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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 423, page id 175905688X:0445
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=445
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.75
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

dec
ueng
ene
113,4
rumum
X alcera im
eationet
EC
plari
EGTIHHII
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aque
DE REDUCETONE AOLUATTONUM. 423
auatur ubique in locum iplius d3 secundae aequarionis: inrenie
Eurque
d+ ∞ ad3 L abdd  a a b d
Peu
a a d d  a ab d =  43 b
a a b d-  ab d d
Hloc est, aabb = a 3b  ab d d = bb d d ∞0
de d d ∞
 a3b - a abb
2ab - 66 Ceu aa; e d ∞ an Peu d -- a ∞ 0.
Si jam hujus d d valor substicuatur in ipsius locum in + ma xequa-
tione, habebitur a a d - a3 =  ab d L a a b ∞0.
Denique Substituatur iplius d ralor a in ejus locum in hac ulti-
mas obcincbitur a 3- 4 3= a ab  a ab ∞ 0.
In hac isicur cum termini omnes se mutuo destruane, indicio est
eam aequationem d3 = a d d - 2 a b d - - 2 a a b ∞ 0 quam
A+ X bb d d F f a ab b ∞ 0 esse dirilibileim per d - a ∞ 0, e
aa
d a ueriu sque maximum communem dirilorem existere. AC-
que adeo, cum dux Propolicae aquationes (vel quantitates) prius
perslinc dirila, manifectum est earundem maximum communem
diriloremtore d = a inc, Peu dC - ac,
Ouodliaurem aliam liceram quam d ceu incognitam quantita-
cem consideremus, licebic similicerillius opc eoldem lemper di-
viloresinvenire. Exempligraciâ, si aucincognita quantitas con-
ideretur, obtinebitur pro
2da Ag.
bbda. F a +
bb- d4 ∞ 0.
vel a  a ∞00, leu a ∞ d.
Subrosetur jam d d ralor iptius aa, per 2dam aequationem inven.-
us in locurena pnta aequationis, ee inrenietur proixla
d da-
a
530.
Aa=
a AC.
d a 
eo
BAHO