Second Cafe of the Cubick Equation x'-qx-r. 917 
14. An Example of the Refolution of a Cubick Equation 
of the aforefaid Form , x % — qx -r } by means of each of 
the three foregoing ExpreJJions . , 
I will here infert a Angle. example cf a numeral equa- 
tion of the foregoing form, x^-qx—r, refolved by each . 
of the three exprefiions above-mentioned, in order to 
fhew that they will all' three bring out the fame number 
for its root. . 
Let -it therefore be required to find the value of x in 
the cubick equation x\- 3 x - 1 8 . 
15. In this equation q is =3, and r is = 1 8. There- 
fore V q is .— %/ 3, and is 2, which is great- 
ly lefs than 18, or r. . Therefore this equation comes 
under the above-mentioned rule, and may be refolved i 
by either of the foregoing exprefiions. 
Refolution -of the equation- x^.—^x - 18 by the Jirft of the 
faid exprejfons . , 
16. The firft of thofe exprefiions is 
, in which s Hands for 
— + j +• 
2 
3v/ 3 I-+ sj 
rrv 
4 *?. 
Now 
