ALGEBRA. 



ADDITION. 



Addition, in Algebra, is connecting the quantities to- 

 gether by their proper signs^ and uniting in simple term« 

 such as are similar. 



In addition there are three cases. 



CASE I. 



TVhen like quaiitliics have like signs. 



R U L E.* 



Add the coefficients together, to their sum join the 

 common letters, and prefix the common sign when nece^;-- 

 sary. 



EXAMPLES. 



* The reasons, on which these operations are founded, will 

 readily appear fi-om a little reflection on the nature of the quanti- 

 ties to be added, or collected together. For with regard to the 

 first example, where the quantities are 3^ and 5^, whatever a 

 represents in one terra, it will represent the same thing in the 

 other ; so that 3 times any tiling, and 5 times the same thing, col- 

 lected together, must needs make 8 times thartfiing. As, if a 

 denote a shilling, then ^a is 3 shillings, and $a is 5 shillings, 

 and their sum is 8 shillings. In like manner — zab and — 7^^, 

 or — 2 times any thing and — 7 times the same thing, make — 9 

 times that thing. 



As to the second case, in which the quantities are like, but the 

 signs unlike ; the reason of its operation will easily appear by re- 

 flecting, that addition means only the uniting of quantities togeth- 

 er by means of the arithmetical operations denoted by their signs 

 j^ and — , or of addition and subtraction ; which being of con- 

 trary or opposite natures, one coefficient must be subtracted from 

 the other, to obtain the incorporated or iinitcd mass. 



As 



