of the Binomial Theorem, 
317 
same denominator with that term in the second column on the 
next lower horizontal line. For the first member, therefore, 
the second letter in the denominator must be raised to the 
next higher letter by substitution ; and for the second member 
the first letter in the denominator must be raised to the next 
higher by substitution. For each denominator, therefore, in 
the first column two equal values must be found accordingly, 
and the first value must be put under the first member, and 
the second value under the second member of the numeratprs. 
Hence the values for the denominators of the first line will be 
obtained in the following manner, from the equations in the 
beginning of this article. For the first term £v==-^xv — y== 
u^v, for a, = 1 ; for the second term a. e v = « x x v = 
therefore follows that 
MDCCXCV, 
Tt 
