MATHEMATICS 31 



Therefore here we see what is the square of the 

 quantity a + b or (a + b) 2 . 



Therefore also, the square root of the product, or, 



J<& + 2 a b + 6 a = a + b. 



Again, if a + b 



be multiplied by a b 



a 2 + ab 



- ab -b* 



The product equals a* b* 



since + ab and - ab neutralise each other. 

 If we multiply i - x + cc 2 - x 3 

 by i + x 



I X + X 2 X S 



+ x - x* + x s - x* 

 The result is i - x* 



The other quantities neutralise each other. 



In algebraical, as in arithmetical, division, the question 

 is to determine how many times one quantity, "the 

 divisor," may be contained in another, "the dividend," 

 which is equivalent to finding out what quantity multi- 

 plied by the divisor will produce the dividend. 



Thus to divide ab by a, is to determine how often a 

 must be taken to make up ab ; that is, what quantity 

 multiplied by a will give ab, and this we know to be b. 



The signs change as they do in multiplication, and for 

 the same reason. If the divisor and dividend have like 

 signs the quotient is + ; but - , if they have unlike 

 signs. 



Thus - ab divided by - a = b ; because - a (the 

 divisor) and + b (the quotient) if multiplied together 

 give - ab (the dividend). 



