THE TRISF.CTION OF AN WOLF. 



39 



Equations (2) and (3) show that the curve is a [)articular case of 

 Pascal's Limacon, as is shown in fig. lY. 



Let us now proceed to the trisection of an angle. 



FIRST METHOD. 



Let OCB be the given angle. 



(See fig. V when 

 given angle is acute or 

 obtuse and fig. VI 

 when it is reflex.) 



With the vertex C as 

 center and with any 

 convenient radius de- 

 scribe the DirectricCir- 

 cle,* cutting the sides 

 of the angle in O and B. 

 With O as origin and 

 OC as axis of y de- 

 scribe the limacon de- 

 termined by equation 



(3)- 



Produce BC to meet the limacon in P. 



Also draw PO and prolong it to H, making OH— OC. 



Then HC trisects <OCB, since <HCO. 



<COP 



*This fact explains the meaning and also the reason for using the nanie '• pirectric 

 Circle " 



