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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 62r, page id 00068201:0123
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(177
da
16)
Hunc valorem
residua, fer:
+ 485]3
cot
t 3uaY 
Est2
+2a7055
c
+ a  at
ipsius ar
Cos
 170
Ergo
a
c0
do
co repertum inserendo in aequatione
2
X + sa a X + 40 a+
c0n
0
incognita X plane evanescet et poterunt omnia dividi
per Xt. Idem est quambeuaque durobus terminis excerptis
G. valor ipsius a quaentur.
Sed quid si tres simul termini nihilo ponantur, v.g. tres
intermedii ponendo:  5 X + 8, IX + a X 1o
c
iet: _ si X + a IX f a)
co
cor 10.
co3
Ul rem excemplo clarius tractemus: Esto aequatio V 4
v
y+ + 4 MV + ad
corsd
al
c025.
Y
+ a cV + de oV B
1
cor
c04
Ponamus Q n Y3 + a x y + a y p0.
cd
co
sive n y + a Xy + a C B0. Euit y
co
cor
(17) Eit s + ea  y + ata
(8)
N
co
v
c n
 ata
+co no qcono
et y + avx
 a S+
∞ 2C0n co
4n
a+o
co
aon
ps es
Ergo inseondo valore ipsius V in aequatione residna y
e
c mvemetur valor ipsius 6, si modo non alia quam
negativa
quadrato qua dratica a quadratica esse ponatur modo scilicet
si Itaque si duo n’in proposito problmate duis obtinere possum
aequatione problema ponatur esse in Numeris et 6 sit quam
titas quadrato quadratica negativa et non nesii uno termino
it
2 0e
reperiatur; in quem y non ducitur et ex 5- o possit
extrahitradii, solutae utqu habebitur utique in  numeris solutio
problematis. Et tanto laris habebitur, si Or sit negativum
quadratum tantum.
X X + ap X
sed ipa satis concta.
d
+ af 5 - a qu=
t
fer
rudicem, fiet: X + a La  qx - ar + Pa etI
extrahendo
Eugo ex AX ar + debet extrahi posse radio, ideoque pro X substimamus
q a Bq + YZ+ da
 et abet extrati radio exaq
ed hoc displicet quoniam extracta radice demuo  facienda esset extractio
u su su aequrtona ins
2
+4 31 
+
11
13)
4)
oumuus.
Ex
a
Uendle euone
s.