[ 64 ] 



Let it be required to find the cubic root of 210, true to 

 twelve places of decimals. The neareft cube number to 210 

 is 216, the cube of 6. Therefore making the binomial 216 — 6, 

 and dividing by 216, the new binomial is i — "77 = 1 ^1 and the 



feries which yields any power of it, is i. ^' \ . ^ ' . 



I . 36 2.36 



3-36 4.36 



■I + I -1-5 



&c. Which reduced to numbers is 



I.. _._^_.__^._±L .jtiL._±2_._±i7. ._±5_, &c. 



3-36 3-36 9-36 9-6 15-36 9.36 21.36 6.36' 

 and the calculation ftands thus : 



1,000 000 000 000 000. ill term, 

 ifl term multiplied by —^ - — 9 259 259 259 259. 2d term. 



+1 



2d term multiplied by — -g 



+S 



5d term multiplied by — ^ - 



+1 



4th term multiplied by g— - - 

 5th term multiplied by ■ g - 

 6th term multiplied by '^{6" ~ 

 7th term multiplied by ^^ , - 

 8th term multiplied by ^ ,- - 



85 733 882 030. 3d term. 



- —I 323 053 735. 4th term. 



— 24 500 995. 5th term. 



- — 499 094. 6th terra. 



- — 10 782. 7th term. 



— 242. 8th term. 



- - - — 5. 9th term. 



Sum of the negative terms 0,009 346 341 206 142 



Sum of all the terms, added? f\ f^-Q fi » 



according to their figns 5 '"" ■'■^ ^ '"-^ ■> 



The fum of all the terms' 

 multiplied by 6 



5,943921 952 763 148 



Having 



