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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 224v, page id 00068196:0444
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 223r); this page is its left half.
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= 200 r 7  H
 (9) + ot e Dd) seumalio. C
- +20B+ B (2) summabilis
y - 2yβ+ B ego
pungantur 1. et 2. ac primum addendo, fier:
+ W β+, 32yDest
y27 3+ 2 5 + β4 = 4y
sue 4B 2( (5) 5
  y ex ap. y 
Jungi possunt subtrahendo, et fiet.
ta se+Berve .
santureu
 =-  e (. (D):
Cujus serici datur urisus summa.
jungantur, Addendo, tei: (OV (C ) + By  ()) 2B est
singantur subtraherdo fiet: B +y + (3 + C3
Hujus ergo seriei + = +  etc. habetur summin,
Idem hujus:  +  +5 + o resi  1o i qua 
quae est series popramidalium, nimirum, omnes numeri cubi radicibus minuti
sunt senarii et divisi per 6. dant numeros pestamidatee
4- 1 9- 1 16-1
duae
15-,. et. A 4
ont A 3 b  g 6i b1
recuml fractionum
potestates exponentium
parium simul sumtae
aequantur tribus quartis.
16 L - = +  - 1 + 1
S
erit. diffecntia:
2 1
Si invicem addantur
Si invicem addantur:
a. ponendo y esse numerum imparem
.5,  seu
s eostaug. in
Aastars fiet: 1
a et a, fiet:  at. qua rubita
e yt inte d+ B +y q er
=+ y ex. Addendo ergo
summ fice 20 =ay Y 5 +  Y ex
quid si sir: S ra
aerrayayr HX, fiet:
ia-  m 25a. + 2avi. 4 5a MM.
qu H  29e, 2292
SyM-41 1r y 1 5
4 +2, 29, 2, + 1 4 - 1 maltiplicetur pereus  72 L. 323  
igiat17, 220- 2, 1x p 83+ ad dipit  2
i nalir qu B du
 2943, -1 V standam d
vertice aliquo, rabit.
4 Equadruplum summae, habetuo ex
ductu hoc differentiorum, cuu 4y aliunde
vi
etur aliquod duci ad summam seriei
3 is su 9s ham
Multiplicentur ista per 3 7. H 15. 19
esto y nuneus impar, erit 1 termines seriei quadratricis
hez: 2y+ 1 - 2y
3 + 1 3-L +  i ex l1s  30nc
40 +4y 1 2y + 27 cujus dinidium  1
Unde auferendo ad  restabit.
qy- 1
(172 ay3 +.
1694 4oyv. 2 16yt 4 - 2
vel ita:  29. 2
 Cay. 212
in6 erc. l. 1  t ipt   vi botaste cujus dimi idium: Qyr. q, addantur adatio ad Aa
Ergo 5 1 s +7 +
Z + f + L + 2 + 
ex 4 +  + 15 +  4 i + 2) B4, ut cdu serimus
Sed 1 - = + L-
1 3 3
fiet 2 f 40 +  F a3) sive   cuus duplum
erit , uet  Hyi. contra
Contra si cddantu slsi ultrum ab altro cnfratur,
cous quodgtum. y -9
1 35   + iont is is
v N 5+b
D a O. restabit.
ayCayd +ad
Cuju seriei habetur summa Addantur
F et 4, fier: y+
y3 - y N y1 257
contra si altra ab altra anferatur, fiet: y - 1
es . 9 i 2 2
n E F2 2o
in3 3 8+ 3+
 summafigurau quae datae seriet
qe