176 



Therefore, in the n differences of the " powers, we have 

 Pf^^xQ^" X R ""^xS^ x&c. with the constant co-efficient 

 1.2.3 n f.(^-l).C?-2) .... (V"-F^) 



1^ x'T?'^ yJJ^' xScc. l.2.3..p-dx l.2.3...d-ex\.2.3..e-fx &c. 

 The several formulae laid down in the following Chapter 

 are deduced from Prop. 4. and the Lemma, in like manner as. 

 the general co-efficient now given, by means of the multi- 

 nomial theorem, which I have stated in the first Essa^', 

 wherein the uncial of powers were deduced from the dif- 

 ferences of powers of numbers, which, having a common 

 difference, are in an arithmetical progression. 



CHAP. 



