Manchester Memoirs, Vol lix. (191 5), No. 13. 



XIII. Trisecting an Angle. 

 By Professor W. W. HALDANE Gee, B.Sc, M.Sc.Tech., 



AND 



Arthur Adamson, M.Sc.Tech., A.R.C.S. 



(Read October ijth, igi2. Received for publication May rjt/i, /g/y.J 



Introductory. The three famous problems whose 

 solution was attempted by the early geometers relate 



to:— 



1. Squaring the circle. 



2. Trisecting an an^le. 

 and 3. Duplicating a cube. 



It was mainly through " a thousand attempts to solve 

 these problems that new propositions and new processes 

 were discovered and geometry made daily progress." 1 

 The first problem has recently been treated by Dr. E. W. 

 Hobson. 2 Circle squarers are now rare, but during the 

 last few years there has been quite a number of enthusiasts 

 who have confidently declared that they had trisected an 

 angle by the use only of a ruler and a pair of compasses. 

 Some of these were brought directly under our notice, 

 with the ultimate result that we decided that a useful 

 purpose would be served by collecting together true or 

 approximate solutions of the problem. As in the case of 

 squaring the circle, the task opens up a little-studied field 

 of Geometry abounding in interesting applications. 



TJie Method of Archimedes:'' One of the ways of 

 solving geometrical problems adopted by the Greek 



1 See J. (low, "A Short History of Greek Mathematics. M 

 - " Squaring the Circle : a History of the Problem." 19 1 3. 



- 1 Circa 2S7-212 B.C. 



October ylli, n)i5- 



