2 INTRODUCTION. 



5. Definition. A negative quantity is of an oppo- 

 site nature to a positive one, with respect to addition or 

 subtraction ; the condition of its determination being such, 

 that it must be subtracted where a positive quantity would 

 be added, and the reverse. 



Scholium. A negative quantity is denoted by the sign of sub- 

 traction : thus if o -f hzza — c, hzz — c and ci= — h. A debt is a 

 negative kind of property, a loss a negative gain, and a gain a nega- 

 tive loss. 



6. Definition. A unit is a magnitude considered as 

 a whole complete within itself. , 



Scholium. When any quantities are enclosed in a parenthesis, 

 or have a line drawn over them, they are considered as one quantity 

 with respect to other symbols ; thus a — {h-\-c\ or a — b-\-c, implies 

 the excess of a above the sum of h and c. 



7. Definition. A whole number is a number com- 

 posed of units by continued addition. 



Thus one and one compose two, 2-|-lzz3, 34-1^^4, or 2+2zi4. 

 Such numbers are also called multiples of unity. 



8. Definition. A simple fraction is a number which 

 by continual addition composes a unit, and the number of 

 such fractions, contained in a unit, is denoted by the deno- 

 minator, or number below the line. 



Thus »-h»-}.^z=l. 



9. Definition. A number composed of such simple 

 fractions, by continual addition, may properly be termed a 

 multiple fraction ; the number of simple fractions compos- 

 ing it is denoted by the upper figure or numerator. 



In this sense f, §, |, are multiple fractions, and fzil, ^=§+^=1+3, 

 or 1^. 



10. Definition. Such quantities as are expressible 

 by the relations denoted by whole numbers, or fractions, 

 are called commensurable quantities. 



