traced upon the Surface of the Sphere. 425 



cos 2 a cos 2 e 

 " ~ sin 2 a q= sin 2 e cos $ 



the upper denoting the ellipses and the lower the hyperbola. Also the pa- 

 rabola, being either an ellipse or hyperbola, should be written 



cos 2 e 



tan ( = 



' cos 6 



The focal radii-vectores make equal angles with the tangent. 

 Let us take P for pole, and the other parts as in the figure, 



Then, per table, 

 rf LMP = 



( cos 2e cos 2(a ip <b) 



-J - i - ' * - 



g 



v J 



) 



cos 2 6 cos 2 (a 

 cos2a cos2(a 



/ g x 



cos 2 a cos 2 e 

 Also, sin* LMP = 1 - cos* LMP = cos a a _ cos 2 (a zp 



cos 2 a cos 2f . . 



2 sin (2a if= 0) sin ^) 



