24 ELEMENTS OF SCIENCE 



as one whole, or collectively. Thus, instead of writing 

 axx + bxx* + cxx, we may write (a + b + c)x, the x being 

 placed outside the bracket. This means that the whole 

 of the quantity contained within the bracket is to be 

 multiplied by x. We may express the same thing thus : 



cx x. 



The sign .-. means therefore, and the sign v means 

 because. 



Numbers as well as letters may be used in algebra. 

 Thus, 2a + 46 - 30 would represent 18, if a 2, b = 8, and 

 c = 6, for twice 2 are 4, and four times 8 are 32, and 

 those two numbers added make 36, while if three times 

 6, which is 18, be taken away (as the minus sign 

 indicates) there remains 18. 



Such numbers or letters prefixed to symbols of quan- 

 tities, are called " coefficients." 



Fractions are written as in arithmetic : e.g., the 



number a of any denomination, b is written r- 



If the denominator be a power of any quantity as 

 ~i> or -g> or ~v then such a quantity may be expressed 



in algebra by what is called a " negative power " of such 

 quantity, that is by a corresponding index* with the 

 negative sign before it. 



Thus, -j may bet written a' 1 . 



~ 

 " a" 



(n, of course, standing for any number.) 



* See ante, p. 15. t See bottom of p. 25. 



