# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/48828/text
# Catalogue record: 48828 — J. Christoph Balcke für Leibniz: ZehrungsRechnung.
# Incipit: 5 Mahlzeiten à 12 g... 1 thlr 24 g
# Date: 1708-04-24
# Sender: Balcke — Addressee: Leibniz
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=48828&katnr=41681
# The Leibniz-Archiv's transcriptions of the letters of 1708 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1708
# Work: https://leibnizlegible.com/work/00068227
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 14
# Folios: Bl. 8v (from the shelfmark LH 35, 3 A 14 Bl. 8v°): 1 page, canvas 16, page ids 00068227:0016 to 00068227:0016
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068227&page=16
# Lines: 29 recognised on 1 of 1 pages, mean confidence 0.79
# 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 8v — 00068227:0016
# Source image: https://digitale-sammlungen.gwlb.de/content/00068227/jpgs/default/00000016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
inestigare duamm quantitatum divisores communi numo dato, numero differente
sit 15da = Cx. 28aa = mx + gam. fil X = 1saa : l = 28aa = tam s: m
fint 15am + aml = 28 al. hinc e a est unitas. ergo M est divisibilis per 4, et
fial m= an, et fiet 15. 4am
am Cal
15~  2.7 4 l fiC FG
2. 7 an + an  et ul =7 al Ergo  n +l divisibilis per
Cum iptur sit
 divisor ipsius 28 divisibilis per 4 eut m - 4, et n = + et dividendo per 4 fiet
2. 4an + 3an + 4nt = 4al + 3al, Ergo l - n divisib. per 4 et nt - l divisib. per 3 so
sed si duior
+ adb
si divisorm differentio sit solum dato numero divis bilis
=l
=M hoc dip cilius: e b = lX aaC = a X m + e mn
aac
ax + eM
eta
aabm = aact = eliun
X = (ab 3l = aaC = emn, : an, et fiet
c= eftag b = eh + K
=a efl + aagl) = elmn, ergo si Km - gl debent esse
divisibiles per C. porro K et g sunt minires quam e
X. 3AG
an + 4p
L sal Lha
hac sntsult MC gal +al
urgo neal dibis. pur
s