COMPUTATION OF SQUARES AND CUBES. J <J 



manner as for the fqiiare, and be equally careful that x -|- « Computation of 



. fquares and 



does not exceed the numbers in the table ; add « -f I . :r^ to cubes. 

 3ax^ ; multiply the fum of thefe two quantities by n— 1 ; to 

 the product add x-{-aY, and multiply this fum by n : this laft 

 produfl will exceed the cube required by n— I .a^. 



If, for example, it be required to find the cube of 53119, 

 or 2.26539+1. : Then « = 2, a = 1, x = 26559, and 2- -|-a = 

 26560, and the cube of 53 1 1 9 = 2 X 



The cube of 26560 



26560)3 _|. 3 .26559)3 -j-3.26559> - I : Therefore, by Mr. 



Councer's table, the cube of 26559 would be 18734200194879 



The fquare of 26559 - 705380481 



18734905575360 

 3 



56204716726080 

 18736316416000 



74941033142080 

 2 



149882066284160 



therefore the cube of 53119 IS - 149882066284159 



Laftly, let it be required to find the cube of 79601, or 



3.26533 4-2: here ti = 3, a = 2, x = 26533, r + a = 



26535 ; therefore, by what has been demonftrated, 7960?)^ 



:=3 X 26535]^ -{-2X 4.26533^^ -|- 6 . 265331 ?| -- 2.8. 



' 26533V = 18679234361437 



265331* = 704000089 

 3 



2112000267 



37358468722874 

 2112000267 



37360580723141 

 4 



149442322892564 

 26535V = 18683458680375 



Therefore the <;ube of 79601 Is 



168125781572939 

 3 



— — III m 



504377344718817 

 504377344718801 

 E. O. 



