# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/60420/text
# Catalogue record: 60420 — [Aufz. zur Algebra]
# Incipit: Methodus pro Investigandis divisoribus aequationum haec est egregia
# Date: 1706
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60420&katnr=57366
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 36 (from the shelfmark LH 35, 13, 1 Bl. 36): 2 pages, canvases 71–72, page ids 00068196:0071 to 00068196:0072
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=71
# Lines: 63 recognised on 2 of 2 pages, mean confidence 0.83
# 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 36r — 00068196:0071
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000071.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
Merhodus ed pro investigandis divisoribus aequationu
e
dgregia, ut idem problema quaeramus diversa via. sen obtinea
musque pro eadem incognita diversas aequationes. aertim quarum
haet est
leinde divisor communis dabit desideratum.
s
si aequatio divisibilis est per aliam rationalem utique sed terminus ultimus
amu
ratio nalis.
aa
dioisibilis
4
ret A +2X + 1x - 18XX
X + 2XX + 1X = 1B = 0 nulti plicetur per XX + 2X + 3
+ 2X + 4X + 2XX - 36X
+3X +6XX + 3X
X+4X + 8 X = I0XX = 33X =54
a
i aequatio sit divisibitis per X
Pro es substituatur V + 1
ponamus aequationem secundum X
potuisse dividi per X+b, erit
aequatio secundum y divisibilis per ytbr
is
ergo comparando duos divisores inter se, aequationis nem ultimi scilices
x et in aeg. seludum, ii demum valebunt, posito
n
termini in aequ. sec
dividi posse per simplicem aquationem, qui differunt unitate
nis
nonamus aequationem drodi posseper. Xx + bx + c et fiat X = y + 1
aequatio dividens
erit ausor
s
y +29+1 Ergo eliu sunt cro otorjores
+ by + D
si divisoo procedit
er adeoque divisor novus secundi termini erit b+et
ergo fiat ad huc Y = 7- 1, et prodibit 3t - 27 +1 pro nova aequatione dividente, ergo divisor
praecedens
divisor ultrmi termini erat c + b +C ergo
e
et 4+ bg b
C
iatum termini est 1 - b + c, et paror erat est
2 +2c quorum dimidium cddermo 
eligendus divisor primi ullimis terminis, C Qui a Rmidia divisorum summa a duobus reliquis summa
summa duorum divisorum ultimi, termini est
CX
distert unitate, ad invenientum uttum aequatio proposita sit divisboris per 49. 2d gradus
porro invento e, habetur et b, cum decur 1b+C=

## Folio 36v — 00068196:0072
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000072.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 11 lines, status machine
rabemus inventionem communisi
visouis sed non aque
alclmus inventionem divisorimqui in datis duobus dividendis
differunt unitate vel alio numerodato quando id possibila
B
a + b X + CXX + d x+ et
et l+ MX + nXX + etc. debent
dividi posse prior per  posteriot per  quaeritur an id fieri possit et quomodo
loc
determinemus
as