# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/40175/text
# Catalogue record: 40175 — [?] für [Leibniz]: Rest einer Abrechnung
# Incipit: Wolffenb. den 29 octobr. Hat | gegeben
# Date: 1680
# Sender: ? — Addressee: Leibniz
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=40175&katnr=41689
# Work: https://leibnizlegible.com/work/00068238
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 25
# Folios: Bl. 5 (from the shelfmark LH 35, 3 A 25 Bl. 5): 2 pages, canvases 9–10, page ids 00068238:0009 to 00068238:0010
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068238&page=9
# Lines: 55 recognised on 2 of 2 pages, mean confidence 0.89
# 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 5r — 00068238:0009
# Source image: https://digitale-sammlungen.gwlb.de/content/00068238/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
solvendia est in integris aequatio
dalus
et 2l = 3m + 1 (unde erus
usum in sched 12 jannar 1687 ubi
de divi periodis decimatibus, poterum
quaerere seriem ubi uga facere
2l + 3m = V, sed malum est quod dunc
locus est  dimensionum nium, seu solidus
seu opus est s non Tabula, sed seme tabu
serie tantum, sed serie seriem, si ducamus
2l 3m M per om unum M, ut 1 per
omnia  et rarsi2 per omnia l ere.
quod si retinendo I quia datum est
(4 variando m, quaeramus C, nempe
2l = 1 = M, _ et omisso l in generaliter
feribamus  2-1
4 -1
6-1
8-1 19-1
19++ Unde sed patet rem esse faciliorem
huc modo 2l = 3M + 1 nam oaes et
solvi problema generatissime sumendo pro
m, quem libet numerum imparem qui triplicatus
manet impar, unde addito I fit par
adeoque fit 2l. si vero esset 3V = 7l +
quaerendum quales sumendi C ut 7 seplenarii unitate
aucti fiant ternarii fiat 3Y = 61 + l + 1, ergo
opus est tantum l esse numerum qui unitate anctus
divedi potest per 3, hoc est pro l sumi posse
ternarium quemlibet unitate minutum ut tes
2, 5, 8, etC. si haberemus 3V = 8l +1, fieret 
3V=6l+ 2l +1. Ergo 2l+ 1= 39. seu fiet
3l - l+ 1= 39. Ergo - l+ 1 = 3Y. seu = 1-3Y
quod est impossibile nisi ponas r=o ergo aquatio
V = 8l + 1 non potest solvi nisi ponendo l=1

## Folio 5v — 00068238:0010
# Source image: https://digitale-sammlungen.gwlb.de/content/00068238/jpgs/default/00000010.jpg
# Model: k3-trocr@runs-615-epoch-5, run 617, 2026-10-30T12:51:04Z — 20 lines, status machine
s
affenb. den 29 octobr. Hat
gegeben
Careon ausgegeben furzu
für mich verzehret
Post hauß -
weg gelt auff der Post¬
u
für Armen Leüten unter
zu Braunschw. in den wirthaus
en
Den 3 November, noch hat er in
en
davon ausgegeben und gek
für spitzzen
für kunnen
aus zu beßern,
für die later
für wachs Stappel
e