# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068194:0309
# Permalink to this reading: https://leibnizlegible.com/page/00068194:0309?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 155r, page id 00068194:0309
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=309
# Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000309.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.83
# 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.

invenire duos cubos quorum summa sit cubus.
X + y aequ Z. Ergo si generaliter solvere volumus, quara
faciamus ut factores ipsius X+y sint cubi, hi autem sunt: xty r
ergo X+y debet esse cubus et Xx-xy+ yy erit cubus. quaeramus hujus
fingatur oaequ. Xx- xytxy et func fiet
quoque factores XX = xG + = YY aequ 477 - yy. seu Xaqu y +7 s-3
ergo factores ipsius XX - xy + yy sunt. X - y -8 : y S- 3 et X - 2 y+ = y 13
ergo ldxty + m S X - 2 y - = y S.3 4 n ~ X - 1y+ 2yS. 3 ∞g V
videamus an ad pradratum deprimere aequationem
primam liceat: CX +y sit aequ bZ fiet:
Xx = yx +  yy aequ b3ZZ aeqo b7 XX+ 2Xy + yy
et faciando x aeque fiet ee = e aequ B ee +2C +1
Ergo ee- et debet esse cubus b3. seu ee et raego b Cetrbe +b3
ee FE
net
seu 1b39C + 2b3e aequ. 1- b3. seu ee +263+1 aequ - 1
b3.  b  egque b2 fii t fergo et +,62 + abbb 
+ 1
e
b2- 1
qi
1263
b2+
b31
b3+4
-41, 16
+413
ab-8b4 4b. 8644
Ergo e b+1 debet esse quadratur  Modo b non sit 1.
aen 4b -1 aequ. 8Lbd
seu quaeritur cubus  cujus radix non sit 2. qui
unitate auctus faciat quadratum
ergol2b + 1 + in 3 2b - 1 - 2 s.3 B  2b- h +1 S.3 equ co
cujus ope evolutis irrationalibus inveniendus valor ipsius, b. Tatioralis
per co. Et ita rem a cubo ad quadratum traduximus
b3 aequ: c0co + epo
possumus vel tres factores ipsius 12 b2-3 multplcare
aequare quadratis, el quantitalibus i invicem ductae faciunt
quadratos; vel duos factores ipsius coco + aequare cullo
verte