# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068083:0003
# Permalink to this reading: https://leibnizlegible.com/page/00068083:0003?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 12
# Folio 2r, page id 00068083:0003
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 1v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068083&page=3
# Source image: https://digitale-sammlungen.gwlb.de/content/00068083/jpgs/default/00000003.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 103 lines, status machine
# Lines: 103 recognised, mean confidence 0.76
# 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.

posfe  li5
L10 95 38
quiguos, L15 1o na
sexies 1 (2 296 3006
uo ne
y = 1y
y =, y - 1 y
1 = 1  3 f + 1 V
y+ = + si - 6 d + 7 V
= 1 f - 10 f) + 2593 - 15 5 +1y0
1Y6 - 15 y 4 95y - 90 5 + 31Y - , y
Iliss
1+2. 3 = 7, 1+2.7= 15 Bc
ubi nunerorum ratio ex Tabula manifesta est, nam 1+ 2. 1 = 3
Et 3+3. 1 = 6 7+ 3. 6 =25 15+ 3. 25 = 90, &tC Et 6+4. 1 = 10. =5+ 4 10 = 95 90 + 4. 95 - 350 
Ande perfacile est potentiarum communium in integris summas mire, nam sy- Y et dyt-
(B quia fy=  a 5ist 19 esc. Hini faet:
 et fg 5y - 5 5 = 5 4 5y -  f 2y + 2s 
Sy -  s Cf  2y 1 5 et fy
. fi - : y
(y = 2= y - 2 f 4+ L 
5y = 5 3 - 8 5 + 7 1 -  y
Etc
esc
dy = 1dy
dys = 121 dy - 1. dy
dy3 = 13 9 dy - 32y y + idy
dyt = 1. 4  sy - 63 y y + 7 y dy
dic et C
sunt autem y idem quod naturales divisi per 1
1-- triangulares..
4.
posito y esse pro-
gressionis Aride
triangulabiaous lies ... . .. . . 1. 2.34 Arhme sica naturalis
3 () pyramidales
Si contra velimus  proucarum expressionem ex potentiis puris
potentiaumque
tentiobimus Methodum similem:
et p = f 9+2 = 1y2 + 1 y
+ 3
= y
+3 d3+ 3.3. y
et S  V.  G - . y + a 3.
et y = y. 9t1 = 1y +17)
= 1 y + 3 y + 2 y
= . y + 6y +10 y + 6 y
+1_ y3+ 4.1d,+ 4. 6 y
et y - f 9a5  F 13, 4 d s 17, 5. 5 3 . 1. 35   1o B  21)
itaque omnibus collectis
F i
(4) = +
isitusro
5 10y+ 35y3+50
 - 196  3y + 8s Ptus tary + 10y
X. 23 45
6a 2 6 24 120
1 3 y 50 274
(V) - y. X = v
V) v aC2 H
CyD. (X)  (y) quodva
nin
pon
a 
∞ 35 3t5
10 ex
p
u d.
Tabula Numerorum
10 35, 50
Nempe
3- 41. 2 + 1
10 = 1.4 +6 35= 6. 4+1 50 = 1. 4 + 6
Ubi jam si fiatit aequationes: l. verb. y - 1 = 0 y - 39+2 =0 y - 6y 4 1 y - 6 =0 y-10 + 35y - 501 +1420
se  e
(14) (∞) XrI
1 vel 2 vel 3 vel 4
15 85 225 274 120
1   ran
1y + 10 y +559450y +24 y
1y+ 15y +  85 y +225 y + res m
Numeri exigui in Tabula
significant quomodo 
tiplicando per ipsos
dertoque majore
uto ad
fextum
duppositi
pleducantur
l sivi udan affiruntici, sed hunc ambir aeguderes
E Erunt radices progressionis arithmeticae: iodem muneri al sint algation
y5 e
qu et. omnium ternionum
5225 sunt somma binionum ab harmonicis;
siit naturalis 1, 2, 3, horum Ergo; + = in 1. 2 = 3 R arsus sint naturales 1, 2,3, horum recipioci L + L + L in 1. 2. 3 = 2.3 + 1. 3 +1. 2 = 11
eo
 in
At1X3, 11,50, 224 ex. sunt summae unt
10, 85 summae ternionum ab Harminicis es. Nempe sint raturales 1, 218
Ergo 1+ = = 3 et = + 2 +3 = 1 et L +  + 3 +  = 50 et  + = +  + 2 + + = 274 Nempe posita
sint n. Nibile eller ali modo
 qua aquatio itonlia est ner qu  l ut s) int sequar lin 
nu aetquatio itculica est, nec quiculeum vine distins naci invonimus Avel  is