# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/43184/text
# Catalogue record: 43184 — [Math. Aufz.]
# Incipit: a²+b²+c² aeqv.
# Date: 1680
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=43184&katnr=39649
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 116 (from the shelfmark LH 35, 12, 2 Bl. 116): 2 pages, canvases 231–232, page ids 00068195:0231 to 00068195:0232
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=231
# Lines: 67 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 116r — 00068195:0231
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000231.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
a + b +c. aqu X
a 16+5 aequ’y
4+ b +C = X aqu. 0. a + 6+ = y aequ. b
a-x, la- in aequ la + 2lab -ma + nx
fint
1
ab +C = X aequ. p. multiplicetur per La + m bit nic -)
fiet aequequ 4)
et ponatur fa+ gb+hC. = G a qu. 0. mulliplicetur
1. per βat) B + se. et fict. (7)
Componantur aequ. 4. et Z.  ponan
fiet aequ. 8. componantur, et 1 et 2
fiet aequ. 9. et somparatius (quam quam
loco aequ 9. sufficiat aequ. 2) conrparent
aequo Z. et g eaque comparatione inveniantu
literae d. l. m. n. b. et f. 9.3. 9
ventaeque la aequationes 1. et 5 solvent
problema. et X atque p.YI manetum
datae quantitates; imo et unus ex
numeris manebit datus nisi forte
postremum si quid deest comparationi
numerorum aliquemet etia in explicare
volumus, ut panter a. b. c inveniantu
ita enum Nota sufficit considerar
duas literas: a. b. ett invenori lon.
et
F 9. 9cum itemue C, quarum
septem, qtantitatum ogie etium termia
se qscilicet  a. b. ab. a. b comp
habuntur, ita ut credam posse C mane
arbitianana. Ecce generabissimum solvendo
moduu

## Folio 116v — 00068195:0232
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000232.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
a + b+ l aequ X. a tb + Caqu. y
 sit C aqu. d rnt ( aequ 4)
ib
fier: a + b equ. y d. f deX  aequac
fint a + b aequ F y +d arbicaerox tic
serit a+ b aequ. yt- s s fiat avr
eut a adu et +y Fc sie
siot l aequl  Ax +C
+
faciamus a ago la et b aqu 1B. et
ex aequ.  fior: 7
la + 1B aqu 4 +c
perculculum inde ad aqu 2 ifficere
possumus, ut ahabeumus tres quadratos
quoru summa. sit aquadratus datus y. itique
possumus datum iquadratoquadratum y dividere
in tres quadratos nam manet
Nam:
C+qd. + l f y (9) t
ergo l (0 4
e
12 L1, 5.
d
line 1B,
ff, and. 0)
sit nominator ipsius l aequ 0 et Y
fintque Cl   ( 9d D. Cec
aequ. D.
eritque l aequi im  eo ex aequ 10 fiet laeqot ny
et ita inveniendo eq resolvendo exsilica trodienus. 3
nempe
ea vel β. n intagus explicando, habebimus
datum quadvitous radiatura not integrum tres qua
patos, entegros s.divesiuu quando
feu