6 Greenhill Gardens,
5/ 1 /66.

My dear M^r Talbot

Since the ellipse & hyperbola
are confocal we must have
suppose, i.e. the distance of the focus from the center the same in each.

Hence the equations of the curves are

Their interaction is the point P where

The other ellipse is found by writing a² + h for a²; and the other hyperbola by writing A² + K for A².

Hence, denoting the intersections as in the figure,

we have

which is the proposition.

Yours truly
P. G. Tait.

H. F. Talbot Esq^re