cardan’s Rule to the fecond Cafe, (grc. 
97 
~ &c * or (if we P ut ttie capital letters a, b, 
c, d, E, F, g, H, &c. for the feveral numeral coefficients 
, &c. of the terms of the 
O 22 I 54 26 x 8 
> 7> U* 243 ? 7 29 ’ 7 5 ~ 6 t? I 3 7,78 
3 T/^t^ T rS 
4- 
r * S SS tS J IO.T 22i 
fenes 1 + 4 - 3 
■54* 
+ 
:6l3i 7 
3c gee 8ic 3 243c 4 729c 5 6561c 6 137,781c 
See. which 
is equal to the cube-root of the binomial quantity 1 +-). 
equal to V‘ i e x the infinite feries 2 a 
2C ss zJLs 4 2 G 1 
aLC° sN' 3 2P’ 
See ; in which feries all the terms after 
the firfl: term 2A, or 2, are marked with the fign -, 
or are to be fubtracted from the faid firft term. 
Art. 18. And, if X is lefs than q —, but greater than 
its half, or and e be put, as before, = -(•> and zz — 
q - it is ffiewn in Art. 31, 32, 33, 34, 35, of the 
faid paper, pages 927 — 936, that the root of the equa- 
tion x 3 - qx-r w 
ill be equal to s/ l e x the infinite feries 
2 + 
2ZZ 202T 
308a 
9CC 243c 4 6561c 0 59049c 8 * 4,782,969c 10 129,140,163c 1 
1 20,646,960^ _ or K / ig x t p e i n q n ite feries 2A+f^- 
8,135,830,269c 14 cc 
2GZ 6 2lz S 2 Lz*° 2Nz J * 2?z'* 2^ 2Tz’ S „ . • ,, • , 
-3- + -? T + -7S-— 7n“+-3T— -?5- + T* &C ’ ln Which 
J8702; 8 ^ 111,8262;’° 
2,358,5122^ 
4~ 
feries the capital letters a, c, e, g, i, l, n, p, r, t, See. 
denote the fame numeral coefficients i , j, ~ T , as±., See. 
as in the laft Article, and all the terms that involve the 
VOL. LXX. 
O 
odd 
