24 Gee AND A DAMSON, Trisecting an Angle. 

 L CAR=2 L RAT= 2 L AFR. 

 arc CR = 2 arc AR. 



Therefore 

 Therefore 



angle ABC= 3 angle ABR. 



The placing of the line BR may be facilitated by describing 

 a semicircle on BA as diameter and making trials until 

 QR is bisected by the semicircle. 



Fig. 17. Lowenthurn's Method (No. 2). 



2. Let ABC {Fig. 17) be the angle to be trisected. As 

 before, describe a circle with centre B and draw the chord 

 AC. Draw AT perpendicular to AC. Place a tangent to 

 the circle so that the length PQ intercepted between AT 

 and AC is bisected at the point of contact D. Join B to D. 

 Then the angle BBC is one-third of the angle ABC The 

 proof is similar to that preceding, for it is easily seen that 

 the chord DC is equal to RC 



