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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 289, page id 175905688X:0311
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=311
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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 0.81
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l5. 851
6 le
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Nant
imparet
COMMEHTARET IN LIDERMIIL 289
narium ipsi addirum.) Nocandum hic est, quod, dum, ausendo
cernario veram radicem aequationis propolicae x =L A X3 = 19
_ X  106X = 120 ∞0, in aequationem incidimus, tres tantum
dimentiones habentem, cujus ideo non nisitres luneradices, nu
merus 3, quo rera radix ae quationis propolita est aucta, (IE se qua-
Jis alicui ex talsis radicibus, ut liquet ex iis, qua ab AuCOrC P. 72
Paulo post explicantur. Ita, quoniam, diminuendo ternario veras
radices aequatiOnIS x = -- 4 X 3- - F9N X - f- 106X - - 12030, in -
cidimus in aequationem p + - L 8 y3 - - + yy - 8 y X ∞ 0, vel
73. 87y - + - 8∞O, innorescit, unam ex veris radicibus
esse z. Et Sic de aliis.
Nimirum, diminuendo veras radices, quantitate coenitâ se- C
cundi termini divisa per numerum dimensionum primi, si unus
ex hisce duobus terminis notatus fuerit sieno es alter sie
no -. Vel etiam hoc modo: Nimirum, diminuendo quanti-
tatem coenitam secundi termini divisam per numerum dimen-
sionum primi, unaquaque verarum radicum; si unus ex hisce
duobus terminis notatus fuerit sieno. 1 es alter signo -. IIc ad
tollendum secundum terminum Equationis X + = = a X 3 + 2 a a
X X = = a 3 X. f a = ∞0, divido 2 a per 4, & provenit ; a: unde
Faciendo = a = x ∞ Z, hoc est, : a - Z ∞ x, Scribendum eAt
 1s a  43Z  = a a k
d ==44 + = a3Z- 3aa
et  a+  2 a3Z  2aa 
Z
Z
de  aaC L aCCZ- c6Z2
et  a+ + 43Z
CUM.  a+
F 164= a3Z.
+aaCC aCC  c6
2 a
2 aZ
3.
PrO
X
PrOnm2_ X3
PFO.  aaX X
PrOm 66 X X
DTO  = A3 X
e exlurget
DO, aquacio,
Secundo carens termino, et ab illa Rutoris difterens tantum in
quartotermino, qui hic per L denotatur, e illic per -. IInde
fic, ut per ea, quae pas. 70 lune ostensa, aequationes ha in eotan-
cum inter se differant, quod Fal(a illius aequales sint veris hujus, da
Contra, atque ita radicum mutua sic reciprocatio. Duod in aliis
Quoque erenire reperietur.
Ubi porro opera pretium est considerare, quod, collendo se-
cundum