V 
(>_> 
Then fliall 5 cc. be always pofitive when the 
Roots are real Quantities, whether they be afFeded 
with the fame, or with different Signs. The Negative 
Coefhcients arife by multiplying thofe in the preceeding 
Corollary, 2,31X530,5' 6,90, by one another* 
PROP. IX. 
Let and m exprefs the fame Quantities 
as in the Co rollaries of the laf Propofttion^and m E* 
m -\-n I X D F a' U 2 p ^ ^ d' 14 .P, 
For by Cor. ii Prop. vi. 
E* =E E',+ 2 C'G' + 2 oB'IT+ 70 A' T 4. *r 
and by the fame "r 7 1 4 --5^ K, 
DF= B'F' +^C'G' + 15 B'R' A' V 4 2rn K>- 
therefore m i x D F =r E' E' + 
m ^n-^ 1 X F^ + m — x n - 
+ XS^' Pf +~m — 47/ 
14 A' I' + ^ — 5* X 4 2^ K = (by fubftituting 
fucceffively for m E' E', m n + 1 . x D' F' 
m — z n + 4 X C' G', m — 3 ;/ -jT^ y. B' H'', 
X A' i' their Values deduced from the 
nrlt Corollary of the lafi: Propofition)-= y _j 
~h S d' -f 14 where the Coefficients prefixed 
^ r tdf'd ri of the Coefficients 
ofE'E', D'F', C' G', B' H', A' i' and K in the Values 
of E* and D F taken from Cor. ii. Prop. vi. being i o, 
^ — 4> 2,0 15'j 70 — and X5'x — , xio. 
X X 2 C' G' 
X 
Cor. 
