[ 6o ] 



Thus : — Let it be required to find the cubic root of 28, true 

 to ten places of decimals. Firfl; make 28=27 + 1, and then divi- 

 ding by 27, a new binomial i H — is had, whofe cubic root is to 



be refolved into an infinite feries. Now any power of it what- 

 ever may be found by the following feries, 



'A . !?!zl . ^=1, &c. 



1.27 2.27 3.27 4.27 5.27 6.27 



where m is the index of the power. In the prefent cafe m=2., and 

 then the above feries reduced into numbers will ftand thus: 



+ 1 



—5 . JUL . -zlL . ^rl . —\^ , &c. 



3.27 3.27 9-27 3-27 15.27 9-27 21.27 



And it is plain that of the terms of the infinite feries, the firft 

 and fecond will be afiirmative, the third negative, and the fol- 

 lowing ones alternately afiirmative and negative : and the work 

 of calculating the terms will ftand thus : 



+1,000 000 ift term. 



This multiplied by -i^, gives +0,012 345 679 0123. 2d term. 

 Which multiplied by -I^, gives — ,0001524157902. 3dterm. 

 And 3d term multiplied by JZL, gives - +3 136 1273. 4th term. 



And 4th term multiplied by Zli, gives 77 4352. 5th term. 



5th term multiplied by IZlI, gives - - +2 1031. 6th term. 

 15.27 



6th term multiplied by Zll, gives - - - — 605. 7th term. 

 And 7th term multiplied by ^Ili^, gives - - - +18. 8th term. 



Having 



