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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 29r, page id 00068217:0059
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 28v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068217&page=59
# Source image: https://digitale-sammlungen.gwlb.de/content/00068217/jpgs/default/00000059.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 97 lines, status machine
# Lines: 97 recognised, mean confidence 0.82
# 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.

X- q aquo 0.
N X + eabiX + fa X t bCX + V a bcX ga X HlaebC XF na bC X+na bext
bC
abc
abc Nab
aC
NpC
abc
+0409,
+D4097
X = 3 aequ. 0
X-
C2
 ib
+6817
et h, 1296
 1 et 2
4096 + 5i3 f +29 + 16h + 20 aequ. 0.. Ergo 3584 - 4809 + 16t - 510d nqu. 0
Y X = 1
2512- 5129-5120 per 1
1292 - 2409 + 8h - 2550 aequ. 0
es jungantur X = et X + 1. fiet . 531441 +5, 17,0561 + 97 57, 81 + h, 16,81 aequ 1 + f, 17, + 9 254 h.6
Ergo
53144P + f, 17, 6560f + 257, 80, 9 + 16, 80, h nqu. 9
6643 + 17,82 f + 2579 +16 h aequ. 0
=17, 8 ~ 1782, 9- 17826 , er 1.
3584 + 4809+ 510
1165 - 4579 - 884 aequ. 0
XX  aqu o. fit 1+ 35 + 2579 7 ibh + 4047 B agu.o sel -3568 +740g +4590 D aqu. 
-17 = 179 -136 - 35841 289+ 5108
9 aequ 1165 - 8840
=1784 +3609 + 2295 aque
9 aequ 1784- 309 22978
229Y360
poteremus hac modo investigare progressionem: Primo em avomodu X. X.
X4. X. X. X. X et exprimantur per a a vel a vel a etc vel a. junctis
rectangulis ab. abc. abed. erc. deinde sumemus X. X. X6. Xd. X et. et videbimus
quomodo exprimantur per a. ae. vel a aeb a. a. a ad. e a junctis aeb
a 12C a bc d. abede inde sumemus X X. ~ X X. et videbimus quomodo expri
mantur omnia per a. a. a. a a5 junctis ab, ab. abCd abCde
Inde sumemus Xt X. N X. et vodeamus quomodo ibi omnia exprimantur per A a. a. a. a
junctis aB. 42b+ 4 44444
item sumemus X. Xio. X. Xo et videamus quomodo
omnia exprimantur per a. 4, a11 a junctis a b. à c. atad
X pu a. ab.  n pa abdabe. A)) X  a. atu abc abid (abide)
X  at.) ab  X pr a ab. abc X  a. ab abe abed X  a. a V a bc à v d: abide.
X per a. a
X. e a). ab.
X per 
e per a
pr a
X per a. a
a
t
X10
a
ad
ecc
ab
 Xaqu. a+b
X jer a. ab abe X a. ab abd. abe X per a. ab. ac. abe d. abede
X per a3. ab
N per ab ab
X7 pr a ab
peur a
ab
+2  a. ab abc
a ab abc
a ab2 abc
a1 ab. abc
a ab abc
sic
Xaequ. at b+c.
+ per a. ab abc
N per a. ab. abc
X per a’àb3. abe
per atab. abc. abid
Xd. ad a V abti abed
XI a ab ab eabed
X6 a. ab 2b Ct. abid
X a ab. abc abid
X per a. ab. (abc. abcd
X per a. ab) abc. abco
X1 per a. 21) abe abc d abide
X aqu. a + b+ C+ d
 aequ
+9535537
=
1+ f + 9 + D aequ. 0
a1
seu fier:
seu dividendo per. 8
Ratio esionis
pese
per a
Xaqu.
Expressio ipsa: