84 AN ESSAY ON THE ROOTS OF INTEGERS, 



(41.) I now proceed with the Arabian. Rule. 



Seek the greatest number with the following conditions— 



1 . That if it be written at the bottom of the Rank of the Latus, that 

 is completely at the bottom of the whole figure and opposite the first 

 period, that is in the same interstice as 6 the units of 168 Par. 38.) 



2. And if it be multiplied into itself, and the product written in the 

 Rank of the Square again opposite the first period. 



3. And if it be again multiplied in this product, and the second pro- 

 duct written in the Rank of Cube again opposite the first period. 



4. And if it be again multiplied into this second product, and the 

 third product written in the Rank of the Biquadrate again opposite the 

 first period. 



5. And if it be again multiplied into this third product, and the 

 fourth product written in the Rank of the Quadratus Cubi again opposite 

 the first period. 



6. And if it be again multiplied into this fourth product that the 

 fifth product be not greater than the first period of the given number. 



Then 2 will be found the number answering these conditions, for 



a. Write 2 in the bottom of the Rank of the Latus, as by Art. 1.) 



b. Multiply this 2 into itself, and write the product 4 in the Rank of 

 the Square, as by Art. 2.) 



