r 8,1 )) 
preceea it> ic.is manifefli that tlie' Term it felf wiH be 
A" -V -r:- • ' . „ • ■ 
~ theSuppofitionDx“-'jsthe 
Correfponding Term in the propofed Equation, and D 
muft be the Sum of. all the Produds that can be made 
by multiplying as many Roots of that Equation by one 
another, as there are Units in r ; and muft be the 
Sum of the like Produds of the Rook of the other 
Equation ; which muft be the greater Qitantity by 
the preceeding Lemmata, becaufe its Roots are equal 
amongfl themfelv«,_and their Sura is equal to the Sum 
S propofed Equation ; and the Sum 
ot luch Froduds is a maximum when the Roots are 
equal amongft themfelves.- By purfuing this Method 
1 it may be demonflrated that 
2 b 
2 
X / muft always 
nxn-^i 
exceed the Coefficient prefixed to the Term At”-' in an 
Equation whofe Roots are all real Quantities affeded . 
with the fame Sign ; providing that r be a Number 
i X 3 
X I 
greater than z ; and alfo that — 
^X^— -IX^ 2 
muft exceed the fame Coefficient, if r be any Num- 
ber greater than 3. 
It is eafy to continue thefe Theorems. 
^ The third Method which I mentioned in the Begin- 
ning of this Letter, is deduced from the Confideration 
of the Limits of the Roots of Equations j and though 
It is explained by fome Authors already, yet as I de- 
M 2 monftrate 
