141 



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 ecpial. Therefore after the 

 subduction, the three first terms will be exterminated, and 

 the next member is of three dmiensions. . ., 



EXAMPLES.rj-- 



Given power IS 1 + ^^ = 1 +w«r + Cat-!- Da; 4-(Xc. 

 Subduct 1 



* mx + Sec. 

 r)mx{^x 



Given power is \-\-mx ■\-Cx + J}x + &c. 



Subduct l + '^x=\-^mx + cx + 8cc. 



* * j-c« + &c. 

 r)rcx{cx 



Given power is l-{-mx + Cx + Dx+8cc. 



:'• 



Subduct {\+'^x)+cxzzl+mx+{c+rc)x+dx+8cc. 



* * * rdx+Scc. 



s s 



ryrdx(^dx 

 u 2 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. 



