141 



th 

 Root multiplied by r. Therefore the third term of the r 



power of the Trinomial and the third term of the given series 



th 

 have the same excess above the third term of the r power of 



the Binomial, and therefore are e(jual. Therefore after the 



subduction, the three first terms will be exterminated, and 



the next member is oi three dimensions. , 



EXAMPLES.^ 



- - --- - . . Oi iL:jj;^ 



Given power is I + x=\ + mx + Qx -{- ux + &c. 

 Subduct 1 



* mx + &c. 

 r)mx{^x 



Given power is \ + mx + Cx + T)x + &c. 



Subduct 1 + yX=i1 + mx + ex + Sec. 



* * rex + Sec. 

 r)rcx(cx 



Given power is !+»?«: + C« + D3:+&c. 



Sabduct (}+yx)+cx—l+mx-{-{c+rc)x+dx+Scc. 



* * * rdx+Scc. 



r)rdx{dx 

 u2 In 



t N. B. In this and in the subsequent Example, the small Roman letters, c, d, &c. 

 t, V, &c. which are used in the Subtrahends, are to be distinguished from the small Italics, 

 c, d, &c. t, V, &c. which are substituted in the Remainders. 



