116 THE REALITIES OF MODERN SCIENCE 



3X4 = 12. The general rule for finding the area 

 would be as follows : Measure the length and the 

 breadth in the same units (e.g. both in inches) and 

 multiply the number of units expressing the length 

 by the number expressing the breadth; the product 

 will be the number of times the square unit of area 

 is contained in the rectangle. 



Such a familar rule may be more concisely stated in 

 symbols as follows: If L, J5, and A express the length, 

 breadth, and area of any rectangle then 



A=LB (1) 



This equation states the relation of the three magni- 

 tudes L, B, and A. Divide both sides of this equality 

 by B and we obtain 



L = j (2) 



This new form of the relation indicates what of course 

 we have known since our early study of arithmetic, 

 namely, that the length of a rectangle is to be found by 

 dividing its area by its breadth. Similarly dividing 

 both sides of the equality (1) by L gives 



B = y (3) 



LI 



which states a similar relation for the breadth of a 

 rectangle. 



Equations (1), (2), and (3) are obviously all the forms 

 in which the relationship of the sides and area of a 

 rectangle may be explicitly expressed. 1 We need to 



T 7? 



1 The relation = 1 is the general but implicit expression of 



A. 



the relationships of equations (1), (2), and (3). 



