t 
C 5 >7 ) 
four Roots of the /Equation x * — B x* C x 2 — 
<Z) x A=o may be impoflible, but if two of the 
Roots of the /Equation 4 # 3 — .3 ^a; 2 -[-2Ca: — 
F) = 0 be impoflible, there muft be at leaft two im- 
poflible Roots in the /Equation x*—~Bx l -\-Cx 2 — 
F) x -f- A — 0. All this hath been demonftrated by 
Algebraical Writers, particularly by Mr. Reyneau in 
his Analyfe 'Demontre , and is eafily made evident by 
the Method of the Maxima and Minima. 
Corolary. Let all the Roots of the /Equation 
a:” — B x + C x n ~~ 2 — T> x n ~ * + Ex n ~* — 
F -f- &c. e x* ±d x* + c x 2 ± b x + 
A=.o be real, and by this Lemma all the Roots of the 
/Equation nx M ~ l — n~—iBx n '~ 2 -{-n — zCx n ~ l — 
n — x n ~ * -\-n — 4 E x n ‘~' s — n — 5 Fx n ~ 6 -f- 
&c. ±5fx*+ ^ex* ± 3 dx 2 + zcx ± b = 0 will 
be real, and therefore (by the fame Lemma) all the 
Roots of the /Equation nxn' — 1 x n ~ 2 — n — ix 
n — z B x n ~ 1 n — 2 x « — 3 C x n ~'* — IT— 3 x 
n — 4 7 ) x n ~ s + « — 4 xn—fE x n ~~ 6 — n — 5 xn — 6 
F x*" 1 + <&c. +20 f x z + izex z ±6 dx + zc = 0 
. or (dividing all by 2) of nx x n ~ 2 — n — ix 
n 
— 2 _ n — 3 
Bx n ~*-\-n — 2 x Cx n ~ 4 — ©r. + 
2 2 ~ 
10 fx l + 6 e x 2 ± 3 d x + c == 0 will be real. After 
the fame Manner all the Roots of the /Equation 
71 
nx 
1 n 
-x - 
X 
n — 3 
— 8 
IX 
71 
2 77 
— x - 
2 3 
B x 11 ~ * 4 - 
3 
