1 6 Gee AND A DAMSON, Trisecting an Angle. 



(3) Use of a parabola. 



This method for trisecting an angle is given by 

 Descartes and is re-stated in Ball's " Mathematical 

 Recreations." 



The parabola 





and the circle 



y = - x 

 4 



I "Z 



x~ +y* — ^ x + 4<2y = 0, 

 4 



intersect at points whose ordinates satisfy the equation 

 1 6/ +/ - 1 3 y 2 + 4ay = 0, 



or 



or 



Hence if 



then 



y = sin a 



will satisfy the equation. 



1 6y* - 1 2 v + 4a = 0, 

 a = $y- 4> :i - 

 <z = sin 3 o, 



Fig. II. Use of Parabola. 



