cardan’s Rule to the fecond Cafe , &c. 93 
it is = whereas 9 — is equal only to which is lefs 
than Therefore the propofed equation • % a* — j may 
be refolved by means of the faid expreflion. 
Art. 10. Now, fince in this cafe q is = 1, and r is 
= 4, we ill all have — , or e, - 4, and = 
3 7 2 * 7 2 7 A v 2 7 3 6 
I 
i©8 1 0 8 
I or) 
36x3 
; that is, zz will be = 
confequently z will be = 
6 6^3^ 6^/3 6^/3 6x3 6x3 
36x3’ 
yd—. Therefore e+z will be = 
6 V3 
v' 3 _ 3+ ^3 3 + ^3 _ 3+ 1 -73^>°5°>8 _ 
6X3 l8. l8 
- - 7 ■- ’° 5 - - ) = .262,891,71; and e-z will be = | - ~~ 
(==ft = ^■°»°- , =^p.>.070,44i,62. There- 
fore the cube-root of e + z is = v 7 ^. 262, 891, 7 1 =• 
.640,607,91 ; and the cube-root of e-z is = 
a/ 3 ]. 070, 441, 62 = .412,993,40; and confequently 
V 3 \e + z + v / 3 | e — z is = .640,607,91 + .412,993,40 = 
1.053, 601, 31- 
Art. 11. It remains that we compute the infinite- 
feries — +^+^+^+-^ 4 r + See. and extract the cube- 
root of <?, and then multiply the faid feries into 4 times 
the faid cube-root. 
Now the cube-root of e is in this cafe = y/ 3 f[ = -d-= 
—f — ; and confequently 4s/ 3 [e is = ~ — . 
1,817,121 7 'X J -T \ 1.817,121 
And. 
