PROPORTION. icy 



and the other on the left for the first number or term ; 

 but if less, write the less of the two remaining numbers 

 in the third place, and the other in the first. 



3. Multiply 



the quotient, of the remainder after division, and of the product 

 of the second and third terms, when it cannot be divided by the 

 first, is obvious. 



6. If the second and third numbers be multiplied together, and 

 the product be divided by the first ; it is evident, that the answer 

 remains the same, whether the number compared with the first be 

 in the second or third place. 



Thus is the proposed demonstration completed. 



There are four other methods of operation beside the general 

 one given ^bove, any of which, when applicable, performs the 

 work much more concisely. They are these : 



1. Divide the second term by the first, multiply the quotient 

 by the third, and the product will be the answer. 



2. Divide the third term by the first, multiply the quotient by 

 the second, and the product will be the answer. 



3. Divide the first term by the second, divide the third by the 

 quotient, and the last quotient will be the answer. 



4. Divide the first term by the third, divide the second by the 

 quotient, and the last quotient will be the answer. 



The general rule above given is equivalent to those, which are 

 usually given in the direct and inverse rules of three, and which 

 are here subjoined. 



The Rule of Three direct teacheth, by having three num- 

 bers given, to find a fourth, that shall have the same proportion to 

 the third, as the second has to the first. 



RULE. 



I. State the question ; that is, place the numbers so, that the 

 fkst and third may be the terms of supposition and demand, and 

 the second of the same kind with the answer required. 



2. Bring 



