COMPUTATION OF SQ.UARES AND CUBES, 1| 



w:e fuppofe it equal to nx-^a, we fliould make x a>; great as It Computation of 



poffibly can be, without being fo large, that when added cubes? ^" 



to the remainder a (as x-\-a), it fliould exceed the numbers 



of which the fquares are given in the table. Becaufe n and a 



are the only numbers by which we have to multiply, and as 



a muft be lefs than n, we fliall always have them as fmall as 



poITible, if we take x according to the dire6lions here given. 



If, for example, it be required to find the fquare of 385618, 



which is greater than twice, and lefs than three times 12S540 



(the greateft number which is fquared by Mr. Councer's 



table) ; here 385618 ZZ 3. 128539 -f 1 ; therefore if « ~ 3, 



XZZ 128539, and aZZ 1, x + a will be ZT 128540, and will be 



within the extent of the table : Hence 



**,or the fquare of 128539, would be by the table 16522274521 

 71-1, or 3-1 - - 2 



33044549042 

 X -fu\*j or the fquare of 128540, would be 16522531600 



49567080642 

 wor3 - - 3 



11870 124 1926 



and as n- 1. a« = 2, the fquare of 38561 8 will be 148701241 924 



If the fquare required were that of 385619, in this cafe a=2, 

 and confequently, if xzz 128539, x-^-a, or 128541, would ex- 

 ceed the extent of the table : therefore n muft, in this cafe, 

 be equal to 4, xzz9 6404, and a rz: 3, and 

 the fquare of 96404 = 9293731216 



3 



27881193648 

 the fquare of 96407 = 9294309649 



37175503297 

 4 



148702013188; but7j~i.a*= 

 3.9. or 27; therefore the") ,4,070001 qifii 

 fquare of 385619 is | 148702013161. 



From this example we fee the neceflity of being careful 

 that x + a does not exceed the numbers in the table : at the 



fame 



