# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/58280/text
# Catalogue record: 58280 — [De triangulo rectangulo numerico]
# Incipit: Summa duorum Quadratorum [primorum inter se] Differentia eorundem
# Date: 1675-12-12
# Akademie-Ausgabe: AA VII,1 N. 082
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=58280&katnr=39561
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 13 (from the shelfmark LH 35, 12, 2 Bl. 13): 2 pages, canvases 25–26, page ids 00068195:0025 to 00068195:0026
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=25
# Lines: 55 recognised on 2 of 2 pages, mean confidence 0.78
# 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 13r — 00068195:0025
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000025.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
xa  x= i 42y GX = n + 3yX X m tay
yem X = m XX = mm + 2mn X = m + 3nin
Nm +amentsnen x = m + smn + 1oM 17
X-ne tmn + 15 m + roni n.
X = m + 7mn + 21 mu + 35n n
Xd=
-m d my + 28 nen 4,6 mn + 7omn
2g
X = in X = m +2y X3= m + 3GX X- m L ymmtbgu
sed um seu = m + 4 yxXCByytoyu- 2yy
Xxhy
X = m + (5y n seu) sy X - 3yX + 109y X seu fit
X3= m5 + 5yX-GyyX
X= m + (6y Mseu)6y X- 4yxx + 2yy
+ (1599 mn seu) 159y Xx - 29 +  207
X= m + 6yx- guyx  2y3
X= m H7y  seu) y X - By X + 5y9X
F(2 yys 1 seu) 219y X - 3 yX + 35y x seu
X = m 4 y yXS - 14yyX3+ 7 B3X
X- m + (8y moseu) dyx -6 yX 199y 29
+(28yys n seu) 28yy X 49Xx + 29y
Hby nonseu s6y ex 2y + 307
X = m + 8yX. 2or  bi)
verte
+56
Summa duorum Zuudratorum
(primorum inter se 
Differentia eorundem
divisa per maximam quamhabent
Nypotenusam
ruplum Rectangulum sub Lateribus et binarium; et Unitas grutia
dividit dabunt
Cathetum vel basia rectum,
communem mensuram, in estants
non, aut per Binarium, neque enim
uiam habere possunt quam unitatem
Basin retlatuetum verbo

## Folio 13v — 00068195:0026
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000026.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 18 lines, status machine
gemu X = mon X = m + 2mn + n, X2= m + gmin + 3mn + N
XI Bntam n+ 6men +am +n Xmsnin
XSM + snin AN FonA+Smn. +n )x- mabriatism sit com asi
Kemrrnhremr u sairuumni sx agu ionuias n silon
Xxnt = R + +x
  Mrina = - 2y X +XX
m+n = + - 3yx = + X
ntant = trgy X -4)X Y X
Wtn = H +syx X - EyX X + X
Men = -2y X +ggupx X byl H + X
m’in = = -7x X +19s X - 1y X X
MEr t X - 1by  Y tuosR H - g H X
 po primi teare
ah
in
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27 1630
9 25 55 106