# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0080
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0080?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 40v, page id 00068198:0080
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=80
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000080.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine
# Lines: 83 recognised, mean confidence 0.77
# 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 + bXX +aCX, ae quari debet quadrato. Itaque patet
 seu X, Xx + bx + ac = agy si ergo sit X =  Ergo
a
L
debebit  abZF ac. ae quari quadratovo Atque adeo
quadato
etiam AbD+  bb aequabitur qeaet B vi + +bb - ac ad
vel bb + ac vocemae fi debet uta tandem ess
+4bZZ+ hadb n ap
94
Adhibeamus irrationales, et.
sit Z= 1(o P ti a) + DRoV+2I, a) + ((30H + 31, a) = O + D + 
fiet 2Z = 00 + DD + 2E + 2(OD+ 02+ D8) G5 O: p E + bBODHEBD, WDB,ADDq
 10al + nb +2, dD + OE+ 2 19
200
10 1
3a
2t
10. 20 P (P. ( on ad  1ua
2030.
182
0.
uad u
30.21
21.50. n.
 2.1. H..
.
31.
2131..
c
e
1. 11 a
4 4 +
1400O
sit a = 12OD F 13OQ+ 23DE7
et fiet aav
=  VV = aa OC (12OV +2. 132390) + 2. 12. 2310 n
1390 +2. 17 ar 2. 13 ar
sit  nDD+ 13C 238 seu
2. 131
2 21.
1210. 20 aa PIBF 15. B 21 ~ I  p. 12 a + 2. 1B. 3P9D + 2. n 3) 99, 3035
13, 10. 30
231 20. 30
11. 20
132. 10 31
23, 20 31
110 5.. +
13. 11.31 X2. 1 ar.. +2. B3ar. +2. 2har.
25, 213)
aarr
itaque Coincitentiati ante omnia Rationate, rrationales primaria
2.3
30..
30.31... 31
in irrationalibus tentanda. Ubi paulo arctius res restricta est
+aC
 Hic seideo e forc  13, 23 = 8. 12 33 = 12. 1 = 2 deni
dende fore. (2 1. 25 4) 31a = 2ab, sed hoc non licel, quia 212 23. 4 =0
48 +(Z. 1 ( 13  ( 1. 23(4 2. 13. 24 4 -
video 1 12, 13, 14 debere aequari ipter se
esse (2) 12 ar = (2). Bar = 3, 23ar = (2) ab Unde
Rursus 2. 13. 23 = 2. 12. 23 = 2. 12. 13 = 4
nam debet
12 = 13=23
sequ 12. 12 = 2 seu ent
12 - t2 12 = 13 = 23 = V2. Ergo Y =  b: 12
supersunt 10, 11, 20, 21, 30, 31, pro cointidentiandis
 Per y quaeratur, et
per 20 quaeratur 21; utrunque rationaliter si commode licet
1p.
sed quiq tandem in sydzue prodiret prodit ODD ider oprt ut hoc evitetur oportat facere
et comparando VV, fint 1010+30. 30 + B,. 10. 30 = 4. 10. 30
vel +a  ar3 30.30 +4. 10. 30 Y 4. 10. 10 = 4. 10. 1B - 10. 10
porro coincidentiando Y, fiat
terminis WR,
aliquuam t)) constantem seu 20 20.
seu 30 = -2.10 +, V3 seu 30 = (2 + 13)10
(0 +30)5 b Lsi l 1 121) (+ 2 (10: 114303)) = 2 21 (10 + 30) (4 2 (10. 31 + 11. 30) a)
sin 10430 = V- , 10.30
Aofioroo)ia  desonun seu (10 + 30) (b + 421 a) + 2. 10 (1 + 2.31) = 2.30 (21(431) =
32
= 80 +20) Z= 6 + 6000 + 4 67 + 120078