Manchester Memoirs ; Vol. lix. (19 15), No. 13. 23 



straight line ADE so that the intercept DE shall be equal 

 to DB. Join ZsZ> and produce EB to /*". Then obviously 

 the angle CBF is one-third of the angle ABC. 



IV. The following two methods are given by G. A. 

 Kenner von Lowenthurn in the course of a correspondence 

 with Huygens (1653-4) 15 : 



Fig. 16. Lowentlmrn's Method (No. 1). 



I. Let ABC {Fig. 16) be the angle to be trisected. 

 With B as centre describe a circle cutting off BA, BC. 

 Draw the chord AC. Through B place a straight line 

 BQR so that A Q shall be equal to the length of the chord 

 AR. Then the angle A BR is one-third of the angle ABC. 

 To prove this, bisect RQ at T, produce RQ to meet the 

 circle at E, join A to F and to T. Then : 



13 See "CEuvres de Christian Huygens." Socictc Hollandaise des 



Sciences. Vol. I. (1S8S.) 



