PROPORTION. 105 



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divided by the other extreme ; and that either mean is 

 equal to the product of the extremes divided by the other 

 mean. 



SIMPLE PROPORTION, or RULE OF 

 THREE. 



The Rule of Three is that, by which a number is found, 

 having to a given numbdr the same ratio, which is between 

 two other given numbers. For this reason it is sometimes 

 named the Rule of Proportion, 



It is called the Rule of Three, because in each of its 

 questions there are given three tiumhers at least. And be- 

 cause of its excellent and extensive use, it is often named 

 the Golden Rule, 



RULE.* 



I. Write down the number, which is of the same kind 

 -vtrith the answer of number required. 



2. Consider 



* Demonstration. The following observations, taken col- 

 lectively, form a demonstration of the rule, and of the reductions 

 mentioned in the notes subsequent to it. 



I. There can be comparison or ratio between two numbers, only 

 when they are considered either abstractly, or as applied to things of 

 the same kind, so that one can, in a proper sense, be contained in the 

 other. Thus there can be no comparison between 2 men and 4 

 days ; but there may be between 2 and 4, and between 2 days 

 and 4 days, or 2 men and 4 men. Therefore, the 2 of the 3 

 given nupibers, that are of the same kind, that is, the first and 

 third, when they are stated according to the rul«, are to be com- 

 pared together, and their ratio is equal to that, required between 

 the remaining or second number and the fourth or answer. 



2. Though 

 O 



