150 Pf SQUARES AND CUBES. 



II. 



^l/y Mdhods of completing the Tables of Squares and Cubes, In 

 a Letter from H. G. 



To Mr. NICHOLSON. 

 SIR, 



Computation of 1N the laft number of your Journal, Mr. Councer's extenfive 



f^uaies: ^^\^\q of fquares is ftated to be deficient from No. 28261 to 



29061. This deficiency may very eafily be filled up by this 



rule. To the fquare of any given root add twice that root 



-f- 1 ; the produ6l will be the fquare of the next root. 



Of cobes; The table of one half the cubes in Mr. Councer's table, may 



half the fenes ; eafily be made, examined, and added to, by the following 



rule : Multiply the cube of any given root by 8 ; the produfl 



will be the cube of twice the next root. 



the other half. T^^ other half of the cubes in the fame table, and alfo all 



thofe already found as above, may eafily be found from any 



two cubes and their roots in fuccefl!ion being given. Thus : 



From the given cube of the largefi of the given roots, fubtraft 



the given cube of the nest lefs given root; to the remainder 



add fix times the largefl: given root, and alfo the given cube of 



the largefi given root ; the fum will be the cube required; as 



will appear from the following example : 



Roots. Cubes. 



p. f 9999zzA=: 999700029999 7 Required the cube 



I Dz=10000=Bzz 1000000000000 3 of the root 10001. 



B — AziCzz 299970001 Remainder. 



6D=: 60000 P'^^'"^^'"'^^^'fg^^ 



( given root. 



J5+C+6 D=l0OO3O00300O,= ] ^t^ltof. "' 



I am. Sir, 



Your moft humble fervani, 

 Eajl SmitJifield. H. G, 



Frolic 



