392 



RESOLUTION OF 



This rule will be found virtually the same as that given by 

 Newton, Raphson, Jones, Simpson &c. and, if applied to the 

 extraction of simple powers, will be found the same precisely 

 as the one usually given in common arithmetic, thus for 



EXAMPLE I. 



Let x3= 



s'=400 - 



By the Rule, 



divisor 

 3x'* = 480000= A 

 ox' = 1200 = B 

 1 = 1 = C 



By the Rule, 



A = divisor 



480000 + 2400x"-f3x"* =634800. 

 B = 1200+3x = 1380. 



C = 1 = 1. 



99252847 

 64000000 



35252847 



28800000 



4320000 



216000 



33336000 

 01916847 



==x'3 



x' =400 



Resolvend. 

 New Equation x"=60 

 480000 xx" 

 + 1200xx"* 



+ix x"3=v— v: 



Subtrahend 

 Resolvend 



New equation x'"=3 

 1904400 = 634800xx'" 

 12420 = 1380 x x'" 2 

 27 = 1 X x'"3 



1916847 Subtrahend. 



Whence x=x'-f-x"-[-x'" = 463, the required Root. 



This form will serve for all numeral equations, and with 

 nearly the same labour; as for 



EXAMPLE II. 



