93 ° 
Extenfwn of Cardan’s Rule to the 
*?• 
s 
8 cc. or 2- - + —^ - ~ + 
4 2 7 rr 10 
2^ 3 
r 4. 3r?* 
27 X 27 Xr 4 64 "H 16 x 27rr 
3 rf 
y?' 
4 X 27 rr 
- &c. which confifts of a much 
4x27x27^ 27 X 27 X 27 r 
greater number of terms than the feries 2 - — 
20 ^ 
2 
9 ££ 243 
3 °?i — . &c. from which it is derived, and in which 
o 5t> 1 tr 
many of the terms are much more complicated than in 
that former feries. Neverthelefs, fm.ce the compound 
quantity 2- — X is equal to ss, the infertion of it inftead 
of ss in the terms of that former feries cannot alter its 
real value, though it will make it much more difficult to 
compute. It muff therefore be true of the new and 
complicated feries 2- — + 21 ,.. — - + 
x 4 27/r 10 
v 
64 
+ Zvf _ 3 y<f + r ? 9 
l6x 27rr 4x27x27 r 4 2 J X 2 J k - 2 jr 6 
former feries 2 
4 X 27 X 27 r 
2 ss 
gee 
4X27 rr 27x27'* 
&c. as well as of the 
20 s 
243 * 
208 ! 
6561 
— &c. that, if it be 
multiplied into e or s/ 1 e, or ^ '-■> the feries thereby 
produced will be equal to the value of x in the equation 
x^-qx-r, or that, if the laid feries be cubed, and alfo 
multiplied into q y and from its cube the product of its 
multiplication into q be fub tracked, the remainder will 
be equal to r, or rather will approximate to the value of 
r, becaufe, as the quantity fubftituted for x in the com- 
pound quantity x z -qx is only a part of an infinite feries 
1 that 
