12 THE SEVEN FOLLIES OF SCIENCE 



In the last number of the Athenaeum for 1855 a corres- 

 pondent says " the thing is no longer a problem but an 

 axiom." He makes the square equal to a circle by making 

 each side equal to a quarter of the circumference. As De 

 Morgan says, he does not know that the area of the circle 

 is greater than that of any other figure of the same cir- 

 cuit. 



Such ideas are evidently akin to the poetic notion of the 

 quadrature. Aristophanes, in the "Birds," introduces a 

 geometer, who announces his intention to make a square 

 circle. And Pope in the "Dunciad" delivers himself as 

 follows : 



Mad Mathesis alone was unconfined, 

 Too mad for mere material chains to bind, 

 Now to pure space lifts her ecstatic stare, 

 Now, running round the circle, finds it square. 



The author's note explains that this "regards the wild 

 and fruitless attempts of squaring the circle." The poetic 

 idea seems to be that the geometers try to make a square 

 circle. 



As stated by all recognized authorities, the problem is 

 this : To describe a square which shall be exactly equal in 

 area to a given circle. 



The solution of this problem may be given in two ways : 



(1) the arithmetical method, by which the area of a circle 

 is found and expressed numerically in square measure, and 



(2) the geometrical quadrature, by which a square, equal in 

 area to a given circle, is described by means of rule and 

 compasses alone. 



Of course, if we know the area of the circle, it is 

 easy to find the side of a square of equal area ; this can be 

 done by simply extracting the square root of the area, pro- 



