CUBIC AND HIGHER EQUATIONS. 373 



Again, suppose 4*^64, and 4*265, and work as follows : 



I St supposition. 2d supposition, 



4*264 ►V 4*265 



18*181696 .V* . 18*190225 



77-526752 ^^ 77-581310 



99*972448 sums 100*036535 



— -o'o275<;2 errors -1-0*036535 



The sum of which is '064087. 

 THen, as '064087 : 'ooi : : 4*264 ; 0*0004299 

 To this adding 4*264 



We have ^ very nearly ==4*2644299 



' 'I 



2. To find the root of the equation ;tf^— i5A;*-j-63;tfi:: 

 '50, or the value of x in it. 



Here it soon appears, that 9C is very little above i. 



Suppose, therefore, 1*0 and i*i, and work as follows : 



1*0 X VI 



63*0 6ja; 69*3 



tp^i5 • — 15A;* 18*15 



I a;' i'33i 



49 sums 52*481 



'—I errors ■4-2*481 



3*481 sum of the errors. 

 A$ 3*481 : 'I ; : i : '029 correct. 



1*00 



Hence x==. 1*029 nearly. 



