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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 3
# Folio 1v, page id 00068048:0002
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v = L0 +
t-t erc  infin  quaeritur vD + bv
 5
7C
v0 =4 F - 2t + 2f - 21
by -et
t
1.3
C
+
L
+
1.5 117
+
+ 27
e
1.9
 25
2
1. 11
+2
14
1. 13
-2+ + 2 t = 2L2 + 2f1
3.3.
35 3.7
117
+t
1. 5
3.9
+
5.7
x =L xtF. X eu
+
3. 11
f14
5. 9
+ 414
1
1. 15
et
etc
et
etc
ek
et
ubi quidem salis apparet compositum non esse valde commodum
ad ingestigandam seriei legem.
AAlia etiam ratione licet novas naucisci arbit
um inderemni
Si scilicet loco t, ponamus aliquem ejus valorem per
V+
rer nomner.  pladet
u vel (ut oterum opus sit serie infinita ) f- axxobure
vel + = Caxx +bx +C ubi rationales prodibunt in valore ipsius vyxtC
ut t = 
vel F+ ht = TaxX+bX+C ubi iterum opus valore ipsius + per seriem
infinitam sed quam scimus esse summabilem
possinus etiam rescato Y addere aliquid ut
ad V addamtus b = at fit b - bF + bF - bt etc
t
+
15
+ L
 eu
bic
= + + -
+ + - + + 15  - +7 + f9 - +1 eM
A
-
n+2
1+4
B: AF = A  n+2: XD8n. nt 3 et C: BF = n + 3. n+ 4: ntZ. nF5
seu n+3: ptr = AF: B MII: n = C: BF n+ 5: n+ 4 ( = (per ypend) BAFI: n = 9u+s: nFq
et fit +r n+ AP = 0. sit n +5n + = P = 0 seu n + 5n+ 25 =  25- + p
p- 9
qn = 5q
seu n+ = =  = ) 254 = 3A( -25C
9- 9
2 A+ - C
quem valorem subitituendo n valore ipsus B habetur absoluta relatio
inter A, B, C. Veum illud jar vdeo, si opus es Et quod
amplius est video in aequatione ita proditura A, B, C per se solus
implere legem homogenearum, itaque sit A et B fierent aequales nihilo
foret etiam C aequalis mihilo, ret quaevis alius terminus ut 
infinitum. Sed exitui hic obstat, quod duaes  terminos
+
faciendo aequales nihilo, reperietur quidem valor ipsius F, et
ipsius n  seu gradus, sed fortasse egeadue numerus in, tiet
non integer quo facto jam non servit nostrae seriei cuius omnes
G. gradus habent ex ponentes integros. Intemm notanda haec calculandi
ratio, nam in stalibus saltem isibus ubi solutio per integros haberi
potest, exitum resterit. Videndum etiam non possit effigiq ut
gradus queant esse irrationale V = (et C: 1+F. sit T- X. fiet:
dt= eX  dx
et t + = e. F et v = e sN.: 1+ X
Itaque (dx. X t X pendet a quadratura (irculi
itaque
it re cstendet a quadratura (irculi
imdleter alia a quadratura Hq perbole pacuriar 21 jum. 19
6
3. 13
6
5. 11
16
d