4 Gee AND ADAMSON, Trisecting an Angle. 



Join AF. With A as centre and AF as radius, describe 

 a circle cutting BF at P. The locus of P is the curve 

 required, since obviously the angle PA C is equal to three 

 times the angle PBA. 



If KAC, denoted by /3, be the angle to be trisected, 

 find //, the point where AK cuts the trisectrix. Join BH. 

 Then the angle HBA (or a) is one-third of the angle 

 KAC. 



II. Use of the Lima con of Pascals 



Let A (Fig. 3) be a point on the circumference of a 

 circle of which B is the centre. Through A draw any 



D 



Fig. 3. Use of Limacon. 



straight line cutting the circle at P t and on this line mark 

 off a length PQ equal to a constant length. The locus 

 of Q is a limacon curve. The special form of limacon 

 used for the trisection of angles is called the " trisectrix," 



6 1 623- 1 662. 



