# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/36613/text
# Catalogue record: 36613 — Recherches sur les équations du troisième degré inéductibles par les formules de Cardan.
# Incipit: (49*7=343)
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=36613&katnr=Cc2+1019
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 57 (from the shelfmark LH 35, 8, 30 Bl. 57): 2 pages, canvases 113–114, page ids 00068124:0113 to 00068124:0114
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=113
# Lines: 149 recognised on 2 of 2 pages, mean confidence 0.73
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 57r — 00068124:0113
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000113.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 102 lines, status machine
ei
1CB
l+ V-2
+ 3 ) - 9- 31 - 3
+ 5,I 1-343, l,3
erum
Xe
X 4E
V = 3X 42
+
(3X - 9X +C
a - 3ab aequ.
+3a6- b aequ mn
+ 245
134
10C
- b aequ +a el
3ab
-3
Savad
2
a
en
3l e aequ. a.
mn + b-9b
aL
seu b aequ. 3
quia
M V- n
l-3.
a aequ.
e
3l +9ba aequ mn + ba
aliter ut inveniamus B, habemus b aequ. hab nn + 3ab
et b aequ.
3a
3a seu 36 aequ a-
binc si e q 1. erit buq
eut
mur
+ 10
a aequ. l+ 3 ab aequ  + 3D aequ. mn +b. Ergo
e
a
Ex +3
30
12
aequle.
A
11+24018 -25
312
aequ ab- l
3 a
Ergi  2 mae a + 3a b
 jam adhuc semel Hagba aequmn +b
sa ponamus a aequ. l. erit baequ e-7 et d absurdum
3a
3
et laequ -3. et m aequ+ et n aequ+
eqe erit b-
b aequ.  a- l
12
=30∞t + _1
aequ C- 124
e
2
Bmna
l+3a-a
a u aequ. mn + 3ab
 8 4 aequ ab - 1b. Ergo
 222.
10
10008
13- 1 a
12
3 2
2
40
342 -2 1- 24 +12-1, v cell 18,9
=D0
H. 902 l 12 3+27-2
e
3a
baequ +mna
1505
24+54- 277 43∞B
=a + l+ 3a.4+3
50
q
18
SeM
1+ P.3 aequ =0
sed non cabsu
s
quod videmmi
3X 42X
343
27
X
a +
l4 3, l, st +301, -1 = 11- 1
anl

## Folio 57v — 00068124:0114
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000114.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 47 lines, status machine
O
25 51- 1
1-
+ 3,2,-
-1
aequ.
+
cepo
Cqu
.
2 + 11= 1 aequ (3) 2 +S-
 11F-1 equ. (2 -1-1
fino videus radicem cubicam ab aliquo
2
2
ita radix cubica ex
+ 1 + - 3
2f-3 - 6
2s-3
Xo
numero etiam multiplicem
esser nam ut radix quadraliva e ex 4
C+ Y- 3.
Niam s A + 4 equ. O. fe hab erit una padix X+2. qua si divi aequ.0. qua si
ividatur
A +8 aequ. 0. fiet:
s
Ergo X = 2X + 4 aequ. 0. seu X - 2X +1 aequ = 3.
t
ergo X = 1 aequ +  - 3. Ergo X equ 1 + - 3
1- S.3 aequ R - 3, 1, 1-3 Y)
vel X aequ1 - 13
3,1, - 3 (= -3 +-3
X +8
ta
tar
aequ. 0)X - 2X + 4
3,
q
+
+
s
12 S-3 aqu - 2 + 2 f-3
x
d l
ene
3 V-