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# Piece: https://leibnizlegible.com/api/records/245/text
# Catalogue record: 245 — Insigne calculi compendium in diophanteis
# Incipit: x + y ⊓ (1) a² x - y ⊓ (2) b². x + z ⊓ (3) c² x - z ⊓ (4) d². y + z
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=245&katnr=59213
# Work: https://leibnizlegible.com/work/00068243
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 30
# Folios: Bl. 9r (from the shelfmark LH 35, 3 A 30 Bl. 9r°): 1 page, canvas 17, page ids 00068243:0017 to 00068243:0017
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068243&page=17
# Lines: 97 recognised on 1 of 1 pages, mean confidence 0.70
# 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.
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# 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 9r — 00068243:0017
# Source image: https://digitale-sammlungen.gwlb.de/content/00068243/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 97 lines, status machine
Insigne calculi compendium in diopeanters
a
X - y p b. X + Z et
(
2
2
X - y p a b
x- Z d
e
X= ZH cd Y. 27e52
Si ultimae tres aequationes efficiantur, et sint X. y. Z. primi inter se
necessario effectae erunt priores omnes.
jungantur 7 et 9. fiet: 
2C11
X H aT+y  Cd +7. Ergo y H Cd + Z - a b, H c5 +Z per 9.
(10)
(12)
Ergo fiet: Cdi a6 + e 
2
(4)
163) Css est + yt Ergo ZH ( Ca b F (X Cd
VH Xab H
2
seu cd
(15)
5+CS ut ante: sit cd p + ab(4) ef + g
(13
fiet cd (ab + cf+ g + +(F) rabes  F 2abg (4) 2efg 1 (a6 + e77)
et abp 97+) 2049
=(+) 2ef =
sit ve xAhx a
X ab + (X 2xh+ h
thd
Cdpi.
=1
2h
2m
ca
2
 et X cd + m ab+h
et 2m A 2h
Aim, -ne  ab +ef2
2h
fiet: ab  2hef +2hm-imiti xhers +tm
ua
2m - 2h
I Am. ph
dA
resu ( 3(Bresu(+ rgest r9
(H2etag
rh
XY CZ+ m effiet ex 8. 2+ 2Zm + m, Z+ Ca
L
n
a
retqe
A() ref =29
fier XC aeb +h. et yp, +ab  +2)ti ab- t
Ek
et Z1 Scd-m
s
-y
e
sunt hes plure sese formulae quadrato aequandae, factum
ex omnibus in se in vicem aequetur quadrato, quod si
illae omnes ponantur primae interse, necesse est
etiam
bXy + CXY + dX
6X t cy + d7
1X
X+y  b
(4 bX  CG X+y ⊓4
Y+ZB C. y- Z H f2
D
ingulas esse quadratas. idem est de Tubo
uod
si hoc aequatio
av
=X
+X y LXG
X-y
X -9V
X7- Xy = 7Z0 + yZV
2
+ et 7V
Axt -g4
XZy) xyt
V7u
solvatur, in numeris integris
strimis inter se, habebitur habentur tres numeri x. y. quaesit
X
qu +yZ2 abedtu
cy
y-
2
1
rutionalite