AS PRACTISED BY THE ARABS. 147 



which is in the Rank of the Cube, and so on until it be multiplied into 

 the sum in the second Rank of the number, and the product written in 

 the Rank of the number this can be substracted from, i. e. is less than that 

 which is opposite to it, and when we have found it, such a number, let us 

 operate with it as I have explained, and let us write the remainder below 

 the latitudinal line drawn over the former period, so that it may be one 

 line with the places of the former period annexed to it. Then let us add 

 the new found top number to that which is in the Rank of the Latus one 

 time after another, for the Rank one after another, and let us operate 

 with it as was done before, and if we cannot find a number with this pro- 

 perty, let us put cypher in its place, and transfer that which is in the 

 Ranks, which are below the Rank of the number, once again to the right 

 hand as was done before, that which is in the second Rank of the num- 

 ber one place, and that which is in the third, two places, and so on. Then 

 let us seek the greatest of the units and operate with it as we have detail- 

 ed above, and so on until the product of the top number placed opposite 

 the units of the original given number into the sum in the second Rank of 

 the number be substracted from that which is written in the Rank of the 

 number, and if nothing remains, that number is rational, and the number 

 written in the external Row, i. e. above the Pulpit Diagram, are its Latus 

 Primum, and if any thing remains then it is Surd, and its Latus Primum, 

 technically speaking, by approximation, is that which is in the external 

 Row, with a fraction of which the numerator is the remainder, and the 

 denominator is that which is between, i. e. is the difference between the 

 power of this said written number, and the power of (this number having 

 unit added to it). Then let us employ the single figure placed opposite 

 the units of the given number as we employed the other numbers, except 

 the transference of them, and let that which is in all the Ranks below the 

 Rank of the number be added together into one sum, and let us add to 

 that unit, and that is the said denominator, and the power produced 



p 1 



