# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068072:0001
# Permalink to this reading: https://leibnizlegible.com/page/00068072:0001?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 1r, page id 00068072:0001
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068072&page=1
# Source image: https://digitale-sammlungen.gwlb.de/content/00068072/jpgs/default/00000001.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 187 lines, status machine
# Lines: 187 recognised, mean confidence 0.75
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

summa potestatum a Naturalibus
Fet(XHC) = X + E X C + es 1
12
P.2 2 + es C. 1, C. 2 7 C. 3 3
C
1. 2. 3
e. 1, C. 2, 2. 3,B 4 4
C e
intelligatur ab X Brmo incusive ad utimum et. lisivel
1.3. 3.4
summa numerica
Ergo X ult. = X prim. : e = sum X et et XC.2C + et C Cs FC + E. 1a sXC  + et e r
et
1. 2, 2 nG
(XC). - X :e = G A e- 1 e 2, L , e-t. C. L p C. 23,
sint X numeri arithunticae crescentes per d sereniani E. Et x pri puemsit ala in 25 qui asumitur, X
p + 8.) s sum XC. 2  e. BB2 3 (um XC2 + .1, e. 2 C 2) _ X
(2)
st 
itinim oslibus fg
siet Xult X prim E sum X verbigr 99. 9  summ x a 49 ad 10 inclusio seu
simolbinst
summa autem intelligitur, ab verbig
ad X. vC
sie erit
sit e = 1. fiet K B x X K X  X ult - X prim = = sum. 1 sed verb. gr. si c =1.
Xult-XprimE
40 terminorum  X, a gu usque ad 10 inclusive vel 5 4t4 3E
et e siet
1, +2
bC= et x pri. X ult sit 6 et X prim. sit 2. fiet  6 22 = b- 8 +5
e
vil G. a +8 274217. 2.
Ergo s, 1+141H1 = 62
A Verb. gr. sit C, 1 et Xult 6, et prim. 2. fiet
6 -2 = 6-5 +5-4 + 4 -3 + 3-2 = ( 2 (6 - 2) 1
+1
sit C =2 siet X ult - X prim, : 2 = C summ. X F sum X
+ 1
6- 2
ab
aequ et 5+4 + 3+2+ 140 = 6. - 5
6-5 +5 _ +4-3 a
uequ
18t2
aequ
a+ q
sit e = 3 fiet X ult - X prim, : d
67253 35
fiet 6- 2 = ape
2545+ 5 = 301
Cs- 36.6- 46+8
216 -8, 13 = 208: 3 =
69+ 3
36, 6 L 216, - 1258
tet
CEx
Au
aequ.
aqu
31 
5.G
adeoque  25 + 15 +9+4:
Eadem methodo 125 +64 + 27 + 8 =
(3 - 2
91;: 3 = 30t 
adeaque 25 + 16+9+4 =
8  2. 27 -7 d 35
+ 53-4
aequ.
16
2. 1
1.219
P-2
+ e3 =
aequ.
 1.2
123,  - 2
1. 2 = 7. 23
6-2 X (72
Eadem meltabo quia 6-  125+ 3 25+ 2. 2 5 + 3. 2. 1 5, seu 6 -5- = 12
et 23 + 16 + 9+4+, +0 = 6-
Eadem nethodo 125+64 + 2718 =6-2 -72
sufficit seponere summaspro calculo, uit enim e = 25 + 2
6-5 = 1Et 65 = 3 +  Et
v. 25
1. 2.3
pro
aequ.
6-2. 21
1. 2.3.C
12
6=5 +2. 1 6-5 et 125=
1. 2 1.2
2.3
3-
2
1. 2.3
1. 2. 3.4
l. F 3
1. 2.3 2
1. 2. 3
g_.. ge2  + g 2 3, e -4
A h
+ t e-4
3.82. 625
1.2.3
1. 2, 3.4
6 -5,: C = 5 +.1 5e 2 +8-1,8- 25C. 3E ( 198-2, C- 35 4 4 (21, c- 2, C. 3, - 4 5-5 +
1, 2. 3. 4.5
1. 2. 3. 4
2.3
.2
1. 2. 3. 4. 5. 6
2. 3,4. 5
1. 2.34
li f-
- 3. 2. 1 6-3
(. + g. C -3, 8 - 4, e-5 .. et
1. 2. 3. 4
+ el B. e- 4, 8-3. .. et
1. 2
h, 6- 507,:, 3 =
sed  = Z = 1. 2. 3, et fiet h_ = 2 -1, C- 2, e, 3
1. 2 1.2
1. 1; 1.2
gF 1.2.3
l= e- 1 e2 2, en 3 en4, = 1, 163, (2.)  1, (.2 3.   (1 2. 3e)
2. 5. 4
M = C = 1, C-2, - h, - 4, B- E,, + 12 (= 1. 1. 3
1
CL) Bra
 = C-1 et C. P-4
1. eK. 4
- 1 (1
et
12 et g - E.1. 82 = e-1, en 2- 1 (L 
1.2
e-1
1.2. 3
at e e  seu d=  (12 = 5) -1, e- 2 Et h = - ( - L) e-t. B- 2 8-Z 4 8-1. 822, e23 = G-1, 8-2, C-)
12 
(e
62
3. 2 6-5X 1 212 2 1. 2L12
1.23 3
5= 6 -5 - + 6- 3 25= 6 25- 6 5 + 1 6-3 125 = 8  5 - 6. 5 + 265 065
t
1,62- 5 3i, 2.2 =
7. 2. 3
6-2 - 63 2 -6-2 + 16, 3
4. 3. 2. 1 et ita porro.
et 6 =5 = 625 + 4- 125 + 4. 3 25 + 4. 3. 2 6 + 1. 2. 3. 45
1.23
1.2.3
Et exempli gratiant
2CC sum. X + 2. 1. C3 summ X. Coterisque te
12   2
6-2-
V
l.h
 . ti 6 (7. 2 2 6 =2 + (3 2 12 1. 2. 9) 627) - 2.1 (6. E - 6 2
-2
tandemus 25 + 16+9+4 = b
2+2
C summ X-
aequ
vi
1.2. 3
et
102
1. 2. 3.4
seu d= ete et h=0
sou d U 1.2: 1. 2. 3
in + - L. = e- 1 et .4 1
1 27 1.2.3 43
25
220
Fi et. Y; 1. 2.3312,
3. 4.50
in
emendodatur
ammonicus
3- -
2
.2. 3
112 1