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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)
# Folio 82, page id 824573315:0294
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en nutegue
PrOP. 107.
uc 2 ad; = = = F 1, vel lc 2 ad 1: (PeF PFOP. 1O1, 102,) (0
lidum ex cocidem planis in
rectarum racione duplicaca
constens, erie leries quadra-
eis lublccundanorum reci
Proca, vel (quod cancun-
der ralec) Ceries Primanio
reciproca, cujus index  
vel i F = _ =  2. Ideo-
queracio hujus solidi ad
cylindrum vel Prilma (Cu-
Per eadem basi xquealcum)
NC 1 24  1 + 1 = 0.
(DETPFOP. XO3.) Nempe illic racio sinica, hic simplicicer inf-
nita.
Siplanum sic Peries Ouadraris Subcercionorum reciproca,
cajus index  5, ejulque rario ad Parallelogrammum in
Tcripium uc 1 ad : = = Z + 1, vel _C Z ad r. (PEF PFOD. 102.)
Colidum ex planis cocidem in rectarum illarum duplicaca racio
ne constans, eric Ceries Biquadratis Subrertianorum reciproca,
cujus index m 3 =-  3  5. _ propterca racio ipsius ad in
Ccripcum exlindrum vel Prilma Cuper eadem bah aeque. alcum,
et X 2d  5 F I = n 3, vel nc 3 ad = 1 (per PrOD. 204.)
Nempe illic rario Enica, hic plusquam intinica.
Si planum sic Peries primanis reciproca, cujus index  1
adcoqueratio quam habet ad Paralleloerammum inscripium
Yad in 1Y 2 =O: C Per PrOP 103) Solidum ex planie in
rectarum illarum racione duplicaca constans, eric leries oundra-
eis Primanorum (hoc cH, Eccundanis) reciproca, cujus index
in 2, _ propcerea racio iptius ad C plindrum rel prilma lupce
eadem baE= que alcum, uc _ ad = 2 t 2, Ccw ucr ad = L. (DeF
P. 104) Nepe illic racio simplicicer infinica, hic plusqua intinica.
Si planum se feries secundanis reciproca, cujur: index = 2,
adcoqueracio quam habet ad parallelosrammum inscripeum
et 1 2d in 2Y1 =  1. Solidum ex coridem planis in recta.
rum illarum racione duplicata conttans, cric Ccrieo omadraris
sccundonorum, hoc est ouarcanis, reciproca, cniuo index
in 4 = in 3 n 2; ejulqueracio ad Cglindrum vel Prisma de-
bi
arithmetica Infinitorum.