360 GEOMETRY. 



Of these* the first is called the antecedent, and 

 the second the consequent. 



The measure or quantity of a ratio is conceived 

 by considering what part pf the consequent is the 

 antecedent ; consequently it is obtained by dividing 

 the consequent by the antecedent. 



54. Three magnitudes or quantities, A,B,C, are 

 said to be proportional, when the ratio of the first to 

 the second is the same as that of the second to the 

 third. Thus, 2, 4, 8, are proportional, because 4 

 is contained in 8 as many times as 2 is in 4. 



55. Four quantities, A,B,G,D, are said to be pro- 

 portionalwhen the ratio of the first A to the second 

 B is the same as the ratio of the third C to the 

 fourth D. It is usually written A : B : : C : D, 

 or, if expressed in numbers, 2 : 4 : : 8 : 16. 



56. Of three proportional quantities, the middle 

 one is said to be a mean proportional between the 

 other two ; and the last a third proportional to the 

 first and second. 



57. Of four proportional quantities, the last is 

 said to be a fourth proportional to the other three, 

 taken in order. 



58. Ratio of equality is that which equal numbers 

 bear to each other. 



59. Inverse ratio is when the antecedent is made 

 the consequent, and the consequent the antecedent. 

 Thus if 1 : 2 : : 3 : 6 ; then inversely, 2:1 : : 6 : 3. 



60. Alternate proportion is when antecedent is 

 compared with antecedent, and consequent with 

 consequent. Thus if 2 : 1 : :- 6 : 3; then by alter- 

 nation, 2 : 6 : : 1 : 3. 



61. Proportion by composition is when the ante- 

 cedent and consequent, taken as one quantity, are 

 compared either with the consequent or with the 

 antecedent. Thus if 2 : 1 : : 6 : 3 ; then by com- 

 position 2 + 1:1:: 6+3 : o, and 2+1 : 2 : 6-f 3 : 6. 



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