m 



CHAP. I. 



Of the Law of the Indices of the Terms in the Binomial 



Theorem. 



If r is any affirmative whole Number, the following will 



be a General Rule for extracting the r Root of 1 + .r,'" or of 



]. + mx + Cx+ Dj + Ei' + &c. + Zx"". 

 th 

 Subduct the r power of the first member of the Root (which 



first member of the Root we know to be an unit) from the given 



ih 



power, divi^le the remainder by r times the r — ] power of 



the first member, the first term of the quotient is the second 



member of the Root. 



th 

 Subduct from the given power the r power of the Binomial 



found, conceived as the first member of the Root, and divide 



— th 

 the remainder by r times the r — 1 power of the Binomial 



found, the first term of the quotient is the third member of 

 the Root. 



ih 

 Subduct from the given power the r power of the Trino- 

 mial found, conceiving the Trinome found to be the first 

 '^ ' member 



