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# Piece: https://leibnizlegible.com/api/records/57457/text
# Catalogue record: 57457 — [De duobus Diophanti problematis]
# Incipit: a + 5 = z². a + 6 = y²
# Date: 1674-08
# Akademie-Ausgabe: AA VII,1 N. 063
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=57457&katnr=39016
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00067993
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folios: Bl. 137 (from the shelfmark LH 35, 2, 1 Bl. 137 (=39017)): 2 pages, canvases 275–276, page ids 00067993:0275 to 00067993:0276
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=275
# Lines: 42 recognised on 1 of 2 pages, mean confidence 0.83
# 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 137r — 00067993:0275
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000275.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 42 lines, status machine
a +5 = Z.
a +6 = y
ap
a= al + 5I = y2
al+51 = y
Aquia Sl = Z
al
b+ 20 + 10b eit Z= b +5) erit l= Z al
Astumatur a = b +20 + 2 b
eritque
Ergo b + 20 + 10b 46-y, a at 
su b+ 6. 11b. + 26- y (vel 67
sal-
y
Xn H b - 10 = Et esto 11 b = quod se si 1b = 10. Z
edt ergo b  1 e a = 20 + to ∞ +
Ergo b 4 26 + 10 b = y ergo 62- y= al
seu b + 25 4, 10b+1., = y ut 62y = a, vel
ideoque ponatur tabat 10 107 - 57= a
b + 10b -1 = C+ 10 C esto jam Z - 4. et 
rgo b4 10b - 1 + 25 = C + 25 + 10C )erit a=
Sb + 10b - 1 + 25, C + 5
Ergo CA f b + 1ob -1 +25, -5 = C
(120- 5= 115
se
Ergo b + 10b - 1 + 25 - 25 = C = , ul pate hoc
ergo pustro.
b  = v = b - d. Et 10b+1+ d = 10c
et d= cb
cb
il
ad penesti
seu 10b4b +1 = 10C- rg 10b + 1 + C= b = 10C
Vy 2 Z = . ego y -  + Z. ponatur Z= X + 2X
iet: y= Sl + 2XI + X et vel y = l + X. sed non
sufficunt ista. Satius eint quaerere valorem non ipsius
s
sed ipsius 7. ita ut extrahi possit ab eo radix
i ipsi
raddatur. Quod cum vanis fieri possit modis recutadanda
est, quo exrifeanto omnes.
137

## Folio 137v — 00067993:0276
# No recognised text on this page (recognized).