C 6^9 ) 
(wim fomewhat deep in the Water,fometimes are catch'd, 
though not often. The Seamen have reached them with 
a Fifgig, a kind of barbed Iron, at the end of a Pole tyed 
faft toaRope, and have made good chear with. them. 
But this is only my Conjecfture, with which I end my 
Journal. B€o Servatori Laus, 
III. A Method of Kaifing an injinite Muhinomtal 
to any gi'ven fovper^ or Extraciing any given 
Root of the fame. By Mr. Ab. De Moivre. 
'^T^IS about two Years fince , that confidering 
1 Mr. Newton s Theorem for Raifing a Binomi- 
al to any given Power, or Extraciing any Root of the 
fame • I enquired^ whether what he had done for a 
Binomial, could not be done for an infinite Multino- 
mial. I foon found the thing was poflible, and efFedted 
it, as you may fee in the following Paper ; I defiga 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 
Dodtfine of Infinite Series, and have feen what Appli» 
cations Mr. Newton has made of his Theorem, may of 
themfelves derive ieveral Ufes from this. 
I fuppofe chat the Infinite Number Multinomial is 
tfz+^zz+^'^'-'Wz^-fz^ &c. m is the Index of the Pow- 
er, to which this Multinomial ought to be Rais'd, or if 
you will , 'tis the Index of the Root which is to be Ex» 
traded : I fay that this Power or Root of the Multi- 
nomial, is fuch a Series as I have expreft. 
For the Underftanding of it, it is only neceflary to 
confider all the Terms by which the fame Power of z. 
is Multiplied j in order there: o I dift ngu fh two things 
in each of thefe Terms ; i° The ProJud of certain 
Powers 
i 
