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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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P. 105, 106.
arithmetica Infinitorum.
cestunc F, 3, 5, _C) auc cuivis denique seriei cujus index
eA umITALCMAJCN UlEPATEL.
PROP. CY.
Theoremao
CY ejusmodi Egura ADBB verticem habens AA inf.
nicum e balin DB dererminatam, rationem ha-
heac ad inseripcum parallelogrammum ADBs majo
rem quam intrnicam; eadem figura ADBB verricem ha-
bens AD infinicum SC Balim sB determinatAM, ra-
eionem habebie ad inseriptum Paralleloorammum
ASBD minorem quam intinitam (finitam nempe:)
Et conera, R Ecu illo considerata racionem habeat mI-
norem quam intinicam; Ciu hoc habebie rationem
majorem quam infinitam: Si deniq; in situ uno ratio
nem habeac simpliciter intinitam (puca neqi majo-
rem neq; minorem) etiam e sicu altero habebitratio.
nem simpliciter intinicam.
Nam verbigracia, in ferie secundanis reciproca, cum sine
(Per PrOD. 99.) recte DB, DB, in diaeErOruM AD, AD,
ratione reciproca duplicata. erum e converlo rectae AD, AD, HOC
cA SB, SB in reCtarUm D B, DB, hoc cR, diametrorum A S,
As, racione reciproca Tubduplicata; adeoque ipla sB.
SB, _C. Cun Ceries secundanis reciproca. BC COnEra. AEqUE
(cum idem eciam in aliis ejusmodi seriebus concingaL) patet
PrOPOtICUm PEF PFOD. 102, &c 104.
In Cerie vero primanis reciproca; eun (ver PrOD. 88.) recta
DB; D B, sinc diameeris AD, AB, reciproee proporcionaleo;
crunc eriam rectae sB, SB diameeris luis A s, A s, recipro.
ce proporcionalen, iplaeque S. B SB, leries icem primanis reci.
Droca. ConHat ergo propOtIEum per PrOP. 103.
D R OP. CVI. Theorema.
lPeries aliqua reciproca per Periem aliam (sive re-
eiprocam Eire directam) mulciplicetur aut divida