195 ' 



is 1 or 2 ; in like manner the numerator of a co-efficient with 

 the sign changed, whose distance from the first is ?«, -vvili be 

 derived from the last differences of the remainders which are 

 deduced from the former remainders by subducting from them 

 the numerator of the co-efficient last found, with the sign 

 changed, multiplied into the powers of the correspondent 

 terms of tlie natural series, the index of which powers is 

 n — m — 1. 



//( 

 If 1.2.3...WX D is the n difference of the divisors of the ab- 

 solute term, or if D is otherwise sought among the numeral 

 divisors of the highest term of the proposed, and if the last 

 differences of the first, second, third, &c. remainders, be 

 viz. 1.2.3...n^ly—p, 1.2.3...M— 2 x — y, 1.2.3...n^x — r, 

 Sec. The polynomial divisor of n dimensions will be 

 X +£^x +Jjv +J_x +&c. or T>x +^x +^x ^rx 



+ &c.+abcflSi.c.=0 



Note. The quantities called remainders are the divisors- 

 subducted from the sum of their own members already dis- 

 covered. The numerator of the required co-efficient must be 

 made to stand in the highest place in those expressions whose 

 differences are to be taken, and this is effected as above by 

 taking away the higher powers which were connected with the 

 preceding co-efficients. 



VOL. XI. 2. D' A«< 



