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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 30
# Folio 20r, page id 00067992:0039
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 17v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067992&page=39
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.84
# 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.

exprimo X3 F2XEy + 5x yt, ubi per x3 intelligo
omnes cubos ex literis X, y, Z; per X2y omnes
quadrato simplices exiisdem; et ita porro maliis
Unde multa generalissima theoremata condinos
sunt, quae locum habent quantus cunque sit nu,
de
merus sit literarum ex or: cubus ab XFG + 2 + Wdc
sins
sed cubo quadratus cum scilicet à majore incipio seu compendiose cubus X est X3 + 3X2y + 6XyZ.
conge aliud mihi desionat, nempe formam pro unde in specie explicando in quatuor literis cubus
ab X +y+ 2+ W0 est 43 +3X2 y46y Unde si plures essent literae, verb gr.
essent literae o
23 3x2Z Exiu ex septem, decem eo immensa oriretur
13 3X y2 6XYW
immensaorietur. W 3 3XZ2 byo moles membrorum quae tamen omnis
C
quae tamen omnis
ype ex gebxy
primitur
inter literas
3X 10
3X 102
3y28
3yX2
3yW0
5G W2
f22W0
32102
 F3Xyt bxi)
sufficienter exprimitur
is
il
benesiclo iustitiae inter literas
observatae.
Interdum lex justitiae propria observatur nr lite
eas quasdam et rursus alia propria nir alias quas,
A. S
dam literas in caltulo occurentes ut sisit formula tae tazisrol
alqas
b
64
y 4 ab xy, patet x et y servare justibiame
inter se item a eb etiam servare justitiam inter
se et si a et X (V. or) interse jurtit ian non servent.
vero
Equationes ut id obiter addam etsio sit plane
sujus coci: duobus modis jurtitiam servant, uno
si oibus quantitatibus ab una parte positis et
nihio posito m altera, oritur formula observas