HISTORY OF ALGEBRA. ITS 



for the purpose of making canals. In this are described the plummet 

 level, and the water level on the same principle with our spirit level. 



Chapter second, on the mensuration of heights, accessible and inaccessi- 

 ble. Under the former of these heads are delivered the common methods, 

 by bringing the top of a pole whose height is known, in a line between the 

 eye and the top of the height required ; by viewing the image of the top 

 in a horizontal mirror; by taking the proportion between a stick of 

 known length, set up perpendicular fo the horizon and its shadow ; and 

 by taking the length of the shadow of the height when the sun's altitude 

 is 45 degrees. The last method is this, " Place the index of the astro- 

 " labe at the mark of 45 degrees, and stand at a place from whence the 

 " height of the object is visible through the sights, and measure from the 

 " place where you stand to the place where a stone would fall from the 

 " top ; add your own height, and the sum is the quantity required." 



For the mensuration of inaccessible heights the following rule is de- 

 livered, " Observe the top of the* object through the sights, and mark on 

 " what shadow line (division) the lower end of the index falls. Then 

 " move the index a step forward or backward, and advance or recede 

 till you see the top of the object again. Measure the distance between 

 your stations, and multiply by 7 if the index is moved a Dhil-Kadam, 

 and by 12 if it is moved a Dhil-As'bd* according to the shadow lines 

 " on the Astrolabe. This is the quantity required. 



5( 



(( 



* This part of the astrolabe consists of two squares put together laterally ; the index of 

 the instrument being at the point of the adjacent angles above. One square has seven, and 

 the other, twelve divisions: the former called Dhil-i-Kadam, the latter Dhil-i-Asbd. The 

 squares are graduated on the outer sides from the top, and at the bottom from the point of 

 the adjacent angles. The divisions on the upright sides are those lines which Chatjoek, in 

 his treatise on the astrolabe, calls Umbra-recta ; those on the horizontal he calls Umbra-versa* 



U s 



