24 THE SEVEN FOLLIES OF SCIENCE 



shall be equal to the area of the circle. The following is 

 the method : 



Draw a line ACB, Fig. 3, equal to half the circumference 

 and half the diameter together. Bisect this line in O, and 

 with O as a center and AO as radius, describe the semi- 

 circle ADB. Erect a perpendicular CD, at C, cutting the 

 arc in D ; CD is the side of the required square which can 



o 



Fig. 3. 



then be constructed in the usual manner. The explanation 

 of this is that CD is a mean proportional between AC 

 and CB. 



De Morgan says : "The following method of finding the 

 circumference of a circle (taken from a paper by Mr. S. 

 Drach in the * Philosophical Magazine,' January, 1863, 

 Suppl.), is as accurate as the use of eight fractional places: 

 From three diameters deduct eight-thousandths and seven- 

 millionths of a diameter ; to the result, add five per cent. 

 We have then not quite enough ; but the shortcoming is 

 at the rate of about an inch and a sixtieth of an inch in 

 14,000 miles." 



For obtaining the side of a square which shall be equal 

 in area to a given circle, the empirical method, given by 

 Ahmes in the Rhind papyrus 4000 years ago, is very 



