( 112 ) 
ways be greater than the' Produdl of the Jerms adja- 
cent to them. ' 
Cor, Multiply either the Square of the fecond Term, or 
the Square of the iourth Term of a Biquadratic iiiqua- 
tion by ^ and if the Produd does not exceed the Pro- 
dudl of the adjacent Terms, feme of the Roots of that 
ytquation muft be impoflible. 
PRO P. V. 
. Oil ■ 
j / 
In an y^quation of any Dimenflon exprefTed by w, 
the Coefficients of the fecond, third, laft, lad but one, 
ahd lad but two Terms, being refpecdively B, £, 
D, C, if the Roots of the Equation are all real, then 
dial] m- — I X always be greater than x m By and m — i x 
greater than xmQ E. 
\ 
I. For fuppofing the Roots to be &c. 
then by Lemma 4, fliall m— i x + m—J X + m— L xc^ 
See. be greater than 1. al-j~ za c -f- ^ ^ and ad- 
ding %m — i. X a h % m — 2 x a c -\~ z m~ ix n d,6^C. tO both, 
the Sum m—\Xa^~\-^‘^n—^xab-\- m~ i xb^ See. ( = w— i 
X a b -j--c -Sec!') mud be greater than zm a I -j- z mac 
x'mad.^Sic. that is, m-ixA^ mud be greater than 
zm B. 
'• 2. In general, it follows from this Demondration, 
that the Square of the Sum of any Quantities whofe 
Number is (w! multiplied’by — {.mud be greater than 
the Sum of all the Prbdu ds can be made by multiply- 
ing any two of them, multiplied by -i m. But it is eafie 
'to fee from the Genefis of z^quations,that C £ is the ^um 
of the Produ<ds can be made by multiplying any tw'o of 
the Term'' whofe Sum D : From which it follows. that 
m-'i X D* mud be always greater than zmC E. 
to he continued. 
V. A 
