th 



According to this arrangement, the " power of the above 

 Multinomial, will be thus expanded, viz. 



(x+Qss+'Rz-\-Sz+&:c.)^= 



m,cy 



■f --'2 ^J2 



1.2 J X I i X 1 



r 



1.2 

 ??— S "-S 



r r" 



+|.g^.g-2..rQy+^.(^l).(?-2)xQR2+&e. 

 las 1.2x1 



r" 



+^.;?-l.^-2.^-3.xQz+&c. 

 12 3 4 



De Moivre has given the Multinomial Theorem in the Phi- 

 losophical Transactions of 1697- His proof, however, from 

 the doctrine of combinations extended only to integral powers 

 which are produced by repeated multiplications; but Newton's 

 Theorem having now been demonstrated, and the Multino- 

 mial Theorem having from thence been derived, it will follow 

 that tlie latter Theorem is as general as the former, whether 



the 



