cardan’s Rule to the fecond Cafe , 6s fc. 87 
lefs than but greater than A, and e be put = — , and 
27 ^ 54 x 2 7 
£3 be put = ~ t -* ie root t ^ ie equation x 3 -qx-r 
2 Qz q 
will be equal to s/ 3 e x the infinite feries 2 + — _ 
- 1 9 ee 243^ 
3082; 6 
b$6ie 6 
&CC, 
Art. 4. The numeral coefficients — , — pf 8cc» 
r 9 7 243 7 6561 7 
0 f f? f Z 1 Sic. in this feries are exactly double of 
ee 7 7 e ' 
A AL Ail &c. which are the numeral coefficients of 
q 7 24.V 6;6i 7 
ee ' er ' e 
10 154 
9 ' 2 AS > 
the fame powers of the fraction A in the feries 1 + - — 
1 e 3 ^ 
^ 81* 3 
IO!?A 2 225 
+ 
54 * 
•618; 
, 4 . s , 6 . o t See- which is equal 
gee sir 243 ^ 729^ bc,bie° 137,78 * 
to the cube-root of the binomial quantity 1 +-; or, if 
the numeral coefficients of the faid latter feries be denoted 
by the capital letters a, b, c, d, e,f, g, h, Sec. refpeltively, 
fo that a fli all be .= 1, b = c = i, d = p, e = a? t , f 
g = f'f, and h = t | Ti ’ t¥T , and fo on, the faid numeral co- 
efficients will be equal to 2 c, 2E, 2 g, &c. 
and the feries mentioned in the laft Article will be 2 A + 
zQzz 
ee 
2E* 4 2G2; 6 
- 8cc. and confequently the root of the 
equation x 3 -qx=r, in the fecond cafe of it, in 'which 
A is lefs than A, will be equal to the expreffion P 3 e x 
the feries 2A + - &c. 
ee t* e 
Art. 5. Now the feries 2 a + + PpL _ See. 
u ee e* e 
IS 
