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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 131r, page id 00068194:0261
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Ne tantum de serebus infinilis loqui
Terminis
videamur, loquamur
seo qui ex infinilis rationibus compo-
nuntur, ut
229942526 etc in infinitum.
1 25 345 etc
Hic F. Hac ratio valet 1.. Nam abjici
potest primum 1. in ferioris, caeteris
inferioris manientibus, quo facto inferia
numerator et nominator sunt aequales
seu fit ratio aequalitatis, id est 1.
sit jam ita:.
25345 26 etc. in infinitum
345526 27. etc. in infinitum
abjectis terminis communibus residuum
manet 2. in sunim nomi numeratore
in nemeratore 1. est ergo tota ratio 2.
contra si sit ply terminus in veg. 2
numer nominatore, qui non est in
numeratore, et ita oestermini un
ita enim pro to valor erit .
in genere abjiciantur termini commu-
nes, licet infiniti, utrinque resid si
finiti restant vel in sumno vel
in imo, vel utrobique, determina-
bunt quantitatem c hujus progressio-
nis complicatae. Et determinare
poterunt veloper modum simplicis
multiplicationis, vel divisionitve vel mixtae cum additine, subtractione, radicu extractione.
sed si in summ No uno termino
sit incultiplicatio, in altero divisio,
productum fit infinite magnum,
vel infinite parvum, ut facile
palet cuivis consideranti.
Sed quid si Termini non coincidant:
ut si sit haec complicatio duarum
progressionum, quarum altera
est Geometrica, altra constat ex
terminis unitate differentibus a Termi-
nis Geometricae. v. g.
20+8216232 etc. in infinitum
137131. etc in infinitu.
ren
Hoc casu determinari nihilominus quantitas qudem
potest, admranda quadam ratione. potest enim ntiortastare
1+1 24XIt 5+  crescit enim ratio in
infinitum, ex causa
1 u 7  2 a paute at 17  fait 64 (3:, quod jam est majus prore,
ideo invertenda est positio, hoc modo:
od ut
15
1 2
31 21
atsu uti sier