# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0355
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0355?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 178r, page id 00068201:0355
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 179v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=355
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000355.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.86
# 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
un multis
modis
indefinite
tentassem fornulam
extrahibilem reddere tandem
+ ab XX + ac
animadverti tale quid obtineri non posse inde-
1
finite. sane ponendo XN = y
ut S dx x+abXx+aec redntur per quadraturam rationalem
haberi possit. vidi tamen postremo id nullo modo posse obtineri
Fiat si placet XX = aG et _ 2Xdx adus su dx= adg: ne fiet
n
debet summari aadus Lynga cy + acve N N
Nempe X + ab XX + ac debet aequari quadrato. _ quod ut fiat explicari debet X
eti Ejus autem formulae factores sunt, x  tam et XX + AX + p posito
sea
L ab et XX + am et Xxtan posit mmen = ab et mn=ac
ergo XXOAMM XXu debet aequari quadrato.  Quod ut obtineqi ten
fetur opertet X explicari rationaliter per valorem a: D posito O et D ess
formulas integrens rationales per novam indeterminatamu; et fiete
si jum O. et D silit formulae lationales simplices per y, qua ascendent quadratum ad
aevi
pro inde Oa
g fecet jam 
jam aa OO = min D)) habet factores ad + mD,  ao=mD, et similiter
est2
+
atum gradum seu poterit concipi esse
aaOD-nnD)) ergo fit  ad +m D, ad - m D, aO + n D, a0 - mD = 4499a
ergo quatur factores unique lateris, in quatuor factores alterius lateris discribuendo,
ita ut efgh sit = at, quo pdo pate Nec refert quaenam alia fiat distributio.
fiet si placet adm D = ( e8 aO - m D = fL
Hoc posito autem pro quatuor literis ∞, D, 8 quantitatibus C, D, 8 9 habetmns
F1
quatuor aequationes. jam epti quia eae servant leges hocuognectum inter se ideo
vel extribus solis aequationibus habetur ratio inter duas quasvis ex ipsis
per constantem valorem, nam a, my n, e, F, oh sunt constantes. sed
ita X quoque fieret constans quod est absurdum. est eum X: a = O: 3
Haec consideratio factorum fent, ut animadverterem eandem
mellidem cabis 
diopanteorum solutionibus inte
osten