Talk:Isogonal conjugate

This article has been around since 2005, yet no one has mentioned the isogonal conjugate of a line with respect to (a vertex, a pair of sides meeting at a vertex, the angle bisector at a vertex ... terminology does not seem to be standard). This is the other line of a pair of isogonal lines. Older papers talk about this as well as the isogonal conjugate of a point. In fact, they define the isogonal conjugate of a point P as the intersection of the isogonal conjugates of the cevians which meet at P. Of course, this terminology conflicts with the view of isogonal conjugacy as a function on the interior points of a triangle, where you would call the isogonal conjugate of a point set the set of isogonal conjugates of the points of the set. In this view, the isogonal conjugate of a line is not a line, it is a circumconic. Unfortunately, both uses of the term are still used and in some cases they are both used in the same paper. I think it is important to bring this up in the article, but I have hesitated in doing so because the article would look radically different if this is incorporated. Any comments? Bill Cherowitzo (talk) 20:37, 29 October 2012 (UTC)

It would be good to see a reference to the well known fact that reflecting in angle bisectors is equivalent to taking reciprocal of trilinear coordinates. Or maybe that is already explained elsewhere in Wikipedia anyway?Billlion (talk) 11:25, 26 January 2017 (UTC)