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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 101r, page id 00068124:0201
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a bc d Radices aequationis quatuor Dimensionum. quod si aequatio secundo termine
careat semper aequatio radices verae sunt aequales falsi, ideoque ponendo tres esse radices, aequa
tionis cubicae, a. b. c. et unam esse veram a, duas falsas b. citunc erit a = b + C, et quia b et
Csunt falsae loco affirmativarum substituantur megetivae, sive a f Ergo poterit dici tres
esse radices b+c, b. c. vel a + b. a - b = 2a.
X = bE N - = b X. rc. X - b - c = 0 X +b = 0 Xt C = 0
a X - bX + ba
X
YX S
LX
X - a IX VX vtX us
= a X + bax - b a
+ aX - b + ba
comparetur cum:
X  WX yX Z
+AX - al X rabisX -b ab ego L +rF o. e rp - t.
=a - b
+  a = X
Ego W FI v - r +5
Q YI vs
Ego vN 3 =
x
X+b =0
bx bc
Ex X abea
b
CC
+X = CX LX be
b -6 - b0
+c rbc
Pbe = 9b - 9c Eigo C17 4b
axy = 9X - qy vel b 1 
X - y
+ 1
= Xy X y sali
s
1 Ermo 223=
9 Xy
e
PC
ertorum
Partinaria
xy vele uds
sign. (
x  CX 2bc s X + derc, b.c, X Bc. ctb
 be bay o bC
-c
=
Pr 1 qui be eEro 91 bep QNsebac 1mb - E B d. Ergo br cAd
Ergo 7 = 3, vel 517 1Z
Ego AXd C. Cab liy   bc.
x
Em a ix de sive
Y = X7. Et  o   C
et Ba r ruk 27.  o Nesta ap u er   + Z sers rader s. bn ir a
la
X =
 a
2a= 
- 1
X X - 4y =
an
1x = 1X (, +.
-y + 4 37
x + 4 - 2 - 0
Vt 8
ui locus Hxperbola est
Unde patet una radicum data
stati in alteram quoque dari
ope circuli, seu sccantum
eae sunt axpliculae hypitoae
101