26 ELEMENTS OF SCIENCE 



Owing to the extremely wide significance these 

 symbols have acquired, it is now also very common to 

 use for either + and - the term " sense " instead of 

 11 signs" i.e., " positive sense " for + , and " negative 

 sense " for - . 



Algebraic addition is partially like, yet in some 

 respects different from, arithmetical addition. 



If similar quantities have different signs, then their 

 difference must be taken into account when they are 

 added together. 



Thus, if to a + b 



a b be added, 



the result is 2 a 



because the + b and the b neutralise each other, while 

 each a remains. 



Similarly, if there are co-efficients, their differences 

 must be taken into account. Thus, by adding together 



3 2 + 460 - e 2 + 10 

 - 5 2 + 6bc + 2e 2 - 15 

 & 2 + 6bc - ioe 2 + 21 



we obtain - 6a 2 + 1 6bc - ge 2 + 1 6 as the result. 



Though convenient, it is not necessary, to write the 

 same letters over each other, but similar quantities 

 must be collected together in stating the result, 

 thus : 



ax* + cz + by* 

 2bx* + cy z + az 



- z + x z + ?/ 2 



ax + 2c + x + + c + + cz + az - z 



This may be written more shortly and conveniently by 



