189. 



Besides, if it happens that several binomials or trinomials 

 are only apparently deducible by the method, we may find a 

 criterion for discovering those which shall not really succeed 

 in the division, if we try whether the quote, which should re- 

 sult from that division, is discoverable in the same manner as 

 the divisor. For this purpose it will be of use to discover a 

 general rule for a polynomial divisor, and the series of num- 

 bers which apparently gives us the divisor, will point out to 

 us the series of factors which should give us the quote ; from 

 whence, by the method of differences, or a numerical sub- 

 duction, we shall avoid the repeated operations of a trial by 

 algebraical division. 



These, and some other advantages, are the practical objects 

 of this Essay, for which the Reader is referred to the second 

 Chapter. In the first Chapter, the general theory of the rule 

 is laid down : it is deduced from the nature of an equation, 

 which is a different view of the subject from that which is 

 usually given by authors. 



c 2 CHAP. 



