Second Cafe of the Cubick Equation x % -qx~r. 909 
that is, either f—a z or a 3 -y, according as — or a 3 is the 
greater quantity. But it has appeared above that a 3 and 
b % together are equal to r; and a is fuppofed to be greater 
than b , and confequently a 3 is greater than b\ There- 
fore a 3 muft be greater, and b l lefs, than Therefore 
a? — -- is the difference of a? and f, and confequently is 
the fquare-root of the quantity j-ra* + a 6 . Therefore 
s = Jfc-*-, and ^ is =E + lETf, confe- 
2 \l4 2 \. 4 27 
quently # is j-y + ~ But £ has been fhewnto 
; and confequent- 
be=— . Therefore £ is = 
3 " 
ly <*+£, or at,, is =\/ 3 (— + ^Vj- — 1 - 
7 * * V l * \I4 *7 - / 3 r 
3 V T + vt~r 7 
Q. E. I. 
6. This expreflion may be rendered more fimple by 
fubftituting the Tingle letter jv in it inftead of - fL. 
For then it will be 
— + s + 
2 
Npli 
+ s 
Synthetick Demonjlration of the Truth of the foregoing 
Solution . 
*/. That this expreflion is equal to a; in the equation 
v3 _ 
X 
