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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 52, page id 824573315:0264
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Arithmeliea Infnitorum.
PrOD. 60
maca Colrimue quae nemo (quancum (cio) antea lulcepic, ne-
dum exleguueus ek.
Elacet aucem: actuc ex Tabellis omnibus praecedenribus
(ProD. 443 54,59.) hoc unirertale Theorema colligere, (9u0d
quidem cohrenie cum Reguta Prop. 46.) Nemve..-
P ROP. CZIV.
TBeorEMA.
I intelligatur series infinita quantitacum, a pun-
eto Icu o inchoatarum, ex continuecrelcentium
proratione cujulcungi porectatis, sive simplicis
sire ex simplicibus compolita; eric totius ratio, ad le
riem rocidem maxime aequalium, ea quae est UInitatis
ad Indicem iltius porellatis unitate auctum.
Primonorum, Secundanorum, PCrtIANOrUM, OMAETAnO.
rum, _C. (livse Porestatis Laceralis, Maadracicx, Cubicae, Biquan
dracicae, _c.) indicem Aatuo 1, 2, 3, 4, esc. Tubsecundanorum
Suocercianorum, Cubquartanorum, ec. (hre Radicum quadra-
dracicarum, cubicarum, biguadracicarum, _C. DrIMAMOTUM.
sire arichmetice proporcionalium) indicem AaEUD Z, 3, 6, _C.
Pocestacis cujulris compoliexe indicem tacio ex componencium
indicibus composicum: Pura Eccundanorum cubi (vel Tercia-
norum ouadreca) indicem habene 6 = 2 2 3: uble-
cundanorum Radices cubicae (vel Subcercianorii Radices Oan-
dracica) indicem habent E == = x ?: C ubi Radicum quadraci.
X Z X E
carum Ouinconorum, indicem habebune 25-
Raciones aurem his. Pocestacibus (in Tabellis) altignata,
unc hujalmodi. Puta, Primanis, Secundanis, Terrianis, Ouar
tanis, _C. 1 ad 2, 12d3, 1204, C ad5, Qc. hoc cA + ad L F 13
2 ad B F 1, 13d 3 F 1, r ad 4 F C, _c. Sublecundanis, Subcer-
rianis, lubgrartonis, sec. 22d3, 3 ad 4, 4 ad5 _c. vel 1 2d 1 23
12d 1 33 12d 1Z, 8ec. HOcCA F ad = F 1, _ 4d = F 1, 1 4d = F F.
_c. Tercianorum oradraris (sirc (extanis) 2ad7, HoC CA,
2ad6 F 2. Tercinnorum Radicibas Ouadraricis 2 2d5, sveF
ad Z, hoc est x adZ F r. Sublccunlanorum radicibus cubicis
Ctive (ub (EXtanis) 6 ad7. Cire F 2d3, hoc est F ad 8 F r. Cubis
radicum quodcaciearum omineanorum, (tire anindecimano
rIM