349 



Mr. P. Nicholson on derivative Analysis. 



which the coefficients of the quotient may be derived from 

 each other. 



Examples. 



Ex. 1. Divide the quantities A by r—a'=s—i'=^—c'= 

 71 — d &c. 



Operatio7u 



Divisors, 

 r— a'=s — 6'=/— c'=?^— £i'=&c. 

 Quotient 



A. 

 A- 



o'A 



rst 

 &C. 



From the operation herewith executed we have the follow- 

 ing derivative equations, viz. 



B. = a'A 



C,=i'B. 



D,=c'C, 



&c. 



Ex. 2. Divide B H h — + — r +&c. (which is the quo- 



r rs rst ^ 1 



tient of the preceding example increased by the quantity B) 



by r— a" =s—b"=t—c" —u—d" &ic. 



B + -+ ?i-+-' +&C. 



' r rs rst 



B 



a"B 



•—a" = s—b"=zt-c"=u—d"=8i,c. 



&c. 



From 



