AS PRACTISED BY THE ARABS. 91 



10. And the sought number be multiplied into this sum, this pro- 

 duct should not be greater than 102,571,800, the first Resolvend by Art. j. 



Then 3 will be found the number answering these conditions. For — 



g. Write 3 in the interstice to the right hand of 12, the upper num- 

 ber by Art. t) in the Rank of the Latus, and it becomes 123, and is now 

 the upper number in that Rank. 



a. Multiply the found 3 into this 123, and write the product 369 in 

 the Rank of the Square opposite to 571,800, the second period, and imme- 

 diately above 60, the upper number by Art. v) in that Rank. 



r. Add the figures in this situation, 369 



60 



and it becomes 6,369. Write this sum opposite to 

 and immediately above 369, and this 6,369 is now the upper number in 

 the Rank of the Square. 



v. Multiply this found 3 into this 6,369, and write the product 19,107 

 ill the Rank of the Cube opposite to 571,800, the second period, and 

 immediately above 160, the upper number by Art. i) in that Rank. 



Add the figures in this situation, 1 9, 1 07 



160 



and it becomes 179,107. Write this sum op- 

 posite to and immediately above 19,107, and this 179,107 is now the upper 

 number in the Rank of the Cube. 



X- Multiply the found 3 into 179,107, and write the product 537,321 

 in the Rank of the Biquadrate opposite to 571,800, the second period, and 

 immediately above 240, the upper number by Art. y in that Rank. 



a 1 



