PROPORl'lON. Ill 



Note 3. It* the first term and either the second or 

 third can be divided by any number, without a remainder, 

 let them be divided, and the quotients used instead of them. 



Direct and inverse proportion are properly only parts o£ 

 the same general rule, and are both included in the pre- 

 ceding. 



Two or more statings are sometimes necessary, which 

 may always be known from the nature of the question. 



The method of proof is by inverting the question. 



EXAMPLES. 



EXAMPLE. 5 



What quantity of shalloon, that is 3 quarters of a yard wide, 

 will line yt yards of cloth, that is it yard wide ? 



4)60 



15 j'ards, the answer. 



The reason of this rule may be explained from the principles of 

 compound multiplication and division, in the same manner as the 

 direct rule. For example : If 6 men can do a piece of work ia 

 10 days, in how many days will 12 men do it ? 



As 6 men j 10 days ; : 12 men : =: 5 </<:yx, the answer. 



And here the product of the first and second terms, that is, 6 

 times 10, or 60, is evidently the time in which one man would 

 perform the work ; therefore 12 men will do it in one twelfth part 

 of that time, or 5 days j and this reasoning is applicable to any 

 other instance whatever. 



