C i 06 ) 
+~d\ &c. is always a Pofitive Quantity,* 
therefore m ~ ix.a - i B is Pofitive, and confequently 
X A greater than B. 
z 
■ Cor. Ttappeat:^ from the Demonflration^thattheExcefs 
of w— I X A above.-i B is always equal to the Sum of 
the Squares ot the Differences of the Quantities a^byc^d^ 
&c. and that when the Quantities a, h, c / &c. are all 
equal, then m-^i xa — 2 . B=o, and with this reflridi- 
on the preceding Lemmata mufl be underflood. 
It is to be obferved, that tho’ we have fuppofed in 
thefe Lemmata the Quantities a^ c^d, &c. JPofitive, 
they are a fortiori true of Negative Quantities, whofe 
Squares are the fame as if they w^ere Pofitive, while 
the Sum of their Produds is either the fame, or lefs 
than it would be, were they all Pofitive. 
PROP. L 
In a Qiiadratic Equation that has its Roots real, the 
' Square of the fecond Term mull be always greater 
than the quadruple Produdt of the third and firfl 
Terms, 
Let the Roots of the Quadratic iTquation be repre- 
fented by ^ and -}- h • and if a- be the unknown 
Quantity, then fhall — ax~\-ah^o 
^ ' — I X 
Now fince -f- is greater than -Lah^ by Lemma i, 
therefore ^ a b greater than r^a h‘, there- 
fore 7^hxx\ the Square of the fecond Term, will be 
greater than a bxx^ the Quadruple Produd: of the 
hrlt and third Terms, 
PROP. 
