Second Cafe of the Cubick Equation x^—qx—r. 913 
- - -- from both fides) ¥ 
4 27 ' 
- q-g and (fubtra<51ing 
will be =fr^Jj-7 7 r Therefore b is =>/ 3 [f-^ 
4 27* 
and a (=1) is 
VI WIB 
, and confequently £+<z, 
or or x, is — >^ 3 |-T — ^ j2T_|i + 
n/‘F 
or 
(if weput^^-jL) 
Ne-s 
+ q . - 
/ \ * 
hC7 
3 V |l s 
Q. E. I, 
Synthetick demonflration of the truth of the foregoing ex - 
prejjion. 
10. Here again we may demonftrate fynthetically, 
that this expreflion is equal to the true value of x in the 
propofed equation x % - qx — r, by fubftituting it for x in 
the left-hand fide of that equation. For, if we make 
that fubftitution, we fliall find that the value of a: 3 - qx 
thence arifing will be equal to r. This may be done in 
the manner following. 
’ ' v 
If x is=J 3 \ -s+ — jy = , or — -j]* 
we 
3 x7V 1 
fhall have a; 3 -—- J+ 3 x - sy x 
+.3 X t” j I Tx 
3 X |— -f 
5 X 
VOL. LXVIII. 
qq 
