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# Piece: https://leibnizlegible.com/api/records/47157/text
# Catalogue record: 47157 — Ad Problemata Numerica in integris solvenda per series.
# Incipit: Esto verbi gratia problema bx + a = yy
# Date: 1714
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=47157&katnr=35784
# Work: https://leibnizlegible.com/work/00068207
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folios: Bl. 59 (from the shelfmark LH 35, 15, 5 Bl. 59): 2 pages, canvases 117–118, page ids 00068207:0117 to 00068207:0118
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=117
# Lines: 67 recognised on 2 of 2 pages, mean confidence 0.78
# 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 59r — 00068207:0117
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000117.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
puis
aotata per B valet, priora non prosuns
problemata sumerica in
eries
at +txx
dulectris
solvenda
lesto pro verbi gratia problima bx +a = 7y ubi
b et a data, quaeruntur X et y. Ponamus seriem sumi ipsarum
 progressionis Arithmeticae, quibus aptemquse b et a
1
C
b dx = 2ydyue + dIdu, et posito ay = 1= fiet  bdx = 2yl + l,
Itaque re reducta ad solam b, oportet (ryt +l, impares ordine sumtis
solos eosquadra
om b ompolles ordine
e
t
1
s
fure isos ax poso, sex datis imparibus 2 ri ad 2yl es dantur y
posse qui divisitiies sint per b
nempe ab imparibus sublinhendo renitatem  Il, et esidum samendo dimidium
Habemus ergo quadratom
vu aquisudctraris a opotetio qui quadrares
.
qui tenglandi a quibus ili sol
Esto
succedent qui detracto 10 relinquime divisibilem
dX +10 = yy
bx + _ = 1 2= bdx. Ergo eligendi
ex +a 
bx + a = 9
Ergo fb
impares sunt divisibiles per
bdx +da = 29+1
si impar sit 13. eut X =6 et quadat
= 36c
bdre = dZ
bx +a = Z
bda + dda = 2 Ergo dax
x progressionis prithmetrcae
sumamus potius
oet
t
az+ a22
= d
 et
bdd de + da
sed bddx= Elgd fiet  ada = ada
+Se a=
impares divitibiles per b. sit b = 13. Ei impares ernul 13, 39, 65
3 horum primus est cy fiet bdx  = 2y4
per b.
ia
- 1
e
0, sed ddp =0
et faciamus bx + a = 2
bdee
d
Cae
 IdasL +2(7d + 2d2cl 7
 + 2ddzauz

## Folio 59v — 00068207:0118
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000118.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 3 lines, status machine
TFRIED WILHELM LEIBNIZ BIBLIOTH
DERSACHSISCHE LANDESBIBLIOTHE
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