Full text: Gravesande, Willem Jacob: Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam

PHYSICES ELEMENTA ut de acceleratione gravium dictum eſt poſt n. 130. , deter-
minari ope trianguli rectanguli PQR, in quo lineæ pa-
rallelæ ad baſin celeritates repreſentant, dum portiones areæ
trianguli ſpatia percurſa deſignant. Hìc autem de eo-
dem ſpatio percurſo ſemper agitur, latitudine nempe ſpatii
attractionis, quia ſolum motum ad ſuperficiem Media diri-
mentem perpendicularem conſideramus; idcirco per por-
tiones æquales areæ trianguli PQR ſpatium hoc percur-
ſum ſemper repreſentatur. Sit portio hæc Pdc quando
cum celeritate o. lumen ſpatium attractionis juxta memora-
tam directionem perpendicularemintrat, id eſt, quando ra-
dius incidens cum ſuperficie media ſeparante angulum mini-
mum format; dc in hoc caſu deſignabit celeritatem attra-
ctione acquiſitam, & quâ lumen ſpatium attractionis exit.

481.1.

TAB. IV.
fig. 3.

Si autem lumen cum celeritate quæ per fg deſignatur
perpendiculariter ſpatium attractionis intret, exibit ſpatium
cum celeritate hi poſitis areis Pdc & fgih æqualibus
inter ſe, ut ex dictis patet. Triangula Pdc, Pfg, Phi
ſunt ſimilia, ideoque horum areæ ſunt inter ſe ut quadrata
laterum homologorum dc, fg, hi ſumma autem arearum
Pdc, Pfg æqualis eſt areæ phi, (propter areas æ-
quales Pdc & fgih); ergo & ſumma quadratorum li-
nearum dc & fg æqualis eſt quadrato lineæ hi; unde
ſequitur tribus memoratis lineis formari poſſe triangulum re-
ctangulum cujus hypotenuſa erit hi. Ergo

In triangulo rectangulo, cujus latus unum eſt celeritas quâ
lumen perpendiculariter ſpatium attractionis intrat, latus
alterum celeritas percurrendo hoc ſpatium acquiſita, quando
lumen celeritate o. hoc intrat, hypotenuſa trianguli deſignat
celeritatem qua lumen ad partem oppoſitam ſpatium attractio-
nis perpendiculariter exit. Quod univerſaliter obtinet, quo-
modocunque mutetur attractio in ſpatio attractionis pro va-
ria diſtantia a planis quibus hoc ſpatium terminatur. Quod
ur probetur,

481.1.

636.

Ponamus ſpatium attractionis in duas partes, ſive æquales
ſive utcunque inæquales ſecari plano parallelo ad ſuperficies
quibus terminatur. Ponamus ulterius attractionem dari diver-

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