^ ^QDCrUTATIOM OP SftUARKS AND CUBES. 



Compuutlonof What li^s been faid may be exemplified by applying it to 

 cubMr ^^ continuation of Mr. Councer's fquares. For 



798684121 is the fquare of 28261, 

 798627600 is the fquare of 28260, 



56521 is their difference, therefore 56523 is 

 iht difference between the fquare of 28261 and the fquare of 

 28262. By the addition in every inftance of 2, we may find 

 the feries of differences ; and by the conftant addition of them, 

 we inay eafily find the fquares. Thus 



798684121 : 

 56523 



798740644 

 56525 



798797169 ZZ 2S263\' 

 56527 



798853696 ZZ 28264\* 

 56529 



798910225 IZ 282651* 



By a fimilar method the table of cubes might be continued 

 jby the addition of differences ; but^ in this cafe, the calcula- 

 tion will be ^ little more complicated : Becaufe, if the terms 

 of any arithmetical progreffion be raifed to the alh power, 

 there will be n orders of differences, and the laft will be the 

 only one of them which will be conflant. For the cube, 

 therefore, where 73 iz: 3, we Ihall have one order of differences 

 piore th^p for the fquare. 



As before, let the progreffion be x -|- 3o, x + 2^* x^a, x^ 



