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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 65, page id 175906937X:0089
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=89
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 recognised, mean confidence 0.83
# 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.

AIIHI
c omnes dd
is equation
b0bi
acque f
159 Scm
1aC COlut
im secundo.
TenCIAM IB.
veram belle
equalem ipte
Orum 1DB
upporendo
mb aquate
15 Det 
 bx
ejuldem 
Lepet lom
consticuuin
IuS ex Ca
latio
A. O U A F F O N U H.
latione secundorum terminorum 0 - b 3 --l, vel l30b -- 6. ITn-
de dilcimus, quod l est differentia inter veram radicem b et Fal-
Camc; ee li cognita tueric Falla c, eric vera b aequalis l. F6; ec (1
Fuerie cognitavera b, Falsa c erit aequalis b -- l.
Porro, per comparationem poltremorum terminorum, ha-
Bebimus mm∞ bc. Unde sequiturmm esse aequale rectangulo
sub vera ee Callaradice; ec, cognita Falsac, veram b esse aequalem
mm
i e cognica rera b, Fallamc esse ∞
3 Propositio.
Procertia supra polica aequatione, Cormemus, per mulciplica-
tionem duarum x = b 3 Oe x -c∞ 0, aequationem (equente
xX =b x. f b6 ∞ 0, et habebic eandem Cormam acque Propo(Ica.
Terria X X =lX Lnm ∞ 0. e consequener ha binx aequationes
erunt ejuldem naturae e constirutionis. Comparemus ersonnam
cum altera, aeque ex collatione secundorum terminorum habe
bimus b. fc∞l. Unde discimus, quod l est summa clIaruM rera-
rum radicum, e liuna earum, exempli gratia, c, est cognita, re-
liqua b aequabieur 1 - 6.
Praeterea ex comparatione ultimorum terminorum habebi-
mus mm∞ bc, hoc est, mm aequale rectangulo sub duabus veris
radicibus, quarum si alceruera eltnota, exempli gratia, c, alcera b
MM
aequabitur.
Ouaneum ad aquatiONeM quadTATAI XN =M M ~O, GuIX
non elt attecta, ipla oritur ex duabus sequentibus N -m DO, e
X-F m ∞ 0. Unde lequitur iplam duas possidere radices, unam
veram, alceram Fallam, quarum urraque ae quatur ip(Im.
C A P u X ILF
Denaiutaconstuutione squationum Cubicarum seu
etra dmensionis, secundo termino carentium.
Mnes lx aequariones reducuntur ad tres sequences Formas:
X3 X - MM X = 113∞ O.
43 X = M M X = 13 ∞ O.
.   M M X   N ∞O.
Pre