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A curious and interesting gem is Frégier's theorem, quoted here from David Wells:

Choose any point $P$ on a conic, and make it the vertex of a right angle which rotates about $P$. Then the lines through the points of intersection, $AA$, $BB$, and so on, will all pass through a fixed point $X$ which lies on the normal at $P$, that is, on the line through $P$ perpendicular to the tangent at $P$.

Who was Frégier, and where can I find the earliest publication of his theorem?

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The theorem of Frégier (Correspondance sur l'Ecole Royale Polytechnique tome III, p.394, 1816) is a limiting case of 144(a) (See footnote on p.324 of "An Introduction to the ancient and modern geometry of conics, being a geometrical treatise on the conic sections with a collection of problems and historical notes and prolegomena" by Taylor, Charles, 1840-1908).

For quick view of the above reference, scroll down to p.394, or use Contents and go to Section 11 for p.394.

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Frégier appears to have published the result in

M. Frégier, Géométrie analitique. Théorèmes nouveaux sur les lignes et surfaces du second ordre. Annales de Mathématiques pures et appliquées, tome 6 (1815-1816), p. 229-241

Here's a PDF.

and what looks like the relevant theorem

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The following article helped me track this down, via some citations in the introduction:

LIPPS, KATHERINE SUE. “Envelopes of Certain Families of Conics.” Pi Mu Epsilon Journal, vol. 2, no. 8, 1958, pp. 359–363. JSTOR, www.jstor.org/stable/24344939. Accessed 27 June 2020.

For anybody who wants to access Gergonne's Annales, there is an index at http://www.numdam.org/item/AMPA/

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