# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068219:0003
# Permalink to this reading: https://leibnizlegible.com/page/00068219:0003?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 6
# Folio 2r, page id 00068219:0003
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 1v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068219&page=3
# Source image: https://digitale-sammlungen.gwlb.de/content/00068219/jpgs/default/00000003.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 72 lines, status machine
# Lines: 72 recognised, mean confidence 0.76
# 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.

superiore, scribatur
e
Nompe aequatione X X, + ab X  a cX +ad X ate X + af
(an)  eah  - ag
2
in
10
sie X + ab X + a dX + af B ac X + a h X + ateX + aG
sentandum est jam an utrobiue extrohi possit radix Cubica, itaque ducenda est in se cubice
quantitas X itaque conferenda pri posteriorque; illa cum formula: _
proos X + 3 al X + 3a V X + a l, poseria cum: aE. N pa X +3aem X + acr
2
213
sive quod idem est, unaquaeque formula determinanda est ad tres radices aequales.
Hinc conferendo primume ei =. Ergo dp 3ab et fp .. Habitis autem
ga
27a2
 d. et f habentur h. et g. Ergo pro tubus quae supersunt collatitiis non nisi una
est incognita m.  An ergo sic forte rectius:
X X + ab X + adX + aef  ranX = ac X + a h+ ate X + a9
ita ut a tentemus utrobique radicem extrahere quadratam; sed ita augetur
quidem numerus incognitae; sed vicissim et numerus aequationum collatitiarum, utrobique
cndraq
inrot quaddutam c
imo remedia huic malo pagina
Resumamus aequationem, nae termino quidem secundo abtato, et ita scribemus:
cur. Tubie
enix sequentiis, subi z
 X X + ab X + ad X + ae XC + af X + ag
n
e
+ a p7. ,+ a4
=atfs
+ a n2...
= ac.
l-a59
om Segungatur haec aequatio in duas partes; ut appareat an habere possint
E
i
h
= ab
X6 A + ab X + ad X + a X +a F X +aG pRX + ab X + aed X rae N +af X +a g
-1 in - al
Unum divisorem communem, fiet:
=am
=aen ap - a4
Jam utramque aequationis partem dividere tentemus per formulam  X + Y.
quod si _ exitum referire potest, ope aequationis data inferioris, aut etium simplicioris;
eo ipso data quaelibet, aut inferior, aut certe simplicior reddi potest
Sed quontum, hic calulus foret prolipus eandem methodum in simplicini aequatione experiamur, ud
appareat an liceat his cum finctu uti, esto aequatio culica:
2 N _ + Ab X +ad X + a
n
+pla
et
+ am 2.
ad.
e+
ae.
EA.
h X + x + bX, + ad X +d e
X +bX +ad X +aC per XI
=am. =an 1
Eodem modo dividendo
Unde aequatio
=h Y + br- ad Y +
C
Y +l Y +an x +an p
1
R.
Sed satis hin uppare, his nihil agi
st n