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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 10
# Folio 2v, page id 00068260:0004
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Data aliqua serie Fractionum, invenire aliam seriem scujus differentias constet
mpossibilitate
ut series 1.  b 10  est duplum  Z  12 10 gdifferentiarum
ita
seriei 1. 2 3 4 5 ∞. ek.
A
Invenienda ergo est talis datae seriei eruntiatio ut Nmintores Numenctor
2
E sint differentiae, Nominatores vero Facti, continue terminorum seriei datae
1
vel statim, vel si cecto quodam modo dividant, aut multiplicent
e
D
E etc. = quaesitum: Z X U S et ratio dividens aut multipli-
Ergo jam 
X
LW
EWxy
vw.
11
A P.
U
t
AT-uW
Wr
V
I Es
rR
et
W 7 R
ans quaecunque ea sit. P
Sed certo sciendum est, seu demonstrandum posse hoc in infinitum continuar
61
si quis huc usque analysin produxeri, ut ista invenore queat, illi
de pe eum plaeimum praestitisse arbitior.
ete
Nam L+  + +  ex = seriebus in
finitis A. B. C. D. et. a quibus si
abjiciantur: L+ L +  etc. restabit
= oi residuo infinities infiniso
incluso. (Ita = initiori iicluso,
et ita de coegis.)
huae 1= terminis omnibus sinu da repehe
seme antea nunc semet tautum sumlis
10 15
16 25 ete H AA
A = D.
= E
ZN 27 b4 ins ete = 1 10 20 3 ete c =F
160 21 25b 610 etc K tr he 70 ete
ete etc etc ete etc etc et er etc
Ck
ilem G. = M. Ergo totum M + N + 0 exe = toti H+ 1. + K etc.
H= A 1 = H ~ D et B  = i H + L = A = D. et 1 + LR = B =. E
et X+ = = C = F Utrobique abjecta intelligante huic Grilline L
patet etiam: AA = DD = HB. et BB= EE = 1:  et CC = FF = K Lo Abjiciantur hinc H
illinc DD. residua erunt aequalia atobique Ergo I+ K = AA. Z. +BB- 1, +CC. + = EE+ FF
Ergo cum in istis infinities infinitis o
in oes termini bis occurrant, denta
media linea notata sic Hmu. un
ex lineae teminis dimidiatis
ete
laodm au un u ex
+M 9
e
 e
e
te
14
28
c M ete eri ere