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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 214r, page id 00068201:0427
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Cum ergo ostenderimus omnem aequationem Cubicam regulis Cardami tractabilem non nisi
unicam habere radicem; reliquas autem quae trisectione anguli perficiuntur radices rales habere tres
ab Alberto Guaido sit animadversum. hinc aequationem (ubicam propositam trium radicum
realium, ad quadraticam attollendo, imypliti plicando scilicet per X +m Habebitur aequatio
quatuor radicum realium, quae inveniantur omnes supposita ipsius m inventioneu
cujus vator realis ope altrius lubicae aequationis unicam radicem realem habentis, habebitur.
Tantum, ubi otium habebimus, excutere operae pretium erit. quid frat si quaeramus valorem ipsius
nn ipsius m Num se novi produentur valores
imaginarigrum
ipsius X, sequetr X plus quam  habere valores, quod cum sit falsum, hinc sequitur debere
Idem quod ante provenire quicunque sumatur valor ipsius n, realis aut amagnarius quo ad tres
illas aequationis utca radices, num quarta accedens, variur, quia est ipsi i
Proposita est aequatio intractabilis
Nunc ad calculi nostitu comprobatio nem veniendum est, o:X X-g X fael0
per quam M regutarum scipionis Ferrei ope inveniatur, fore Xp m (+) S3m  (49E-9 m 4 i a lm gg
assumta aequatine
videamus nunc per rogressum, an ex aequationibus n X 129 m 48aC 10. et valore
roposita
ipsius X praescripto inveniri possit aequatio: X  -g2X f al, p0.
Nempe: E6X - m X( mi  (3 m 59) C+D4 S-gem 4 vt alm + 4gt. et quadando ruvus
x baA = b+m X
 4
16 m) X its
649.. Jogal
dec
F16m).. + (8 m X
F32mg.)
et
n
i
jam m = 129 n 78a l. une 8mrj 3239 im 764a
focunus
(4 
+Ct,
4qgem
ot
1697)
ne absolutis destructionibus, et
divisa aequatione per 64, fier:
X =m X - g X- GMX Falm po.
+ al.
qua per x= sed deberet loco et
=mx3 esse F mX, ut per
 X + m. dixidendo prodeat X- g X+ a l p0.
Ideoque hic tandem detegitur error, sane insignis: quod scilicet Hac expluni
in calculo per +m cum debuissem explicare per m.
Cui tamen malo remedium inest ut infra dicam.
sit aequatio.
X X - g2X + ae l. ponendo X p  y + a
Unde explicando: V + 3bac V2 + 3baY + a3C3
s g bd
-92bd2.
l. g’ac 2 - 29 acd
3a ld + 3aetd2
b = gb + a l
=g’acd2
=d. mgal b , et 3.9a Y b. -99 b + ralg b
1299
e
V + d
er X
6y + 2bac VpaC
BEV24 3bV +3bd c V ac
y2F 2dy F d et X  y243dy + 3d2y+ 43
7 + 2dy + d
by + ac
by3 + eay +bd Y
+ac.. + 2acd. + acd
+ a Id
Unde Terminus secundus hujus aequatim aequabitur nihilo
Tnminus tertius erit:
+3, 49 b3
1169
2929
9b7 - 6g2 b5 + g b
= 3a 169 .. - 96
+29gib.
99.. . 1969 .. +5 -992b
0 Y + bacxaec
+ d
by ey 1 ae2
+b. +dbaco + daec
ubi tollendo terminum setundum
A ponemu ac p, 29 b- 3 al
3b2
e erit a  a9b- 19 bal 49 p
9b - 6b292 +94
8gd-129b3a l +69b9a- 7 a 13
2762-301, -27691 +96 9t dg
3
2934 19
+a 19b = a 169b + al9