Add 



Sum Sa 



26a X — loy 



5- 



As to the third case, where the quantities are unlike, it is 

 plain, that such quantities cannot be united Into one, or otherwise 

 added than by means of their signs. Thus, for example, If a be 

 supposed to represent a crown, and b a shilling ; then the sum of 

 a and b can be neither 2a nor 2b, that Is, neither 2 crowns nor 2 

 shillings, but only i crown plus 1 shilling, that Is, a-{'L 



In this rule, the word addition is not very properly used, being 

 much too scanty to express the operation here performed. The 

 business of this operation is to incorporate into one mass, or alge- 

 braic expression, different algebraic quantities, as far as an actual 

 incorporation or union is possible ; and to retain the algebraic 

 marks for doing it in cases, where an union is not possible. 

 When we have several quantities, some affirmative and others neg- 

 ative, and the relation of these quantities can be discovered, in 

 whole or in part ; such incorporation of tv/o or more quantities 

 into one is plainly effected by the foregoing rules. 



It may seem a paradox, that what is called addition in algebra 

 should sometimes mean addition, and sometimes subtraction. But 

 the paradox wholly arises from the scantiness of the name, given 

 to the algebraic process, or from employing an old term In a new 

 and more enlarged sense. Instead of addition, call it incorpora-^ 

 Hon, union, or striking a balance, and the parado^f vanishes. 



