Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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7658

Lect. VIII.

I QUæ radiis obveniunt à longinquo puncto manantibus, adc-
óque quaſi parallelis, ex reflectione peripheriam ad circula-
rem peractâ; ubinam & quouſque vel ſibimet ipſis occurrunt, vel ax-
em interſecant; quo loco radians oculo ubicunque conſtituto repræ-
ſentant, in poſtremis eſt diſſertatum. ad punctum jam accedimus ra-
dios ejiciens ſenſibiliter divergentes. Et hujuſmodi quidem puncto,
quanquam ſeu in obverſas circuli Convexas partes ſeu ad concavas
radiet communia pleraque ſymptomata conveniunt; tamen communi
fretus _Opticorum_ exemplo, præſertímque majoris evidentiæ causâ,
caſus iſtos diſtinctè proſequemur; illum fuſiùs imprimis, hunc aliquan-
to conciſiùs. ad rem.

II. In circuli BNP (cujus centrum C) convexum à puncto A
quilibet incidat radius AN, íſque reflectatur in NG; patet reflex-
um GN productum axi AC occurſurum. nam ductâ CNE patet
GN productum angulum ANC ſecare; nec non ideò trianguli
ANC baſin AC; puta in K; quo poſito.

III. Dico fore AC. AN : : KC. KN. Nam ducatur KH ad
CN parallela. eſt igitnr ang. KHN = CNP = CNK = NKH.
hoc etiam è ſuperiùs generatim oftenſis conſectatur. adeóque NH
= NK. itâque cùm ſit AC. AN : : KC. HN. erit etiam AC.
AN : : KC. KN.

IV. Corollarii loco notetur (ductâ CP) fore NH = NK;
& triangula HNK, NCP aſſimilari; vel eſſe HK. HN : : NP.
CN.

V. Porrò, conftantibus iiſdem, dico fore AC. KC : : ACq
- ANq . CNq. Nam eſt NP. CN + AN. CN = HK.
HN + AN. CN = HK x AN. HN x CN = AN.

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