199 



CHAP. II. 



The practical Application of the foregoing general Rules. 



h OR an example of the method of finding divisors, let the 



proposed equation be 18:r-15T-12;i + 10T-108.r+90.r+42cr-35=0, 

 and let the roots be diminished by the terms of the natural 

 series; 



1 

 3|24310 I 13,34, 442,55,715,1870,1 13,3/?+^— 7,<Scc. 



2 1 665 I 7,19, 133, 5, 35, 95,| 7,2^3+^^— 7,&c. 



1 i -10 I 1, 10, 10, -1, -1, -10,1 1, l/3±l/^,&c. 



o| -35 I -5, 7, -35, 1, -5, +7,1 -5, +^^,&c. 



l| 110 1-11, 10, -110, -1, 31, -10,1-11, V^+y^Ac, 



21-1615 I • 



-3 I -43010 



-21-1615 1-17, 19,-323, 5, | 



Thus, to find a divisor of one dimension : 

 13 g 3x6—13 = 5 



7q 2x6—7 = 5 



1 g D=6 1x6— 1=5 p=~5 

 -5 g 0x6+ 5 = 5 



-11 -1x6+11=5 



The divisor is x—^ or which is the same thing, 6x — 5=0. 



To 



