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# Piece: https://leibnizlegible.com/api/records/58576/text
# Catalogue record: 58576 — Tres quadrato[-]quadrati progressionis arithmeticae
# Incipit: Hoc problema solvit Osannam.
# Date: 1674-06
# Akademie-Ausgabe: AA VII,1 N. 045
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=58576&katnr=723%2FB
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 44 (from the shelfmark LH 35, 8, 30 Bl. 44): 2 pages, canvases 87–88, page ids 00068124:0087 to 00068124:0088
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=87
# Lines: 53 recognised on 2 of 2 pages, mean confidence 0.74
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 44r — 00068124:0087
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000087.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 30 lines, status machine
tria latera.
ita ut duorum quorum libet
invenire tres quadratos, quorum differentia sit quadratus et intervallum laterum
ex duobus quibuscunque sit eriam quadratus:
tres quadati a b
a b
v
s
a = b = (d.)
a c - b
a - C = (C.)
bc
1
2
e
2
2
b - c = f.
81. 729
81 = 27 3
ta
128
256
12
120
156
si2
72
2107
u1

## Folio 44v — 00068124:0088
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000088.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 23 lines, status machine
Tres quad pulo quadrati progressionis
:C
e at aequ 2B
seu a- b aequ b- C
anthmeticae
for problem
solvit csannam
sit a + b aequ l b4)c. Ergo 4 a + b, a b  Fb+C, btc
seu 1 a 7b
m
V(4)c
s
b+C
at b
M
=b+c pna + mb
ponc in aequ. l. et nea m ergo si
et M’a aqu. d) fiet: b + c7 d + dfa
urgo ac tata t
et
amb tube b a
b()C
l