COMPUTATION OF SQUARES AND CUB&S. 



18736316416000 ZZ 265 60V Computation of 



2I163804S1 1ft Diff. Tubes/ '"'^ 



18738432796481 ZZ 263 6 iV 

 2116539847 1ft D. 



18740549336328 zr 26562V 

 2116699219 ift D. 



18742666035547 ZZ 26563\» 

 2116858597 ift D. 



18744782894144 ZZ 2656?)^ 

 2117017981 Ift D. 



18746899912125 ZZ 2656515 



The methods here ftated are, probably, the eafieft which 

 can be devifed for conftruding an extenfive table : but it muft 

 frequently happen, that the calculator will want the fquare or 

 cube of fome number which is greater than any which is con- 

 tained in the table. It may be ufeful, therefore, to confider 

 the affiftance which the table may afford him in facilitating the 

 computation. 



It is well known, that x^ x 3/" zzl]?]'". * Therefore, if we 

 want to find the fquare of a number which is e double of any 

 contained in the table, we have only to multiply the given 

 fquare by 4. In the fame manner, if we want to find the 

 fquare of a number which is exactly three or four times asi great 

 as any contained in the table, we may find it by multiplying 

 the given fquare by 9 or 16. Thus, for example, 



16522531600 ZZ the fquare of 128540; 



66090126400 ZZ the fquare of 257080; 



16522274521 rz the fquare of 128539 ; 

 9 



148700470689 ZZ the fquare of 385617. 



* I do not know whether it is worth while to mention the cii> 

 cumftance, but your correfpondent H. G. has made a mlftake in 

 the application of this rule. For he fays that, if we " multiply 

 the cube of any given root by 8, the produft will be the cube of 

 twice the next root :^^ whereas the produ^ will be the cube of twice 

 the giveiv root. 



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