22 THE SEVEN FOLLIES OF SCIENCE 



practical purposes. One of the oldest of these makes the 

 ratio 3y to i. Using this ratio we can ascertain the cir- 

 cumference of a circle of which the diameter is given by 

 the following method : Divide the diameter into 7 equal 

 parts by the usual method. Then, having drawn a straight 

 line, set off on it three times the diameter and one of the 

 sevenths ; the result will give the circumference with an 

 error of less than the one twenty-five-hundredth part or 

 one twenty-fifth of one per cent. 



If the circumference had been given, the diameter might 

 have been found by dividing the circumference into twenty- 

 two parts and setting off seven of them. This would give 

 the diameter. A more accurate method is as follows : 



Given a circle, of which it is desired to find the length 

 of the circumference : Inscribe in the given circle a square, 

 and to three times the diameter of the circle add a fifth of 

 the side of the square ; the result will differ from the circum- 



Fig. i. 



ference of the circle by less than one-seventeen-thousandth 

 part of it. Another method which gives a result accurate 

 to the one-seventeen-thousandth part is as follows : 



Let AD, Fig. i, be the diameter of the circle, C the 

 center, and CB the radius perpendicular to AD. Continue 

 AD and make DE equal to the radius ; then draw BE, and 

 in AE, continued, make EF equal to it ; if to this line EF, 



