1 758 3 
•value is fought, be conceived to be compofed of 
three others. 
> y, a -f b%px + c x/7 2 + dxfx** + exjw\6cc, 
+ + + &C. 
■j x a -{- b x r x 4~ c x rj? -f* d x ri? 3 --j - ^ x v > & c ' 
having all the June jom, and the fame coefficients 
with the feries firft propofed, and wherein the con- 
verging quantities px y qx y rx, are alfo in a determi- 
nate (tho* yet unknown) ratio to the original con- 
verging quantity x. Now, in order to determine the 
quantities of thefe ratios, or the values of />, q y and r, 
let the terms containing the fame powers of *, in the 
two equal values, be equated in the common way ; 
So (hall, 
\by.px-\- J zby.qx-{-^bxrx=o 
|cx p 1 x 2 -j- -j c x q z x z -f- 7 c x r z x 2 = o 
■j d x /> 3 * 3 + 7 d x y 3 * 3 -\--jdy. r l x z — dx l 
ffx p*x* 4- -J e x y 4 Ar 4 + 4 e x r 4 A <4 = o 
&c. 
And confequently, 
/>+ y + r = o 
P z -\-q z + r 2 = o 
p iJ r y 3 + ^ = 3 
P 4 + S ' 4 + r 4 = o, &c. 
Make, now, /> 3 = r, y 3 = 1, and r 3 = 1 ; that is, 
let p y and r, be the three roots of the cubic equa- 
tion z 3 = r, or 3 3 — 1=0: then, feeing both the 
fecond and third terms of this equation are wanting, 
not 
