Re: [HM] Gossard's Theorem on Euler lines

John Conway (conway@math.Princeton.edu)
Fri, 3 Dec 1999 12:42:08 -0500 (EST)

On Fri, 3 Dec 1999, Antreas P. Hatzipolakis wrote:

> The only reference I located is:
>
> Deaux, R.: Quadrilateres de Zeeman.
> Mathesis 69 (1961) 399-405

Thanks, Antreas. Julio has already confirmed my guess.

> I found in the Greek student periodical _Supplement of the Bulletin
> of the Greek Math. Society_, Febr. 1963, pp. 134 - 136, the theorem
> (without references):
>
> The Euler line of a triangle ABC intersects AB, AC at B', C',
> respectively. Prove that the Euler line of the triangle AB'C' is
> parallel to BC. (The proof in the periodical is nice and purely
> synthetic)
>
> And the theorem in the same form as yours above, in the book:
> I. G. Ioannidis: Plane Geometry. Athens 1965, p. 380

Did this include the congruence-by-reflection statement, which I
wasn't quite sure about?

John Conway