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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 133v, page id 00068201:0266
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Ergo aequatio
sit intractabilis.
t aequatio sexti grabu exipsis habebit quatuor 2
Tubica
Aequatio plana assumta  habet duas radices
voles; aequatio ergo quadrato- quadintica habebit religvas du as
radices reaes, duasue alias imaginarias.
idendum jam an omnis aequatio quadrato-quadratica quae duus tantum
taabiem
an vero revocetur ad tiradicalem. Utroque modo lucrabimur, nam si revocatur
in triradicalem poterimus aequationem duas medias proportionales invenir
per trifectio nem anguli, duplim, si  ad ractabilem, poterimus trisectionem
X= + bX + C
+ b2).
x b2)..
N= - ( X ∞ qu
∞b X
 b3.
X+ X +CX2 - ebX - 4
-12.. - 86.
=e b.
 qN Yx +5)
b11   1) se - d - q
vel
assumta est, tractab
anguli invenire per Mesolabum
X + bX +c
X X +cX
Ci
 ed p L-)
u
C - d -
2
unde et -d ac- 9C = 25 5 1Y
ubi memorabile est nanc calculum
sic terminari, cum iderus cale
quaerendo y. ultimo lodo
terminetur in cubicam.
ung
unde generalis habetur nota, in aequatione quadrato- quad ratica sacundo
-
L d2 62
termino carente, non nisi duae sunt radices reales
quandocunque signus terminorum tertis et ultimi
cont Tertii Termini signum est affirmativum
compludiosioris calculi causa faciamus
b
4C,b2
= c2b0
traectabilis. Generaliter ponendo ex tore terminum tectium fict,
Aliud exemplum: ponendoque dYC4 teb
erit terminus tertius p0. mamente secundo
unoc term. quartus e (F eb3 - cb - b3
eb) et altimque erit:
bt - 206 - ebce
ubi rursus sibicae
productae terminus
penullimus resula-
ater fiet affirma.
tivus, Acredibile
Follatur aequationis ciusmo quadhaticae generalis tertrinus quantus
cini tertius, faciendo X 4+ pX2 +
frei: N2+ ay
ultimi signo contra existente negativo
quae revocaxitur cut cubicam hanc:
quae aequatio reduora dat quadrato
quadraticom A Xh  N. X
ulus
u
q
X +
+ +BY + p+
+ py exEY +3 pB Y +B
excitatae
ss v. et
esse nactubilem;
VFap etp
+ c2b4
b
W0 X ++C W
YW
Unde lubica:
quae aequatio semper  +tCb
+ b X
2 + C X
2
+ b. X3
12
1
... + eb..
d ab.
Unde fier subica: 
Uende per Tubica:
est, etim cum sic
negalivus, tamen
aequationem (ubicum
10 cd. X +4C tsd +ocd, W0 etc
+4 eb
 ate
D
eb2