# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068197:0025
# Permalink to this reading: https://leibnizlegible.com/page/00068197:0025?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 13r, page id 00068197:0025
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=25
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000025.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 91 lines, status machine
# Lines: 91 recognised, mean confidence 0.71
# 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 Mee = culae,  sit y = x +v, fietque
X +bXX X + ac X + aae = (X + 3Xx V + 3XVV + V3
ac 3VV
et fiet XX (b - 31) + (ac - 3VV) = v3 - aae, seu XX + ac- 30VX + qu
b- 3V
~, b- 3V
= aacc 6ac vD + qu + +bV - 12V ea-4aabe + 12aaev, compendi
sit nacc - 4aabe = aF et 4b Et Xx _ ac +3xP V+ rbv.ba B, idueb 7
4, qu  b- 31)
st
= 2b- 6v
 In formula sub radice tollatur terminus itimus, faciendo v=  q et fiet
exea f(- D
a -34
summ
L1xA. 13YYZZ +12543 34
Et fiit
u s V = ga = Y = aa- YZ
 et ex prodibit in vinculo 2
+12 aaC7 -12 aaer) 340 a Z)arr Z2 aaY  51 4, 4
BaarrZ- P2 bac 2Z + 12ac YZ - 6ac)
 4baaZ
+ 1Z
a
a
=12brZZ Tabrr 22-6b
2673 baaztor
X
+ a5+
393
aa
 = acq + 3a 6aaZ+ ac  +c
_
ea
+4 bgA - 126+, 122 + 12bnZ - 4br
=3a + 12aaYZ = tgrZL
c
t
a y3
4 12
s
e
et fiat p + 4)
Dq
60
.a
 naabmZ. ab1
6aZ tnarZ- 6aC1Y.
a en
4
4
+121 (Z= 12A1Z
es
Aad
e
a)-0
1 in elqe bna 16ih
CZ-3a +6aarZ + 3N - ac DZ (-346 +12a YZ- et
r+ 2acMHaaeY -
X - adque t 34 6497 +2n72
2bZZ-6aaq trt2b), 
vades
7Z, 2b-61 = 2( 263 - baa + brz
3a412a7Z- 184 rr7Z + 12aap13
+44 bze - 12a br7G + 12aab p93
-6aC74 + pa cYZ
Vp
4
93
3a +baar
tandem
s
-6aaZ + (6r + 2b) 22
quaeritur autem y dx, fit Xdx + (a a - YZ: Z) ax, Et sydx=
x+ saa- Yax
quae summa involvit irrationalem trimam.
Rursus sit X = a si in aequatione prima tollamus faciamus X = aa -q, et substitut
V
valore tollamus summum terminum, W03, res eo redit ut radix cubica extrahatur
ex WW + mW + an, seu quaeritur 3(WW+ MWtan)=
sit avWo + ZmWo an = W t3 + 3cutEa + ta ZWba taan (t an)
et divisis omnibus per WF W, fiet  W1o t + 3W (At Vaan -a) + 3 a (t aan -am)
luw +mi van potest reduci ad  coco + pco et quantur
Cacoco +pC) sit co= P fiet 2((3, a + aap) et -  ( + aap)
Faap Z cubo 3 + 3888+, 3880+ a X 3 fir _ +90. + E∞:2 - dap: 3E
e
11)
taap = (8 +3983PhGEEH F 3GGracp + 38 aep F X  323 Saap F 35 a Yaep F aap)
83
(07
everte