22 ELEMENTS OF SCIENCE 



Various symbols are used to denote, not quantities, 

 but certain relations between them. Thus the symbol 

 = shows and indicates " equal to." Other symbols are 

 useful as follows : 



+ (plus, or added to) - (minus, or taken from) 



x (multiplied by) 4- (divided by) 



Thus 6 + 3 = 9. 9-4 = 5- 3x2 = 6. 10-4-5 = 2. 



These signs are of special use in algebra, as we shall 

 shortly see. 



This explanation of the fundamental conceptions and 

 simplest practices of the arithmetical part of mathe- 

 matics will suffice for our purpose, which is but to show 

 (i) what are the truths at once the simplest and the 

 most universal, because applicable to all objects which 

 can be enumerated, and (2) to make if clear that by 

 working with such symbols we can arrive at definite 

 results which correspond (with perfect exactness and 

 certainty) to real relations existing between objects of 

 all kinds. 



For information respecting the manifold, complex, and 

 most ingenious processes and devices whereby the labour 

 of counting and calculating is lightened, the reader is 

 referred to explicit treatises on the rules and practice 

 of arithmetic. 



Arithmetic concerns itself with definite numbers, 

 whole or fractional, and each symbol it employs denotes 

 some quantity or other. But, since the Middle Ages, a 

 much wider and more searching branch of mathematics 

 has been widely cultivated namely, Algebra. 



Each arithmetical operation applies only to certain 

 numbers, but each algebraic operation is, at one and the 

 same time, good for all numbers, whole or fractional 



