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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 57r, page id 00068255:0113
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=113
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 72 lines, status machine
# Lines: 72 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

s
ax  nat
9
An ex natura differentiarum constantium in Arithmeticis
replicatis et seuen Columnarum dyadicarum inveniri possitt
Columnarum
12 3 4 5 6 78 9, 10 ete Hic lex nota est, et simplicissima
videndum.
sit alia serres progressiones iae uprimae differentiae constantes
ete
 h+a n+ 2a h+3a hiqu htsa ec. Fiet ergo ex Termino seriei N
en
fiet terminus respondens seriei Nte si  fiat gna + h = n
jam summe Naturalium quaerantur et seu trrangulares, et smiliter
6C 3 6 10 15, 21 28 36 45 55. pyramidales, et videatur quonam
a +1 - b = 0
vela -120
unde a+a =abua- 1+ b
seu a + b = ab =0
de+ Offeantis
ld duc
vil2
3 4
8
sit lex columnarum. Undel
e
 Note
einde omne
o
alrae progress
0110011 010d 1. 1b ∞) od V  oa summes colmmnes
10 10101010
0 1 11 1000101 1 1 1000 datmr hic
progressus
10 1 111111 10000000
dc b ad c b a d c b
21.D
o
vel 2 a
ob b- a = 1 est a=0 b =1 c=1
e
408710 ex
a+b ab = aseu a et b ob bua + fit a + b ab =0  sed absemper 0
si  b - a = 1 vel 2 - a = q e B erunt b et a inaequales et fit b  a = 1
sed si C- b =0 erit c= b a =d b = 1- a C = A - a d = a
Alibi nifallor
sitione dipertitom
Rursus ex lege dupbisectionis columnae est, C= a- 1, ut jam, sed _ d ab. 1. Ergo b- 1 = a
seu b- a+1 seu supra b = a 1 sed C = 1 - a quod jam habemus, et d = 1 - b,
ergo 1- b = a. Ut supra. Notendum quod bisectio nil dat nov
Caeterum a invenimus facile ex primo termino.
esset
,m, n, p, 4, 75, t
essetque
11001100110011001100
401000100105 00lD1 00
i 1 1 1000l0r1 11000
11 11 10000000
1111 11 11 1 10 00000001000 00d
10 01+f.1 100
000011 I O1141000
s si
enti
demonstratio
cla de oppo
puncta significant
ex secunda zla quadde
maecedentis trans
Fraustata in puimum
idam estiam et hurus
Et suppleas punctis
d11t1111000000011