# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068269:0014
# Permalink to this reading: https://leibnizlegible.com/page/00068269:0014?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 20
# Folio 7v, page id 00068269:0014
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 8r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068269&page=14
# Source image: https://digitale-sammlungen.gwlb.de/content/00068269/jpgs/default/00000014.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 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.

20D. II
ecelavum factum extribus numeris
unitate differentibus non potest ess
quadratus,
Nam isti tres numeri sae exprimi possunt.
M= 1. M.
M+ 1.
jam
factum ex his est MZ m. quod non potest
esse quadratus. per prop. 1.
Prop. III. factum ex quatuor numeris
quorum tres sint progressionis arithmeticae
quartus sit rumddifferentia progres
sionis non potest esse quadratus.
ii sint quatuor numeri 
V X- y.  X+ y
ex quibus tres posteriores sunt progressionis Ari
thmeticae, primus vero est differentia
pujus progressionis ajo factum ex ipsis
quatuorn se invicem ductis non posse esse
quadeatum.
Hoc ita probo. Ostendemque
in se itvice puductos non posse producere
l
e
prop. 2. hos tres non posse quadratum:
X - 1.
2.
 4
Ergo nec si productum si ductus factus ex
nam differunt dunitate.
his tribus ducatur in facta quartum 2 seu
unitatem quia  multiplicare per unitatem
nil mutat. Ergo factus ex his quatuor
e
3-
X
 + non
non potet esse quadratus.