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# Piece: https://leibnizlegible.com/api/records/51572/text
# Catalogue record: 51572 — Leibniz an P. Aug. Th. a S.Josepho
# Incipit: Prioribus adjicere volui plenam solutionem ejus casus nostri problemat
# Date: 1713-11-11
# Sender: Leibniz — Addressee: Augustin Thomas à S.Josepho
# Akademie-Ausgabe: AA III (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=51572&katnr=35771
# The Leibniz-Archiv's transcriptions of the letters of 1713 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1713
# Work: https://leibnizlegible.com/work/00068207
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folios: Bl. 49 (from the shelfmark LH 35, 15, 5 Bl. 49 (=35772)): 2 pages, canvases 97–98, page ids 00068207:0097 to 00068207:0098
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=97
# Lines: 193 recognised on 2 of 2 pages, mean confidence 0.72
# 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 49r — 00068207:0097
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000097.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
vienna
l Norembus 17 B
mist abgang est eror
everendissime
sin
d.
Augus mothoncae
osetho piarum
schilarum
vicefectori
Horna
prioribus
adjicerq volui mtenam solutione
nostri problematis, qua ubi
postulatur etiam x integer, licet y sit
fractus. Ago tanc a et d semper
hic rursus
habere communem divisorem Hic duo possunt
esse casus, unus ut a et x suit promi inter jes
alter ut habeant communem divisorem
si
si a et X integr, sint integri prigui inter si
binos quodam
necesse est ut a datus habeat confactores
qui sunt etc, quorum differentia sit duplus
iaten, quos comput. etiam la et Is
quadratus 2cocd, et eri sem cded et a bc
a sit be et bac  cocd,
et bC coco j por con actores ipsiusa non dntur proole
equod si toles
egi
et X habegtes communem divisorem
erit, ex  coco sint
tendetur an tentetur divisores ipsius a, et d
est impos sple
d sina
examisenturalio sumtis binis confeturitus bc quibusdauc
a
ea
estt
veluli b et C, et smmendo ani
cica
minsdest C mino. Pous
prodo R hoc qumutato in peliquae.
itrum res succedat raerendro papet quod si in ul
omnes solutiones
en
samendeX
X
confraciorem
lomum
aequale
faciendo
quod si e succedat habentur
possibiles, sin minus problema est imposibile
sed majoris molis est prooem. perfecte so vere cum
x potest esse fractus permissum est  esse fractum
a c, v. existente in tegro permissum est X esse tractu
ractum. Reperi autem tunc si X et v reduet
est fenctus: 1t
quocasu etian neressarios.
sunt ad tractines minimorum terminorum, ras quid
practiones non posse habere communem denomina
torem, earum tamen denominatores hatere divisore
vale
communem

## Folio 49v — 00068207:0098
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000098.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 127 lines, status machine
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