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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 11
# Folio 9v, page id 00068082:0018
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VX y+Y
qui  v
3
xt
Quaeritur eodem modo summe seriei
assumatur ... . . . . . . .
ot + 1F + 1b + + 81 + +25b +gep Gp sy4
1t + 16t+81 1 +2561 1625 15 He Sx4
HR. Y SxtXyEX F+C+ Soy6yy7
3E +6C + 4A +S
AF+1E +6C + 4 A + 5
jam H-Gp O. et HFBG. vel Hn G
vel Hp O+ G. Ex
Ergo O + GB G. Ergo G50
 vel Gp 0S
3E 4 36
4253st S
et
Ergo O  4E +5C + 4 A +S
X Hct
XtLX+I
3y1694 47 +
yt Xy+y
yx HS+2+Y
9 +
A-G1 SXY HKX+XV AXy +y
AF+ C+ (X ytXy
S2y3+37+)
EE 4
HF + 3E 4 3C +1
Op
F+ 3E-
A
+SA
Eodem modo supra: F. EH D. A D + 2C + A. Ergo D + 2C + 3A +S
AG
Unde patet si quis prosequi A  velit, nova semper compendia
Et methodus inveniendi compendia in talibus huc redit, primum invenienda in ipsis nasci.
X+ X y + XY + Y e, et similibus, inde transitu facto quaerendum compendrum
seu progressio ipsis C vel D.  id est H - G vel F- E, vel D-C vol B- A. simpliciter ex-
pressis relentis B. D. F. H. erc. inde quaerenda progressio eliminatis his, B. D. F. H
et re ad solas S. A. C. C. G. reducta. atque ita denique apparebit etiam
progressio, eliminatis A. C. 2. G. seu re ad solas ipsius S. potentias reducta
ita enim psc per gradus apparebit quomodo progressio una ex alia derivetur
Cum alioqui non statim liceat ad progressiones et compendia pervenine per saltum.
Spt + t+ t+ F tKC B + F
AHot rItG E 13tE, H A Sy. Fr.
ppota t : 4+  mbt e A5 L
+
F+
stoneus Quilibet terminus est +
id est potestas ab a + cujus
coneu y+1. posito & esse ovel 1 vel 2 vel 3. etc
et D it +49’erc seu p SByri, +2. +
Appellamus y + 1 aequ. X
Ap Sy, tM. s B1 (y+1 FY+ E B- AB S+ 5. seu B⊓ S+ A
sit ergo si (+tp
Ergo seriei summa est
  t +, 1t e seu ( sy+, L1. F.
BH St
(vel BF 5y. + = ot otian este 311, t.
D- C aequ. Siyr1, t
quiaot aequ. 0
seu Dn C+ 2 A + S
LveI
quam aliunde constat
esse
1- +
.Et ita porro
Ergo A, VRII,t
C aqu. sy. +r H. Daqu. sn 
Caqu. Sy, + D aqu. sy, t - oF. Erga C ag. D. Ergo DBC. Ergo C1 2A +5,  = se 2A+ S, 5 sc. 2S75
+-
Eaqu. Sy . Faequisa F7
G aequ. f73 +r Haego. (X F, +7 H aequ. G et G aequ. 4E +6C + 4A + 5, 5
Et ita porro Sed ut inde fiat Tabula: Sit:
progressio ubi inventa, fuerit, quod
continuato labore labulae facile erit
tunc utilissimum apparebit hoc inventum
ad summas serierum, quales sint
  +F -t et ac similes vide schedam
serie non nisi duobus
modis scilice
additionibus et substracto
nioque intoris tantamus
X....
Has tabula
A paulo nitur
scripta et
S opus conti
anata, facile
progressio
apparebit
Nota nanquaeque
linea aequivalet
sed summa continet
explicationem per
fectam, hac explica
tionum gra datione
Series optime inve
niuntur
et muetiplicationib
ac divisionibo
constantium ()4I2C
tractari possu
lem divultionib
in alias series
125
125es
is
3575G 35,51.
.. .t
5+65, d
45 25, 12Sid, +65, 5 1455
15
.. 2 L 25 05 +eA +65, 5 455 15.
C
--
A... 15.
Notu: patos eadem methodo etiam inveniri posse summas serierum yit. Namm tantum v.g. 0r + 1t + 46 + 9 ec.
Scil.
Sit
a( L mo vide id difficilius, quia ne quidem habemus, vel et + 2F + 2t+ 9t
+ 1 + ++
adjectam, signo (1)