CHAP. IV.] 



OVAL CURVES. 



97 



tangent to the oval, and CE the radius is perpendicular to it ; then by 

 Prop. 8 Corollary, sine DCE : sine ACE : : (DT : TA : :) power of A : 

 power of B. 



As the ratio of the sines of incidence and refraction is invariable 

 for the same medium, and as this ratio is as 2 to 3 in glass ; and as in 

 the oval at Fig. 1 the powers of the foci are as 2 to 3 ; if the oval 

 were made of glass, rays of light from B would be refracted to A. If 

 now a circle be described from A, the case will not be altered, for the 

 rays are perpendicular to the circle as in fig. 2. 



The ellipse and hyperbola, figs. 3 and 3 [&&], cause parallel rays to 

 converge, for (Prop. 3) they are ovals with one of the foci at an infinite 

 distance. 



Fig. 4 is a combination of 2 hyperbolas, and rays from A are 

 refracted to B. 



H 



