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# Piece: https://leibnizlegible.com/api/records/39992/text
# Catalogue record: 39992 — Leibniz an Johann Friedrich Leibniz
# Incipit: Literas à te indies expecto, ut rei Altenburgicae confectionem discam,
# Date: 1682-03
# Sender: Leibniz — Addressee: Leibniz, J.Fr.
# Akademie-Ausgabe: AA I,3 N. 560
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=39992&katnr=42018
# AA I,3: 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-i-3
# In the Akademie-Ausgabe: AA I,3 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdI3.pdf#nameddest=560
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 47r (from the shelfmark LH 35, 8, 30 Bl. 47r°): 1 page, canvas 93, page ids 00068124:0093 to 00068124:0093
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=93
# Lines: 69 recognised on 1 of 1 pages, mean confidence 0.84
# 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 47r — 00068124:0093
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000093.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 69 lines, status machine
int. 1682
credo absolutum esse
problema osannae invenire tresquadratos, ita ut
duorum quorumlibet differentia sit quadratus, et differentia laterum
olim
sit etiam quadratue facilius solvi potest, quado tunc uihi videbatur
sufficit enim effici ut differentiae ipsorum quadrutorum sint quadrati
inc enim per se sequitur
etiam differentias laterum fore quodvatos
modo, summae et differentiae laterum sint simper primi inter se quod
fiet, etiam si ipsa latera sint prina inter se ut X+ y et x - y erum
primi inter se, si X et Y sint prima inter se, pone enim X +y aequ bv
et X - y aequ b7 erit: _X aequ bv + bZ et B erit bv = bZ
ergo si b alius sit quam 2 habebunt X et y etiam communiem divisorem
Ergo opus est sallem solvi haec tria problemata: U- mn aequ et
Si
U - un aequ gg et mm - un aequ lih. sit  aequ. f eb. Ergo
per 1 et 4 fiet: fC2fb + bb c-mur aequ f seu faego bb + un
6
2b
et l aequ. nm - bb. eodem modo faciendo M aego ha - c ex aequ. 3 et 7.
fiet. haeqo ccann, et et maego nn-cc
2C
2C
a
supoerest
solvenda aequatio 2, quod  ut fiat faciamus tam
l+n aequ da quam
(10
l=n aequ. Ce ita enim fiet g aequ ed
erit ergo n aequ dd- ee cet l’aeqo da + ee. Qui valor aequandus valori
(141
ipsius d, jam reperto seu fiet in aequ. 6. et erit nm - bb aequ dd + ee
et pro in substituendo valorem ex aequ. 8. et in ea pro n valorem ex aequ. 12. fier
2(1 (21 dd -ee - cc = bb aequ. dd + ec. addatur ejus lateri dextrot 25bb - 25 bb
2C
seu scribatur: (2C
15
..-.
16
sus
4+25bb -256b - bb aequ dd + ee quae divellatur in duns:
(18
.. .. - 25 bb aqu. 0. et (+25b6 - b6)  bb aequ dd + ee
8
7)
Ex aequ. 17 fit (2(5 ad -ee - cc Eeqo E bc
(20)
seu b aequ. 3 (2) dd - ee - 3C
c
(22
et aequ. 18 per aequ321 fiet=
Rursus in aequ: 18. faciendo  b aequ -eAK. fiet 16bb aequ eet KK - 2 et seu C aequ KK dd
2K
(21)
et 4b aequ 2kR = KK + dd seu Ab aequ 3kK +dd quibus valoribus 24 et 23 substitutis in aequ. 20
(22
(24)
fiet: 5KK + dd aequ (2(sdd - (.(XX dd
sumto
itaque satius resumue
F
L 4cc
c. Sed hec non minus difficilis quam aequ. 15
(16) imo maxi nihil ergi. divulsio javit
(1
exeso 15 et 16, tiec _  C -ec aqu  Cb + repErgo) cdd 1eeL CPP HECPP
2
verte