144 AN ESSAY ON THE ROOTS OF INTEGERS 



period, is, in my demonstration, called the first ; and what he calls the 

 former or preceding period, is, in my demonstration, called the next, or 

 following period, and so on. It must also be noticed, that throughout this 

 Extract, the word breadth means across the page from right to left, and 

 length means down the page from top to bottom. 



50). Translation. 



" Chapter Tenth. From the Book called the Ayoun-ul-Hisab, or 

 Sources of Arithmetic. Of the extraction of the Latus of Powers 

 generally. 



Let us draw a Pulpit Diagram of ascending steps, the number of 

 which steps is equal to the number of periods of the given Power. Then 

 let us divide the breadth of each step into places, the number of ivhich are 

 according to the number of the Index, except the highest step, and we 

 are to divide that according to the number of the places of figures which 

 are found in the last of the periods. Then let us draw from the points 

 of division longitudinal lines, ivhich, with the lines which f 07 m the height 

 of the step, are to be drawn to such a distance as the operation may re- 

 quire. Then let us produce the breadth of the step to the most left hand 

 of the longitudinal lines, and let us divide the most right hand of the 

 longitudinal lines into divisions, or ranks, according to the number of the 

 Index of the Power, and it is sufficient that the length of the divisions 

 be great enough to contain the same number of figures as the height of all 

 the steps, and the length of the lowest of them be great enough to contain, 

 in length, one period of the given Power. And let the lowest of the divi- 

 sions be called the Rank of the Latus, and tlie division above it the Rank 

 of the Square, and the division above it the Rank of the Cube, and so on 

 till we reach the Rank of the number ; and the figures exterior to the 

 Diagram are called the external Row, and then to the division which is 



