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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 420r, page id 00068196:0835
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in 682
caltutus deges smnodiffere trabs ni pumlis ao. e
 -Saa +bx + CXX + Vaa + b X + b dx +, C,XX + 2CXdx +cdX aequ e
(4)
var
fiet ee (+ a a)t bX L CXX)  -2C Saa + bx + exx aego (aax+c + cax
et 4 eeaa + 4ec bx + 4CC CXX aequ e + 4 Cee d accxdx 
si esset caequio. fieret
seu
qu
4. 2 ee bdx ∞ Ab Cxdx + 2bcdx
+b
et + reebd + bbd
et +2ec b dx + bb dx aequ 
ee b X _ abbx dx
eAee aa _abaa dx
+bbXX
+ 8baax
9a
=ab bx dx
qbaa ex
+ 4bb Xx
+DbanX
seu ec = b dx, = 2bx - raa aequ Vaa  + 8baax + 4bbXY - 4baa dx - 4bb 2 1
si jam ponamus ex esse constantem, ut ex aqu a et faciamus etiam baqui
fiet: Ce = aa = 2ax aequ  X 4aa XX + 4aX.
seu erit e aequ. S aa + rax + 2aS XX + ax
Redinchoaudo fuisset: B, Saa + ax esaa + ax ead aeque.
seu ee( aa +a r e tantur aequiaar aoaax aequ
et fiet: ee 2 faa tax 4aatax aequ aa axtado
seu eaqu Saararan  saaran, faciamus aa adx aquo se
fiet et sit a aequ. 1. fiet ego et de aequ. 1. fet X s + X. iago e
eago fr  vel Sibi vel Fquo vel 14 vel 556s6 
sumnae Si  si 13 s+ s5
su
summa si 12 13 S4 se
seriessumabilus sis 21S Sis Sas
Ii - 1 aqo 1+ s2
seu Cog det
x
d 2 aequ 4 + 8
si+ ex s  aqu e. Ergo re x ago eet rosx
Ergo A4X aequ C + sa et 1X aequ eet rerx +x. Redeunt priora
Ergo nihil hinc fuit erior
pisa 1(1.X + X  2 X + XX aequ ee. Ergo C aer 1+ 2X +, X+XY
ovel
Faciamus a aequ. 1 et dx aequ. 1. seu X ogr Tvel 2 vel 3 vel 4 se
fieret. Saatax erit Lt Si vel S2 vel 53 vel 14. HC
et  Saa tax - Taa + ax = adx eut, S2- Sivel Se t2tc
equ.
seu eago Si +X = sx. Ego ee aequ 1+ x  2 SX + X + X
ergo eaequ. s1 + 2X + 2SX+XX
Ergo  summae erunt
52
V3
Sq si 16
Ergo series summatix erite si
series summabilis erit sirito Bri Sir Sinta sortio axsio
seu sirto hrgi Ssa Syt 15.b (9+0 vits
at
rrgo 1+ 13 + (8.1 4. 15 + 18. 3 + (2 + 18. 6. + (9+ B3. 10 + S11 + 18. 15. an 50q
aqu f5