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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 111v, page id 00068201:0222
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Oidendum esst an radice cubica acedente aliquid fieri possit constat si bC4. c L b + bc multi-
plicentur per b -c fieri B - c2. Itaque sit:
aequatio multipluanda per X +hs Abatac
a3ce
+2sd sae  15) abracsae
-a dae
X s ab ressae X
+d tae
+ h Seab
=l 52 ac sae
-h d’ac sae
sit jan si sin duce radices cubica unia ex aliqua quantitate, altera ex ejus quadrato
tunc cubus earum radice cubica ceret Ubiue, quadracum ejus nusquam ine s +  By. ejus
cubus ent .aetey   qae sac Py), + 3ae sae ( (197 + tactac y Error 10
b +c p. 3 + 36c +3bc2 + c3
b7 4 ct.  u+ 7 13. c et L. +   3
erit 91 3 - . et u  9 - 6 +  ergo 69 - +  ) H
Eive.  6r = 5 Y + 1. sive x r - 5 Y + 25
quod in numeris fieri non potest.
4, 36
binonium iabenire ex radicibus, quae cubice multiplicatae carcant radice cubica, sint nomina
b+ b c7. fici:
multphieanda per:
YX - ssy X
fiei X _-sse X C sN)X
sin  X +35+7 N X +s’r
- 139377
+ + 7..
+s5
F par
+Sot 
13.) abedidu
sit iam aequatio data Z  ah Z + ael po
+8sV
+ Sxt 7
+ C256
F So +
+ S3t
(- + 7 (2514)
- + 3 73
1) a  n 2, a a + 3Y at
a a haer raarer
_C sap + 3 sap + 4
E ap sap +
(X +ab B X + Y. Ergo
(∞ ab  (4 + 2rX + v. et fiet:
X = fiet r2 ab - 2X -2X X ral
et repab - 2X - 2X 1X +ab. adeoque
Sxitab  ab 2X- X IXrab +X
C5 (+ 7s5FD urat
Fiat Z 7 2 6. fiet X  + v su aliX +   L B. erit 3s t Z e v h. punendo ses p va ves fiet n A  ar
fiet xco +Zppha.. et + 7 r vta. et collatis terminis ultimis, fiet: Co N- N h a  val N
sibe S - 27 a l a 5e + 27, 27a 12
adeoque sch = 27 a1
1 27, 27 ao l + 4c 27, +, at2
1f27, 27 a 13.54 h2a
adeoque s⊓1 B =Sia 1   h a3 + 47 a.
co s02
sed calculum cum tanti sit momenti, explicatis jam literis resumere operae pretium erit
Nempe
= c0 e
+aha.
co2 +
alti
+ o ox
(sit jam aequatio data Z3 X abiZ +ael B
or fiet Xa X ah Xa + ael 5 et musti-
plicata aequatione per  fiet. X X Nh X +,0. quam
aequationem conferendo priori -  X NH X + cor
habebimus aequationem collatitiam unicam
nempe
NN7
ati. adeoque
03
7294 4, 27 a h
Ubi ad determinationem scipionis Ferrei nihil tale suspi-
cantes redivimus. Videamus an liceat evitare,
2740
17a6 = a4, scilicet
er diveundo: XL n mra 216 n. adcom  S2 27 al 7 cos
altera aequationis paus residua: m  co A6
15 27a0
N Cos
ut i inie.
17a  a  sive fiet:
adeoque  729 a
+ a 
Me -rampa rH 27a  h3
Adesque M a + a
 
  ab rratetae
hd sae  16) ab + ac vac
Muctipuletur per
in
 aelioa
+o hcoo
= cose at
 nati
Nh X