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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 59, page id 824573315:0271
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PrOD. 74.
Arichmictica insinitorum.
cA Z = 2 + =;) quae eAt ad feriem tocidem maximae aequalium,
Uc 22d30 == Z + +, vel uE3 ad 20. Puta A respectire malipIL
eetur
Series
Oa 10 4 a3
9a _c.
in Teriem N Ob, ~ 1b, N  2b, V 3b, _C.
hoc cA Ccries  20a, V 2 1 a2, V 6402, V ? 729 a, &C.
in Teriem N 30b, V 1b, V 2b, V 3b, _c.
prodibic leries
d
20a 7 b, N 3 x47 b, V 128a b, ~ 2187 a b, _C.
Icem, S lerieo Sublecundanorum (cujus index Z) respecti
ve mulciplicetur in seriem subguincanorum ( cujus in-
dex 5,) eric produeta Peries Radices Decimanae Seprismanorun,
cujus index 2. - = + 5.)e propcerea rationem habebie, ad seri-
em maxima agualium, cam quam habec a ad 25 == 20 t 5, vel
10 ad 17. Puta hrelpective mulciplicetur.
Scries. N 200 N =1a. N 2 2a, V 2 Z0, EEC.
in Ccriem NOb, V3 2b, a 32b, V E3b, _c.
hOc cA, Cerieo
V
20 45, 1 2 1a, V 13203, V 10243 a3 _C.
in Teriem ~ 2 OB2, V e 1B2, V 2 4b 2, V 209b 2 _C.
prodibic leries
Y 1e Oa 3 b 2, Y2e F4EB=, V 128 a b=, V02187a l2, etC.
Ex similicer in aliis ejulmodi mulciplicationibus concinget.
P R O P. LZXIV. Corollarium.
Deogi. Vbi Aegrecatum Indicum serierum invicem re-
spective multiplicatarum idem est, ibi et idem erit In-
dex seriei producta.
Txsempli gracio. Si lerieo cerrianorum in Periem Ter-
tianorum, vel scries secundencium in Ecricm OuarZ
norum, vel series Primanorum in Periem Omintanorum,
vel Ceries Aqualium in seriem sextanorum, respectire nulri
liceum ProdibitCeries (excanorum. Ouia nempe intngulis
I K 2
288EC