Steede — On Curvature of Pedal and Reciprocal Curves. 127 



"WTien two curves touch the angle ^ for the point of contact, being 

 the same for both curves, the equation 



pp' sin^<jf) = Jc^ 

 shows that — 



9. If two curves touch, the radii of curvature at the point of con- 

 tact are inversely as the radii of curvature of the reciprocal curves at 

 their corresponding point of contact : 



10. Hence, by reciprocation, it may be proved that, if two conies 

 have double contact, the ratio of the radii of curvature of the conies at 

 one point of contact is the same as that at the other point of contact. 



