# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068261:0038
# Permalink to this reading: https://leibnizlegible.com/page/00068261:0038?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 11
# Folio 19v, page id 00068261:0038
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068261&page=38
# Source image: https://digitale-sammlungen.gwlb.de/content/00068261/jpgs/default/00000038.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 183 lines, status machine
# Lines: 183 recognised, mean confidence 0.58
# 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.

 e= 5 +
L2
 2 C
25
8. =5
1
2 =
=2
C5
 e
= E
2
dd
2
C = sC.
X 2 =
E.
2∞
FL. =
C
X. F. 2
u
C
825
F
E  5  
22
 5 2 
22
S. c51
E 2
 
x+ 2 E
3
e
a
e
.d
  e
= 3
= d c E
H +8 0
5,
2
S 
Ce
de 2763
.  2
R= re  ∞ 
22
e
CEEE
2
= = 2 F:
e
2= +CEC
xi
2 2
4 d
e
S+
0.
 E . = 7 3
6 31. L.
2c5
3. 2
S.
2.
2ec
C3
35
2 Z
E8
l
c
13
2i3
sivII esit divisibilis per cotedeba, oportet ut idem dividenius sit,
si(ti 13 s bE d
11
95 edcba
Y q pnmL
I. k 8 E5Yβ0
N P s dl a
Y9 pnmt
sec
Yd B
e 1B8
Optimum est, quaei non residaorum serem
sed quotientium qui sunt unius hotae, cum
redeunt quotientes finut 6000, qot opo
sint tolea l tint solle prines taom
si jamdivisio ipsius Budet
instituatur per abc, erc
E, 5Cd
5+ F 
F 5 = + +
5
3=
5 2
-2
EF it u
2
5E
5
== eiE 5S
m =
1. 1
53
d 2
+ 
3it e
3 =
-C F
∞ F 3. ∞ 3
c
e
noiso si
(t quonens P. Nam ei Asit.
quia a et 1. hinc si BC sit 1
erit et quotons 1, et si Bst
oeut et quotiens c. corgo
quotient est β, ergo per B
multiplicetur fint subtrahend
aβ. b(. 2B eta. Hinc quia aB= β
s dit 999g Henme
 l= D et  M = Y (nam 3b~0)
(BFn = d seu c- bc +n = 1- d et
a+ I = al) a- 2al a - 2al = 1, fit 1= a - 1, : 2a 
b1, fiet ax at Eal  a 1t 4al = a -1, i2 bd quid a = 1 fit l -0
b+m e= d bm) b - 2bn b - 2bm = 1
et fiet M = b - 1 si. b sit 0 fit M = 1, Si b sit 1 fit M =-
fit b - 1 = 1 - b, 2b -1 = (2b) 1= 26) + b quod est verum
C+ n = cn. E -2n. Hl. fit eodem modo B = 1-C
a + I= ( 1.. 1B = H- 2al fit B- a = lac
C12a
β et a aequales lest 0, si sint inaequales, quidatu ec
a B. a est A, I, et quadratur a porro quadratur ab 1- 2a
semper . + 4a = 4a deu semper est 1. Ergo si β set a
sunt inae pales U, vel semper est 1. itaque si
A3 Li B et a sunt aequales l est 8, si suit inaequales l’est 1.
Ergo _ l= Y + ( BBa 2 aB ( a + B- 2a (
 = a + β = 2 a β, nam B a = at B- 2aβ
1.2
lo. 15
Hoc mogeodice inveniri poterat, seu (=a poterit aequari integros
=M et
is aon pblest esse nisi 10β+ na + 12aB, et fut 10β +na tnaB = β-a
Ergo  10 = 1 et 11 = 1 et fint
p= 1 -d e+ bc CB+n = CB+n - 2C(2 L
jura
ua 1B2 aB
I2. 2dB
12 aβ - 10. 2aβ = 12 aβ =0 seu 12 = 10. 2- 12. 2 =0 seu 12 - 2-120
et Cβ + p - 21βH = d fit n = SL CB:, 1 - 2c =
seu  =2 - 12 =0, seu 12 = =2. Et fit _ B. a, = βt a- 2 aβ-
rum ex e aedi inc, e na es tame
depicand, ita ut B
ta
= Cβ+ d 2Be et esta 1d A+ eBS, quodi
8+ cB = 2(3cd, et CBn = cBd +C(+ 23cd = cβ- βc = βcd
8 + c- 2 3C + 2BCd =8 - Cc + 20.d
Ergo m = lee 1- b et bm2O
1-b bocemus B, 1-C vocemus V, et 1 - C vocemus
ROB non nempe
subtra
(et e 2b4VF
1b -1
1a + ab + 12 ab
1- 2b= a- b= 10 a +ub + 12 ab b
a
oe
2. 10ab
fit 10=1 et 1~ 1 - 2. ub 2. 12 ab
6 - 12 - 2. 10 =0 Ergo 12 = 
ro aut rb= a Fba mab
2.
2
18  2
E
=1
l
recto