190 Mr. Morton oh the Focus of a Conic Section. 



difficult to perceive, that these vertices, and these only of all 

 points without the plane of the section, have with regard to it 

 properties analogous to those Avhich characterize the focus only 

 of all points in that plane, and which have been demonstrated 

 in Propositions I and II of the present Paper. Thus, in every 

 conic section, the distances PV, PY of any point P from the 

 vertex of the cone, and from the straight line YB (fig. 1, 2, 3.) 

 in which the plane of the section cuts a plane passing through 

 the vertex of the cone perpendicular to the axis, are to one 

 another in a constant ratio : and, mgain, in such as have a 

 centre, the sum or the difference of the distances of the vertex 

 of the cone from the extremities of any diameter is always 

 equal to the sum or to the difference of f^J and f^'^', the 

 sum in the case of the ellipse, and the difference in that of the 

 hyperbola. 



PIERCE MORTON. 



Middle Temple, 

 Jan. 15, 1829- 



