SQUARING THE CIRCLE. 323 



at the ends of two diameters, AOB, COD, at right 

 angles to each other, and join CA ; let COAE be 

 one of the quarters of the circumscribing square, and 

 from E draw EG, cutting off from AO a fourth part 

 AG- of its length, and from AC the portion AH. 

 Then three sides of the circumscribing square together 

 with AH are very nearly equal to the circumference 

 of the circle. The difference is so small, that in a cir- 

 cle two feet in diameter, it would be less than the 

 two-hundredth part of an inch. If this construction 

 were exact, the great problem would have been solved. 



One point, however, must be noted : the circle is 

 of all curved lines the easiest to draw by mechanical 

 means. But there are others which can be so drawn. 

 And, if such curves as these be admitted as available, 

 the problem of the quadrature of the circle can be 

 readily solved. There is a curve, for instance, in- 

 vented by Dinostratus which can readily be described 

 mechanically, and has been called the quadratrix of 

 Dinostratus, because it has the property of thus solv- 

 ing the problem we are dealing with. 



As such curves can be described with quite as 

 much accuracy as the circle for, be it remembered, 

 an absolutely perfect circle has never yet been drawn 

 we see that it is only the limitations which geome- 

 ters have themselves invented that give this problem 

 its difficulty. Its solution has, as we have said, no 

 value ; and no mathematician would ever think of 



