Second Cafe of the Cubick Equation x'—qx-.r. gig 
Refolution of the fame equation by the fecond and third of 
the foregoing exprefions. 
17. We are now to refolve the fame equation x 3 - 
- 1 8 by means of the two other expreffions, to wit, 
[?f7 l . ? 
s + 
and ^ |f+ 7 + s j : 
~-s. 
z 
Now, lince r is = 1 8, and s has been ffiewn to be 
=\/8o, or 4^ 5, we ffiall have ^~s— 
, and — j = 3 * ~ a v ’X Therefore 
=3><EZi, and 
J 7~ *7 A + 45 - 5 d; 
8 
W : 
— s is 
z 
4\f 
iS =— J=r= 3 X 
3x3-^ 
3x3- V'j 3 -^S* 
Confequently jf — j~+ 
is — 
3-^S , 2 — 3-/3X3-/5 + 4 _ 9- 6 V , 5 + S + 4 _ :i 8-6^3 _ 9-3 
2 3 “ v'j 2 x 3 - a X 3 — y 5 2X 3 — V^S 3 — v's 
3 X 3 -y's_- 
3-^5 
3. Therefore a; is = 3, as it was found to be 
by the firft expreffion. 
1 8. The third expreffion f^-+ 7 +^ 3 [~- s is in the 
prefent cafe = 3 -^~ + ~^ = 7 = 3 * Therefore by this 
expreffion, as well as by both the former, the value of 
. . 
x in the equation x 3 -$x~ 1 8 comes out to be 3. 
6 19. Note. 
