942 Extenfion of Cardan’s Rule to the 
is lefs than 4, or e'e, in the proportion of about 6 to 
40, which is a pretty large proportion of minority, and 
much larger than the proportion of ss to ee in either 
of the former examples. Confequently the feries e* x 
20 s 
208 
2 -J- 
gee 243^ 6 $ 6ie 6 
8cc. will converge with a greater 
degree of fwiftnefs than in either of thofe examples. 
Therefore the equation ar 3 — 5 x=r may be refolved by it 
as follows. 
44. Here ^ is = — — .157,407 ; and confe- 
quently s - is = .024,777, and - 6 is = .003,900. There- 
fore £ is = - -ilMii = .034,979, and ^ is = 
gee 
20 X ,024,777 
243 
J.20I,200__ 
9 9 
495,540 ,1 
2 43 
= 002,039, an d 6^677 is ~ 
243^ 
308 x .003,900^ 
656; 
, . -.000,182, and confequently 2+— - 22 L. + 
0301 1 ^ J gee 243^ 6 5 6 1 e 
is = 2 + .034,979 -.oo2,039 + .ooo,i82 = 2.o35,i6i- 
.002,039= 2. 033,, 122. And or V l e, is = v/ 3 2 = 
1.259,921. Therefore ^ x the feries 2+ — - 
20s 
308^ 
20 J 4 
9^ 243^ 
3085 
6^617 “ &c '. iS = 1-259,921 x 2.033,122 = 2.561,573 ; 
that is, the root of the propofed equation x l - 5^=4 is 
2-561,573 ; which is true to five places of figures, the 
error being in the fixth place of figures, or the fifth 
place of decimal fractions, where the figure ought to 
