Second Cafe of the Cubick "Equation x'-qx-r. 941 
I* 1 3733 > that is, the root of the propofed equation 
x 3 -x=j is 1.137,33; which is true to four places of fi, 
gures, the error being in the fifth place of figures, or 
the fourth place of decimal fractions, where the figure 
ought to be an unit inftead of a 3, the more accurate 
value of x being 1.137,158,164, which differs from 
the value of it here found by lefs than .00017, or 
— — — -parts of an unit, .which is lefs than the 668q tIv 
IQOjOOOP x 
part of 1.137,1 58,164, or the true value of x\ 
EXAMPLE in* 
43. Let it be required to find the root of the equation 
x ' " n 
x 3 - 5^ = 4. 
Here 7 is = 5; ris=4; -f, or<?, is = 2; C, or ee, is 
= 4; 7 3 is = i25, and q — is — l -hi — 4.629,629,629, 8cc. 
which is greater than 4, or Therefore this equation 
cannot be refolvedby cardan’s rule, but may by the 
infinite feries e'x [2 +— - — 4 + - See. in cafe that 
I gee 2436* 05016'. 
feries is a converging one. 
Now, fince — is 4.629,629,629, 8tc. and -is ■■= 4, 
2 7 4 
we fixall have .p - p or ss, = ,629,629,629, See. which 
‘ is- 
