114 AN ESSAY ON THE ROOTS OF INTEGERS, 



And this operation is analogous to that of g". 



(_s. Then add together the upper numbers in each Rank as found 

 by Arts. <j- £_ J j * and an additional Unit. The sum of all these will 

 be the Denominator of the Fraction, to be added to the integral Root as 

 required. 



And performing these operations in this example with the last figure 

 of the Root 7, the Result will be as follows : 



The upper number in the Rank of the 

 4,260,747,694,908,334,607,381,985,642. Quadratus Cubi. 

 45,410,774,905,552,940,176,81 5. Biquadrate, 



258,125,396,471,245,260. Cube. 

 825,325,162,335. Square. 

 1,407,402. Latus. 



1. The additional Unit. 



4,260,793,105,941,366,382,119,977,455. The sum or Denominator. 



Hence, then, finally, the approximate 6th Root of the given number. 

 166,571,800,758,593,887,308,296,025,335,490 

 is the mixed number. 

 987,654,321 



234,567 



4,260,793,105,941,366,382,119,977,455 



And this concludes the operation according to the Arabian method. 



(42). I now proceed to show the conformity of the above operation 

 withthedemonstrationofPar.il). et seq. and for this purpose must 

 premise the following Lemmas. 



