cardan’s Rule to the fecond Cafe , &lc. 
+ &c. are - + '^+ u , + , 
e '° e + e gee 6 $ 6 ie 4,782,969^° 8,135,830,269^ 
or, in decimal fractions, .111,111,111, 8ec. x — + 
ee 
•023,472,031, See. x ~ + .011,690,017, See. x + 
.007,414,542, See. x p-. Therefore the root of the 
cubick equation x z -qx~r, in the fecond cafe of it (in 
which ~ is lefs than ^), is equal to \/ } je+z +v / 3 U-«|+ 
^e x the feries ~ + ^ + Jmf -+ /°’^’ 48o f , 4 + Sec. 
* gee 6$6ie° 4,y82,g6ge l ° 8,135,830,269# 4 
ad infinitum , or \/ 3 ^ + «| + + 4%/ % x the feries 
*111,111,111, 8ec. x ^ + .023,472,031, Sec. x 7 + 
z 10 z 1 * 
.011,690,017, Sec. x jrs + *007,414,542, 8ec. x + 
Sec. ad infinitum . 
O/ the heft Manner of Proceeding to the Computation of 
more Perms of the f aid Series , if required. 
Art. 8. If more than four terms of this lafl feries 
are required, it will be neceflary to compute the feries 
_ . a aa ez 3 jo z* 22 % 3 1 
1+ + > 
^5+ Sec. (which is^\/ } 1 +— )) 
y gee ' 8 ie 3 2$y* ‘ -jige 3 6561c 6 ' ' c (/> 
to more than fifteen terms ; in order to which it will be 
convenient to exprefs the terms of that feries in thfe 
following manner, to wit, i+|x— -|x B — + |x 
Cz 3 8 
A Z 
3-7-6* 7 + t*7 
P_* 4 -i- *_»_ y EgS li y Fz6 t 12 •• G%1 - Ig. x j 11 v *** - 2 6 O KgI ° -f 
N a 
1 2 
if* 
.it 
