I wonder when was discovered the nine point conic. English Wikipedia article about it https://en.wikipedia.org/wiki/Nine-point_conic is misleading. The nine point conic wasn't discovered in 1892.

In the book Trilinear Coordinates, by William Allen Whitworth, published in 1866(https://ia801405.us.archive.org/21/items/trilinearcoordin029731mbp/trilinearcoordin029731mbp.pdf) one can see that the proof of the existence of the nine point conic is proposed as an exercise (page 473, exercises 438 and 439).

My rough guess is that the nine point conic was discovered in the very beginning of the nineteen century.

Any ideas?

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    $\begingroup$ Well, Feuerbach described the nine-point circle only in 1822, but he was only aware of six points, and Terquem described the remaining three soon after. After that anybody with some knowledge of projective geometry would have been aware of the nine-point conic. I am guessing Bôcher was first to go into details of it. $\endgroup$
    – Conifold
    Sep 21 '18 at 0:11

Bocher, the author of the 1892 article cited in Wikipedia, published a follow-up note:

I find that in the Educational Times for March, 1864, Clifford refers incidentally, in the solution of a problem set by Prof. Sylvester, to the "nine-point conic;" thus showing that this conic, to which I called attention in the March number of the ANNALS, was then familiar to English mathematicians. I have not been able, however, to find any earlier mention of the subject.

So it seems to have been in the "folklore" as early as the 1860's.

Update: It's referred to in Salmon, Conic Sections, 3rd Edition (1855), Art. 154, pg 137, Ex. 4.. It is a special case (shown later in the book) of the theorem that the locus of a pole of a fixed line with respect to the conics through four points is a conic.

It also comes up in the Second Edition (1850), pg 309, Ex. 10, but only six of the nine points are mentioned.

It's worth pointing out, as Bôcher does in the note cited above, that although the "nine point conic of a quadrangle" was known much earlier, his "nine point conic of a triangle and a point" connects it more closely with the nine point circle of a triangle.


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