve" xml:id="note-0721-09" corresp="note-0721-09a" n="*" anchored="true" place="margin">1384.</note>
              <note xml:space="preserve" xml:id="note-0721-10" corresp="note-0721-10a" n="*" anchored="true" place="margin">1385.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Mutationes inclinationis Axeosnimium ſunt exiguæ, ut ob-<lb />
<ptr xml:id="note-0721-11a" corresp="note-0721-11" type="noteAnchor" />
ſerventur: </s>
          <s xml:space="preserve">tranſlatio autem lineæ Æquinoctiorum, &amp; </s>
          <s xml:space="preserve">mo-<lb />
<ptr xml:id="note-0721-12a" corresp="note-0721-12" type="noteAnchor" />
tus Axeos, qui ex hac ſequitur, cùm ſemper verſus eandem <lb />partem dirigantur, tandem ſenſibiles ſunt; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ex his Phœno-<lb />mena antea explicata <ptr type="noteAnchor" /> ſequuntur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0721-11" corresp="note-0721-11a" place="margin">1388.</note>
              <note xml:space="preserve" xml:id="note-0721-12" corresp="note-0721-12a" place="margin">1389.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1185. 1186.</note>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XIX.</head>
        <head rend="italics" xml:space="preserve">De Æſtu Maris.</head>
        <p>
          <s xml:space="preserve">Ut Æſtum Maris ex principiis traditis explicemus, conſi-<lb />derandum eſt, Tellurem, ut &amp; </s>
          <s xml:space="preserve">etiam omnia corpora <lb />in hujus viciniis, in Lunam gravitare <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò particulæ aqueæ,
<ptr xml:id="note-0721-14a" corresp="note-0721-14" type="noteAnchor" />
in Telluris ſuperficie, quæ verſus centrum Telluris tendunt, <lb />(hìc enim negligimus conſiderationem n. </s>
          <s xml:space="preserve">1371.) </s>
          <s xml:space="preserve">cum hac ver-<lb />ſus Lunam feruntur. </s>
          <s xml:space="preserve">Cùm etiam ſolida Telluris maſſa ad Lu-<lb />nam feratur, juxta leges, quæ locum haberent, ſi omnis mate-<lb />
<ptr xml:id="note-0721-15a" corresp="note-0721-15" type="noteAnchor" />
ria ex quâ conſtat in centro coacta daretur<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">poterunt demon-
<ptr xml:id="note-0721-16a" corresp="note-0721-16" type="noteAnchor" />
ſtrata, in capite 16. </s>
          <s xml:space="preserve">de actione Solis in Lunam, verſus Tel-<lb />lurem cadentem, dum cum hac Solem petit, applicari ad <lb />actionem Lunæ in particulas aqueas in Telluris ſuperfi-<lb />cie, cum Telluris maſſa non cohærentes, ſed verſus hujus
</s>
          <pb facs="0722" n="192" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
centrum tendentes, &amp; </s>
          <s xml:space="preserve">cum hujus maſſà, etiam verſus Lu-<lb />nam continuò cadentes; </s>
          <s xml:space="preserve">quâ vi, ut vidimus <ptr type="noteAnchor" />, Tellus reti-
<ptr xml:id="note-0722-01a" corresp="note-0722-01" type="noteAnchor" />
netur in orbitâ, circa commune gravitatis centrum hujus &amp; </s>
          <s xml:space="preserve"><lb />Lunæ.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0721-14" corresp="note-0721-14a" n="*" anchored="true" place="margin">1206.</note>
              <note xml:space="preserve" xml:id="note-0721-15" corresp="note-0721-15a" n="*" anchored="true" place="margin">1126.</note>
              <note xml:space="preserve" xml:id="note-0721-16" corresp="note-0721-16a" place="margin">1390.</note>
              <note xml:space="preserve" xml:id="note-0722-01" corresp="note-0722-01a" n="*" anchored="true" place="margin">1280.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Sit S Luna; </s>
          <s xml:space="preserve">ALBl ſuperficies Telluris, cujus maſſa ad <lb />
<ptr xml:id="note-0722-02a" corresp="note-0722-02" type="noteAnchor" />
Lunam tendit, quaſi tota in T eſſet coacta; </s>
          <s xml:space="preserve">ex actione Lu-<lb />
<ptr xml:id="note-0722-03a" corresp="note-0722-03" type="noteAnchor" />
<ptr xml:id="note-0722-04a" corresp="note-0722-04" type="noteAnchor" />
næ particulæ aqueæ A &amp; </s>
          <s xml:space="preserve">B verſus T majorem acquirunt gra-<lb />vitatem <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">contra particulæ in L, l, ex gravitate amit-
<ptr xml:id="note-0722-05a" corresp="note-0722-05" type="noteAnchor" />
tunt <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Unde deducimus, ſi tota Tellus aquâ obtegatur,
<ptr xml:id="note-0722-06a" corresp="note-0722-06" type="noteAnchor" />
æquilibrium non dari, niſi magis elevata ſit hæc aqua, in <lb />punctis L &amp; </s>
          <s xml:space="preserve">l, quàm in toto circulo ab his punctis 90. </s>
          <s xml:space="preserve">gr. <lb /></s>
          <s xml:space="preserve">diſtanti; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ideò per puncta A &amp; </s>
          <s xml:space="preserve">B tranſeunti. </s>
          <s xml:space="preserve">Idcirco, a-<lb />ctione Lunæ, aqua adipiſcitur figuram ſphæroidis, forma-<lb />
<ptr xml:id="note-0722-07a" corresp="note-0722-07" type="noteAnchor" />
tam ex revolutione ovalis circa Axem majorem, qui conti-<lb />nuatus per Lunam tranſit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0722-02" corresp="note-0722-02a" place="margin">1391.</note>
              <note xml:space="preserve" xml:id="note-0722-03" corresp="note-0722-03a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0722-04" corresp="note-0722-04a" place="margin">fig. 1.</note>
              <note xml:space="preserve" xml:id="note-0722-05" corresp="note-0722-05a" n="*" anchored="true" place="margin">1287.</note>
              <note xml:space="preserve" xml:id="note-0722-06" corresp="note-0722-06a" n="*" anchored="true" place="margin">1296.</note>
              <note xml:space="preserve" xml:id="note-0722-07" corresp="note-0722-07a" place="margin">1392.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ponamus Lunam in Æquatore; </s>
          <s xml:space="preserve">omnes Sectiones Telluris <lb />parallelæ ad Æquatorem, cùm etiam ſphæroidis axi parallelæ <lb />ſint <ptr type="noteAnchor" />, ſunt ovales, quarum axes majores per Lunæ Meridia-
<ptr xml:id="note-0722-08a" corresp="note-0722-08" type="noteAnchor" />
num tranſeunt; </s>
          <s xml:space="preserve">unde ſequitur, Tellure quieſcente, in circulo <lb />
<ptr xml:id="note-0722-09a" corresp="note-0722-09" type="noteAnchor" />
quocunque latitudinis, aquam magis elevari in Meridia-<lb />no in quo Luna datur, &amp; </s>
          <s xml:space="preserve">in Meridiano oppoſito, quàm in <lb />Locis intermediis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0722-08" corresp="note-0722-08a" n="*" anchored="true" place="margin">1392.</note>
              <note xml:space="preserve" xml:id="note-0722-09" corresp="note-0722-09a" place="margin">1393.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve"><hi rend="small caps">Definitio</hi>.</head>
        <p>
          <s xml:space="preserve">DiesLunaris, eſt tempus lapſum interreceſſum Lunæ à Me-<lb />
<ptr xml:id="note-0722-10a" corresp="note-0722-10" type="noteAnchor" />
ridiano &amp; </s>
          <s xml:space="preserve">acceſſum ſequentem ad eundem. </s>
          <s xml:space="preserve">Dies hæc in vi-<lb />ginti quatuor horas Lunares dividitur. </s>
          <s xml:space="preserve">Superat diem natura-<lb />lem 50. </s>
          <s xml:space="preserve">minutis.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0722-10" corresp="note-0722-10a" place="margin">1394.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex motu Telluris circa axem, ſingulis diebus Lunaribus, loca <lb />ſingula per Meridianum Lunæ &amp; </s>
          <s xml:space="preserve">Meridianum oppoſirum tran-<lb />ſeunt, id eſt bis ibi tranſeunt, ubi aquâ ex actione Lunæ eleva-<lb />
<ptr xml:id="note-0722-11a" corresp="note-0722-11" type="noteAnchor" />
tur, &amp; </s>
          <s xml:space="preserve">bis ubi ex eâdem actione deprimitur <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſic in die lu-
<ptr xml:id="note-0722-12a" corresp="note-0722-12" type="noteAnchor" />
nari Mare bis elevatur, bis deprimitur, in loco quocunque.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0722-11" corresp="note-0722-11a" place="margin">1395.</note>
              <note xml:space="preserve" xml:id="note-0722-12" corresp="note-0722-12a" n="*" anchored="true" place="margin">1393.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ex motu Telluris circa axem, continuò aqua elevata à Meri-<lb />
<ptr xml:id="note-0722-13a" corresp="note-0722-13" type="noteAnchor" />
diano Lunæ recedit; </s>
          <s xml:space="preserve">actione tamen Lunæ, Sphæroidis axis <lb />per Lunam tranſit<ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò agitatur continuo aqua, ut eleva-
<ptr xml:id="note-0722-14a" corresp="note-0722-14" type="noteAnchor" />
tio, ex motu Telluris, remota, infra Lunam inſtauretur. </s>
          <s xml:space="preserve">Ideò <lb />
<ptr xml:id="note-0722-15a" corresp="note-0722-15" type="noteAnchor" />
<ptr xml:id="note-0722-16a" corresp="note-0722-16" type="noteAnchor" />
ab A &amp; </s>
          <s xml:space="preserve">B continuo verſus L &amp; </s>
          <s xml:space="preserve">l ſluit aqua. </s>
          <s xml:space="preserve">dum ex motu
</s>
          <pb facs="0723" n="193" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XIX.</fw>
Telluris elevatio ab L verſus B &amp; </s>
          <s xml:space="preserve">ab l verſus A fertur; </s>
          <s xml:space="preserve">id eſt, inter <lb />L &amp; </s>
          <s xml:space="preserve">B, ut &amp; </s>
          <s xml:space="preserve">inter l &amp; </s>
          <s xml:space="preserve">A, dantur duo motus contrarii, quibus <lb />aqua accumulatur; </s>
          <s xml:space="preserve">ita ut elevationes maximæ inter hæc pun-<lb />cta, ad latus Lunæ &amp; </s>
          <s xml:space="preserve">puncti oppoſiti, dentur. </s>
          <s xml:space="preserve">Id eſt, in locis <lb />quibuſcunque aqua maximè eſt elevata, duabus aut tribus <lb />
<ptr xml:id="note-0723-01a" corresp="note-0723-01" type="noteAnchor" />
horis poſtquam Luna per Meridianum loci, aut Meridia-<lb />num oppoſitum, tranſivit.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0722-13" corresp="note-0722-13a" place="margin">1396.</note>
              <note xml:space="preserve" xml:id="note-0722-14" corresp="note-0722-14a" n="*" anchored="true" place="margin">1392.</note>
              <note xml:space="preserve" xml:id="note-0722-15" corresp="note-0722-15a" place="margin"><hi rend="small caps">TAB. XXV</hi>.</note>
              <note xml:space="preserve" xml:id="note-0722-16" corresp="note-0722-16a" place="margin">Fig. 6.</note>
              <note xml:space="preserve" xml:id="note-0723-01" corresp="note-0723-01a" place="margin">1397.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Elevatio ad partem Lunæ paululum excedit oppoſitam <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0723-02a" corresp="note-0723-02" type="noteAnchor" />
Minuitur aſcenſus aquarum acceſſu ad Polum, in quo nulla <lb />
<ptr xml:id="note-0723-03a" corresp="note-0723-03" type="noteAnchor" />
aquarum agitatio datur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0723-02" corresp="note-0723-02a" place="margin">1398.</note>
              <note xml:space="preserve" xml:id="note-0723-03" corresp="note-0723-03a" n="*" anchored="true" place="margin">1390. 1295.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" place="margin">1399.</note>
        <p>
          <s xml:space="preserve">Quæ de Lunâ demonſtrata ſunt, ad Solem applicari poſſunt; <lb /></s>
          <s xml:space="preserve">ideò, ex actione Solis, ſingulis diebus naturalibus, bis e-<lb />
<ptr xml:id="note-0723-05a" corresp="note-0723-05" type="noteAnchor" />
levatur Mare, bis deprimitur <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Agitatio hæc multò minor
<ptr xml:id="note-0723-06a" corresp="note-0723-06" type="noteAnchor" />
eſt, propter Solis immenſam diſtantiam, quàm quæ à Lunâ <lb />
<ptr xml:id="note-0723-07a" corresp="note-0723-07" type="noteAnchor" />
pendet; </s>
          <s xml:space="preserve">iiſdem tamen legibus ſubjicitur. <lb /></s>
          <s xml:space="preserve">
<ptr xml:id="note-0723-08a" corresp="note-0723-08" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0723-05" corresp="note-0723-05a" place="margin">1400.</note>
              <note xml:space="preserve" xml:id="note-0723-06" corresp="note-0723-06a" place="margin">1401.</note>
              <note xml:space="preserve" xml:id="note-0723-07" corresp="note-0723-07a" n="*" anchored="true" place="margin">1395.</note>
              <note xml:space="preserve" xml:id="note-0723-08" corresp="note-0723-08a" place="margin">1402.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Non diſtinguuntur motus ab actione Lunæ, &amp; </s>
          <s xml:space="preserve">Solis, pen-<lb />
<ptr xml:id="note-0723-09a" corresp="note-0723-09" type="noteAnchor" />
dentes, ſed conſunduntur, &amp; </s>
          <s xml:space="preserve">ex hujus actione tantùm muta-<lb />tur Maris ſluxus lunaris: </s>
          <s xml:space="preserve">quæ mutatio ſingulis diebus va-<lb />
<ptr xml:id="note-0723-10a" corresp="note-0723-10" type="noteAnchor" />
riat, propter inæqualitatem inter diem Naturalem &amp; </s>
          <s xml:space="preserve">diem Lu-<lb />narem <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0723-09" corresp="note-0723-09a" place="margin">1403.</note>
              <note xml:space="preserve" xml:id="note-0723-10" corresp="note-0723-10a" place="margin">1404.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1394.</note>
        <p>
          <s xml:space="preserve">In Syzygiis elevationes, ex amborum Luminarium actioni-<lb />
<ptr xml:id="note-0723-12a" corresp="note-0723-12" type="noteAnchor" />
bus, concurrunt, &amp; </s>
          <s xml:space="preserve">magis elevatur Mare; </s>
          <s xml:space="preserve">minus adſcendit <lb />Mare in Quadr aturis; </s>
          <s xml:space="preserve">nam ubi aqua Lunæ actione elevatur, <lb />deprimitur ex actione Solis, &amp; </s>
          <s xml:space="preserve">vice versâ. </s>
          <s xml:space="preserve">Idcircó, dum Lu-<lb />
<ptr xml:id="note-0723-13a" corresp="note-0723-13" type="noteAnchor" />
na à Syzygiâ ad Quadraturam tranſit, elevationes quotidia-<lb />næ de die in diem minuuntur: </s>
          <s xml:space="preserve">augentur contrà in motu à <lb />Quadraturâ ad Syzygiam. </s>
          <s xml:space="preserve">In Novilunio etiam, cæteris pari-<lb />
<ptr xml:id="note-0723-14a" corresp="note-0723-14" type="noteAnchor" />
bus, elevationes majores ſunt, &amp; </s>
          <s xml:space="preserve">quæ in eodem die ſeſe <lb />mutuò ſequuntur, magis differunt, quàm in Plenilunio <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0723-12" corresp="note-0723-12a" place="margin">1405.</note>
              <note xml:space="preserve" xml:id="note-0723-13" corresp="note-0723-13a" place="margin">1406.</note>
              <note xml:space="preserve" xml:id="note-0723-14" corresp="note-0723-14a" place="margin">1407.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1398. 1402.</note>
        <p>
          <s xml:space="preserve">Elevationes maximæ &amp; </s>
          <s xml:space="preserve">minimæ non obſervantur, niſiſe-<lb />
<ptr xml:id="note-0723-16a" corresp="note-0723-16" type="noteAnchor" />
cundâ, aut tertiâ, die poſt Novilunium, aut Plenilunium, <lb />quia motus acquiſitus non ſtatim ex attritu, &amp; </s>
          <s xml:space="preserve">aliis cauſis, de-<lb />ſtruitur, quo motu acquiſito adſcenſus aquarum augetur, licèt <lb />minuatur actio quâ Mare elevatur: </s>
          <s xml:space="preserve">ſimile quid circà calorem <lb />alibi <ptr type="noteAnchor" /> demonſtravimus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0723-16" corresp="note-0723-16a" place="margin">1408.</note>
            </div>
          </body>
        </floatingText>
        <note xml:space="preserve" n="*" anchored="true" place="margin">1174.</note>
        <p>
          <s xml:space="preserve">Si nunc Luminaria ex Æquatoris plano recedentia conſidere-<lb />mus, videbimus agitationem minui, &amp; </s>
          <s xml:space="preserve">minorem dari, prò <lb />
<ptr xml:id="note-0723-18a" corresp="note-0723-18" type="noteAnchor" />
</s>
          <pb facs="0724" n="(194)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
majori luminarium declinatione. </s>
          <s xml:space="preserve">Quod clarè patet ſi hæc in <lb />Polis concipiamus; </s>
          <s xml:space="preserve">tunc enim Axis figuræ ſphæroidis cum Axe <lb />Telluris coincidit; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">omnes ſectiones ad Æquatorem paral-<lb />lelæ ad Axem ſphæroidis ſunt perpendiculares; </s>
          <s xml:space="preserve">ideòque cir-<lb />culares. </s>
          <s xml:space="preserve">Ita ut, aqua, in ſingulis circulis latitudinis, ubique <lb />eandem habeat elevationem; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ſic in motu Telluris non mutatur <lb />altitudo Maris in locis peculiaribus. </s>
          <s xml:space="preserve">Si ex Polo recedant Lumi-<lb />naria agitationem continuò magis ac magis augeri, facile vi-<lb />demus, donec omnium ſit maxima, revolvente ſphæroide cir-<lb />ca lineam ad Axem perpendicularem, poſitâ ſphæroidis axe in <lb />plano Æquatoris.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0723-18" corresp="note-0723-18a" place="margin">1409.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Hinc liquet, quare in Syzygiis, prope Æquinoctia, Æ-<lb />
<ptr xml:id="note-0724-01a" corresp="note-0724-01" type="noteAnchor" />
ſtus omnium maximi obſervantur, ambobus Luminaribus in <lb />Æquatore aut prope hunc verſantibus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0724-01" corresp="note-0724-01a" place="margin">1410.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Actiones Lunæ &amp; </s>
          <s xml:space="preserve">Solis majores ſunt, quo minus hæc cor-<lb />
<ptr xml:id="note-0724-02a" corresp="note-0724-02" type="noteAnchor" />
pora à Tellure diſtant <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">cùm autem minor Solis diſtantia
<ptr xml:id="note-0724-03a" corresp="note-0724-03" type="noteAnchor" />
detur, hoc verſante in ſignis auſtralibus, ſæpe ambo Æſtus ma-<lb />ximi Æquinoctiales in illo ſitu Solis obſervantur; </s>
          <s xml:space="preserve">id eſt ante <lb />Æquinoctium Vernum &amp; </s>
          <s xml:space="preserve">poſt Autumnale; </s>
          <s xml:space="preserve">quod tamen non <lb />ſingulis annis obtinet; </s>
          <s xml:space="preserve">quia ex ſitu orbitæ Lunaris, &amp; </s>
          <s xml:space="preserve">diſtan-<lb />tiâ Syzygiæ ab Æquinoctio variatio dari poteſt.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0724-02" corresp="note-0724-02a" place="margin">1411.</note>
              <note xml:space="preserve" xml:id="note-0724-03" corresp="note-0724-03a" n="*" anchored="true" place="margin">1354. 1390.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">In Locis ab Æquatore diſtantibus, receſſu Luminarium ab <lb />
<ptr xml:id="note-0724-04a" corresp="note-0724-04" type="noteAnchor" />
Æquatore, inæquales fiunt ejuſdem diei elevationes. </s>
          <s xml:space="preserve">Sit <lb />
<ptr xml:id="note-0724-05a" corresp="note-0724-05" type="noteAnchor" />
<ptr xml:id="note-0724-06a" corresp="note-0724-06" type="noteAnchor" />
PP Telluris Axis; </s>
          <s xml:space="preserve">EE Æquator; </s>
          <s xml:space="preserve">L l circulus latitudinis; <lb /></s>
          <s xml:space="preserve">AB axis ſphæroidis figuræ, quam format aqua: </s>
          <s xml:space="preserve">quando locus <lb />in circulo Ll, datur in L aut l, datur in eodem Meridiano cum <lb />axe ſphæroidis &amp; </s>
          <s xml:space="preserve">aqua eſt maximè elevata, in utroque caſu; </s>
          <s xml:space="preserve">in L <lb />tamen magis quàm in l; </s>
          <s xml:space="preserve">nam CL ſuperat Cl, quæ lineæ altitudines <lb />aquarum, id eſt diſtantiæ à centro, menſurant: </s>
          <s xml:space="preserve">æquales hæ <lb />forent ſi AL &amp; </s>
          <s xml:space="preserve">B l diſtantiæ ab axe ſphæroidis forent æquales, <lb />minor autem eſt Cl, quia Bl ſuperat AL, quod ex inclina-<lb />tione Axeos ſphæroidis ad Æquatorem oritur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0724-04" corresp="note-0724-04a" place="margin">1412.</note>
              <note xml:space="preserve" xml:id="note-0724-05" corresp="note-0724-05a" place="margin">TAB. XXV.</note>
              <note xml:space="preserve" xml:id="note-0724-06" corresp="note-0724-06a" place="margin">fig. 8.</note>
            </div>
          </body>
        </floatingText>
        <p rend="italics">
          <s xml:space="preserve">Quamdiù Luna ad eandem partem Æquatoris cum loco <lb />
<ptr xml:id="note-0724-07a" corresp="note-0724-07" type="noteAnchor" />
datur, id eſt, ad partem lineæ CA continuatæ, aquæ eleva-<lb />tio maxima ſingulis diebus obſervatur, poſt tranſitum Lunæ <lb />per Meridianum Loci, maxima enim datur elevatio, ubi locus <lb />pervenit ad L; </s>
          <s xml:space="preserve">ſi autem Æquator ſeparet Lunam &amp; </s>
          <s xml:space="preserve">locum, <lb />
<ptr xml:id="note-0724-08a" corresp="note-0724-08" type="noteAnchor" />
</s>
          <pb facs="0725" n="(195)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XIX.</fw>
de quo agitur, id eſt ſi detur illa ad partem lineæ CB conti-<lb />nuatæ, aqua iterum in L, ad maximam pertingit altitudinem, <lb />&amp;</s>
          <s xml:space="preserve">, ſingulis diebus, maxima Maris datur elevatio, poſt <lb />tranſitum Lunæ per Meridianum oppoſitum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0724-07" corresp="note-0724-07a" place="margin">1413.</note>
              <note xml:space="preserve" xml:id="note-0724-08" corresp="note-0724-08a" place="margin">1414.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Omnia quæ huc uſque fuere expoſita, exactiſſimè obtine-<lb />rent, ſi tota Telluris ſuperficies Mare obtegeretur; </s>
          <s xml:space="preserve">cùm autem <lb />non ubique Mare detur, mutationes inde oriuntur, non qui-<lb />dem in Mare aperto; </s>
          <s xml:space="preserve">quia ſatis extenditur Oceanus ut memo-<lb />ratis motibus ſubjiciatur. </s>
          <s xml:space="preserve">Sed ſitus littorum, freta, multa-<lb />
<ptr xml:id="note-0725-01a" corresp="note-0725-01" type="noteAnchor" />
que alia, à peculiari locorum ſitu pendentia, generales regulas <lb />turbant. </s>
          <s xml:space="preserve">Generalioribus tamen obſervationibus conſtat, Æſtum <lb />leges explicatas ſequi. </s>
          <s xml:space="preserve">Supereſt, ut ipſas vires quibus Sol &amp; </s>
          <s xml:space="preserve">Lu-<lb />na Mare agitant determinemus, ut pateat has valere ad me-<lb />moratos edendos effectus, &amp; </s>
          <s xml:space="preserve">illorum corporum actiones in <lb />pendula &amp; </s>
          <s xml:space="preserve">cætera corpora inſenſibiles eſſe.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0725-01" corresp="note-0725-01a" place="margin">1415.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Augmentum gravitatis Lunæ in Quadraturis, ex actione <lb />
<ptr xml:id="note-0725-02a" corresp="note-0725-02" type="noteAnchor" />
Solis, eſt ad ipſam Lunæ gravitatem in Tellurem, ut 1. </s>
          <s xml:space="preserve">ad <lb />178, 73. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> in quâ computatione poſuimus, Lunæ diſtantiam me-
<ptr xml:id="note-0725-03a" corresp="note-0725-03" type="noteAnchor" />
diam à centro Telluris eſſe 60. </s>
          <s xml:space="preserve">ſemid. </s>
          <s xml:space="preserve">Telluris <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">gravitas ergo
<ptr xml:id="note-0725-04a" corresp="note-0725-04" type="noteAnchor" />
Lunæ eſt ad gravitatem in Telluris ſuperficie, ut 1. </s>
          <s xml:space="preserve">ad 60 x <lb />
<ptr xml:id="note-0725-05a" corresp="note-0725-05" type="noteAnchor" />
60 = 3600 <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Eſt idcirco augmentum memoratum ad gravi-
tatem in Telluris ſuperſicie, ut 1. </s>
          <s xml:space="preserve">ad 643428.</s>
          <s xml:space="preserve">, in quâ com-<lb />putatione error datur corrigendus.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0725-02" corresp="note-0725-02a" place="margin">1416.</note>
              <note xml:space="preserve" xml:id="note-0725-03" corresp="note-0725-03a" n="*" anchored="true" place="margin">1291.</note>
              <note xml:space="preserve" xml:id="note-0725-04" corresp="note-0725-04a" n="*" anchored="true" place="margin">1285.</note>
              <note xml:space="preserve" xml:id="note-0725-05" corresp="note-0725-05a" n="*" anchored="true" place="margin">1208.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Exacta foret computatio hæc, ſi augmentum, de quo agitur, <lb />eſſet ad vim, quâ Tellus verſus Solem deſcendit, ut diſtan-<lb />tia Lunæ 60. </s>
          <s xml:space="preserve">ſemid. </s>
          <s xml:space="preserve">Telluris ad diſtantiam Telluris à Sole <ptr type="noteAnchor" />;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0725-06a" corresp="note-0725-06" type="noteAnchor" />
ſed eſt ut vera media Lunæ diſtantia, 60 {1/2} ſemid. </s>
          <s xml:space="preserve">Telluris, ad <lb />diſtantiam Telluris à Sole. </s>
          <s xml:space="preserve">Quare augmentum ſtatim determi-<lb />natum parte {1/120} augeri debet, &amp; </s>
          <s xml:space="preserve">ſe habebit ad vim gravitatis <lb />in ſuperficie Telluris; </s>
          <s xml:space="preserve">ut 1 {1/120} ad 643428, aut ut 1. </s>
          <s xml:space="preserve">ad <lb />638110,4.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0725-06" corresp="note-0725-06a" n="*" anchored="true" place="margin">1287.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Augmentum hoc gravitatis Lunæ in quadraturis ex actione <lb />Solis, eſt ad augmentum gravitatis aquæ in ſuperficie Telluris, <lb />in locis à Sole 90. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">diſtantibus, ex eâdem Solis actione, ut <lb />60 {1/2} ad 1. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> ideo augmentum hoc gravitatis ad ipſam aquæ
<ptr xml:id="note-0725-07a" corresp="note-0725-07" type="noteAnchor" />
graviratem, ut 1. </s>
          <s xml:space="preserve">ad 38605679. </s>
          <s xml:space="preserve">Diminutio gravitatis ſub Sole, <lb />&amp; </s>
          <s xml:space="preserve">in loco oppoſito, eſt dupla hujus augmenti <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò eſt ad
<ptr xml:id="note-0725-08a" corresp="note-0725-08" type="noteAnchor" />
</s>
          <pb facs="0726" n="(196)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
gravitatem, ut 1. </s>
          <s xml:space="preserve">ad 19302839, &amp; </s>
          <s xml:space="preserve">tota mutatio in gravita-<lb />
<ptr xml:id="note-0726-01a" corresp="note-0726-01" type="noteAnchor" />
te, ex actione Solis, eſt ad ipſam gravitatem, ut 1. </s>
          <s xml:space="preserve">ad <lb />12868560.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0725-07" corresp="note-0725-07a" n="*" anchored="true" place="margin">1288.</note>
              <note xml:space="preserve" xml:id="note-0725-08" corresp="note-0725-08a" n="*" anchored="true" place="margin">1296.</note>
              <note xml:space="preserve" xml:id="note-0726-01" corresp="note-0726-01a" place="margin">1417.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut actionem Lunæ cum actione Solis comparemus, expe-<lb />
<ptr xml:id="note-0726-02a" corresp="note-0726-02" type="noteAnchor" />
rimenta ſunt inſtituenda in locis, in quibus, propter angu-<lb />ſtias, Mare ſenſibiliter elevatur. </s>
          <s xml:space="preserve">Prope Briſtoliam tempore <lb />Autumnali &amp; </s>
          <s xml:space="preserve">Verno, in quo agitatio Maris eſt maxima <ptr type="noteAnchor" />,
<ptr xml:id="note-0726-03a" corresp="note-0726-03" type="noteAnchor" />
adſcendit aqua in Syzygiis, plus minus, pedibus 45.</s>
          <s xml:space="preserve">; in Qua-<lb />draturis pedibus, plus minus, 25.</s>
          <s xml:space="preserve">, qui numeri ſunt inter ſe, <lb />ut 9. </s>
          <s xml:space="preserve">ad 4.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0726-02" corresp="note-0726-02a" place="margin">1418.</note>
              <note xml:space="preserve" xml:id="note-0726-03" corresp="note-0726-03a" n="*" anchored="true" place="margin">1410.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Facillima foret determinatio virium, quas quærimus, ſi <lb />elevationes maximæ &amp; </s>
          <s xml:space="preserve">minimæ exactè in Syzygiis darentur, <lb />quod non obtinere antea vidimus <ptr type="noteAnchor" />,
<ptr xml:id="note-0726-04a" corresp="note-0726-04" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0726-04" corresp="note-0726-04a" n="*" anchored="true" place="margin">1408.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diſtantia autem Lunæ à Syzygiâ, aut à Quadraturâ, non <lb />ſemper eſt eadem in maximâ aut minimâ elevatione; </s>
          <s xml:space="preserve">nam va-<lb />riat hæc diſtantia, quia Luna nunc magis nunc minus à Me-<lb />ridiano diſtat, quando per Syzygiam aut Quadraturam tran-<lb />ſit. </s>
          <s xml:space="preserve">Diſtantia media Lunæ à Syzygiâ, aut Quadraturâ, ad <lb />quam obſervationes memoratæ referri debent eſt circiter 18. <lb /></s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">30′; </s>
          <s xml:space="preserve">ita ut non tota Solis actio, neque cum Lunæ actione <lb />conſpiret in Syzygiis, neque contrariè agat in Quadraturis. </s>
          <s xml:space="preserve"><lb />Etiam in tali caſu, ſi in Syzygiâ, ambo luminaria in Æquatore <lb />fuerint, in memoratâ diſtantiâ à Quadraturâ, declinatio Lu-<lb />næ eſt plus minus 22. </s>
          <s xml:space="preserve">gr. </s>
          <s xml:space="preserve">13′; </s>
          <s xml:space="preserve">quo minuitur Lunæ vis ad <lb />Mare movendum <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Ulterius, cæteris paribus, diſtantia
<ptr xml:id="note-0726-05a" corresp="note-0726-05" type="noteAnchor" />
Lunæ à Tellure in Syzygiis minor eſt, quàm in Quadratu-<lb />ris <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">unde etiam actio Lunæ in Quadraturis minuitur <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">ad
<ptr xml:id="note-0726-06a" corresp="note-0726-06" type="noteAnchor" />
<ptr xml:id="note-0726-07a" corresp="note-0726-07" type="noteAnchor" />
quæ omnia attendendo detegitur, vim mediocrem Solis ad <lb />
<ptr xml:id="note-0726-08a" corresp="note-0726-08" type="noteAnchor" />
Mare movendum ſe habere ad vim mediocrem Lunæ ad i-<lb />dem agitandum, ut 1. </s>
          <s xml:space="preserve">ad 4,4815. </s>
          <s xml:space="preserve">Sed vis Solis eſt ad vim <lb />
<ptr xml:id="note-0726-09a" corresp="note-0726-09" type="noteAnchor" />
gravitatis, ut 1. </s>
          <s xml:space="preserve">ad 12868560. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare vis Lunæ eſt ad ean-
<ptr xml:id="note-0726-10a" corresp="note-0726-10" type="noteAnchor" />
dem vim gravitatis, ut 1. </s>
          <s xml:space="preserve">ad 2871485. </s>
          <s xml:space="preserve">Ex quibus ſequitur, <lb />vires has Lunæ &amp; </s>
          <s xml:space="preserve">Solis nimium eſſe exiguas, ut in pendulis &amp; </s>
          <s xml:space="preserve"><lb />aliis experimentis ſint ſenſibiles; </s>
          <s xml:space="preserve">has autem ipſas valere ad Ma-<lb />re agitandum facile probatur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0726-05" corresp="note-0726-05a" n="*" anchored="true" place="margin">1409.</note>
              <note xml:space="preserve" xml:id="note-0726-06" corresp="note-0726-06a" n="*" anchored="true" place="margin">1310. 1311.</note>
              <note xml:space="preserve" xml:id="note-0726-07" corresp="note-0726-07a" n="*" anchored="true" place="margin">1411.</note>
              <note xml:space="preserve" xml:id="note-0726-08" corresp="note-0726-08a" place="margin">1419.</note>
              <note xml:space="preserve" xml:id="note-0726-09" corresp="note-0726-09a" n="*" anchored="true" place="margin">1417.</note>
              <note xml:space="preserve" xml:id="note-0726-10" corresp="note-0726-10a" place="margin">1420.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diminuendo gravitatem parte {1/289} Mare elevatur ad altitudi-<lb />nem pedum Rhenolandicorum 88902. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />, perticæ enim ſin-
<ptr xml:id="note-0726-11a" corresp="note-0726-11" type="noteAnchor" />
</s>
          <pb facs="0727" />
          <s xml:space="preserve">
</s>
          <pb facs="0727a" />
          <s xml:space="preserve">
<ptr xml:id="fig-0727a-01a" corresp="fig-0727a-01" type="figureAnchor" />
</s>
          <pb facs="0728" />
          <s xml:space="preserve">
</s>
          <pb facs="0729" n="(197)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA LIB. IV. CAP. XX.</fw>
gulæ continent pedes duodecim: </s>
          <s xml:space="preserve">unde detegitur <ptr type="noteAnchor" /> ope regulæ
<ptr xml:id="note-0729-01a" corresp="note-0729-01" type="noteAnchor" />
proportionum, Solis actionem mutare Maris altitudinem <lb />
<ptr xml:id="note-0729-02a" corresp="note-0729-02" type="noteAnchor" />
pedibus duobus, &amp; </s>
          <s xml:space="preserve">hanc ex Lunæ actione mutari pedibus <lb />
<ptr xml:id="note-0729-03a" corresp="note-0729-03" type="noteAnchor" />
8,95 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">ex ambabus actionibus conjunctis agitatio me-
<ptr xml:id="note-0729-04a" corresp="note-0729-04" type="noteAnchor" />
diocris eſt circiter undecim pedum, quod cum obſervationi-<lb />
<ptr xml:id="note-0729-05a" corresp="note-0729-05" type="noteAnchor" />
bus ſatis congruit; </s>
          <s xml:space="preserve">nam in Oceano aperto, pro ut Mare magis <lb />aut minus patet, elevatur aqua, ad altitudinem ſex, novem, <lb />duodecim, vel quindecim pedum; </s>
          <s xml:space="preserve">in quibus elevationibus etiam <lb />differentia datur ex profunditate aquarum. </s>
          <s xml:space="preserve">Elevationes verò, <lb />quæ has multum excedunt, locum habent, ubi magnâ vi <lb />
<ptr xml:id="note-0729-06a" corresp="note-0729-06" type="noteAnchor" />
Mare freta intrat, in quibus impetus non frangitur, niſi <lb />majori adſcenſu.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0726-11" corresp="note-0726-11a" n="*" anchored="true" place="margin">1368.</note>
              <figure xml:id="fig-0727a-01" corresp="fig-0727a-01a">
                <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0727a-01" />
                <label>0727a-01</label>
              </figure>
              <note xml:space="preserve" xml:id="note-0729-01" corresp="note-0729-01a" n="*" anchored="true" place="margin">1417.</note>
              <note xml:space="preserve" xml:id="note-0729-02" corresp="note-0729-02a" place="margin">1421.</note>
              <note xml:space="preserve" xml:id="note-0729-03" corresp="note-0729-03a" place="margin">1422.</note>
              <note xml:space="preserve" xml:id="note-0729-04" corresp="note-0729-04a" n="*" anchored="true" place="margin">1419.</note>
              <note xml:space="preserve" xml:id="note-0729-05" corresp="note-0729-05a" place="margin">1423.</note>
              <note xml:space="preserve" xml:id="note-0729-06" corresp="note-0729-06a" place="margin">1424.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">CAPUT XX.</head>
        <head rend="italics" xml:space="preserve">De Lunæ Denſitate &amp; Figurâ.</head>
        <p>
          <s xml:space="preserve">Vires Solis &amp; </s>
          <s xml:space="preserve">Lunæ ad Mare movendum, ſunt inter ſe in <lb />
<ptr xml:id="note-0729-07a" corresp="note-0729-07" type="noteAnchor" />
ratione compoſitâ, ex ratione quantitatum materiæ in <lb />his corporibus <ptr type="noteAnchor" />, (ſingulæ enim particulæ agunt) &amp; </s>
          <s xml:space="preserve">ratione in:</s>
          <s xml:space="preserve">
<ptr xml:id="note-0729-08a" corresp="note-0729-08" type="noteAnchor" />
versâ cuborum diſtantiarum Solis &amp; </s>
          <s xml:space="preserve">Lunæ à Tellure <ptr type="noteAnchor" />,
<ptr xml:id="note-0729-09a" corresp="note-0729-09" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0729-07" corresp="note-0729-07a" place="margin">1425.</note>
              <note xml:space="preserve" xml:id="note-0729-08" corresp="note-0729-08a" n="*" anchored="true" place="margin">1207.</note>
              <note xml:space="preserve" xml:id="note-0729-09" corresp="note-0729-09a" n="*" anchored="true" place="margin">1390. 1402.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quantitates materiæ ſunt in ratione compoſitâ, ex ratione <lb />
<ptr xml:id="note-0729-10a" corresp="note-0729-10" type="noteAnchor" />
voluminum, id eſt cuborum diametrorum, &amp; </s>
          <s xml:space="preserve">ratione denſita-<lb />tum <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quare vires memoratæ ſunt directè ut denſitates &amp;</s>
          <s xml:space="preserve">
<ptr xml:id="note-0729-11a" corresp="note-0729-11" type="noteAnchor" />
cubi diametrorum, &amp; </s>
          <s xml:space="preserve">inversè ut cubi diſtantiarum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0729-10" corresp="note-0729-10a" place="margin">1354.</note>
              <note xml:space="preserve" xml:id="note-0729-11" corresp="note-0729-11a" n="*" anchored="true" place="margin">288. 79.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Diametri apparentes corporum, id eſt, anguli ſub quibus <lb />videntur’, creſcunt ut ipſæ diametri, &amp; </s>
          <s xml:space="preserve">minuuntur ut diſtantiæ; <lb /></s>
          <s xml:space="preserve">id eſt, ſunt directè ut diametri, &amp; </s>
          <s xml:space="preserve">inversè ut diſtantiæ; </s>
          <s xml:space="preserve">id-<lb />circo ratio compoſita ex ratione cuborum diametrorum appa-<lb />rentium Solis &amp; </s>
          <s xml:space="preserve">Lunæ, &amp; </s>
          <s xml:space="preserve">ex ratione denſitatum, erit ratio vi-<lb />
<ptr xml:id="note-0729-12a" corresp="note-0729-12" type="noteAnchor" />
rium, quibus hæc corpora Mare movent. </s>
          <s xml:space="preserve">Ideoque horum cor-<lb />porum denſitates ſunt directè ut vires, quibus Mare movent, <lb />&amp; </s>
          <s xml:space="preserve">inversè ut cubi diametrorum apparentium: </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">dividendo <lb />vires per cubos harum diametrorum, datur ratio denſitatum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0729-12" corresp="note-0729-12a" place="margin">1426.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Vis Solis eſt ad vim Lunæ, ut 1. </s>
          <s xml:space="preserve">ad 4,4815, <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">media diame-
<ptr xml:id="note-0729-13a" corresp="note-0729-13" type="noteAnchor" />
ter apparens Solis eſt 32′. </s>
          <s xml:space="preserve">12″, &amp; </s>
          <s xml:space="preserve">media Lunæ diameter ap-<lb />parens eſt 31′. </s>
          <s xml:space="preserve">16 {1/2}″. </s>
          <s xml:space="preserve">id eſt, ſunt inter ſe, ut 3864 ad 3753. </s>
          <s xml:space="preserve">Eſt <lb />igitur denſitas Solis ad Lunæ denſitatem, ut 10000 ad 48911.</s>
          <s xml:space="preserve">: <lb />
<ptr xml:id="note-0729-14a" corresp="note-0729-14" type="noteAnchor" />
quæ Lunæ denſitas cum Jovis, Saturni, &amp; </s>
          <s xml:space="preserve">Telluris den-
</s>
          <pb facs="0730" n="(198)" />
          <s xml:space="preserve"><fw type="head">PHYSICES ELEMENTA</fw>
ſitatibus poteſt conferri <ptr type="noteAnchor" />, eſtque Luna Tellure denſior.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0730-01a" corresp="note-0730-01" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0729-13" corresp="note-0729-13a" n="*" anchored="true" place="margin">1419.</note>
              <note xml:space="preserve" xml:id="note-0729-14" corresp="note-0729-14a" place="margin">1427.</note>
              <note xml:space="preserve" xml:id="note-0730-01" corresp="note-0730-01a" n="*" anchored="true" place="margin">1260.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Quantitates materiæ in duobus corporibus ſunt inter ſe in ra-<lb />tione compoſitâ denſitatum &amp; </s>
          <s xml:space="preserve">voluminum <ptr type="noteAnchor" />, id eſt, ſi de ſphæris
<ptr xml:id="note-0730-02a" corresp="note-0730-02" type="noteAnchor" />
agatur, in ratione compoſitâ denſitatum &amp; </s>
          <s xml:space="preserve">cuborum diametrorum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0730-02" corresp="note-0730-02a" n="*" anchored="true" place="margin">288. 79.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Lunæ &amp; </s>
          <s xml:space="preserve">Telluris denſitates ſunt inter ſe, ut 48911. </s>
          <s xml:space="preserve">ad <lb />
<ptr xml:id="note-0730-03a" corresp="note-0730-03" type="noteAnchor" />
39214. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">diametri ut 11. </s>
          <s xml:space="preserve">ad 40,2. </s>
          <s xml:space="preserve">ideò quantitates materiæ
<ptr xml:id="note-0730-04a" corresp="note-0730-04" type="noteAnchor" />
in his corporibus, ut 1. </s>
          <s xml:space="preserve">ad 39,13. </s>
          <s xml:space="preserve">Licèt denſitates detegan-<lb />tur, poſitis corporibus homogeneis, quantitates materiæ re-<lb />ctè definiuntur, quamvis corpora homogenea non ſint; </s>
          <s xml:space="preserve">nam <lb />illam determinamus denſitatem, quam corpus haberet, ſimateria, <lb />ex qua corpus reverâ conſtat, per hoc æqualiter diſpergeretur.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0730-03" corresp="note-0730-03a" place="margin">1428.</note>
              <note xml:space="preserve" xml:id="note-0730-04" corresp="note-0730-04a" n="*" anchored="true" place="margin">1427. 1260.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Gravitates in ſuperficiebus Telluris &amp; </s>
          <s xml:space="preserve">Lunæ determi-<lb />
<ptr xml:id="note-0730-05a" corresp="note-0730-05" type="noteAnchor" />
nantur, multiplicando denſitates per diametros <ptr type="noteAnchor" /> id eſt ſunt in-
<ptr xml:id="note-0730-06a" corresp="note-0730-06" type="noteAnchor" />
ter ſe, ut 2,93. </s>
          <s xml:space="preserve">ad 1.</s>
          <s xml:space="preserve">, aut ut 407,8. </s>
          <s xml:space="preserve">ad 139,2. </s>
          <s xml:space="preserve">qui nume-<lb />rus etiam exprimit relationem gravitatis in ſuperficie Lunæ, <lb />cum gravitate in ſuperficiebus Solis, Jovis, &amp; </s>
          <s xml:space="preserve">Saturni <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0730-07a" corresp="note-0730-07" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0730-05" corresp="note-0730-05a" place="margin">1429.</note>
              <note xml:space="preserve" xml:id="note-0730-06" corresp="note-0730-06a" n="*" anchored="true" place="margin">1230.</note>
              <note xml:space="preserve" xml:id="note-0730-07" corresp="note-0730-07a" n="*" anchored="true" place="margin">1258.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Centrum commune gravitatis Lunæ &amp; </s>
          <s xml:space="preserve">Telluris, circa <lb />
<ptr xml:id="note-0730-08a" corresp="note-0730-08" type="noteAnchor" />
quod ambo corpora moventur, determinatur; </s>
          <s xml:space="preserve">nam hujus à <lb />Telluris centro diſtantia, eſt ad diſtantiam intra centra ambo-<lb />rum corporum, ut quantitas materiæ in Lunâ ad quantitatem <lb />materiæ in ambobus corporibus <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">itaque 40,13. </s>
          <s xml:space="preserve">ad 1. </s>
          <s xml:space="preserve">ut Lu-
<ptr xml:id="note-0730-09a" corresp="note-0730-09" type="noteAnchor" />
næ diſtantia à Tellure ad diſtantiam quæſitam centri gravitatis <lb />à centro Telluris, quæ detegitur 5126950. </s>
          <s xml:space="preserve">perticarum, ut <lb />ex notis Telluris diametro <ptr type="noteAnchor" />, &amp; </s>
          <s xml:space="preserve">Lunæ diſtantiâ deducitur.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0730-10a" corresp="note-0730-10" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0730-08" corresp="note-0730-08a" place="margin">1430.</note>
              <note xml:space="preserve" xml:id="note-0730-09" corresp="note-0730-09a" n="*" anchored="true" place="margin">234. 235.</note>
              <note xml:space="preserve" xml:id="note-0730-10" corresp="note-0730-10a" n="*" anchored="true" place="margin">976.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Ut Lunæfiguram determinemus, examinanda eſt figura, quam, <lb />
<ptr xml:id="note-0730-11a" corresp="note-0730-11" type="noteAnchor" />
ſi fluida foret, acquireret <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si Lunam ſolam conſideremus qui-
<ptr xml:id="note-0730-12a" corresp="note-0730-12" type="noteAnchor" />
eſcentem, ſphærica erit <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Si actionem Telluris in Lunam con-
<ptr xml:id="note-0730-13a" corresp="note-0730-13" type="noteAnchor" />
ſideremus, acquireret Luna figuram ſphæroidis, cujus axis per <lb />Tellurem tranſiret <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Vis Telluris ad Lunæ figuram mutandam
<ptr xml:id="note-0730-14a" corresp="note-0730-14" type="noteAnchor" />
eſt ad vim Lunæ in Tellurem, ut 39,13. </s>
          <s xml:space="preserve">ad 1. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> &amp; </s>
          <s xml:space="preserve">ut diameter
<ptr xml:id="note-0730-15a" corresp="note-0730-15" type="noteAnchor" />
Lunæ ad Telluris diametrum <ptr type="noteAnchor" />, quæ ſunt inter ſe, ut 11 ad 40.</s>
          <s xml:space="preserve">2.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0730-16a" corresp="note-0730-16" type="noteAnchor" />
eſtque ratio compoſita ex his 10,7. </s>
          <s xml:space="preserve">ad 1. </s>
          <s xml:space="preserve">Hæc vis Lunæ eſt ad <lb />gravitatem in ſuperficie Telluris, ut 1. </s>
          <s xml:space="preserve">ad 2871485 <ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">quæ gra-
<ptr xml:id="note-0730-17a" corresp="note-0730-17" type="noteAnchor" />
vitas in Telluris ſuperficie eſt ad gravitatem in ſuperficie Lu-<lb />næ, ut 407,8. </s>
          <s xml:space="preserve">ad 139,2. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" /> aut ut 2871485′, ad 980028.</s>
          <s xml:space="preserve">;
<ptr xml:id="note-0730-18a" corresp="note-0730-18" type="noteAnchor" />
quare actio Telluris ad mutandam Lunæ figuram, ad gravita-<lb />
<ptr xml:id="note-0730-19a" corresp="note-0730-19" type="noteAnchor" />
tem in ſuperficie Lunæ, ut 10,7. </s>
          <s xml:space="preserve">ad 980028, aut ut 1. </s>
          <s xml:space="preserve">ad 91524.</s>
          <s xml:space="preserve">
</s>
          <pb facs="0731" n="(199)" />
          <s xml:space="preserve"><fw type="head">MATHEMATICA. LIB. IV. CAP. XXI,</fw>
mutatâ gravitate, in Telluris ſuperficie, parte {1/2871485}, aqua <lb />elevatur pedibus 8,95. </s>
          <s xml:space="preserve"><ptr type="noteAnchor" />; </s>
          <s xml:space="preserve">ideò, ſi gravitas parte {1/91524} mutare-
<ptr xml:id="note-0731-01a" corresp="note-0731-01" type="noteAnchor" />
tur, elevatio foret pedum 280,7, ut regulâ aureâ detegitur: <lb /></s>
          <s xml:space="preserve">ſi, ſervatâ hac diminutione gravitatis, de corpore minori a-<lb />gatur, minuenda eſt hæc altitudo in ratione diametri; </s>
          <s xml:space="preserve">ideò, <lb />ex actione Telluris, elevatio in Lunâ eſt pedum 76,8.</s>
          <s xml:space="preserve">: &amp; </s>
          <s xml:space="preserve"><lb />æquilibrium non dabitur, ſi Luna ſit bomogenea, niſi axis <lb />
<ptr xml:id="note-0731-02a" corresp="note-0731-02" type="noteAnchor" />
ſphæroidis ſuperet diametrum ad bunc perpendicularem pe-<lb />dibus 153,60.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0730-11" corresp="note-0730-11a" place="margin">1431.</note>
              <note xml:space="preserve" xml:id="note-0730-12" corresp="note-0730-12a" n="*" anchored="true" place="margin">1358.</note>
              <note xml:space="preserve" xml:id="note-0730-13" corresp="note-0730-13a" n="*" anchored="true" place="margin">1359.</note>
              <note xml:space="preserve" xml:id="note-0730-14" corresp="note-0730-14a" n="*" anchored="true" place="margin">1392.</note>
              <note xml:space="preserve" xml:id="note-0730-15" corresp="note-0730-15a" n="*" anchored="true" place="margin">1428. 1207.</note>
              <note xml:space="preserve" xml:id="note-0730-16" corresp="note-0730-16a" n="*" anchored="true" place="margin">1390. 1354.</note>
              <note xml:space="preserve" xml:id="note-0730-17" corresp="note-0730-17a" n="*" anchored="true" place="margin">1420.</note>
              <note xml:space="preserve" xml:id="note-0730-18" corresp="note-0730-18a" n="*" anchored="true" place="margin">1429.</note>
              <note xml:space="preserve" xml:id="note-0730-19" corresp="note-0730-19a" place="margin">1432.</note>
              <note xml:space="preserve" xml:id="note-0731-01" corresp="note-0731-01a" n="*" anchored="true" place="margin">1420. 1422.</note>
              <note xml:space="preserve" xml:id="note-0731-02" corresp="note-0731-02a" place="margin">1433.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Unicâ proportione detegitur, ex notâ elevatione Maris <lb />
<ptr xml:id="note-0731-03a" corresp="note-0731-03" type="noteAnchor" />
ex Lunæ actione, elevatio in Lunâ ex Telluris actione; </s>
          <s xml:space="preserve">nam <lb />ſunt hæ elevationes in ratione duplicatâ inverſâ gravitatum <lb />in ſuperficiebus illorum corporum.</s>
          <s xml:space="preserve" />
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0731-03" corresp="note-0731-03a" place="margin">1434.</note>
            </div>
          </body>
        </floatingText>
        <p>
          <s xml:space="preserve">Si, poſitâ hac Lunæ figurâ, partes cohærere concipiamus, <lb />æquilibrium inter Lunæ partes non dabitur, niſi axis ſphæ-<lb />
<ptr xml:id="note-0731-04a" corresp="note-0731-04" type="noteAnchor" />
roidis ad Tellurem dirigatur; </s>
          <s xml:space="preserve">unde videmus, quare Luna <lb />eandem faciem ſemper Telluri obvertat; </s>
          <s xml:space="preserve">quâ continuâ agi-<lb />tatione, Luna tandem acquiſivit motum circa axem, de quo <lb />
<ptr xml:id="note-0731-05a" corresp="note-0731-05" type="noteAnchor" />
antea egimus <ptr type="noteAnchor" />: </s>
          <s xml:space="preserve">qui motus neceſſario eodem tempore peragi.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0731-06a" corresp="note-0731-06" type="noteAnchor" />
tur, in quo Luna revolvitur; </s>
          <s xml:space="preserve">nam ex actione memoratâ, ſe <lb />ad celeritatem talem neceſſariò conſtituit; </s>
          <s xml:space="preserve">ſi enim major fo-<lb />ret celeritas, vi, quâ eadem facies ad Tellurem ſemper di-<lb />rigitur, continuò retardaretur; </s>
          <s xml:space="preserve">acceleraretur continuò ſi <lb />minor foret. </s>
          <s xml:space="preserve">Vis tamen hæc non eſt ſatis magna, ut in ſin-<lb />gulis revolutionibus æquabilitatem motus acquiſiti circa <lb />axem ſenſibiliter turbet: </s>
          <s xml:space="preserve">Ideò motus circa axem æquabilis eſt, <lb />
<ptr xml:id="note-0731-07a" corresp="note-0731-07" type="noteAnchor" />
licèt motu inæquali in orbitâ moveatur Luna <ptr type="noteAnchor" />. </s>
          <s xml:space="preserve">Situs etiam
<ptr xml:id="note-0731-08a" corresp="note-0731-08" type="noteAnchor" />
axis Lunæ, non vi memoratâ ita poteſt mutari, ut ad Planum <lb />orbitæ, dum hujus inclinatio mutatur <ptr type="noteAnchor" />, ſemper perpendi-
<ptr xml:id="note-0731-09a" corresp="note-0731-09" type="noteAnchor" />
cularis ſit, idcircò ad Planum orbitæ aliquando inclinatur <lb />
<ptr xml:id="note-0731-10a" corresp="note-0731-10" type="noteAnchor" />
axis Lunæ, ut antea vidimus <ptr type="noteAnchor" />.</s>
          <s xml:space="preserve">
<ptr xml:id="note-0731-11a" corresp="note-0731-11" type="noteAnchor" />
</s>
        </p>
        <floatingText>
          <body>
            <div type="float">
              <note xml:space="preserve" xml:id="note-0731-04" corresp="note-0731-04a" place="margin">1435.</note>
              <note xml:space="preserve" xml:id="note-0731-05" corresp="note-0731-05a" place="margin">1436.</note>
              <note xml:space="preserve" xml:id="note-0731-06" corresp="note-0731-06a" n="*" anchored="true" place="margin">970. 1092.</note>
              <note xml:space="preserve" xml:id="note-0731-07" corresp="note-0731-07a" place="margin">1437.</note>
              <note xml:space="preserve" xml:id="note-0731-08" corresp="note-0731-08a" n="*" anchored="true" place="margin">966.</note>
              <note xml:space="preserve" xml:id="note-0731-09" corresp="note-0731-09a" n="*" anchored="true" place="margin">1345.</note>
              <note xml:space="preserve" xml:id="note-0731-10" corresp="note-0731-10a" place="margin">1438.</note>
              <note xml:space="preserve" xml:id="note-0731-11" corresp="note-0731-11a" n="*" anchored="true" place="margin">1093.</note>
            </div>
          </body>
        </floatingText>
      </div>
      <div type="section">
        <head xml:space="preserve">FINIS LIBRI QUARTI.</head>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0731-01" />
          <label>0731-01</label>
        </figure>
        <pb facs="0732" />
        <fw type="head">CORRIGENDA.</fw>
        <note xml:space="preserve" place="margin"> <lb />Pag. # lin. # dele # lege <lb />(2.) # 25. # major # majus. <lb />(3.) # 3. in fine # Non tamen differentiam hanc in\vitto Anglicano obſervate potui, ni-\ſi illis diebus in quibus propter aëris\conſtitutionem languida eſt electri-\citas. <lb />(4.) # 25. # abc # abd <lb /># 27. # turquæ # tur, quæ <lb />(7.) # 5. # lamella # tabella <lb /># penult. &amp; ult. # obteguntur &amp; firmantur # obtegitur &amp; firmatur. <lb />(8.) # 16. # Gypſeis # ex Succino <lb />(25.) # 30. # IL # IG <lb />(28) # 6. # ſupra aqua # ſuper aquâ <lb />(36.) # 5.6. # O magis diſtet # O, magis diſtas <lb />(44.) # 18. # aquens # aqueus <lb />(47.) # 21. # inte # inter <lb />(66.) # 29. # diametrum # diameter <lb />(94.) # 33. # FG # FH <lb />(101.) # 9. # radiir eftectuntur # radii reflectuntur. <lb />(110.) # 24. # ipſer # ipſe <lb /># 29. # antecedentiâ # conſequentiâ <lb />(112.) # 8. # 60 {2/9} # 60 {1/2} <lb />(113.) # 27 # 340069. # 3400669. <lb />(117.) # 31. # videtur # videtur in conſequentiâ, <lb />(128) # 20. # Luna # Solis <lb />(130) # 5. # videtur # videtur in antecedentiâ <lb />(134) # 16. # fuperficies # ſuperficiem <lb />(135.) # 29. # Stella fixa # corpora caleſtia <lb />(146.) # 12. # horum # harum <lb />(173.) # 24. # inverſâ # inverſâ quadratorum <lb />(174) # 15. # Ll # l <lb />(185.) # 29. # ſequitur # ſequuntur <lb />(187) # 24. # AB; # AB; <lb />(189.) # 24. # centrum ducta # ſuperficiem perpendicularis <lb />#### IN MARGINE. <lb />(16.) # 33. # 291. # 190. <lb />(60.) # 27. # 191. # 190. <lb />(64) # 8. # TAB. XXI. \\ fig. 4. <lb />(128) # 24. # fig 4. # fig. 5. <lb />(138) # 14. # 191. # 192. <lb />(187) # 24. # <ptr type="noteAnchor" />232.
</note>
        <figure>
          <graphic url="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0732-01" />
          <label>0732-01</label>
        </figure>
        <pb facs="0733" />
      </div>
      <div type="section">
        <head xml:space="preserve">INDEX <lb />RERUM, <lb />Numeri (1), (11), deſignant Tomum pri-<lb />mum &amp; ſecundum, p. denotat paginam, <lb />&amp; n. numerum in margine.</head>
        <note xml:space="preserve" rend="italics" place="margin"> <lb />A. Acceleratio gravium: (1) p. <lb /> # 38. n. 129. &amp; ſeq. <lb /># --corporum ſuper <lb /># plano inclinato devol-<lb /># ventium. p. 42. n. 144. <lb /># &amp; ſeq. n. 135. &amp; ſeq. <lb />Æoli Pila. (11) p. 16. n. 606. 607. <lb />Æquatio Temporis (11) p. 138. n. 1145. <lb />Æquator (11) p. 129. n. 1075.. p. 134. <lb /># n. 1114. <lb />Æquinoctia. (11) p. 139. n. 1155. <lb />borum præceſſio. p. 143. n. 1186. p. <lb /># 144. n. 1193. <lb />motus bujus explicatio. p. 190. n. 1382. <lb /># &amp; ſeq. <lb />Aër inter fluida refertur. (1) p. 153. n. <lb /># 417. &amp; ſeq. <lb />--ponderatur. p. 163. n. 442. <lb />--Elaſticitatem babet. p. 155. n. 426. <lb /># &amp; ſeq. <lb />--ex particulis ſeparatis conſtat. p. <lb /># 158. n. 431. <lb />--experimenta bunc ſpectantia. p. <lb /># 163. n. 442. &amp; ſeq. <lb />--eſt vebiculum ſoni. p. 181. n. 504. <lb />--bujus actio in ignem. vide Ignem. <lb />Albor. (11) p. 90. n. 870. <lb />--ex permixtione colorum. ibid. n. <lb /># 871. &amp; 872. <lb />corpus album citius aliis incaleſcit. p. <lb /># 104. n. 909. <lb />Altitudo ſiderum. (11) p. 133. n. 1105. <lb />--Poli. p. 135. n. 1126. <lb />Amplitudo ſiderum. (11) p. 133. n. <lb /># 1104. <lb />Angulus incidentiæ (11) p. 21. n. 621. <lb />--Refractionis. ibid. n. 623. <lb />--Reflectionis. p. 59. n. 781. <lb />Animalia ad vivendum aëre indigent <lb /># (1) p. 169. n. 463. <lb />--in aëre compreſſo. p. 170. n. <lb /># 465. <lb />Annulus Saturni (11) p. 111. n. 963. <lb /># p. 124. n. 1034. <lb />Antlia Pneumatica. (1) p. 160. n. 435. <lb /># &amp; ſeq. <lb />Antliæ vulgares. (1) p. 172. n. 472. <lb />Aphelia Planetarum. (11) p. 109. n. <lb /># 935. <lb />Apſides Planetarum. (11) p. 109. n. <lb /># 937. <lb />linea Apſidum. n. 938. <lb />Aqua eſt glacies liquefacta. (11) p. 15. <lb /># n. 604. <lb />Arcus coeleſtis. Vide Iridem. <lb />Aſcenſus fluidorum in tubos capillares, <lb /># (1) p. 10. n. 35. <lb />--etiam in vacuo. n. 36. <lb />--inter duo vitrea plana. n. 37. <lb /># 38. <lb />Aſteriſmi. (11) p. 108. n. 1190. &amp; ſeq. <lb />Æſtus Maris. vide Mare. <lb />Atmoſphæra. (1) p. 153. n. 418. <lb /> # (Cc 2) <lb /></note>
        <pb facs="0734" />
        <note xml:space="preserve" place="margin"> <lb />Attractio. (1) p. 9. n. 31. <lb />-- bujus leges. ibid. <lb />-- ex gravitate. (11) p. 147. n. <lb /># 1210. <lb />Attractionis ſpatium. (11.) p. 23. n. 632. <lb />Auges. vide Apſides. <lb />Axiomata circa motum. (1) p. 15. n. 58. <lb /># &amp; ſeq. <lb />Axis Planetæ. (11) p. 110. n. 949. <lb />Axeos Telluris motus. vide Æquino-<lb /># ctiorum præceſſionem. <lb />Axis in Peritrochio. (1) p. 28. n. 112. <lb />-- hujus proprietates. n. 113. &amp; ſeq. <lb />-- libræ. p. 20. n. 84. <lb />B. <lb />Bilanx vide Libram. <lb />C. <lb />Calor. (11) p. 10. n. 579. 580. p. 11. <lb /># n. 584. <lb />Calorem non ſequi proportionem ignis. <lb /># p. 12. n. 588. <lb />Calore corpora lucent. p. 12. n. 591. <lb />-- corpora dilatantur. p. 13. n. 596. <lb /># 597. <lb />-- corpora quædam liquefiunt. p. 15. <lb /># n. 602. <lb />-- corpora quædam Elaſticitatem ac-<lb /># quirunt. p. 15. n. 605. <lb />quæ corpora citius incaleſcant. p. 104. <lb /># n. 908. <lb />Camera obſcura (11) p. 42. n. 711. p. 67. <lb /># n. 817. <lb />Celeritas. (1) p. 15. n. 53. <lb />-- relativa. p. 55. n. 175. <lb />Centrum libræ. (1) p. 21. n. 85. <lb />Centrum gravitatis. (1) p. 23. n. 95. <lb />-- hujus proprietates. n. 96 &amp; ſeq. <lb />-- oſcillationis. p. 47. n. 161. <lb />-- percuſſionis. p. 48. n. 162. <lb />Centrales vires (1) p. 76. n. 220. <lb />harum proprietates. n. 221. &amp; ſeq. <lb />harum comparatio. p. 82. n. 231. &amp; <lb /># ſeq. <lb />Centrifuga vis. (1) p. 76. n. 218. <lb />Centripeta vis. (1) p. 76. n. 219. <lb />Chordarum conſonantiæ. (1) p. 185. n. <lb /># 532. &amp; ſeq. <lb />-- motus aliis communicatus. p. <lb /># 186. n. 536. &amp; ſeq. <lb />Cochlea interior. (1) p. 33. n. 121. <lb />-- exterior. ibid. <lb />harum uſus. ibid. <lb />Cochlea perpetua. (1) p. 34. n. 123. <lb />Cœlum quid ſit. (11) p. 115. n. 986. <lb />-- quare cœruleum. p. 116. n. 987. <lb />Cohœſionis lex. (1) p. 9. n. 31. <lb />Color objectorum. (11) p. 84. n. 859. <lb />-- Radiorum. ibid. n. 860. <lb />-- immutabilis hic eſt. p. 85. n. 863. &amp; ſeq. <lb /># p. 89. n. 869. <lb />Colorum ordo ex diverſâ refrangibili-<lb /># tate. p. 84. n. 861. <lb />Colores permixti. p. 91. n. 873. 874. <lb />unde Colores vividi &amp; fuſci; p. 105. <lb /># n. 911. 915. <lb />unde Colores in quibuſdam corporibus <lb /># varii ſint, pro oculi ſitu. ibid. n. 914. <lb />mutatio Colorum in liquidis permixtis. <lb /># p. 106. n. 916. <lb />liquidum Coloris diverſi, ſi radiis re-<lb /># flexis aut tranſmiſſis videatur. ibid. <lb /># n. 917. <lb />Colores Nubium. ibid. n. 920. <lb />-- tenuium lamellarum &amp; horum <lb /># affectiones. p. 98. n. 887. &amp; ſeq. <lb />-- corporum unde oriantur p. 104. <lb /># n. 907. p. 105. n. 910. <lb />Cometæ (11) p. 114. n. 979. &amp; ſeq. <lb />Cometarum motus explicatio. (11) p. <lb /># 169. n. 1276. <lb />Conjunctio corporum cœleſtium. (11) <lb /># p. 119. n. 1010. <lb />Conſonantiæ. (1) p. 185. n. 525. &amp; ſeq. <lb /></note>
        <pb facs="0735" />
        <note xml:space="preserve" place="margin"> <lb />Corporis proprietates. (1) p. 3. n. 8. &amp; <lb /># ſeq. <lb />Crepuſcula. (11) p. 139. n. 1149. &amp; <lb /># ſeq. <lb />Cryſtallus montana ex attritu lucida. <lb /># (11) p. 2. n. 552. <lb />Cuneus. (1) p. 31. n. 118. 119. <lb />Curſus ſluminis. (1) p. 143. n. 392. &amp; <lb /># ſeq. <lb />hujus celeritatis menſura. p. 146. n. 399. <lb /># &amp; ſeq. <lb />D. <lb />Declinatio Sideris. (11) p. 129. n. <lb /># 1079. <lb />Denſitas. (1) p. 106. n. 284. <lb />Denſitatum ſluidorum determinatio. (1) <lb /># p. 113, n. 309. &amp; ſeq. <lb />-- ſolidorum comparatio. p. 116. <lb /># n. 315. &amp; ſeq. <lb />Denſitates Planetarum. (11) p. 164. <lb />-- n. 1260. p. <lb />Dies Naturalis. (11) p. 137. n. 1141. <lb />--artificialis. p. 138. n. 1147. <lb />harum differentiæ. p. 139. n. 1152. <lb /># &amp; ſeq. <lb />Lunaris Dies. p. 192. n. 1394. <lb />Dilatatio ex Calore. Vide Calorem. <lb />Ditonus. (1) p. 185. n. 530. <lb />Diviſibilitas Materiæ. (1) p. 3. n. 10. <lb /># p. 6. n. 17. &amp; ſeq. p. 8. n. 26. <lb />Durum corpus. (1) p. 8. n. 28. <lb />E. <lb />Echo. (1) p. 187. n. 542. <lb />Eclipſis Satellitis. (11) p. 124. n. <lb /># 1033. <lb />-- Lunæ. vide Lunam. <lb />-- Solis. vide Solem. <lb />Ecliptica linea. (11) p. 118. n. 999. <lb />Eclipticæ planum. p. 109. n. 940. <lb />Elaſticitas. (1) p. 13. n. 44. <lb />-- perfecta. p. 56. n. 177. <lb />Elaſticitatis lex. (1) p. 90. n. 251. <lb />Fibrarum Elaſticitas. p. 88. n. 244. &amp; <lb /># ſeq. <lb />Laminarum Elaſticitas. p. 95. n. 262. &amp; <lb /># ſeq. <lb />globi Elaſticitas. p. 96. n. 266. <lb />Elaſticitas ex calore. vid. Calorem. <lb />Electricitas. (11) p. 2. n 551. <lb />--Tubi vitrei. p. 2. n. 554. 555. <lb />--Globi vitrei. p. 4. n. 559. &amp; ſeq. <lb />Conjecturæ circa hujus cauſam. p. 5. n. <lb /># 563. &amp; ſeq. <lb />Elongatio Planetarum. (11) p. 119. n. <lb /># 1012. <lb />-- maxima. ibid. n. 1013. <lb />Excentricitas Planetarum. (11) p. 109. <lb /># n. 932. <lb />Extenſio. (1) p. 3. n. 8. p. 4. n. 13. <lb />F. <lb />Fibrarum Elaſticitas. (1) p. 88. n. <lb /># 244. &amp; ſeq. <lb />-- Vibrationes. p. 93. n. 257. &amp; ſeq. <lb />Flamma. (11) p. 11. n. 587. p. 12. n. 592. <lb />Fluidum. (1) p. 8. n. 30. <lb />Fluida, in quo cumſolidis congruant. (1) <lb /># p. 97. n. 270. <lb />Fluidorum proprietates. p. 98. n. 272. <lb /># &amp; ſeq. <lb />-- actiones in fundos &amp; lateravaſe-<lb /># rum. p. 101. n. 280. <lb />horum motus. (1) p. 127. n. 354. <lb />Fluida proſilientia verticaliter. p. 129. <lb /># n. 358. &amp; ſeq. vide fonticulum. <lb />-- proſilientia obliquè p. 133. n. 368. <lb /># &amp; ſeq. <lb />-- ex vaſis profluentia. p. 138. n. <lb /># 378. &amp; ſeq. <lb />comparatio temporum quibus vaſa eva-<lb /># cuantur. p. 139. n. 379. &amp; ſeq. <lb />Solida fluidis immerſa. p. 107. n. 290. &amp; <lb /># ſeq. <lb />-- graviora. p. 108. n. 292. n. 296. <lb /># &amp; ſeq. <lb /></note>
        <pb facs="0736" />
        <note xml:space="preserve" place="margin"> <lb />-- leviora. p. 112. n 306. &amp; ſeq. <lb />Fluiditas, unde oriatur. (1) p. 97. n. 269. <lb />-- an à calore pendeat? (11) p. 15. n. <lb /># 603. <lb />Flumen. (1) p. 143. n. 390. <lb />hujus ſectio. n. 391. <lb />hujus curſus. n. 392. &amp; ſeq. <lb />Focus. (11) p. 29. n. 650. <lb />Fonticulus Heronis. (1) p. 172. n. 474. <lb />-- ex aëris compreſſione. p, 168. n. <lb /># 459. <lb />Fonticuli duo. p. 167. n. 457. p. 168. n. <lb /># 458. <lb />Fumus. (11) p. 11. n. 587. p. 12. n. <lb /># 592. <lb />G. <lb />Gradus latitudinis accedendo ad po-<lb /># los augentur. (11) p. 189. n. 1374. <lb />Gravia non ad centrum Telluris tendunt. <lb /># (11) p. 189. n. 1371. <lb />Gravitas. (1) p. 18. n. 73. (11) p. 147. <lb /># n. 1206. &amp; ſeq. <lb />Gravitatis Phœnomena. (1) p. 18. n. 72. <lb /># p. 19. n. 75. 77. <lb />Gravitas reſpectiva. (1) p. 108. n. 295. <lb />-- ſpecifica. (1) p. 107. n. 287. <lb />-- univerſalis eſt. (11) p. 146. n. <lb /># 1206. <lb />hujus leges. n. 1207. 1208. <lb />probatur. p. 147. n. 1211. &amp; ſeq. <lb />propoſitiones hanc ſpectantes. p. 151. n. <lb /># 1226. &amp; ſeq. <lb />non tribuenda eſt impactui nobis noto. p. <lb /># 153. n. 1238. <lb />Gravitas in ſuperficiebus Planetarum. <lb /># p. 62. n. 1258. <lb />Gutta fit Sphærica (1) p. 9. n. 33. <lb />Gypſum in vacuo lucet. (11) p. 8. n. 570. <lb />H. <lb />Heterogeneum corpus. (1) p. 107. <lb /># n. 286. <lb />Heterogenei radii. (11) p. 78. n. 850. <lb />Homogeneum corpus. (1) p. 106. n. <lb /># 285. <lb />Homogenei radii. (11) p. 78. n. 849. <lb />Homunculi vitrei in aquâ ſaltantes. (1) <lb /># p. 169. n. 462. <lb />Horizon. (11) p. 132. n. 1096. <lb />I. <lb />Ignis proprietates. (11) p. 1. n. 544. <lb /># &amp; ſeq. <lb />Ignem corporibus contineri. (11) p. 2. <lb /># n. 552. &amp; ſeq. <lb />Aëris actio in Ignem. (11) p. 9. n. 577. <lb /># p. 13. n. 593. 594. <lb />Inclinatum Planum. (1) p. 41. n. 139. <lb />Inertia corporis. (1) p. 3. n. 12. <lb />Iris, quando detur. (11) p. 96. n. 884. <lb /># 885. <lb />ſæpe duæ obſervantur. p. 98. n. 886. <lb />explicatio motus luminis in Iride forman-<lb /># dâ. p. 92. n. 875. &amp; ſeq. <lb />Judicium de diſtantiâ &amp; magnitudine <lb /># objectorum. quære Viſum. <lb />-- de magnitudine Solis &amp; Lunæ <lb /># prope Horizontem. (11) p. 49. n. 735. <lb />Jupiter. (11) p. 111. n. 962. <lb />hujus pondus. p. 163. n. 1255. <lb />gravitas in hujus ſuperficie. n. 1258. <lb />hujus denſitas. p. 164. n. 1260. <lb />-- vis in Saturnum. p. 167. n. <lb /># 1270. <lb />-- in Martem. p. 168. n. <lb /># 1273. <lb />Jovis ſigura. p. 186. n. 1363. <lb />L. <lb />Laminarum elaſticitas. (1) p. 95. n. <lb /># 262. &amp; ſeq. <lb />Latitudo corporis cœleſtis. (11) p. 118. <lb /># n. 1006. <lb />-- loci. p. 134. n. 1118. <lb /></note>
        <pb facs="0737" />
        <note xml:space="preserve" place="margin"> <lb />circulus Latitudinis. p. 135. n. 1119. <lb />Lex Naturæ. (1) p. 2. n. 4. <lb />-- quomodo leges Naturæ detegan-<lb /># tur. ibid. <lb />Lens vitrea. (11) p. 38. n. 692. <lb />Lentium affectiones. (11) p. 38. &amp; ſeq. <lb />-- convexarum. p. 39. n. 698. &amp; <lb /># ſeq. <lb />-- cavarum. p. 41. n. 704. &amp; <lb /># ſeq. <lb />-- polygonarum. p. 53. n. 759. <lb />Libræ proprietates. (1) p. 21. n. 87. &amp; <lb /># ſeq. <lb />-- perfectio. p. 25. n. 102. <lb />-- falacia. p. 22. n. 92. <lb />Bilanx Hydroſtatica. p. 98. n. 271. <lb />Lignum lucidum. (11) p. 10. n. 578. <lb />Liquefacta corpora. vid. Calorem. <lb />Locus. (1) p. 14. n. 48. 49. 50 <lb />Longitudo corporis cœleſtis. (11) p. 118. <lb /># n. 1003. 1004. <lb />-- loci. p. 135. n. 1121. <lb />Lucernæ Magicæ deſcriptio &amp; uſus. <lb /># (11) p. 72. n. 837. &amp; ſeq. <lb />hujus perfectio. p. 74. n. 839. <lb />Lumen. (11) p. 10. n. 581. &amp; ſeq. <lb />Lucent corpora calore. vide calorem. <lb />Luminis Radius. vide Radium. <lb />-- motus. (11) p. 12. n. 589. 590. <lb />-- celeritas in variis mediis. p. 27. <lb /># n. 640. <lb />-- inflectio. p. 17. n. 611. &amp; ſeq. <lb />-- Refractio; vide Refractionem. <lb />-- Reflectio. vide Reflectionem. <lb />Lunæ motus, diſtantia, &amp; c. (11) p. <lb /># 112. n. 967. &amp; ſeq. <lb />-- dimenſiones. p. 113. n. 977. <lb />-- diſtantia, ſi in ſuo tempore perio-<lb /># dico, circa Tellurem quieſcentem move-<lb /># retur. p. 161. n. 1253. <lb />-- Phœnomena. (11) p. 124. n. 1035. <lb /># &amp; ſeq. <lb />quare major prope Horizontem appareai. <lb /># p. 49. n. 735. <lb />circa axem rotatur. p. 112. n. 970. p. 131. <lb /># n. 1092. <lb />eandem faciem T’elluri obvertit ſemper. <lb /># n. 1092. <lb />Eclipſis Lunæ. (11) p. 125. n. 1047. <lb />-- quando detur n. 1049 1051. <lb />-- Partialis. p. 126. n. 1052. <lb />-- Totalis. n. 1053. <lb />-- Centralis. n. 1054. <lb />Lunæ gravitas in Tellurem. p. 150. n. <lb /># 1225. <lb />-- denſitas. p. 197. n. 1427. <lb />-- gravitas in ſuperficie. p. 198. n. <lb /># 1429. <lb />-- Pondus. n. 1428. <lb />-- figura. n. 1431. <lb />-- motus explicatio Phyſica. p. 170. <lb /># n. 1285. &amp; ſeq. <lb />Virium Lunam turbantium determi-<lb /># natio. p. 173. n. 1291. p. 147. n. <lb /># 1296. p. 177. n. 1306. 1307. p. 182. <lb /># n. 1336. <lb />Lunæ Apſidum motus. p. 112. n. 970. p. <lb /># 180. n. 1325. <lb />-- motus Nodorum. p. 112. n. 970. p. <lb /># 183. n. 1341. &amp; ſeq. <lb />-- Excentricitatis mutatio. p. 112. <lb /># n. 968. p. 181. n. 1328. 1329. <lb />-- inclinationis orbitæ mutatio. p. 112. <lb /># n. 969. p. 183. n. 1345. &amp; ſeq. <lb />M. <lb />Machinæ ſimplices. (1) p. 25. n. 103. <lb /># p. 28. n. 112. p. 29. n. 115. p. 31. <lb /># n. 119. p. 33. n. 121. <lb />-- compoſitæ. p. 34. n. 122. &amp; ſeq. <lb />Machina, qua Cunei proprietates demon-<lb /># ſtrantur. (1) p. 32. n. 120. <lb />-- ad accelerationem corporum caden-<lb /># tium determinandam. p 39. n. 132. <lb /></note>
        <pb facs="0738" />
        <note xml:space="preserve" place="margin"> <lb />Machina quaplani inclinati proprietates <lb /># demonſtrantur. (1) p. 41. n. 143. <lb />-- qua experimenta de percuſſione in-<lb /># ſtituuntur. p. 50. n. 170. <lb />-- pro experimentis de motu compo-<lb /># ſito &amp; percuſſione obliquâ. p. 63. n. <lb /># 191. <lb />-- pro potentiis obliquis. p. 67. n. 197. <lb /># p. 70. n. 203. 204. <lb />-- progravium projectione. (1) p. 73. <lb /># n. 210. <lb />-- ad vires centrales demonſtrandas. <lb /># p. 77. n. 222. <lb />-- qua experimenta circa Elaſticita-<lb /># tem inſtituuntur. p. 89 n. 249. <lb />-- quibus preſſiones fluidorum de-<lb /># monſtrantur. p. 101. n. 281. p. 104. <lb /># n. 282. p. 105. n. 283. <lb />-- quibus denſitates fluidorumdete-<lb /># guntur. p. 114. n. 312. p. 115. n. <lb /># 314. <lb />-- quibus denſitates ſolidorum confe-<lb /># runtur. p. 116. n. 317. p. 117. n. 318. <lb />-- ad experimenta circa reſiſtentiam <lb /># fluidorum inſtituenda. p. 124. n. <lb /># 346. <lb />-- quibus experimenta circa fluida <lb /># proſilientia inſtituuntur. p. 128. n. 356. <lb /># p. 133. n. 370. <lb />-- quafluminis celeritas menſuratur. <lb /># p. 146. n. 398. <lb />-- Pneumatica. p. 160. n. 435. &amp; <lb /># ſeq. <lb />-- qua corpora invacuo dimittuntur. <lb /># p. 19. n. 77. <lb />-- qua corpora in vacuo circumvol-<lb /># vuntur. (11) p. 6. n. 567. <lb />-- qua experimenta in aëre compreſ-<lb /># ſo inſtituuntur. (1) p. 166. n. 454 <lb />-- qua Urinatores utuntur. p. 168. n. <lb /># 461. <lb />Machinæ variæ, quarum effectusab aëris <lb /># actione pendet. (1) p. 170. n. 467. &amp; ſeq. <lb />-- quaglobus vitreus circumvolvitur. <lb /># (11) p. 3. n. 556. <lb />-- qua luminis inflectio demonſtra-<lb /># tur. p. 17. n. 611. <lb />-- quibus refractio luminis demon-<lb /># ſtratur. p. 21. n. 630. p. 28 inprinc. <lb /># p. 32. in med. p. 35. in fine; p. 40. n. <lb /># 702. p. 41. n. 708. <lb />Maculæ albicantes in cœlis. (11) p. 146. <lb /># n. 1205. <lb />Magnitudo apparens. vide Judicium &amp; <lb /># viſum. <lb />Maris Æſtus. (11) p. 192. n. 1395. &amp; <lb /># ſeq. <lb />-- -- ab actione Lunæ &amp; Solis <lb /># derivatur. p. 191. n. 1390. &amp; ſeq. <lb />vires bædeterminantur. p. 195. n. 1416. <lb /># &amp; ſeq. <lb />Mars. (11) p. 111. n. 961. <lb />Materia cœleſtis eſt ſubtiliſſima. (11) p. <lb /># 156. n. 1243. <lb />-- --non movet corpora. n. 1244. <lb />Materiæ quantitates in Planetis. (11) <lb /># p. 163. n. 1255. <lb />Medium Luminis. (11) p. 19. n. 15. <lb />Menſis Lunaris Periodicus. (11) p. 124. <lb /># n. 1037. <lb />-- --Synodicus. n. 1038. <lb />Mercurius in vacuo lucet. (11) p. 8. <lb /># n. 571. &amp; ſeq. <lb />-- Planeta. (11) p. 111. n. 958. <lb />Meridiani. (11) p. 129. n. 1077. p. 134. <lb /># n. 1114. 1116. <lb />primus Meridianus. p. 135. n. 120. <lb />Meridiana linea. (11) p. 133. n. 1101. <lb />Molle corpus. (1) p. 8. n. 29. <lb />Mobile eſt corpus. (1) p. 3. n. 11. <lb />Motus. (1) p. 14. n. 47. <lb />hujus quantitas. p. 15. n. 54. <lb />-- directio. n. 55. <lb />-- leges. p. 36. n. 124. &amp; ſeq. <lb /></note>
        <pb facs="0739" />
        <note xml:space="preserve" place="margin"> <lb />Motuum comparatio. (1) p. 16. n. 62. <lb /># &amp; ſeq. <lb />Motus acceleratus. (1) p. 37. n. 127. <lb />-- retardatus. p. 38. n. 128. <lb />-- compoſitus. p. 63. n. 190. &amp; ſeq. <lb />-- reſolutio. p. 65. n. 192. <lb />-- relativus. (11) p. 115. n. 985. <lb />-- apparens. n. 985. p. 117. n. 992. <lb /># &amp; ſeq. <lb />-- in conſequentiâ. p. 110. n. 946. <lb />-- in antecedentiâ. n. 947. <lb />-- diurnus. p. 129. n. 1074. p. 130. <lb /># n. 1081. &amp; ſeq. <lb />-- fluidorum. (1) p. 127. n. 354. <lb /># &amp; ſeq. <lb />-- Luminis. vid. Lumen. <lb />-- quantitas in mundo non ſemper <lb /># eadem. (1) p. 61. n. 187. 188. <lb />Mycroſcopium. (11) p. 54. n. 760. <lb />-- amplificat objecta exigua. ibid. <lb /># n. 761. <lb />-- compoſitum magis amplificat. <lb /># p. 55. n. 763. <lb />Myops. vide Oculum. <lb />N. <lb />Nadir. (11) p. 133. n. 1100. <lb />Nigredo. vide Reflectionem. <lb />-- corpora nigra tardius cæteris <lb /># incaleſcunt. (11) p. 104. n. 909. <lb />Nodi Planetarum. (11) p. 109. n. 941. <lb />-- linea Nodorum. n. 942. <lb />Novilunium. (11). p. 125. n. 1042. <lb />Nubeculæ duæ in Cœlis. (11) p. 145. <lb /># n. 1201. <lb />O. <lb />Occaſus Siderum. (11) p. 132. n. <lb /># 1089. <lb />Occidentis punctum. (11) p. 133. n. <lb /># 1103. <lb />Octava. (1) p. 185. n. 527. <lb />Oculi explicatio. (11) p. 43. n. 712. <lb />Oculus Artificialis. (11) p. 45. <lb />mutationes in Oculo p. 46. n. 719. &amp; <lb /># ſeq. <lb />vitium Senum corrigitur. p. 52. n. <lb /># 756. <lb />vitium Myopum corrigitur. p. 53. n. <lb /># 758. <lb />Opacum corpus. (11) p. 42. n. 709. <lb />Opacitas a poris pendet. p. 76. n. 843. <lb />Oppoſitio corporum cæleſtium. (11) p. <lb /># 119. n. 1011. <lb />Ortus Siderum. (11) p. 132. n. 1097. <lb />Orientis punctum. p. 133. n. 1102. <lb />P. <lb />Phænomena Naturalia. (1) p. 1. <lb /># n. 2. <lb />Paralaxis Syderum. (11) p. 133. n. 1106. <lb /># &amp; ſeq. <lb />-- annua. p. 144. n. 1187. 1188. <lb />Partium ſubtilitas. (1) p. 7. n. 20. &amp; <lb /># ſeq. <lb />Pellucidum corpus. (11) p. 75. n. 840. <lb />Pellucidæ ſunt omnium corporum partes. <lb /># ibid. n. 841. <lb />Pellucida corpora ſeparatione partium <lb /># ſiunt opaca. p. 77. n. 844. <lb />Pendulum. (1) p. 44. n. 153. <lb />-- compoſitum. p. 47. n. 161. <lb />Pendulorum motus. p. 45. n. 154. &amp; <lb /># ſeq. <lb />Penumbra. (11) p. 127. n. 1060. <lb />Percuſſio directa. (1) p. 49. n. 166. <lb />-- corporum non Elaſticorum. p. 53. <lb /># n. 171. &amp; ſeq. <lb />-- corporum Elaſticorum. p. 56. n. <lb /># 179. &amp; ſeq. <lb />-- obliqua. p. 65. n. 193. &amp; ſeq. <lb />Perihelia Planetarum. (11) p. 109. n. <lb /># 936. <lb />Phoſphorus urinæ. (11) p. 9. n. 575. <lb />-- in vacuo. (11) p. 13. n. 595. <lb />Phyſica. (1) p. 2. n. 3. <lb /></note>
        <pb facs="0740" />
        <note xml:space="preserve" place="margin"> <lb />Piſces aëre indigent. (1) p. 169. n. 464. <lb />Planetæ. (11) p. 108. n. 926. <lb />-- Primarii. ibid. n. 927. <lb />-- Secundarii. ibid. n. 928. <lb />-- inferiores. p. 112. n. 964. <lb />-- ſuperiores. ibid. <lb />Planetarum inferiorum apparentiæ. p. <lb /># 119. n. 1015. &amp; ſeq. <lb />-- ſuperiorum apparentiæ. p. 122. <lb /># n. 1024. &amp; ſeq. <lb />-- figuræ determinantur. p. 186. <lb /># n. 1360. <lb />-- diſtantiæ. p. 111. n. 956. &amp; ſeq. <lb />-- dimenſiones. p. 113. n. 975. p. <lb /># 163. n. 1256. <lb />-- pondera. p. 163. n. 1255. <lb />-- denſitates. p. 164. n. 1260. <lb />-- motus. p. 108. n. 929. &amp; ſeq. <lb />-- actionum mutuarum effectus. <lb /># p. 168. n. 1274. <lb />Planetæ revolvuntur circa centrum gra-<lb /># vitatis totius Syſtematis. p. 166. <lb /># n. 1264. <lb />horum orbitæ quieſcunt. p. 166. n. <lb /># 1265. <lb />-- motuum explicatio Phyſica. p. <lb /># 169. n. 1275. <lb />ſecundariorum motus diſtantiæ &amp; c. <lb /># p. 112. n. 965. &amp; ſeq. p. 123. n. <lb /># 1130. &amp; ſeq. <lb />-- horum motuum explicatio. p. 169. <lb /># n. 1277. &amp; ſeq. <lb />Plenilunium. (11) p. 125. n. 1043. <lb />Poli Planetæ. (11) p. 110. n. 953. <lb />-- Mundi. p. 129. n. 1073. <lb />-- Arcticus. p. 131. n. 1090. <lb />-- Antarcticus. n. 1091. <lb />-- Eclipticæ. p. 119. n. 1007. <lb />Circuli Polares. p. 131. n. 1091. p. <lb /># 134. n. 1114. <lb />Potentia. (1) p. 15. n. 56. <lb />hujus intenſitas. n. 57. <lb />actionum Potentiarum comparatio. p. <lb /># 18. n. 67. &amp; ſeq. <lb />-- obliquarum determinatio. p. 67. <lb /># n. 196. &amp; ſeq. <lb />Præceſſio Æquinoctiorum. vide Æqui-<lb /># noctia. <lb />Projectio gravium. (1) p. 72. n. 208. <lb /># &amp; ſeq. <lb />Puncta quietis in chordis agitatis. (1) <lb /># p. 185. n. 538. 539. <lb />Q. <lb />Quarta. (1) p. 185. n. 529. <lb /># Quinta. (1) p. 185. n. 528. <lb />R. <lb />Radians punctum. (11) p. 29. n 645. <lb /># Radius luminis. (11) p. 17. n. <lb /># 610. <lb />Radii divergentes. (11) p. 28. n. 643. <lb />-- convergentes. p. 29. n. 648. <lb />-- incidens. p. 20. n. 620. <lb />-- refractus. p. 21. n. 622. <lb />-- reflexus. p. 59. n. 780. <lb />-- Homogenei. p. 78. n. 849. <lb />-- Heterogenei. ibid. n. 850. <lb />-- per curvas in aëre moventur. p. <lb /># 126. n. 1056. <lb />Reflectio luminis d corporibus. (11) <lb /># p. 42. n. 710. <lb />-- à ſuperficie politâ. (11) p. 59. <lb /># n. 779. <lb />-- hujus leges. ibid. n. 783. &amp; ſeq. <lb />-- cum refractione relationem ha-<lb /># bet. p. 63. n. 795. &amp; ſeq. <lb />corpora nigra lumen non reflectunt. p. <lb /># 78. n. 845. <lb />Refractio luminis. (11) p. 19. n. 616. <lb />-- quando detur. ibid. n. 617. <lb />-- unde oriatur. ibid. n. 618. <lb />-- hujus leges. p. 21. n. 624. &amp; <lb /># ſeq. <lb />conſtansratio inter ſinus incidentiæ &amp; <lb /># Refractionis p. 27. n. 639. <lb /></note>
        <pb facs="0741" />
        <note xml:space="preserve" place="margin"> <lb />Hujus effectus cauſa. n. 633. &amp; ſeq. <lb />Leges Refractionis mediis ſuperficie <lb /># planâ ſeparatis. p. 28. &amp; ſeq. <lb />-- -- mediis ſuperficie ſphæricâ-<lb /># ſeparatis. p. 31. &amp; ſeq. <lb />Siderum Refractio. p. 134. n. 1110. &amp; <lb /># ſeq. <lb />Refrangibilitas diverſa in variis radiis. <lb /># (11) p. 78. n. 847. <lb />-- in ſingulis conſtans eſt. p. 83. <lb /># n. 855. <lb />-- quo major eſt, eo radii facilius <lb /># reflectuntur. p. 88. n. 868. <lb />Regulæ philoſophandi. (1) p. 2. n. 5. <lb /># 6. &amp; 7. <lb />Res Naturales. (1) p. 1. n. 1. <lb />Repulſio. (1) p. 11. n. 40. &amp; ſeq. <lb />Reſiſtentia fluidorum. (1) p. 118. n. <lb /># 319. &amp; ſeq. <lb />Retardatio corporum adſcendentium <lb /># verticaliter. (1) p 40. <lb />-- -- adſcendentium ſuper pla-<lb /># no inclinato. p. 44. n. 151. &amp; ſeq. <lb />Retardatio corporum in fluidis moto-<lb /># rum. (1) p. 120. n. 329. <lb />Retardationum comparatio. n. 331. &amp; <lb /># ſeq. <lb />-- collatio cum gravitate. p. 121. <lb /># n. 336. <lb />Retardatio penduli in fluido. p. 122. n. <lb /># 339. &amp; ſeq. <lb />-- corporis in fluido deſcendentis. p. <lb /># 125. n. 347. &amp; ſeq. <lb />-- corporis in altum adſcendentis. p. <lb /># 126. n. 351. &amp; ſeq. <lb />Rotæ dentatæ. (1) p. 29. n. 114. <lb />S. <lb />SAtellites. vide Planetas Secunda-<lb /># rios. <lb />Saturnus. (11) p. 111. n. 963. <lb />hujus pondus. p. 163. n. 1255. <lb />hujus gravitas in ſuperficie. n. 1258. <lb />-- denſitas. p. 164. n. 1260. <lb />-- vis in Jovem. p. 168. n. 1272. <lb />Seſquiditonus. (1) p. 185. n. 531. <lb />Signa Zodiaci. vide Zodiacum. <lb />Sipho. (1) p. 170. n 467. 469-p. 171. <lb /># n 470. <lb />Sol exiguo motu agitatur. (11) p. 111. n. <lb /># 957. p. 166. n 1266. <lb />-- hujus motus effectus. p 166. n 1267. <lb />-- circa axem rotatur. p. 111. n. 957. <lb /># p. 128. n. 1071. <lb />--motu Telluris moveri videtur. p. <lb /># 117. n. 996. &amp; ſeq. <lb />quare major prope Horizontem appa-<lb /># reat p. 49. n. 735. <lb />Eclipſis Solis. p. 125. n. 1046. <lb />-- diverſa eſt in variis locis. p. 128. n. <lb /># 1065. <lb />--quando detur. p. 127. n. 1059. <lb />--Partialis. p. 128. n. 1067. 1068. <lb />--Totatis. n. 1067. 1068. <lb />--Centralis. n. 1068. <lb />--Annularis. n. 1070. <lb />Solis pondus. p. 163. n. 1255. <lb />--gravitas in ſuperficie. n. 1258. <lb />--denſitas. p. 164. n. 1260. <lb />Soliditas Materiæ. (1) p. 3. n. 9. <lb />Solſtitia. (11) p. 139. n. 1155. <lb />Sonus ab aere pendet. (1) p. 181. n. 504. <lb />hujus intenſitas. p. 184 n. 515. &amp; ſeq. <lb />augetur in aere compreſſo. p. 184. n. 516. <lb />Soni celeritas. p. 182. n. 508. &amp; ſeq. <lb />Spatium. vide Vacuum. <lb />Specula plana. (11) p. 64. n. 799. &amp; <lb />-- ſphærica convexa. p. 65. n. 806. <lb /># &amp; ſeq. <lb />-- ſphærica cava. p. 66. n. 813. &amp; <lb /># ſeq. <lb />-- uſtoria. ibid. n. 814. <lb />-- cylindrica &amp; conica. p. 71. n. <lb /># 863. <lb /></note>
        <pb facs="0742" />
        <note xml:space="preserve" place="margin"> <lb />Sphæra parallela. (11) p. 135. n. 1123. <lb /># 1124. <lb />-- obliqua. n. 1125. &amp; ſeq. <lb />-- recta. p. 137. n. 1138. &amp; ſeq. <lb />Statera Romana. (1) p. 22. n. 91. <lb />Stellæ fixæ. (11) p. 108. n. 923. p. 144. <lb /># n. 1190. &amp; ſeq. <lb />-- maximo numero Teleſcopiis dete-<lb /># guntur. p. 145. n. 1202. <lb />-- quædam ſunt periodicæ. p. 146. <lb /># n. 1203 <lb />-- quædam apparuere &amp; in totum <lb /># evanuere. n. 1204. <lb />Suſpenſionis puncta. (1) p. 21. n. 86. <lb />Syſtema Planetarium. (11) p. 107. n. <lb /># 922. <lb />hujus explicatio phyſica. (11) p. 169. <lb /># n. 1275. <lb />Syzygiæ. (11) p. 125. n. 1044. <lb />T. <lb />Teleſcopium. (11) p. 56. n. 768. <lb />-- Aſtronomicum. ibid. n. 769. <lb />-- rebus terreſtribus videndis ap-<lb /># tum. ibid. n. 772. p. 58. n. 776. <lb />quare minus ſunt perfecta Teleſcopia <lb /># p. 88. n. 867. <lb />Tellus inter Planetas refertur. (11) p. <lb /># 111. n. 960. <lb />hujus motus &amp; diſtantia. n. 960. p. <lb /># 117. n. 996. &amp; ſeq. p. 130. n. 1081 &amp; <lb /># ſeq. p. 143. n. 1183. &amp; ſeq. p. 157. <lb /># n. 1244. &amp; ſeq. p. 171. n. 1281. <lb />--dimenſiones. p. 113. n. 976. <lb />--figura. p. 186. n. 1360. &amp; ſeq. <lb />-- --ex menſuris non poteſt deter-<lb /># minari. p. 189. n. 1375. <lb />-- elevatio ad Æquatorem determi-<lb /># natur. p. 189. n. 1370. <lb />in Telluris ſuperficie gradus acceden-<lb /># do ad Polos augentur. p. 189. n. <lb /># 1374. <lb /></note>
        <note xml:space="preserve" place="margin"> <lb />Tempeſtates annuæ. (11) p. 142. n. <lb /># 1176. &amp; ſeq. <lb />-- in Zonâ Torridâ. n. 1179. &amp; <lb /># ſeq. <lb />Tempus. (1) p. 15. n. 51. 52. <lb />-- medium. (11) p. 138. n. 1145. <lb />Thermometrum. (11) p. 14. n. 598. <lb /># 599. <lb />Tonus. (1) p. 185. <lb />-- gravis. ibid. <lb />-- acutus. ibid. <lb />Trochlea. (1) p. 20. n. 82. 83. p. 29. n. <lb /># 115. &amp; ſeq. <lb />Tropici. (11) p. 130. n. 1089. p. 134. <lb /># n. 1114 <lb />Tubuli pulvere nitrato farti. (11) p. <lb /># 17. n. 609. <lb />Tuba Stentoria. (1) p. 187. n. 543. <lb />V. <lb />Vacuum poſſibile eſt. (1) p. 4. n. <lb /># 13. <lb />--hujus proprietates. (1) p. 5. n. 15. <lb />-- datur. (11) p. 153. n. 1239. &amp; <lb /># ſeq. <lb />Vectis. (1) p. 25. n. 103. 104. <lb /># hujus proprietates. n. 103. &amp; ſeq. <lb />Velocitas. (1) p. 15. n. 53. <lb />Venus. (11) p. 111. n. 959. <lb />Via lactea. (11) p. 145. n. 1199. <lb />-- eſt congeries Stellarum. n. 1200. <lb />Vibrationes Pendulorum. vide Pen-<lb /># dula. <lb />-- Fibrarum. vide Fibras. <lb />Viſus. (11) p. 45. n. 716. <lb />Viſio diſtincta. ibid. n. 717. p. 47. n. <lb /># 724. p. --48. n. 728. <lb />confuſa. ibid. n. 718. <lb />judicium de diſtantiâ. p. 48. n. 729. <lb /># &amp; ſeq. <lb />magnitudo apparens. ibid. n. 733. <lb /></note>
        <pb facs="0743" />
        <note xml:space="preserve" place="margin"> <lb />judicium de magnitudine. ibid. n. 734. <lb />quidam objecta propinqua, &amp; longin-<lb /># qua, diſtinctè vident, intermedia <lb /># confuſe. p. 47. n. 725. <lb />Viſio per vitrum planum. (11) p. 50. n. <lb /># 739. &amp; ſeq. <lb />--per lentem convexam. ibid. n. 745. <lb /># &amp; ſeq. <lb />--per lentem cavam. (11) p. 53. <lb /># n. 757. <lb />objecta in aquâ viſa ampliſicantur. <lb /># (11) p. 50. n. 744. <lb />Vitra uſtoria. (11) p. 41. n. 703. <lb />Vitrum lucidum ex atritu. (11) p. 2. n. <lb /># 553. p. 5. n. 557. 558. p. 7. n. 568. <lb /># 569. <lb />Unda in fluidi ſuperficie. (1) p. 147. n. <lb /># 403. <lb />hujus latitudo. p. 148. n. 404. <lb />harum motus, reflectio &amp;c. p. 147. n. <lb /># 402. p. 148. n. 405. &amp; ſeq. <lb />harum celeritas. p. 152. n. 415. 416. <lb />Unda in aëre. p. 174. n. 476. <lb />harum motus, celeritas &amp;c. p. 175. <lb /># n. 477. &amp; ſeq. <lb />Uniſonus. (1) p. 185. n. 526. <lb />Z. <lb />Zenit. (11) p. 133. n. 1099. <lb />Zodiacus. (11) p. 119. n. 1008. <lb /># 1009. <lb />-- hujus ſigna. n. 999. p. 144. n. <lb /># 1191. 1192. <lb />Zonæ. (11) p. 140. n. 1159. &amp; ſeq. <lb />phænomena Zonarum Frigidarum. n. <lb /># 1165. 1170. &amp; ſeq. p. 142. n. 1176. <lb /># &amp; ſeq. <lb />-- Temperatarum. n. 1 65. &amp; ſeq. <lb /># p. 142. n. 1176. &amp; ſeq. <lb />-- Torridæ Zonæ n. 1163. 1@67. <lb /># p. 142. n. 1179. &amp; ſeq. <lb /></note>
      </div>
      <div type="section">
        <head xml:space="preserve">FINIS.</head>
        <head xml:space="preserve">CATALOGUE</head>
        <head xml:space="preserve">Des LIVRES Nouvellement Imprimez à LEIDE, chez <lb />PIERRE <hi rend="small caps">VANDER</hi> Aa.</head>
        <p>
          <s xml:space="preserve">Index alter Plantarum quae in Horto <lb />Academico Lugduno-Batavo aluntur, <lb />conſcriptus ab Hermanno Boerhaave, in 4°. <lb /></s>
          <s xml:space="preserve">2 voll. </s>
          <s xml:space="preserve">cum figuris.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">-- Sermo Academicus de Chemia <lb />ſuos Errores Expurgante, quem habuit, <lb />Quum Chemiæ Profeſſionem in Acade-<lb />mia Lugduno - Batavâ auſpicaretur XXI. <lb /></s>
          <s xml:space="preserve">Septembris 1718. </s>
          <s xml:space="preserve">4.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Oeuvres diverſes de Phyſique &amp; </s>
          <s xml:space="preserve">Me-<lb />chanique, de Mrs. </s>
          <s xml:space="preserve">C. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">P. </s>
          <s xml:space="preserve">Perrault, de <lb />P Academie Royale des Sciences &amp; </s>
          <s xml:space="preserve">de l’ Aca-<lb />demie Françoiſe. </s>
          <s xml:space="preserve">in 4. </s>
          <s xml:space="preserve">2 voll. </s>
          <s xml:space="preserve">avec figures.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">La plus Nouvelle Academie Univerſelle <lb />des Jeux, ou Divertiſſemens innocens, <lb />contenant, les Regles des Jeux de Car-<lb />ies permis; </s>
          <s xml:space="preserve">des Echecs, du Trictrac, du <lb />Revertier, du Toute-Table, du Tourne-<lb />Cafe, des Dames Rabatues, du Plain &amp; </s>
          <s xml:space="preserve"><lb />du Toc, comme auſſi, celles du Billard, <lb />du Mail, de la Courte-Paume, de la Lon-<lb />gue-Paume, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">avec des Inſtructions <lb />@ciles pour apprendre à les bien joüer. <lb /></s>
          <s xml:space="preserve">Derniere Edition revûe, corrigée, aug-<lb />mentée &amp; </s>
          <s xml:space="preserve">enrichie de Figures en taille-dou-<lb />ce. </s>
          <s xml:space="preserve">in 12°. </s>
          <s xml:space="preserve">2 voll.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Recueil de pluſieurs Machines, de nou-<lb />velle invention. </s>
          <s xml:space="preserve">Ouvrage Poſthume de <lb />Mr. </s>
          <s xml:space="preserve">Claude Perrault, de l’Académie <lb />Royale des Sciences, Docteur en Me-<lb />decine, dela Faculté de Paris. </s>
          <s xml:space="preserve">in 4°. </s>
          <s xml:space="preserve">avec <lb />figures.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Les Colloques d’Eraſme, Owvrage très-<lb />intéreſſant; </s>
          <s xml:space="preserve">par la Diverſité des Sujets, par <lb />l’ Enjoument, &amp; </s>
          <s xml:space="preserve">pour l’Utilité Mo ale: <lb /></s>
          <s xml:space="preserve">Nouvelle Traduction, par Monſr.</s>
          <s xml:space="preserve">
</s>
          <pb facs="0744" />
          <s xml:space="preserve"><fw type="head">CATAL. DES LIVR. NOUV.</fw>
Gueudeville, avec des Notes, &amp; </s>
          <s xml:space="preserve">des figu-<lb />res trèsingenieuſes. </s>
          <s xml:space="preserve">in 12°. </s>
          <s xml:space="preserve">6 voll.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Voyages tres-renommées des S<hi rend="superscript">rs</hi>. </s>
          <s xml:space="preserve">Olearius <lb />&amp; </s>
          <s xml:space="preserve">Mandelſlo, en Moſcovie, Tartarie, <lb />Perſe, Indes Orientales, &amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">&amp;</s>
          <s xml:space="preserve">c. </s>
          <s xml:space="preserve">avec tres-<lb />belles figures, in folio, 4 voll.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Les Comedies de Plaute, nouvellement <lb />Traduites en Stile libre, naturel &amp; </s>
          <s xml:space="preserve">naif; <lb /></s>
          <s xml:space="preserve">avec des Notes &amp; </s>
          <s xml:space="preserve">des Reflexions enjouées, <lb />agreables &amp; </s>
          <s xml:space="preserve">utiles, deCritique, d’ Antiqui-<lb />té, de Morale &amp; </s>
          <s xml:space="preserve">de Politique; </s>
          <s xml:space="preserve">par Monſieur <lb />Gueudeville. </s>
          <s xml:space="preserve">Enrichi d’ Eſtampes en Taille-<lb />douce à la Tête de chaque Tome &amp; </s>
          <s xml:space="preserve">de cha-<lb />que Comedie. </s>
          <s xml:space="preserve">Diviſées en dix Tomes. </s>
          <s xml:space="preserve">en <lb />grand douze.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Principia Trigonometriæ; </s>
          <s xml:space="preserve">ſuccinctè <lb />demonſtrata; </s>
          <s xml:space="preserve">Auctore Joh. </s>
          <s xml:space="preserve">Wilſon. </s>
          <s xml:space="preserve">8°.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Moſis Maimouidis Conſtitutiones de <lb />Siclis; </s>
          <s xml:space="preserve">quas Latinitate donavit &amp; </s>
          <s xml:space="preserve">notis <lb />illuſtravit Joannis Eſgers, 4°.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Recueil des belles Tailles douces, en ma-<lb />niere Noire, Peints, Deſſinées, ou Gravées <lb />par les celebres Maitres, F. </s>
          <s xml:space="preserve">Parmens, Spa-<lb />gnolet, W. </s>
          <s xml:space="preserve">Vaillant, J van Soomeren, D. <lb /></s>
          <s xml:space="preserve">Teniers, P. </s>
          <s xml:space="preserve">Picart, &amp; </s>
          <s xml:space="preserve">autres. </s>
          <s xml:space="preserve">in fol.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Divers Owvrages de belles Figures; </s>
          <s xml:space="preserve">Peints, <lb />Deſſinées, ou Gravées par divers Maîtres <lb />très Renommez, ſavoir: </s>
          <s xml:space="preserve">A Carats, G. </s>
          <s xml:space="preserve">Re-<lb />ni, A. </s>
          <s xml:space="preserve">Corregio, J. </s>
          <s xml:space="preserve">Callot, Guarcin, S. <lb /></s>
          <s xml:space="preserve">Vouet, J. </s>
          <s xml:space="preserve">le Pautre, Rembrant, A. </s>
          <s xml:space="preserve">F. </s>
          <s xml:space="preserve">Van-<lb />der Meulen, A. </s>
          <s xml:space="preserve">Collart, &amp; </s>
          <s xml:space="preserve">autres. </s>
          <s xml:space="preserve">in fol.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Marmorea Baſis Coloſſi Tiberio Cæ-<lb />ſari erecti ob Civitates Aſiæ reſtitutas <lb />poſt horrendos terræ tremores. </s>
          <s xml:space="preserve">Primus <lb />trans Alpes vulgavit, revocavit, notis <lb />uberioribus &amp; </s>
          <s xml:space="preserve">novis obſervationibus ac <lb />nummis illuſtravit Laurentius Theodo-<lb />dorus Gronovius, in Octavo.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Vaillant diſcours ſur la ſtructure des Fleurs, <lb />leurs differences &amp; </s>
          <s xml:space="preserve">l’uſage de leurs Par-<lb />ties; </s>
          <s xml:space="preserve">pr@noncé à l’Ouverture du Jardin Royal <lb />de Paris, le X. </s>
          <s xml:space="preserve">Jour du Mois de Juin 1717. <lb /></s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">l’ Etabliſſement de trois nouveaux Genres <lb />de Plantes, l’Araliaſtrum, la Scherardia, <lb />la Boerhaavia. </s>
          <s xml:space="preserve">Avec la Deſcription de deux <lb />nouvelles Plantes, rapportée au dernier <lb />Genre, in 4°.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Scamozzi Oeuvres d’ Architecture, conte-<lb />nuës dans ſon Idée de l’Architecture Univer-<lb />ſelle; </s>
          <s xml:space="preserve">dont les Regles des cinq Ordres, que <lb />le ſixiéme livre contient, ont ététraduites en <lb />François par Mr. </s>
          <s xml:space="preserve">Auguſtin Charles d’A-<lb />viler, &amp; </s>
          <s xml:space="preserve">les autres parties traduites nouvel-<lb />olement par Mr Du Ry; </s>
          <s xml:space="preserve">avec les Planches <lb />riginales: </s>
          <s xml:space="preserve">Le tout revu &amp; </s>
          <s xml:space="preserve">exacte ment cor-<lb />rigé ſur l’Original Italien. </s>
          <s xml:space="preserve">On y a joint auſſi <lb />pluſieurs nouveaux Deſſeins des plus beaux <lb />Edifices de Rome, dont l’Auteur parle dans <lb />ſon Ouvrage. </s>
          <s xml:space="preserve">in fol.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Poſt Oewvres d’Architecture, in fol. </s>
          <s xml:space="preserve">avec <lb />très belles figures.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Vignole Regles descinqOrdres d’Architectu-<lb />re, avec pluſieurs Augmentations de Michel <lb />Ange Buonaroti, Nowvellement revûës, <lb />corrigées &amp; </s>
          <s xml:space="preserve">augmentées par Mr. </s>
          <s xml:space="preserve">Dury, 8°.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Vingboons Oewvres d’Architecture, conte-<lb />nant les plans, elevations &amp; </s>
          <s xml:space="preserve">deſcription des <lb />principaux &amp; </s>
          <s xml:space="preserve">desplus nowveaux Edifices par <lb />lui ordonnéz dans le dernier agrandiſſement <lb />de la Ville d’Amſterdam &amp; </s>
          <s xml:space="preserve">autres endroits <lb />de ces Provinces, fol. </s>
          <s xml:space="preserve">2 voll. </s>
          <s xml:space="preserve">avec figures.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Delices de la Suiſſe, ou l’on void tout ce <lb />qu’il y a de plus remarquable dans la Suiſſe, <lb />&amp; </s>
          <s xml:space="preserve">dans ſes Alliez qui compoſent le Louable <lb />Corps Helvetique: </s>
          <s xml:space="preserve">la deſcription des Villes, <lb />Bourgs, Chateaux; </s>
          <s xml:space="preserve">la nature de l’air &amp; </s>
          <s xml:space="preserve"><lb />du terroir; </s>
          <s xml:space="preserve">les Antiquitez du Pays, &amp; </s>
          <s xml:space="preserve">les <lb />raretez de la Nature; </s>
          <s xml:space="preserve">le Naturel, les Mœurs <lb />&amp; </s>
          <s xml:space="preserve">la Religion des habitans; </s>
          <s xml:space="preserve">leurs Gouver-<lb />nemens differens, leurs Alliances mutuelles <lb />&amp; </s>
          <s xml:space="preserve">leurs interëts communs; </s>
          <s xml:space="preserve">avec un Memoi-<lb />re inſtructif ſur les cauſes de la guerre qui eſt <lb />arrivée en Suiſſe, dans l’ An 1712. </s>
          <s xml:space="preserve">Par le <lb />Sr. </s>
          <s xml:space="preserve">Gottlieb Kypſeler de Munſter, le tout <lb />enrichi de très belles figures. </s>
          <s xml:space="preserve">&amp; </s>
          <s xml:space="preserve">CartesGeo-<lb />graphiques deſſinées ſur les originaux in, <lb />12°. </s>
          <s xml:space="preserve">4 voll.</s>
          <s xml:space="preserve" />
        </p>
        <p rend="italics">
          <s xml:space="preserve">Oewvres de Mr. </s>
          <s xml:space="preserve">Mariotte, de I’Acadé-<lb />mie Royale des Sciences; </s>
          <s xml:space="preserve">Diviſées en <lb />deux tomes, comprenent tous les Traitez de <lb />cet Auteur, tant ceux qui avoient déja paru <lb />ſéparément, que ceux qui n’avoient pas en-<lb />core été pubiez; </s>
          <s xml:space="preserve">Imprimées ſur les Exem-<lb />plaires les plus exacts &amp; </s>
          <s xml:space="preserve">les plus complets; <lb /></s>
          <s xml:space="preserve">Revuës &amp; </s>
          <s xml:space="preserve">corrigées de nouveau. </s>
          <s xml:space="preserve">in 4°. </s>
          <s xml:space="preserve">2 voll. </s>
          <s xml:space="preserve"><lb />avec figures.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">FINIS.</head>
        <pb facs="0745" />
        <pb facs="0745a" />
      </div>
      <div type="section">
        <head rend="italics" xml:space="preserve">Tom. II. In fine poſt Indicem.</head>
        <head xml:space="preserve">USUS TABULÆ.</head>
        <p>
          <s xml:space="preserve">CUm ſolus tomus primus de novo editus ſit, <lb />inde reſpectu tomi ſecundi duo effluxere <lb />incom moda, 1. </s>
          <s xml:space="preserve">numeri in margine, qui propo-<lb />ſitiones primi tomi indicant, propter mutatos <lb />numeros in ſecunda editione, innutiles fiunt. <lb /></s>
          <s xml:space="preserve">2. </s>
          <s xml:space="preserve">Eadem de cauſa Index rerum, qui toti operi <lb />deſtinatus eſt, tantum in tomo ſecundo uſu venit. </s>
          <s xml:space="preserve"><lb />Tabella adjecta ambo hæc tollit incommoda; </s>
          <s xml:space="preserve"><lb />ubi in margine tomi ſecundi numerus datur mi-<lb />nor 543.</s>
          <s xml:space="preserve">, qui ultimus eſt tomi primi in editione <lb />prima, quærendus hìc eſt in prima columna <lb />Tabellæ, &amp; </s>
          <s xml:space="preserve">numerus qui in ſecunda ipſi reſpon-<lb />det eſt numerus in ſecunda editione quærendus.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Eodem modo ubi in indice agitur de tomo <lb />primo, pag. </s>
          <s xml:space="preserve">negligenda eſt, ſed numberus, qui <lb />n. </s>
          <s xml:space="preserve">notatur, quærendus eſt in hac tabella, ut <lb />habeamus numerum in margine ſecundæ editio-<lb />nis quærendus, &amp; </s>
          <s xml:space="preserve">qui propoſitioni in indi-<lb />ce indicatæ reſpondet.</s>
          <s xml:space="preserve" />
        </p>
        <p>
          <s xml:space="preserve">Compendii cauſa tantum in hac tabella no-<lb />tantur numeri, qui aut in margine tomi ſecun-<lb />di, aut in indice ad calcem hujus, reperiuntur.</s>
          <s xml:space="preserve" />
        </p>
      </div>
      <div type="section">
        <head xml:space="preserve">TABULA</head>
        <head rend="italics" xml:space="preserve">Demonſtrans quorundam numerorum 1<hi rend="superscript">æ</hi>. &amp; 2<hi rend="superscript">dæ</hi>. Editionis <lb />convenientiam.</head>
        <note xml:space="preserve" place="margin"> <lb />Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. # Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. # Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. # Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. # Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. # Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. # Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. # Ed. 1<hi rend="superscript">a</hi>. # Ed. 2<hi rend="superscript">a</hi>. <lb />1 # 1 # 44 # 70 # 105 # 175 # 158 # 290 # # # 272 # 707 # 356 # 797 # 463 # 1120 <lb />2 # 2 # 47 # 86 # 112 # 186 # # # 225 # {354 \\ 396 # 280 # 720 # 358 # 801 # 464 # 1121 <lb />3 # 3 # 48 # 87 # 113 # 188 # 161 # {296 \\ 311 \\ 551 # # # 281 # 722 # 368 # 815 # 465 # 1121 <lb />4 # 4 # 49 # 88 # 114 # 190 # # # # # 282 # 726 # 370 # 817 # 467 # 1124 <lb />5 # 6 # 50 # 89 # 115 # 192 # 162 # 552 # 226 {355 \\ 397 # # 283 # 729 # 378 # 827 # 468 # 1125 <lb />6 # 7 # 51 # 90 # 118 # 200 # 166 # 476 # # # 284 # 733 # 379 # 837 # 469 # 1126 <lb />7 # 8 # 52 # 93 # # # # # 231 # 361 # 285 # 734 # 390 # 856 # 470 # 1127 <lb />8 # 9 # 53 # 94 # 119 {204 \\ 205 \\ 212 # # 170 # {490 \\ 491 # # # # 286 # 735 # 391 # 857 # 472 # 1130 <lb />9 # 10 # 55 # 96 # # # # # 232 {363 \\ 409 # # 287 # 736 # 392 # 858 # 474 # 1133 <lb />10 # 11 # 56 # 97 # # # 171 # 519 # # # 288 # 737 # 398 # 868 # 476 # 1136 <lb />11 # 12 # 57 # 104 # 120 {206 \\ 215 # # 175 # 473 # 234 # 367 # 290 # 742 # 399 # 869 # 477 # 1137 <lb />13 # 15 # 62 # 450 # # # 177 # 557 # 235 # 369 # 292 # 748 # 402 # 872 # 502 # 1168 <lb />14 # 17 # 63 # 447 # 121 # 208 # 179 # 565 # # # 295 # 753 # 403 # 873 # 504 # 1170 <lb /># # 64 # 470 # 122 # 217 # 190 # 246 # 236 {371 \\ 408 # # 296 # 754 # 404 # 874 # 508 # 1182 <lb />15 {19 \\ 20 # # 67 # 107 # 123 # 218 # 191 # 615 # # # 306 # 769 # 405 # 875 # 515 # 1190 <lb /># # 72 # 113 # 124 # 243 # 192 # 604 # 237 # 373 # 309 # 774 # 415 # 889 # 516 # 1191 <lb />20 # 25 # 73 # 114 # 125 # 245 # 193 # 612 # # # 312 # 778 # 416 # 890 # 525 # 1200 <lb />26 # 23 # 75 # 116 # 126 # 247 # 196 # 220 # 239 {376 \\ 409 # # 314 # 781 # 417 # 1050 # 526 # 1201 <lb />28 # 48 # 77 # 118 # 127 # 249 # 197 # 223 # # # 315 # 784 # 418 # 1051 # 527 # 1202 <lb />29 # 49 # 78 # 119 # 128 # 250 # 198 # 221 # # # 317 # 786 # 424 # 1060 # 528 # 1203 <lb />30 # 50 # 79 # 120 # 129 # 251 # 203 # 232 # 241 {381 \\ 411 # # 318 # 788 # 426 # 1063 # 529 # 1204 <lb />31 # 51 # 82 # 123 # 131 # 255 # 204 # 233 # # # 319 # 891 # 429 # 1066 # 530 # 1205 <lb />33 # 55 # 83 # 124 # # # 208 # 326 # # # 320 # 956 # 431 # 1092 # 531 # 1206 <lb /># # 84 # 125 # 132 {276 \\ 546 # # 210 # 328 # 243 {385 \\ 390 # # 330 # 942 # 435 # 1093 # 532 # 1207 <lb />35 {56 \\ 78 # # 85 # 126 # # # 217 # 343 # # # 331 # 957 # # # 536 # 1211 <lb /># # 86 # 127 # 139 # 235 # 218 # 344 # 244 # 668 # 334 # 954 # 439 \\ 440} # 1096 # 538 # 1214 <lb />36 # 57 # 87 # 128 # 143 # 239 # 219 # 345 # 249 # 673 # 335 # 958 # # # 539 # 1215 <lb /># # 91 # 135 # 144 # 263 # 220 # 346 # 251 # 675 # 336 # 928 # 442 # 1099 # 542 # 1218 <lb />37 {59 \\ 85 # # 92 # 137 # 151 # 273 # 221 # 347 # 257 # 686 # 339 # 971 # 454 # 1111 # 543 # 1219 <lb /># # 95 # 143 # 153 # 278 # 222 # 348 # 262 # 692 # 346 # 977 # 457 # 1114 # #  <lb /># # 96 # 144 # 154 # 279 # 223 # 349 # 266 # 697 # # # 458 # 1115 # #  <lb />38 {58 \\ 80 # # 102 # 155 # # # 224 # 351 # 269 # 702 # 347 \\ 351} # 965 # 459 # 1116 # #  <lb /># # 103 # 172 # 157 {288 \\ 307 # # # # 270 # 704 # # # 461 # 1118 # #  <lb />40 # 61 # 104 # 174 # # # # # 271 # 705 # 354 # 794 # 462 # 1119 # #  <lb /></note>
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