# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/755/text
# Catalogue record: 755 — [Aufz. zu Exponentialgleichungen]
# Incipit: [x+a]z aequ.: xz + z, xz-1a1 + z, z-1, xz-2, a² + z, z-1 z-2 xz-3a³
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=755&katnr=58333
# Work: https://leibnizlegible.com/work/00068033
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folios: Bl. 10 (from the shelfmark LH 35, 5, 15 Bl. 10): 2 pages, canvases 19–20, page ids 00068033:0019 to 00068033:0020
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068033&page=19
# Lines: 30 recognised on 2 of 2 pages, mean confidence 0.85
# 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 10r — 00068033:0019
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000019.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 29 lines, status machine
X +a
st eumer sit
2 2
aqu: Xt + 7, X a +Z, Z- 1, X, a + Z2 Z 2X a
qui Numeri quidem sunt finiti Quae sor la
formula est finita s si Z sit numerus integer
se infinita si fractus aut irrationalis. Quaerendus
est modus exprimendi potentiam totius per potentias
partium finitas etsi Notentiae exponens
id enus fi non non sit integerlatio-
nalis
Exemplicausa an posit: Xta
exprimi per X +  Xa + a
YX + l Yxa + sa equ. 1X+a
seu
fic 2Xa  X2 e8
debet
+Tasa + Yxta
X + 2lVXa + 2Vxa a
er
restat:
ta
+lsxa +2(7Xa + (a)
Lc
a
l, Ixa ; 2 X + 2 Y xa aequ. 0.
+BVae +
quod non procedit universaliter; seu sine
ipsorum X et a de terminatione

## Folio 10v — 00068033:0020
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000020.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 1 line, status machine
es