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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 273v, page id 00068201:0546
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+aer
Cl agX ⊓ aq ( d’e
pX H
+pet..
+2pl..
1 3deo..
321...
(1) 10 (210
+ aq  de + aql
+ pd ..
+ 2pl3..
+3det..
+d
eda
6(70
5
+2pdet.
+pt
a
d’e
de
6de 14
() 10
subtrahendo jam aequationem 3. ab aeq. 2. fiet  3et sdl
si gp. Eut Ir. 
et (C) +6e 7 1dc
sive de P, eri
altime aequatio
L. Ex (B +B
d +P
d
atre n
snc d  gar d . .) + Bira
P 1+4, a r(+
ego at  vr +1b p quanticas
affirmativa sunt autem
3el + pe - 3dl = pd B sive dividendo per e- d. cunqu in nostra sit
fiet 3l + P B o ergo sel + pe 10. et 3d l + pd p0: et his ex aeq. 2. et 3,
et ipsius e
et ep -3a9+ 2p. Unde valore ipsius de n ag. 4. inserto
ap Y+p = 3aqd + 2pd + 3 a9 12 aqu 4
81 d
 aequatio q plana, quae semper est possibilis quandocunque
dimidius terminus dtertius. s u
aut aerandecunue
ut sit
X3 + pX + aqX + ar p0. sint
XN H = f. fiet 8 - dp  + 3 e y
Quod adeo verum est, ut exhibeat
adhuc minus. Nimirum quandocunque
secundus tertius terminus productae in aequatione:
semato s cujus secundus sublatus est
est affirmativus, tunc aq  = pr.
+ p .. a2p.
erg et a al non ieo semper et a p Lp. fiet
+aq
+ a9
Ergo ut aliquando hoc calculo exitum non reperiamus quem fardanico
-
+ P
=aqu
3
4. 2p3
=ags
+ar
non reperissemus. Contra cum nostro primur reperinus, letim Cardanico reperiemus. Haec differentia e
nimitum dabuntur exempla quibus aquationes eaedem radices et imaginarie in speciem et realiter exhibeantur,
quae comparatio aliquam credo lucem praebebit. Nisi forte in reliquo calento ad idem reditur
anter Extrorendum. Quod abitior. De seequo  si ponams
P H0.
triduere asfirmatio nelu cui velimus sequereE
sublatis, res idua aequationum 2. 3. inter se coincident, et habebitur
+ a Y 4.aqe 
fiet: destinetur in eo 2pde + del, et fiei
non nisicu
3
signa ipsorum contraria.
aequatio. a9 f -  P +. 3de, 0. sive - 3 a9 + 2p 7 de.
1d
=aqX  - a9 + 13 b
+
X
H+3Fa ps.
X P
ege 1960
lri
+ -a9f 1( bet
9
apate...
de
+ 5b0
de enajs errore calculi mihi suspecta est, si tamen nullus subest, hinc rem ducemus memorabilem,