93 * 
'Extenjion of Cardan’s Rule to the 
i 
rr i 
powers of the difference - , to wit, 
* 27 4 7 7 27 4' 27 
rr 
4*' ' 27 4' 27 4 
&c. will con lift of the very fame terms, or the fame 
powers, products, and multiples of the two original 
quantities If and q — , and with the fame figns + and - 
prefixed to them, as were before contained in the even 
powers of the oppofite difference ~ — L , when ~ was 
greater than Thus, for example, the fquare of f- - 
in the former cafe was 4 — + — - — ; and in the pre- 
fent cafe the fquare of - — i s — - 22-2 + r —. which 
con fills of the fame terms, and with the fame figns pre- 
fixed to them, as were contained in the fquare of - — — , 
4 27 
and differs from it only in the order in which the ex- 
treme terms r — and — - — 
10 27 X27 
are placed. And the fame ob- 
fervation is true concerning all the other even powers of 
the oppofite differences — - — and - — — * 
iL 4 27 27 4 
Alfo the odd powers of the difference to wit, 
- — - itfelf, and 2- - -] 3 ? 21 _ !l| 5 , 8cc. will confifl of the 
27 4 27 4 27 4 
fame terms, or of the fame powers, products, and multiples 
of the two original quantities and as were contained 
in the fame odd powers of the oppofite difference 
rr 
