Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

GP _a_, HP δ ità diſponantur, ut latera PG, PH ſibi congruant (un-
de major angulus GP _a_ minorem HP δ comprehendet) tum centro P
per δ deſcribatur circulus E δ F ipſas PG, P _a_ ſecans punctis F, E; item
connexâ EH, centro H per δ tranſeat circulus HMN ipſas HP, HE
ſecans punctis N, M; denuò connexa E δ cum PG conveniat in L. Eſtque jam ang. _a_ P δ. ang. δ PH: : ſector EP δ. ſector δ PF & gt; triang. EP δ. triang. δ PL: : Eδ. δ L : : triang. EH δ. δ HL & gt; ſector MH δ. ſector δ HN : : ang. EH δ. ang. δ HP. eſt igi-
tur ang. _a_ P δ. ang. δ PH & gt; ang. EH δ. ang. δ HP. ergóque
compoſitè ang. _a_ PG. ang. δ PH & gt; ang. EHP. ang. δ HP. per-
mutandóque ang. _a_ PG. ang. EHP & gt; ang. δ PH. ang. δ HP. eſt
autem HP. PE : : HP. P δ : : I. R : : GP. P _a_. adeoque EH ad
_a_ G parallela; vel ang. EHP = ang. _a_ GP. ergò erit ang. _a_ PG. ang. _a_ GP & gt; ang. δ PH. ang. δ HP. hoc eſt ang. _a_ BG, _a_ BP
& gt; ang. δ BH. ang. δ BP. vel componendo ang. GBP. ang. _a_ BP
& gt; ang HBP. ang. δ BP. Quod erat demonſtrandum.

11.1.

Fig. 27, 22.

12. _Corol_. 1. Ang. _a_ BG. ang. _a_ BP > ang. δ BH. ang. δ BP.
2. Ang. _a_ BG. ang. PBG > ang. δ BH. PBH.

Opportunum eſt hoc Theorema conciliandis cum experientia pro-
poſitis refractionum legibus. Ut demirari ſubeat nuperrimum Opticæ
ſcriptorem, virum alioqui diffuſè doctum, hujuſmodi ratiocinio leges
iſtas impugnàſſe: “In majoribus tamen angulis inclinationis (Ipſiſ-
"ſima ſunt ejus verba) falſum eſſe conſtat (principium nempe no-
"ſtrum;) in his enim angulus refractionis major eſt ſubtriplo an-
"guli inclinationis; quod mihi aliiſque ex luculentis experimentis
"compertum eſt. Hæc, inquam, ille ταντοεπ@. Quaſi verò dixiſſet; numeri 6 & 4 ſimul accepti non conficiunt 10, quia numerum effici-
unt majorem quam 8. planè ſimilis eſt diſcurſus; non ovum ovo ſi-
milius. Nam in refractionibus ex. gr. ad vitrum factis ſi ponatur ad
quamvis inclinationem (puta graduum 15.) quòd ſit angulus refra-
ctionis ſubtriplus anguli inclinationis (quem ille vocat, incidentiæ nos
angulum appellare ſolemus) neceſſariò, ſicuti modò demonſtratum
eſt, è principio noſtro conſequetur, quòd ad aliam quamcunque ma-
jorem inclinationem refractionis angulus major erit ſubtriplo anguli
inclinationis; nominatim acceptâ graduum 30 inclinatione juxta di-
ctum principium inſtitutus calculus angulum præbebit reſractum
19. 24'; angulúmque proinde refractionis 10. 36', qui 30 graduum
trientem exuperat. Quare cùm Clariſſimus vir Hypotheſin hanc (à

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