# Leibniz Legible — https://leibnizlegible.com
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# Title: LBr. 705 · Overbeck
# Folio 91r, page id DE-611-HS-861255:0181
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=181
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000181.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 89 lines, status machine
# Lines: 89 recognised, mean confidence 0.73
# 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.

 2I
9
c
E
e
1 2 3 4 5 6 7 8 9 10 11 le. 13 14 15 16 17 18 19 2 21 22 23 24 X
0 1 4 9 16 25 36 49 64 81 100 1 14 169 196 225 256289324 901 400 141 44 529 570
0 a 0 6 000 100 0 0
1 d0
 0 60 
e
8
8
0
6 6 0  00 5 6 0 6 0 6 5 0 V 6 50000 c0 C0
0 0 1 1 2 2 3 3 4 4 5. 5 6 6 7 7 88 9 9 16 10 i 11 b
0 0 2 4 8 12 16 24 32 40 50 60 72 54 98 112 129 14 1l2 180 20 no 242 264 238
0 1 0 10 1 0. 10 1 0 10 10 1 0 10 10 10
c
0 10 10 10 10 1 0 1 0 1 0 10 101 0 10 10
0 D0 6 1 1 1 1 222 2 3 3 3 3 4 4 4 4 5 5 5 56
0 0 1 2 4 6 9 12 16 20 25 3d 6 42 47 5b 64 72 d1 90 l 1 R) BI s)
0 1 2 3 0 1 2 30 1 2 30 1 2 30 1 2 36 1 27
6 1 0 1 0 10 1 0 10 10 10 1 c 10 1 0 1 c 1 C
0 b ∞ 0 00001 11 1 1 1 1 1 LZLLF7
1
∞0  1 23 4 6 8 10 12 15 18 2)2428 3236 40 45 50 50y60 6p 72
0 1 2 3  5 6 7 8 4 2 3 4 5 6 2 d 1 2 3 4 5 6 7
O
0 1 a 1 0 1 41 0 1 4 1 e 14 (0 1 41 0 1 4 1 9
0 000000000c00000 1 11 1 1 1
6 0 0 0 1 123 4 56 79 10 12 14 V 1820 222527 30 83 36
d12 3 4 5 6 7 59 10 11 12 13 14 15 0 1 2 345 6 7 8
0 1 4 9 0 441 0 +490 94 1 0 14909 4 10
6 0 0 0 0 00000000000000000018
d 4 ∞ 0 d 0 11 2233 4 5 6 7 8 9) 10 11 121 15. 16 18
8
1 2 3 4 5 67 8 9 10 1 1 13 14 15 1b 17 18 19 20 22 23 24
0 14 3 16 25. 4 VB  4 25 1b9 4 1 0 1 4 9 1b 25 4 17 0
dE
X = 28+5 XX = 29+ Y = 288 + 2 8p + 55. Ergo 55. r = q- 288 -285
+
si primam periodum investigemus tot notarum quot sunt in 2, fiet 8 - x et B = d et
fiet q = XX - Y,: 2 seu XX = 2q+Y, quod jam habuimus. Rursus XX + 2X +1 = 2 (q) HV)
siet 29+ Y + 2X +1 = 2 (9) + (Y). Est autem (9) majo quam 9, et fiet
(9 - 9 = r - (r) + 2X + 1,: 2 Ergo Y -(Y) + 2X +1 est numerus par. jam
jam 2x+ 1 est impar Ergo r - (Y) est numerus vet (Y) - Y, seu differentia residuot
a propimis quadralis semper est impar
0134591625  170 17 4 25 1694 10
= 21 13 - 17
resid (Y + 2X + 1) = (Y) seu Y. + 2X + 1 = R + p. K 2 + (Y)
4 2 9 + re
2x +) = 2 (9) + (Y)
Duo
e e en quadratis nota
p
(5f, 9
25
k = (9) - 9
qeal priore consent sunt aequalia posteriorius.
seu XX  usque ad X = ZC-
=1. et XX 2= -1 + X habent eadem re sidua
XX = 24+Y a X +X ( q X): = 2 F +Y =B seu 2. + Z C  .XXM- 3
122
2 +2  (+ XX - 23 (+XX - 2eg
 xer fict 29
u
ope harum duarum aequationum
Eti fu
C+ + X = 3- 9
9 8- 252.2 9= 2. 2 + 17 (5 + 9) = 3. 19 4 17 f 8+9 = 19- 2 verum
en + -X _)  = LB 2 X +Y = 2e. 2- qet x + XX Et XX = E q+ Y
22 +X = Z-9
fiet E X (+Y - 2e- ex + F g(D fiet X = =- x + 9 se q  = 2 +X
6 = 12
probundum est residua opposita inter se aequari _  sit X = 28 + 5 et XX = 2 88+  8 (+
Hinc E a X Q -X -  2X
-
2 X + XX
XX = 29 +r (2C -1 - X) = = 2
XX = YY in itaque residnum ipsius (B1-x
eest in XX. sed  in prima citodo reverae X Y eru et Y, vel XX itaque idem resionum est quadrasu
 2
20-2
ruecn
-X _, qu = 2
ab X, et quadrati a (2=1 - X)
t X 4 189 +
2IX +XX = XX = ~9+Y