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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
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CAP. 10.
 semicirenli.
LoCcementi opposici. Seu, quod icem cR, Anoulus in perixte
ria legmenco inlistens, cAt a qualis anculo iltius ACEN CHEI CU
BMAIRIT.
20 Idem sc crincitur. AneuluS B AC caMIUS CA guante
Temistis Feripheriae BC, per 20c3, hoc eHt, angulus B AC cA
ad quacuorrsdus, uc lemistis peripherix B C, ad inceeri circuli
Peripheriam.) Idcogi Li coulgi diraricentur AB, AC, doncc
iptum P CEcctionis punctum) perveniet ad punctum A, (iplaq;
A B degcneret in punctum,) eric anguloB A C, oppolicusince.
per semicirculor; idcCgs angulus. B AC. rectus cAt. CC, quoni-
am idem acciderer in quoris lemicirculo, igitur anguli lemicir
culorum lunc aqualce, nempe recti omnes. Sed _ idem cMendi
Porek, eciam in aliis lrvilibus scgmencis. Ergo similium les
mencorum ansuli lunc aequales; canci nempe quantus iltorum
Peripheriarum lemiscs.
40 Idem hoc modoprobatur. Ouoniam in lemicirculo an
gulus ABC rectus cA, per 31 c 3; ideog: anguli B A C, BCA,
limul, aequales recto, Per 32 c 1: Siigirur recta A B moreatur
vg; dum perveniat 2d sicum A C, angulus B A C cranelcie
sive nullus eric, idcog; B C A (qui jam hc angulus Termiciren.
11) rectus eric; nam quod auteriur angulo B AC, additur 27-
gulo B C A, ur nempe ambo aquentur uni recto. ACq; idem
ostendi porcA in aliis segmeneis lirnilibus; naM, Per 32 C1, c-
rUnEB A C. BC A, CimuI, aquales retduo onsuli ABC ad
duos rectoe; idcoq; cum A B C, in eodem vel similibus sexmen-
eis, semper idem mancas, erie lumma angulorum BC A, BAC,
eadem; adebq; cum B A C prortus eranclcit eric reliquus
BC A ipE Cummae 2qualis. Similium igitur sexmentorum an
Eulisune aquales.
50 Idem argum exnatura Pa.
rallelitmi. Nam, ductis pluri.
buscirculis concenericis, recta
per eenerum illos secans Faciet
ansolos alcernos aequales. Ideo
Temicirculorum anguli a, an
quamris inaequalium aequales
Tunc.
Dicetur Forlan, il lud quidem
valere in parallelis rectis, pex