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# Piece: https://leibnizlegible.com/api/records/58137/text
# Catalogue record: 58137 — [De divisione per binomia]
# Incipit: Si quis divisiones per binomia vel apotomos in divisiones per simplici
# Date: 1673
# Akademie-Ausgabe: AA VII,1 N. 112
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=58137&katnr=Cc2+1094
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00067993
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folios: Bl. 199–200 (from the shelfmark LH 35, 2, 1 Bl. 199-200): 4 pages, canvases 399–402, page ids 00067993:0399 to 00067993:0402
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=399
# Lines: 158 recognised on 3 of 4 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 199r — 00067993:0399
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 200v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000399.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 44 lines, status machine
+
b+c
+1
1t 3
te
V17 it
Ergo a) - a-
a
E
go
ab
+C
1=
5 3
6is
Ergo ab
6tc
1 =
f
6
X + 2
2
4 = 16
16. Si 4 = 16 erit 36 =8
+2
Sed at ex hac hypothesi falsa non pt pervenori ad aequaonem
vel proportionem.
Ita a = a - f si f= ca f
b+c
f = c a- f Ergo fb =  c a-f seu fb = ca - cf.
Ergo fb + cf = ca. Ergo b +c = ca Ergo b+c = =
ca
Ergo ca = f. Ergo a  ca seu B - ca
b+c
b+c
b+c
b
bFC
b
bgch = a ba
C27 BC Et hoc ipsum adimendum, rursus
eodem modo tractari ist in infinitum, et habemus infinitas raves aequales
propositae
verte 

## Folio 199v — 00067993:0400
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 200r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000400.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 53 lines, status machine
a
entandum est semper an fier possit, ut id ponatur productum
per peoren divisore arbitrarium
divitionis arbitrarium, quod ductum in altrum divisorem aeguet
residuum nempe
ponatur quotiens assumi d ita ut ( - 9 seu a -g
b.
equetur ita ut a - 8 f. a-  =tur
blb.
b
detractum ab a seu
Sed si = (9 erit c = b. id ergo non procedit nisi inm
c9.
Ergo g-
d
a - g = cg E. ab - gb = cg. E. ab = c9 + bg. E. ab = C +b. g.
b +c
ab
(+1.
b+c
ab
b cb. item 
te 
Si nota notis hoc est aequade aliqua ad data exposita
sit, ratio  duorum nominum divisoris, ut bc
1 = dc = b
trc itq 
 ac al
ab
C+b
b.
fitit
H1 cb +b2 in quo ni hil est lueri
e
et
Haec oris vicari quotientis g. substitutio
utilis esse p.
vel 5.
1
E. ab = B. Ergo pro a potesta ssemi
c+b
aequatus hum haeri f -gq
a
b
ita ut g b = g. aequetur C9 a -g = c 
termini componentes divasorem sunt aequales.
1- cg ergo L= 
+c
iti bc
te ab
bpC
acb.
be

## Folio 200r — 00067993:0401
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 199v); this page is its right half.
# No recognised text on this page (recognized).

## Folio 200v — 00067993:0402
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 199r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000402.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 61 lines, status machine
d +
vel aposomos
si quis un divisiones per binomia in divisiones per simplicia
resolveret rem magnam praestaret, ut
b + c
invertatur ratio erit
b + c.
quaeratur ratio rationum; primum praeposita rave
vinomium puaeponente
H
b +c
boc fiet b+c b+C a = b + C.  - b +c + 2bc
a
c
a
a
B+c
a BtC
a
Deinde praeposita rade binomium postponente:
buc -
a b+C -
a
ar
b+ e
a--
b4C2 (2b btc
btc btc a b+c b +C +2bc 1bec X1 2tC bE B+C
e
Hinc intilis, in fallor e axis duci potest. Accidit nonnunquam, H
libenter velimus convertere a in btc sed non possimus,
b+c
a.
quia per consequens etiam alter terminus aequationis invertendus
esset, qui fortasse sic fieret et vicissim divisus per binomium
nullo lucro ut ad a d+ c = a Ergo b+C = 1
quod nobis saepe inusmodum ut expertus sum. btc
a atc.
En ergo methodum, ut invertere, et tamen oppositi in dersio
ne abstinere possis. Inverte ravem, et substitutam divide
per priorem, per productum multiplca altu terminum
aequationis manebit aequatio.
ut: d + e = a. Ergo b +c = d + e b + C + 2bc
b+C
seu dac db d re b+ c + 2bC= b +c 
seu dte b+c+ 2bC = b +c
a
seu d+e  b +c+ 2bc = ba tcb +C, a.
seu d+ e  b +c = a.
1
bte
la
Nota a- est Unitus divisa per b +C sirgo si oppositus
1+C
b+c malliplicetur
terminus, divid per terminum cundem btc. pro
a
prodctum d+ e, ea = +. Et d te = 1 et b+C - a.
+C
btc a ate
b+c = 1. Otc Ergo a= atebtC