■2 7 



Gee AND A DAMSON, Trisecting an Angle. 



describe a circle cutting the circle HVK at P' . Draw 

 MP" perpendicular to HK. With H as centre describe 

 a circle passing through P" cutting HK at R. Trisect 

 MR at X and Y. With // as centre and HY as radius 



y v /y. 24. Diirer's Approximate Method. 



describe a circle cutting the circle HVK at P. Similarly 

 obtain the points Q\ Q" and Q. Draw BP y BQ. BP 

 and BQ are then the approximate trisectors of ABC. 

 The arcs HP', P" Q" and QK are obviously exactly 

 equal, and to each of these is added an approximation to 

 one-third of the sum of the arcs P'P'\ Q'Q". 



Method F. — Although the construction of method E 

 gives a very close approximation to trisection, a much 

 closer approximation is obtained by the following varia- 

 tion devised by one of the writers. 



Let ABC {Fig. 25) be the angle to be trisected. With 

 B as centre and any radius describe a circle ERG cutting 

 BA at E and BC at G. With B as centre and radius 

 equal to three times BE describe a circle H VK cutting 

 BA at H and BC at K. Join EG, HK. Now with H as 

 centre and radius equal to EG describe an arc cutting 

 HK at M and the circle HVK at P' . Join E to M and 



