g COMPUTATION' OF. SQUARES AND CUBES. 



Computation of and 26560, and, by what has been obferved above, the fecond 

 fquwsand difference of the three cubes will be* 6. 26560 ~ 159360; 

 which, added to the difference between the cubes of 26559 

 and 26560, will give the difference between the cubes of 

 26560 and 26561. So far we ftiould proceed exadtly in the 

 ileps which are traced out by your correfpondent H. G. ; but 

 I differ from him in this refpeft, that I Ihould by no means re- 

 commend this method for the folitary calculation of any parti- 

 cular cube; it is only mentioned here for the fake, of (hewing 

 how to afcertain the numbers by which we muft commence the 

 feries of differences, when we want to continue a table which 

 has already been calculated to a certain extent. For the third 

 diflference is conftantly 6 ; therefore if we take an arithmetical 

 progreffion, of which the terms differ from one another by that 

 number, and which begins with 159360 (fuch as 159360, 

 159366, 159372, S^c. ^^c), vve fhall afcertain the fecond dif- 

 ferences of the cubes which we want to find, Thefe fecond 

 differences mufl be added to the refpedive firft differences, 

 and, by that means, we fliall find a feries of numbers, which, 

 added to each particular cube, will give us the cubes of the 

 numbers next above it. Thus 



26560\3 IZ 18736316416000 

 26559\ « ZZ 18734200194879 



^KKT 



2116221121 ~*26560]3 - 2655913 

 159360 2d Difference. 



2116380481 ZZ 2656l)3 ~ 265 60]^ 

 159366 2d Difierence. 



2116539847 ZI 26562)3 

 159372 2d D. 



2116699219 — 26563\^ - 26562] ^ 

 159378 2d D. 



2116858597 ZZ 26564)3 - 26563)3 

 159384 2d D. 



2117017981 z: 26565)3 - 26564^3 



Having thus afcertained the firfl differences, we may plo* 

 ceed to add them to the cubes : 



♦ The dot (.) between the figures is here ufed as the iign of 

 multiplication. N. 



