Mr. P. Nicholson on derivative Analysis. 251 



Ex. 5. Divide the quantity A by the binomial v — e. 



Divisor. 



A- 



he 



V — e 

 Quotient 

 A B. , C, , D, 



&c. 

 By this operation we have the following derivative equa- 

 tions, viz. 



B, = ^A 



C. = .B. 

 . D.= ^C, 



&c. 

 Hence it appears that any quotient figure is equal to the 

 product of the next preceding quotient figure by the second 

 part of the divisor. 



Ex. 6. 



A B C D 



Divide the series B + - — I ^+ — H '- + &c. 



V V- t)3 d' 



(which is the quotient in the preceding example increased by 

 the quantity B) by the binomial v—e (which is the same divi- 

 sor as in the preceding example. 



Divisor. 



V—e 



Quotient 

 1 + ^+^ 



+ &C. 



D, 



li2 



By 



