4 ** — 4 
( 5*7 ) 
jS = o = y = 5', therefore 
4+ ixy— 4+ i 
xE 2 
or 
— £ a exceeds T> x A by L'^~ 1 
5 - 44 - 1 x 5 -— 44 -i 
i- a =±z_. 
1 5 
xZ — 
_ ^ I 
^ — — -X — abceV 4- 
io io 11 
io 
y^abed — bcde\* 4 - &c. which is a politive 
Number when the Roots are real Numbers. 
Proposition II. 
Let x^—B x n ~ l -{-Cx n -~ 2 — 2) x tl ~ i -\-Ex i ~ 4 
&c. -^A~o be an ./Equation of any Degree, whole 
Roots with their Signs let be expreffed by the Let- 
ters by c, dy e , f 9 &c. let M reprefent any Coeffi- 
cient of this ^Equation, L , N the Coefficients adja- 
cent to M ; K, O the Coefficients adjacent to L , N; 
I, T thofe adjacent to K, O 5 H, ^ thofe adjacent 
to IyT, and fo on. Let m reprefent the Exponent 
of M and let Z (as in the preceeding Proportion) 
reprefent the Sum of the Squares of all the poffi- 
ble Differences between the Terms of the Coeffici- 
ent M. Then the Produft of the Square of any 
Coefficient M multiply’d by the Fraffion x 
'L 
I 
doth 
n x 
n 
- x 7 i 
X &c. x - — 'L 1 
m 
always 
