126 ARITHMETIC, 



In these questions (here is always given an odd number 

 of ternivS, as five, seven, or nine, Sec. These are distin^ 

 guishcd into terms of jupposiihfi, and ten^s of dcmandy 

 the number of the former aKvays exceeding tji;it of the lat- 

 ter by one, which is of the same kind with the term of 

 answer sought. 



This rule is often r.awied the Douhle Rule of Three^ be- 

 cause its questioi?s are sometimes performed by two opera- 

 tipns of jthe rule of three. 



RULE* FOR STATING^ 



i» "Write the term of supposition, which is of th^ samt 

 kind with the answer, for the middle term. 



2. Take one of the other terms of supposition, and one 

 of the demanding terms of the same kind with it ; tktii 

 place one of them for a first term, and the other for a 

 third, according to the directions given in the rul-e • o* 

 three. Do the sanie with another term of supposition and 

 its correspondent demanding term ; and so on> if there be 

 more term$ of each kind ; writing the terms under eacl^ 

 other, which fall on the same side of the middle term. 



METHOD OF OFERATJQl/, 



I. By several operations.-rr-TTike the two upper terms and 

 the middle term, in the same order as they stand, for the. 

 first stating of the rule of three ; then take the fourth 

 number, resulting from the first stating, for the middle 

 term, and the two next terms in the general stating, in the 

 same order as they stand, for the extreme terms of the 



second 



* The reason of this rule for stating, and of the methods of 

 operation, may be easily shewn from the nature of simple propor- 

 tion ; for every line in this case is a particular stating in that rule. 

 And, therefore, with respect to the second method, it is evident^ 

 that, if all the separate dividends be collected into one dividend, 

 and all the divisor^ into one divisor, their quotient must be tha 

 answer sought. 



