928 ExtenJIon of Cardan’s Rule to the 
dud of e | into the feries 2- — — - 3 ° 8 % - 8ec. ad 
1 <)ee 243 e 4 6561/ 
infmitum , is equal to the root x. Now there are two 
different ways of computing this feries, which (though 
not equally Ihort and convenient in practice) are never- 
thelefs equally juft and true: and therefore they muft 
both produce the fame refult for the value of the feries. 
The firft way of computing it is the common one, which 
confifts of the following procelfes; to wit, firft, to 
compute the quantities and q — , as was done in the 
foregoing example, art. 26, where ~ was found to be 
= 1, 1 10,916, and|^ to be 1000,000; 2dly, to fubtrad 
^ from ft-, in order to get the quantity ss, which is equal 
to their difference, and which in the foregoing example 
was 110,916; 3dly, to divide ss by ee, fo as to obtain 
the value of the fraction as in the foregoing example 
we found the fraction to be = .0998; 4thly, to 
compute the powers of the value found for the fradion 
ft; as in the foregoing example we computed thofe of 
.0998, and found its fquare to be .009,950, and its 
cube to be .000,992; 5thly, to multiply—, audits 
€€ 
powers - 4 > 4 > &c. into the co-efficients - > — , , 8cc. 
* * 9 2 43 656!’ 
refpedively, 
