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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 12
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Ut autem pro summis talium serierum generalem Methodum
demus, aetem icique calculi differentialis a lineis ad numeros
transferamus generaliter sic licebit procedere: sit  du differentia
ipsorum y. Et  significet exponentem gradus potentiae quam pla-
cet imitatione veterum quorundam Arithmeticorum vocare pronicam
Gradus Ii Directis primus
in Directis
y-y
secundus Tertius
in Reciprocis  -y
Quartus
J. yrty. g y. ytag. 9 r2ty - 2 y. V2oh. 92 . 19 +rctus - 
.- 5
y. yt ay
1. gitus. yreous
in Reciproris autem Generalier autem Y oy =  yta et Y yeF  - 1
(2) pr
y. praty. 9 Atgs. 9 43Ey
in nerunt pa etauralis et  ya  +Idy = y iti  senis at + s dre piscis
 Ergo subtrabendi a4 ex aqu. 1. ab aequatione 2
st et y y - pri dus =
y p+1
Et subtrahendo aequationes l et 2 a se invicem fiet:
y+ u  - y B = PFI Ay. Y. ser. S y su =
in Directs pinittr VC. j = 9+ y et y. y apnus =
In directis alio opus est artificio
PF1
tale quid
siniliter in directis alia arte nonnihil procedendum est, ut idem
pe
concludatur, nempe tau. yrius yrdus et y. 9+ p- idus =
nempe yra. et y = y et B ) podu et et y rdy. y du = y +du
odatasum tat syt (seu fy S y+ tu dus = Y + 4y. seu s ylay =
Generaliter ergo y dy = 
er
1P+1
Ly et1
ar
 in Nrumerois
p
Josito p este exponentem potentiae pronicae, et  valere in tirectis,  in neciprocis.
peute vi
ipso p existente numero gradus in directis positivo, in reciprocis privativo. Quod
ipsum in linera verum est pro. potentiis communibus;
perae pretium autem erit potentias communes revocare ad
q pronicas selssgntas seu aritimetice afsectas.  vig. gta estt L y
 ab (2) in Exponente significal potentiam pronicam. Ergo y9+y = . yl)
 Erqu. y =   y - y
ubi notandum y et  seu y esse idem
jam y - y+1 -1 et y g4 = E ) ergo fiet
y C2d - so). rursus y = y+2 - 2 = y+ 1 - 1 e y2 in P - y. fiaetus
3 13 + 2. 3y2)
2) - 3 y + y0
-6 f4y ce
+ 7
2γ
egosis)
- y a- 5. d 1 410)
+25 - 25.3)  15. 2g21
= 5 - 6 y +  1 - 1 y
.∞ +1 y
(2) (1)
p  10 3 +25 - 15y + y
  - Y y 73y tog.  et = y + 1 3 3 Y 3y Ea y, =   1)
V = 1. 2 s y - y et y - 943- 3. Ergo y=
Generalius ergo y. _ =
yy =
fietue ist = y - 21
∞1. +y=
sid -3
4 (4)
s 1   g  2 9e 3 9. 3et. 18 1)
in dinctis pa 1oe 2 eet 3
Hocest in direcie si iste atae
seu differtalia
sie
Et qud in Reciprocis
 
si seriti e
progressione aricha
proudere ineum
sse e
umma
uuda sit
s
moium
quaeritum, aen cum  infinito)