Mtfcellanea Curiofa. 183 



<A JMethod of ILaifmg an infinite 

 Multinomial to any given € Po<wer 1 

 or Extradling any given Root of 

 the fame. 



By Mr. A. De Moivre." 



* r I ^IS about two Years fince, that confi- 

 JL dering Mr. Newton's Theorem for 

 Railing a Binomial to any given Power, or 

 Extracting any Root of the fame; I enquir'd, 

 whether what he had done for a Binomial, 

 could not be done for an infinite Multino- 

 mial. I foon found the thing was poffibley 

 and effected it, as you may fee in the follow- 

 ing Paper; I defign in a little time to fhew 

 the Ufes it may be applied to : In the mean 

 while, thofe that are already vers'd in the 

 Doctrine of Infinite Series, and have feen 

 what Applications Mr. Newton has made of 

 his Theorem, may of themfelves derive fe- 

 veral Ufes from this. 



I fuppofe that the Infinite Number Multi- 

 nomial is az, +■ bz.z. "\- czj -f dz* jr ?£% *&c. m 

 is the Index of the Power, to which this 

 Multinomial ought to be Rais'd, or if you 

 will, 'tis the Index of the Root which is to 

 be Extracted s I jay that this Power or Root 

 of the Multinomial, is fuch a Series as I 

 have expreft. 



N 4 For 



