# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068220:0027
# Permalink to this reading: https://leibnizlegible.com/page/00068220:0027?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 14r, page id 00068220:0027
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 16v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068220&page=27
# Source image: https://digitale-sammlungen.gwlb.de/content/00068220/jpgs/default/00000027.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
# Lines: 64 recognised, mean confidence 0.79
# 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.

Qoe
quintiogrudus X ADX H2X X4X Haequo
vul quaesivi din aequationem quadrato quad naticam ad aliam
revocare in qua X haberi posset pro absolate per aequationem gradus quarti
10 5
A. X. Xx
verum difficultas in eo occurrit, quod non adsunt sufficientes arbitrariae.
Nam si multiplicemus aequationem X +_  X +X 4X  aequ. 0
perarbitrariam formulam X + X +LX et. habemmus arbitrarias quidem
15. sed terminis opus est 16. termini tollendi post termini sollendi sunt 16
ad
10
17
X
 X X
(3 ~
et XD XX X X X X gx ut
s
16
nempe X3. 
possimus qui tant sunt enini tollendi ut aequasio propencta hanc formam
sem
possemus qudem pri aequationem
aecipiat
Xo 1 xi X X
propositamo inaliam transmatare. X H X Z X +BX + X A5S9. 0.
a 
in aliam transmutare pro X ponendo
ut scilicet statim multiplicando per V
yg. i vel etiam qu
Ae. seuundus cerminus evanescate
nempe  p bx erc pond sulsoliendo pro X substituendo y-i fiet:
X id
stequilgodata
X
24X
6)d +(0
s
(9 +(Ny- 11
V+ (5) hy  + (1o)hr y + (10)h3 y 4(5) h2 y +h
+21. y + (4 ) uh. y + (6juh y tasik y +us
+22, y H)h y  stb) +2
∞ 3 t(9Thy +23h2
essra y +2a. h
+25
 Numeri paret
Resibus inclus
ut (5). (10)
Hoc aequatio jam mullipli canda esserper per aequationem
in producta
V+ (5) 18y4 +2 y +3 y en aequ d. et tollendi omnes termini
15
qui non afficiunt pera hrabent exponentem divisibilem per 5
Et ut hoc efieret faciliusi minoreque calculi labore, utile esset
praeformationem institui Nempe aequalio:
X3 + 31X + 32 X + 33X + 34X + 35 aequ 0. multiplicet  per
AaiX
1C
Et a XIS + 1 X  4 2X 3 + 3 X Y 4 4 X IB + siX +6X) + 7X + 8X +9X +10 X FuFr 
+14 X + 15 47,0. Mabiplicandae in se invicem:
_ X
aequ. 0.
significant
veros numeros