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Document number: 6253
Date: 05 Jan 1866
Recipient: TALBOT William Henry Fox
Author: TAIT Peter Guthrie
Collection: British Library, London, Manuscripts - Fox Talbot Collection
Collection number historic: Acc 38764
Last updated: 8th November 2012

6 Greenhill Gardens,
5/ 1 /66.

My dear Mr Talbot

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

Hence the equations of the curves are
mathematical equation

Their interaction is the point P where mathematical equation

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,
mathematical equation
we have
mathematical equation
which is the proposition.

Yours truly
P. G. Tait.

H. F. Talbot Esqre

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