VIII. On the Focus of a Conic Sectioji. 



By pierce MORTON, Esq. B.A. 



OF THE MIDDLE TEMPLE, AND FELLOW OF THE CAJUBRIDGB 

 PHILOSOPHICAL SOCIETY. 



[Read March 2, 1829.] 



Perhaps no property which is known to pertain to the 

 plane section of a cone, is more striking than that which 

 characterizes the focus. Not being aware of any simple and 

 direct mode in which the existence of so remarkable a point 

 is established, I have felt interested to discover a solid con- 

 struction which might accomplish this object. The result to 

 which I have been led, is exhibited in the following pro- 

 positions : 



Prop. I. 



If a right cone be cut by a plane; and if a sphere be 

 inscribed, touching the plane in a point S, and the conical 

 surface in a circle the plane of which is produced to cut the 

 plane of the conic section in a line RX; the distances SP and 

 PR of any point P in the conic section from the point S and 

 the line RX, shall be to one another in a constant ratio. 



Vol. III. Part I. A A 



