272' COMPUTATION QF S<^yA9BS AND CUBES, 



798853696 = 2826-40* 798910225 = 282651'^ 



Perhaps it may be obje6led to my ftatement, that the calcii, 

 later would be aware that 28264.. 2 =: 28263 .24-2 = 2826:2 

 .2 -j- 4, &c. or that he muft (oim difcover this law of conti- 

 nuation ; and therefore, that he would not proceed in every 

 iaftance to the adtual mulliphcation of tlie root by 2. Such 

 an objection, however, will avail nothing again ft my argu- 

 ment, for in tl)at cafe he will no longer work by the rule 

 given by H. G. in P. 150, Vol, VIII.; but if he proceeds to 

 find the difference by addition, he muft virtually purfue the 

 method which I recommend : the only difference will be, that 

 the pra^ice of calculation will have (uggefted to him an im-,, 

 provement which he might have originally derived from firft 

 principles. 



I ftiali not enter into the queftion, whether addition is, or 

 is not, a iimpler procefs than (ubtradion. The prefent quef- 

 tion may be decided Independently of it. For grantir^ that 

 there is no reafon to prefer one to the other, yet the two me^, 

 thods by which we lind the firft differences of the c\jbes, 

 might be; fairly put to iffue upon the number of figures ufed in 

 e.ach. To find them according to the mcfthod recommended 

 by H. G. in p. 150, Vol. VIII. we muft fubtra6t the whole 

 of one cube from the whole of the other ; whereas I find them 

 b,y theconftant addition of the fecond differences, which muft 

 neceffarily be much frnaller no^mbers. Thus to find the fitft 

 difference between the cubes of 26561 and 26560 : 



According to H. G, According to E. O. 



18738432796481 2116221121 



~ 1873^316416000 + 159360 



21163804S1 2116380481 



It is ftated, indeed, by H. G. that he avoids the continual 

 repetition of firft differences; By this we muft not underftahd 



that 



