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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 41, page id 824573315:0253
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is o
PxOD. SL.
Arithmetica Infinitorum.
merice proportionales. Vel eciam, quia si recta sinE Serics
Ouarcanorum, Ouincanorum, _c. Plana timilia ad has LCccas
timsilicer polica, crunt leries Octaranorum, Decimanorum, _c.
quibus conrenit racio 3 ad9, 1 ad 11, _C.
SCAOLLV M.
Acq: hoc pacto Rsurarum solidarum superficiebus curris
comprehenlarum insens mulcicudo recuci poltune ad aliasu.
Superticiebus planis comprehenlas;  corpora non modo conic:
(quod docuerunt rereres) sed _ alia quamplurima conoidica,
ad eylindrum reduci. Guod vescio an quilpiam alius ancehac
ostenderit.
PROP. LI. Lemma.
Exta eandem regulam (prop. 46, 47.) Si expONA-
tur series quancitatum quarumlibet, juxta quam-
libet Tabellae Seriem; de illarum radicibus qua-
draticis, cubicis, ac. aut quibulris intermediis pore-
Ctacibus, paricer inguirendum exit.
Exlempli gracia; s exponantur infinica ouadrata (rel quae-
libec plana similia) juxca seriem Cmartanorum; (cui astigMaCUT,
in Tabella, racio 1 ad 5:) series lacerum (vel rectarum in illis
similicer politarum) racionem habebit (ad leriem aequalium)
2ad 3: quia 1, 3, 5, lunc arichmecice proportionalia: vel eci-
am, quia ubi plana tunc series Ouartenorum, eorum lacera
erunc series secundanorum, quibus assignacur in TebcIla racio
1ad 3.
Sic, s exponantur cubi infinici (vel ouxlibec similia Colida)
suxca Ceriem sexcanorum, quibus in Pabella consruie racio 1ad
; eorum laceribus cubicis (vel rectis in his lmilicer poticis)
conreniet racio 1 ad 3; e horum lacerum quadracis (vel planis
in cubis illis similicer posiris) rario 1 2d5; quia euarum medi-
arum arichmecicarum incer 1 _ 7, minor cR 3, MajOrS, (LUINE
enim 1, 3, 5, 7, arictmetice proporcionalia: duns aucem medias
Arichmecicas interxono incer 1_7; quia colidem supponimus
medias Geomerricas inter unicacem _ cubUM, MEnIPC LACUIS
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