# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068194:0348
# Permalink to this reading: https://leibnizlegible.com/page/00068194:0348?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 174v, page id 00068194:0348
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 175r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=348
# Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000348.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.87
# 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.

ut destruatur oepo. 4 ultinus cinim
ro speciali igitur solutione faciamus
7
ut destr
Sc Ysb + C: 4b d = 0 seu X  +e -c
X  4be - C.: 4b 1b
Ergo ex aequ. 4
destructio fiet: A 4bed - cC - e + 816tbd0- 8bcd +cc
seu a - 16bbc0 + 4bcc + 4be
4 bb
16bb de - 8bcd +CC
1663
Possumus autem ex fer matii Methodo
primme
jam pro valore ipsius y sumere aliam iucognilam
ipsius y
valore hoc invento auctam; et substituendo hac
hanc quantitatem in locum ipsius, simili net methodo
habebunus aliam alium novum valorem
pat
Quod cum ita sit ad videamus quid ab initio
in fonnulas
si pro b  cy + dyy + ey, substiturtemus
b pro y substituamus co + V et siet
ce
+ b + ccd + dcocd + e c aeq. quadrato 77
d +2d. + 30..
d
etseo
_+Z leb)
 C: 4(6)
seu per compendi fut
B) + (C) co + (d) cotd + (esed = 22
unde fieta n +
12C: 16 a +Z )
C
b+ 19 + dyy+ ey
=d seu
patet
Hinc si (6) (posset aequata quadrato, haberi novum
valorem, nam poterit destini terminus ultimus
quia seu haberi valor ipsius Z rationalis unde
etiam ipsius  valor rationalis habetur Vecum
patet si ipsius  y valor determinate habeatur, etiam
ipsius 7 valorem sie haberi. adeoque et ipsius cd valorem
interum id comme Caeterum prto hanc methodum
ducere ad  impossibilitatum demonstrationum, re
redacta ad meros integros; dure
ditur sugponi _ temper praerequiri minorem aliquid
desi deratum praestantem, nam in integris non
licet a imminuere in infinitum
tanc Methodum etiam altiores gradus adaptemus