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# Piece: https://leibnizlegible.com/api/records/481/text
# Catalogue record: 481 — Propositiones de triangulis rectangulis numericis
# Incipit: AB ⊓ b² - d². BC ⊓ 2bd. AC ⊓ b² + d².
# Date: 1675-12-12
# Akademie-Ausgabe: AA VII,8 N. 055
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=481&katnr=58058
# AA VII,8: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-8
# In the Akademie-Ausgabe: AA VII,8 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII8.pdf#55
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 51 (from the shelfmark LH 35, 8, 30 Bl. 51): 2 pages, canvases 101–102, page ids 00068124:0101 to 00068124:0102
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=101
# Lines: 35 recognised on 2 of 2 pages, mean confidence 0.81
# 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 51r — 00068124:0101
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000101.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 20 lines, status machine
AB, l2-d.
BCp, 2bd.
32
 ACp b2+ dc.
Intera Ti Rectantuli, numeric
Atren Triung.li Tli erit bd - bd3. Aet F reniclus non posse aequari quadrato, et hanc
aequatione bd - bd3 H X. esse in numeris impossibilem. sit kY) be+ de,
od
b d - bd
numeris
asa
2
e + abdet +
 et b + ed.
12
a
fier.
E et dividendo utrobique per b +d. fier aequatio haec
aequatio impossibilis et b2d- bd  b+d aequatio rursus impossibilis cu
1

## Folio 51v — 00068124:0102
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000102.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 15 lines, status machine
y  quaediato
(6+ 9 125
impossibile est, si qua duo quadruta face
um quad ratum punctum altrutri eorum
differentiam, quadiato quadrutorum esser
est rum quadratorum progressionis Arith meticae
impossibile est
impossibile
face ruisus quadratum
quadratum
di perenti esset
O
quadratu
F
C