# Leibniz Legible — https://leibnizlegible.com
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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 413, page id 175905688X:0435
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=435
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000435.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
# Lines: 64 recognised, mean confidence 0.70
# 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: the recognised lines in reading order, one per line.

12
comm
lepenun
duc
decteu
vel ut
6
enumqu
idir
Duo
moout
ecteactione
tA AII
et CDM.
RCMI
151
ect, De
12
minator ekt v o, e in qua conttones omnes allumprae, sive sup:
policiones, lune adimpletx, illa, quam ex Propolica resuleare
DE R EDRCFEOHE A OUATTONUM. 473
denominatores mulciplicare. Ouo peracto, erie equario haec, in
qua scilicet nulla amplius repericur tractio liceralis, cujus deno-
CLC0
empa
CX
a a
E OHATTOHES PROPOSITA.
EX LCC∞ O. (UPPONREUFCNO
b
C _   X   30.
t- -bb
e
CCa
a + B 2a f b
D
∞
SEQDAETOHES RESBLTAHFFS.
X X = bX = a a 20
+ab
tCX- ccb ∞ O, leux F b ∞ O.
N N - f a X ∞O, TeUX. F A ∞C
  - 3 O, tCI1 N = 6∞0
udm ab
2u b _ d
ccb3
b3a3
3aa- ab   a F B∞0.
Cuppolita3 a - b 00:
ab
Ende, supposirione 3 a ∞ b adimpletâ, resultat
 = a 6X - - 27 a At 66∞ O.
a a
(.063
∞0.
dec cancu hsel BBletrondum in aequationibus, led etiam in
quanticatibus compolitis, quarum communis mentura, vel diri-
Por, relradix peritur. Uc, exempli gratia, s inquirere relis, num
YC extrahi BONTIECXCC -: Cd - f d d -F 5c -: cd.  ad L = bb, ec in
cum Finem suppoluilies 50 -6d- dd ∞ 0: rerinendum esserb+
non autem 2 bb. Si enim  bb retineres, concludendum Foret,
FiFE 3
WBCatBS
XX