Second Cafe of the Cubick Equation x 3 -qx-r. 943 
be a 5 inftead of a 7. For the accurate value of x in 
this equation is - -f— , or — -- , ^ 3 ’ I ° 6 , or —N I0( \ or 
2 -5 6 i >55 35 which differs from 2.561,573, or the va- 
lue of x found by the foregoing feries, by only IO - 0 2 o ° 0Oth > 
or io ojooth * P arts of an unit 3 or lefs than the 1 28,000th 
part of 2.561,553, orthevalxieof x itfelf ; which is 
a great degree of exactnefs. 
45. Note. That x, or the root of the equation a; 3 - 
$x=r, is accurately equal to will appear by fub- 
llituting —'pi inftead of x in the compound quantity 
a; 3 - 5 at, and obferving that it will make that quantity 
become equal to 4. For, if x is = we fliall 
^- 1 +3X'^ i y+3Xi7 + i7XA/i 7 _ ;2 + 2QX a/x7 _ i 3 + 5^17 an( j 
8 8 2 * 
5#=— , and confequently a; 3 — ^x- ^p - 
| = 4. Therefore CLpl i s = x. Q. E. D. 
46. Thefe examples fufficiently prove that the ex- 
preffion e$ x the feries 2 + — — - Sic- (which 
* gee 243^ 656 ie ° N 
We derived from the other feries el x 
20s 4 3085® 
243c 4 6561^ 
See. 
by the peculiar train of reafoning ufed in Art. 33, 343. 
and 35,) gives the true root of the cubick equation x 3 — 
qx=r 
