1 ; J INTROl* 8 



ere w - J66., approximately y, the ratio of the 



inference of a circle t<> it> <liaineter; and 



-2.71828182... -1 + J + 



approximately y, the base of the Naperian system of loga- 



rithi: 



. arbitrary constant is a number which retains the same 

 valu- liout li. <*f a given problem, but 



may have a diflVn-nt ii\ in another problem* 



i independent variable is a numbi -r that may take any 

 value whatever witliin limits prescribed by the conditions of 

 the problem under consi.i 



A dependent variable is a number that depends for its 

 value upon the values assumed by one or more independent 

 



A number that is greater than any assignable number, 

 however great, is an infinite number; one that varies and 

 becomes and remains smaller (numerica merely alge- 



braical 1 assigned number, however small, is 



an infinitesimal number. All other numbers are finite. 



3. Functions. A number so related to one or more other 

 numbers that it depends upon these for its value, and takes 

 in general a definite value, or a finite number of definite 

 i us, when each of these other numbers takes a definite 

 value, is a function of these other numbers. E.g.* the cir- 

 cumference and the area of a circle are functions of its radius; 

 distance traveled by a railway train is a function of its 

 and rate; ifyseSx^ + Sa 8, then y is a function of *. 



All thee kind* of nornbem will be mrt and better illustrated in 

 ing chapters of thtobook. .9, aw Art. 66, Note. 



