Ill 



THE TRISECTION OF AN ANGLE 



HIS problem is not so generally known as that of 

 squaring the circle, and consequently it has not 

 received so much attention from amateur mathe- 

 maticians, though even within little more than a 

 year a small book, in which an attempted solution is given, 

 has been published. When it is first presented to an un- 

 educated reader, whose mind has a mathematical turn, and 

 especially to a skilful mechanic, who has not studied theo- 

 retical geometry, it is apt to create a smile, because at first 

 sight most persons are impressed with an idea of its sim- 

 plicity, and the ease with which it may be solved. And 

 this is true, even of many persons who have had a fair gen- 

 eral education. Those who have studied only what is 

 known as "practical geometry" think at once of the ease 

 and accuracy with which a right angle, for example, may 

 be divided into three equal parts. Thus taking the right 

 angle ACB, Fig. 4, which may be set off more easily and 

 accurately than any other angle except, perhaps, that of 

 60, and knowing that it contains 90, describe an arc 

 ADEB, with C for the center and any convenient radius. 

 Now every schoolboy who has played with a pair of com- 

 passes knows that the radius of a circle will " step " round 

 the circumference exactly six times ; it will therefore 

 divide the 360 into six equal parts of 60 each. This 

 being the case, with the radius CB, and B for a center, 



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