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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 28r, page id 00068217:0057
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 120 lines, status machine
# Lines: 120 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.

denique per gendo per gradus, supponendo scilicet primum b aequ. d
singulas
b. c. aequ. 0. deinde tantum C aequ. v. denique o supponendo aequales 1. vel 2.
 gradibus valituras deprehendemus, ut hoc loco  fit semper ftg. aequ. 1. in
377 omnibus gradibus in infinitum ut patet.
X- Q aequ 0.
X9ud
X - 1 aequ. 0.
X - 2 aequo
ea X - 2 equ. 0
X + e abc X + fa    Gab 94 aqu. 0. quaritur e. f. g. g. h.
 
XX
256 XF 0
256 XX 0
65536 X+
+f, 256
+f, 32
+5, 32, 256
+ haH4
2u
+ g aequ. 0. fit f+g aequ. - 1.
+9, 256 aequ. 0. fit ftg. aequ. - 1
+9, 2 aequo. fit 256132f +.9 + h aequ. 0.
+ h, 1
+92256 aequ. 0. fit 206 rf eg th. aequ. 0
+Rersb
ut ante.p
Htinc patet, ut obiter dicam si semel adhibuerimus X aequ. 1+1 nihil nos novi discere, N
postea assumamus X a9u. 2 +2. vel X aequ. 3+3, sed ipsam radicum relationem
inter se variandam esse.
6561 X + 0
+f, 1377
+f, 17
+9, 257 aequ. 0 fit 6561 4137, f. 4 2579 +16h
+ h, 16
+9, 257 aequ. o fit 1 + 17f + 2579 + 6h. a q. c
+h, 16
Quia ergo p invenimus per X4. X - 1 aequ. 0. esse f +9, aqu. 0
et per ∞ =  aequ. 0 esse. 256 +32 f +29 + h aequ. 0. ac denique per X = 1 aequ. 0
esse 1+2f + 2579 + 16h aqu. 0. Hinc pro tribus incognitis f. g. h. habemus tres
aequationes per _ aequ 1 fit f aequ - 1 -9; quo nalore substituto in aequ. 2 fit
256 2. 329 +29 +h aequ. 0. seu 224 - 309 + h aequ. seu
h aqu. 20g - 224. at per aequ. 3. idem h ae qu - 1 = 17f 87579, Sesruse
Seu bengu. 
explicano f, h aequ - 1 + 17,  + 179 - 25b9. seu h qp. 1 - 15.9. qui valor
si aequetur priori aequ. 9. fit 45 = 9 aequ 225. seu 9 aequ. p600
substituatur in aequ. 10. fit h aequ. 72)  15,  = 225 9 seu -5850+ aq.
et per aequ. 4. fit f aqu. -4331
727
721
1031954000 432His jam valoribus inventis videamus  an succevant aequationes 1. 2.2
2s) debet esse per aequ. 1. et 12 et 15. 4321 + 3600 +721 aequ. 10 quod et
(verum est, item per aequ. 2 et 12. 14. 15. debet
256, 721 - 32, 4321 + 7d 53504 aequ.v. suc  2
serp - 2, 131+ 4+ 25 13344
72+(seu 5y68 = 432) + 225 = 1672 aequ. 0 quod et verum est
57602) denique per aequationes 3. et 12. 1415. debet esse
26404+195) 257 721 ∞7, 4321 + 257, 3600 -53504 a qu. 0 Eror
3XYx2
y3
1028
56563
a 5bI
216
f+g + 1 aequ. 0 25 + huf + ng + h aequ. 0.
f aequ - g - 1.
1672
24
58+
1000
g aequ l+h - m
m = n
C∞ mg-H+ng + h aequ. 0 1∞vg- v L xg tytrop
Ergo h aequ. +lo - lX + mX.
.9719 ag. 9
t Xgryh
1 + yh - v lv- IX + h V. hX C. m D + mX
v - x
n +A, = vX a
+3 M = ynC
V + X (A
+240
per X = 1 aequo. ( juncta X = 1 aequo fit
vide ex pagina vertanda
136f aequ. 656
993
4321
672
5993
e
216 X7
protest aequatio: - a bF y-5xZ t3 - ab + yt 4XZY +4)2y + 2_ g. aequo 65536F omnia ordine nullo negotio inveniemus. Etiam regulas generales pro omnibus
  atquita.
X = 1 aequ. 0
X = 1 aequ. 0.
agudo
X + 1 aequ. 0.
224 16, 30
i 3700
10094
100036,2
5350
affootris
N2F0+225
es 
240
884
10094
fer16656
 334+
A ++34 +13 4 26 51q
t414
h
1672
130
M - n Auho yhu C vm + pX
lXFV m +n
 - 229 257 56615
= yn