AS PRACTISED BY THE ARABS. 145 



below the Rank of the number there is applied the name of second Rank 

 of the number, and to that Rank which is below it there is applied the name 

 of third Rank of the number, and so on till we reach to the Rank of the 

 Latus. Then let us begin from the right hand, and let us write the first 

 period of the number in the Squares of the first step, and the second 

 period in the Squares of the second step, and so on till we have written 

 all the places of figures in the small Squares, each place in a Square. 

 Then let us seek the greatest number of the Digits, which being involved 

 to the Index of the given number, can be subtracted from, i. e. is less than 

 the last dotted place, and the figures to its left hand. Now, if we were to 

 arrange in a Table the Powers of the numbers from 2 to 9 to the Quadratus 

 quadrati cubi cubi which is to the Index 10, that would facilitate the find- 

 ing of this sought number. And when we have found it, let us place it in 

 the external Row, and call that the top number which hence is the first found 

 figure of the Root, and let us also put it in the lowest part of the Rank of 

 the Latus, opposite to the last dotted place, and call that the bottom num- 

 ber, and let us write its Square (and that is the product of the top number 

 into the bottom) in the lowest part of the Rank of the Square, and 

 let us write the product of the top number into the Square, and that is its 

 Cube in the lowest part of the Rank of the Cube, and thus, until we multi- 

 ply the top number into that which is in the second Rank of the number. 

 Then let us write this product in the Rank of the number below what 

 was written there and below that, there is written the products in the 

 Ranks, so that their units should all be opposite the single top figure. 

 And let us subtract the last product from that which is opposite it in the 

 Rank of the number, and let us write the Remainder below the latitudinal 

 line drawn above the former period, so that it may be one line with this 

 period. Then let us add the top number to that which is in the Rank of 

 the Latus, once, for the second Rank of the number, and let us multiply 

 it, the lop number into the sum, and let us add the product to that which 

 is in the Rank of the Square, and let us multiply it into the sum there, 



