© **“ ’ + E S x"~ 4 _ &c.±A = 0 . Then if all 
the Roots of the ./Equation are real, the Square of 
any Coefficient multiply’d by the Fraction whicli 
ftands above, will be greater than the Reftangle un- 
der the adjacent Coefficients. This Corolary doth not 
hold converfly, for there are an Infinity of /Equa- 
tions in which the Square of each Coefficient multi- 
ply d by the Fraction above it, may be greater than 
the Reftangle under the adjacent Coefficients, and 
notwithftanding fome or perhaps all of the Roots may 
be impoffible. Therefore when the Square of a Coeffi- 
cient multiply’d by the Fraflion above, is greater than 
the Reftangle under the adjacent Coefficients, from this 
Circumftance nothing can be determined as to the 
Poffibility or Impoffibility of the Roots of the /Equa- 
tion : But when the Square of a Coefficient multiply’d 
by the Fraftion above it, is lefs than the Rectangle un- 
der the adjacent Coefficients, it is a certain Indication 
of two impoflible Roots. From what hath been faid, 
is immediately deduced the Demonllration of that 
Rule which the mod illuftrious Newton gives for de- 
termining the Number of impoffible Roots in any gi- 
ven iEquation. J & 
Scholium. 
Let the Roots of the iEquation x* B x n ^ 1 JL 
Cx"-‘—‘Dx*-> + E x"~* — Fx—< -f &c. ± 
A = o (with their Signs) be reprefented by the Let- 
ters a, b, c, d, e,f,g, &c. then (as is commonly 
known) B will be the Sum of all the Roots or = a + 
b + c + d -f-e-f-/-f (Sc. C the Sum of theProdu&s 
A a a a z 0 £ 
