MATHEMATICS 25 



Points are made use of to denote proportion, thus 

 A : b : : c : d signifies that a bears the same proportion to 

 b as c does to d. 



There are certain evident truths or simple axioms 

 which the student must bear in mind, thus : 



1. If equal quantities be added to equal quantities, 

 the sums will be equal. 



2. If equal quantities be taken from equal quantities, 

 the remainders will be equal. 



3. If equal quantities be multiplied by the same, or 

 equal quantities, the products will be equal. 



4. If equal numbers be divided by the same, or equal 

 quantities, the quotients will be equal. 



5. If the same quantity be added to and subtracted 

 from another, the value of the latter will not be altered. 



6. If the same quantity be used both to multiply and 

 divide any quantity, the value of the latter will not be 

 altered. 



It may be useful here to observe that the signs + and 

 - , have in our day acquired an exceedingly wide significa- 

 tion. They are now used to denote all sorts and kinds of 

 opposition, not only with regard to quantity, but oppo- 

 site relations of all kinds time, space, velocity, or any 

 other property. So if + be applied to any operation t 

 direction, or quality then - will denote the inverse 

 operation, the opposite direction and the most opposed 

 quality. Thus if + refers to North, to increase, to 

 stability, &c., - will denote South, decrease, instability, 

 &c. 



A specially algebraic illustration may be derived from 

 the fact that since a means a times any unit, a 1 which is 

 a taken one time, signifies i multiplied by a, and since 

 the negative sign denotes the opposite operation a~ l 

 must denote i divided by a. 



