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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
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P. E C T. IV.
autem procedentis cujusris racii (cen A N) retractus N a cum ip(q A P
(protractus utique, vel rerractuS) conveniat in R; dico FOrC NR.
N A: : T. R. (Neque non inverse, si fuerit NR. N A:: I. R:
exit R N a iplius N A retractuS.)
Hloc e superius ostensis immediate COn(CCEatE. Fic hinc etiam ParIS
apparet, quoniam (id quod bene noretur, uc paltim in sequentibus a(-
sumendum) ansulus NV A B, x quarur angulo incidentix; (quippe cum
is complementum sit anguti A N B;) _c angulus N R B (comple
mentum videlicet anguli K _I B) aequarur anoulo retractO. C urs ita-
C1. 34 53. Que sic hinc sinus ansuli N A B (vel ansuli deinceps N A R) ad (1-
num anguli N R A, uE P ad R; etiam in criangulO N A R latuS N R ad
LaFuS N. A sese habebit ur l ad R. uod F. D. Ouinetiam li latera
N R, N A sC habeant uE L. ad R; eriam dictorum angulorum linus ita
se habebunt; unde constabir iplam R N a ad A N pertinere.
V. Flinc parricularis emergir expedirissimus modus hujusmodi quor-
cunque retractos delignandi. Nempe per radians punctum A ducatur
A B retringenti F F perpendicularis; _ HaE AB. ZB:: R. I; tum
Der. Z duCatuT reCta G HI ad. F P parallela. Proponatur jam quilibet
incidens AN, cui conveniens delignandus est retractus. Pum lic de-
delignareris. Protrahatur N A (B OpuS) ut cum C H conveniar in
5S; _ centro N per S deseribatur circulus ipsam A B secanS in R (Pe-
cabit urique (i retractus aliquis ad incidentem A W pertincat) erie con
Rexa RN, protractaque radio AH debitus retractus. Litenim est
RN. AN:: SN. AN:: ZB. AB:: I. R:: RN. AI. unde
liquet (e prxecedente) proxolicum.
VI. Extiinc etiam hujusmodi refractionis prxecipua sympromata
pertacili colliguntur Negorio; qua scorlim acceptis, de quae se
cum mutuo collatis accidunt retractis; hoc imprimis: In primo casu
(quum nempe retraceio sic c rariori in densius, seu quum IE R)
concurlus retractorum cum recta A B (quam subinde radiationis hujus
axem appellare licebic) supra punctum Z existir. Nam connexâ HL;
quoniam ang. NZ S rectO B L S major est, erit NIS (vel NR) C
NZ; adeoque B RC BZ. Trem, in secundo casu (quum media
contrarie se habent) dictus concursus intra punctum Z ezistit. Fire-
nim rursuS Connexa NIZ; est ang. NISZ reCtO A ZS (interno) ma-
jOr, adeoque AZ = NS, vel NR; _ ideo BL C BR.
VII. Llinc liquet punctum Z esse limitem ulera vel cirra quem (re-
C) omnes retraeri cum axe AB COnCUITuNE. Quimito quod
ipsive
Fect. 3. num).
518. 35.