9 1 B Extenfion of Cardan’s Rule to the 
Now, lince q is — 3, A will be = |= t, and confequent- 
ly — , or the cube of A will alfo be = 1. And, lince r 
is = i8, we lhall have — = 9, and~=8i, and confequent- 
ly — --=8 1- 1 =80; that is, ss will be =80. There- 
1 4 27 ’ ’ 
fore j is = s/8o = \/i6xv / 5 = 5 ; and f+ s is = 9 + 
4^/5 = h — — 27 + 2 7 ^s + 4 3 + . fys . an( j confequently 
4~~ ~ ~ 
3 \r . 2 -f- \/ f 
— + S is= — 
2 2 
. Therefore 3 x j-h+J is 
3^3+A 
and 
Vi 
IS = 3 X 
+ r 
3x3 + </ 5 3 +^S 
; and 
+ S + 
is = 3 -t£i + 
1 3 * V fl X 3 -f */$ + _4 -2 
3+^5 2x3+7? 
iS 
^6x3+ 6 ^ . 
= 4-3. Therefore 3 is 
3 \/ 3 |f +lf 
9 +6i/ j + 3 4 - 4 
2 x f 7 + 7 ? 2X l 3+7 5 2X[ 3 + v's 
the value of a? in the equation' v 3 - 3V= 18. And fo we 
lhall find it to be upon trial: for, if x is taken =3, we 
fhall have a? 3 = 2,7, and 3^=3 x 3=9, and a? 3 - 3^= 27 - 
9 = 18. , And thus we fee that the firft of the three fore- 
q has 
going exprefiions, to wit, ^J 3 j—+ s + 
4 
— + s 
2 
•given us the true value of x in this equation. 
Refolutim 
