POMFUTATION OF SQUARES AND CUBES, 171 



VII. 



Concluding JRemarks on the Computation of Tables of Square* 

 and Cubes. In a Letter from E. O. 



To Mr. NICHOI^SON. 

 SIR, 



1 AM ferry to trouble you again on a fubjeft which I fear On the compu. 

 can afford but little intereft to the generality of your readers; ^^^ cubes, 

 but I niuft requeft the admiffion of a few remarks upon 

 the letter which you publiftied in your laft number from 

 p. G. 



Your correfponderit is certainly miftaken when he aflerts 

 that our methods of calculating fquares are ** precifely the 

 fame :" Both, indeed, are derived from the principles of the 

 binomial theorem ; but I conceive that there is a material 

 difference in our manners of applying thofe principles to prac- 

 tice. As we find the fquare of the given number by adding a 

 certain quantity to the known fquare of the number next be- 

 low it, it follows, that in both methods the quantity fo added 

 muft be the fame ; but there is a confiderable difference in the 

 operations by which we find this number : I do it by the re- 

 peated addition of the fmall number 2, whereas H. G. finds 

 the fame quantity by the repeated doubling of a number, 

 which is conftantly changing, and may poffibly confift of many 

 figures. To fhew the difference more clearly, I will calculate 

 feveral fquares according to the direftion given in P. 150, 

 Vol. VIII. and I will take for my example the fame which I 

 Jiave taken in P. 6, Vol. IX. that your readers may the more 

 eafily form the comparifon for thenafelves. 



