( 70 ) 
C 0 Fv. Since ^ = n — r x r therefore nA^\ 
Y 
— ^-|-ixr+ i ; and confequently X 
n T _ 4- I 
; — X E* muft always be greater than D F the 
, r -j- I ^ ° 
Produd of the Coefficients adjacent to E ; and hence 
the Fradions are deduced, that in Sir Ifaac Newton's 
Rule are placed over the Terms of the Equation, which 
multiplied by the Square of the Terms under them, 
muft always exceed the Produds of the adjacent Terms 
of the Equation, when the Roots are real Quantities : 
For it is manifeft that the Fradion to be placed over 
the Term Ea? according to that Rule is the Quo- 
.n — r — r + I 
Ucnt or divided by 
r + 1 ' r 
PROP. X. 
T'he fame E^prejfwns being allowed as In the pre- 
ceedtng Propo/ltlons^ it will he found in the fame man'‘ 
nefthat as n-\~\ fo 
w — j— I X DF xCGmr - 
m — zn-\- 4 xCG — xBH— - - c’-j- 5 i'-j^zoe' 
m — 9 xBH — 7n-\-j^7t-\-i6 y.K\'=. - - - d-j~ •} e' 
m — 4«-f-i5xAI — ^ - - - - . ^e\'‘ 
Thefe Theorems are eaffly deduced from the Theo- 
rems given in the fecond Corollary of Prop. vi. and the 
firft Corollary of the viihi^ PropoQtion *, and the Co- 
efficients prefixed to a\h\c'^d\e\ are the Differences 
of the Coefficients of the correfponding Terms in the 
Values of E%D F, C G, B H, A I and K in Cor. ii. 
• Prop. vi. 
^ Cor. 
