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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 118v, page id 00068196:0234
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6) =
sit c= tab et b d = aa: Vab
e= scd f = CE : NCd. Ergo e = a f = ab: a = b
Ergo hc erravit Gregorius, putans hanc feriem convergentem
c = Vab d = 2ab:, a + tab seu d = 2CC:, a + C
e= sed f- rec:, C+C cd = 28: a + ergo C = c YC :, a+C)
 = 2(cc 29:, a +C): (C) + H(2C: , atC) seu f - + ab:, a + vab, 14 at hab
seu C = tab AE tab : 3 at +ab)  f = 4ab: a + fab + 2 +ab
seu f- 4ab., a + 3tab
e = sCd f = 2cd; C+ sed
= 2ec: c+ C
e = H2 ab Vab:, at rab) f -  4 ab tab 
seu f= 2ab tab
a vab + ab + rab tab
seu f=
2ab
4ab vab
2644 4025 +el
sit E = cd feri a
ab Vab
Trabrab
atrab
b+ Sab + Y(E ablabrelb.
a= ad + cd = 2cc. fit a = 2Cc = cd, id
d = 2 ab: 7 a +C
(2cC - cd, :d) seu b = cd:
2cc ed
b =
2es
at rab:, sab
atab + ab + Y (raab sab + 2 aa bb)
cc = ab d = 2Cc:, a+c
a  b = cc: a
et b = cc:
a =
a
b
Rcd
2C - d
a
2c = d
408 - 2ccf
2ef-s
rec -ef d=
es
bes
20-f
2dc = cr a = a = 21dc = c. 2cd - 1
c
i
2ad
seu s 20d - 1, 28 - 1
simplicior, si  a: b = (6) c: d = (d) et ita ponro
videtur res reddi
fiet
rec-cdrcd
25dd
25d) -1
a cb7
et a = c, 21d) -1 et (b) = qu. 2(8) -1,
ita et si serres non sit lonvergens.
tamen si in ipsa haberi posset relatio
ila constans, haberetur utique nova proprietas
Notandum hoc modo a et b) ex ipsis c etd)
habentur non modo rationaliter sed et integre
in indeterminatis.
S.
seniei per
Hinc amplus
7) ete per se spectatae datur relatio
spuplicior, sit enim (b) = qu (2() -1) se se 
b
d
seu 26=  qu (2) -1) Ergo proter terminis
c
b, (C), (3) (6), (d) (f) ete assumamus 26) ,  2(d), 2)f)
XA, et fiet (() = qu 20
et fiet (2) = 2 β = qutd 1) aquod est simplicissimum
ultinum est
scribendo β, id G,
siet (3) = qu (G=1) Ergo = qu (qu (es 1) 1)
1S +B+1 = 8. Vercor nesit ersor, nam ut est2
d= 2cc:, a + c
ad + cd = 2cc a = 2cC - cd 2 d b = fc d:, 21c- +d
d= Zab: a + fab
sit c 2a b =B et 2 ci d a S fiot na iam 2 bi sit a : b = (b) et c: d = (d)
Calculus resumatur c= sab
fit (6) = (24c = Ed, : d) : ((d :, 2c- 8) = (2C = d,: D) qu = (2() - 1) qu
CC = ab ergo b = cC: a
tabemus ergo broprietatem simplicissimam seriei (b), (d) (), qua est
(b) = qu (2d-1). Hinc dem quod verum in casu convergentiae
ubi (b) = (d) = 1. Restituendo a, b, c, fiet 4 = qu (2C - 1)
E
propr i0 a
A3 GGreg. Quadr. Cin et Wyp prop. 10
B = 6)=
o
a2