HISTORY OF ALGEBRA, I75 



over the well which shall serve for its diameter ; from the center of this 

 diameter drop something heavy and shining till it reach the bottom, and 

 make a mark at the center ; then look at the heavy body through the two 

 sights of the astrolabe, so that the line of vision may cut the diameter. 

 Multiply the distance from the mark on the diameter to the .place where 

 the line of vision cuts it, by your own height, and divide the product by 

 the distance from the place where the line is cut to the place where you 

 stand. The quotient is the depth of the well.* 



Book eighth. _ " On finding unknown quantities by Algebra. In this 

 book are two chapters. 



** Chapter first. Introductory, Call the unknown quantity Shai 

 (thing,) its product into itself Mdl (possession,) the product of Mdl into 

 Shai, Cab (a die or cube,) of Shai into Cab, Mal-Mdl ; of Shai into Mal- 

 i-Mai , Mai-Cab ; Shai into MdUi-Cdb, Cdb-i-Cdb ; and so on, without 

 end. For one Cab write two Mdl, and from these two Mdls one becomes 

 Cab ; afterwards both Mdls become Cab. Thus the seventh power is 



* The impossibility of attaining accuracy 

 in either of these operations is abundantly ob- 

 vious. The first depends on the principle, 

 that on a level plain, two places, which with 

 a given height of the observer's eye have the 

 same dip below the horizon must be at equal 

 distances. The second is thus : let the body 

 drop from a to e / and let the observer at c d 

 observe it in the line d e which Cuts a c in b. 



WKnbc>.cd::ab*.ac = f ^^. 



b c 



