> One of Clark's correspondents (was it Cyril Parry?) pointed out that
> this seemed to be connected with the concept of "Zeeman quadrilateral"
> that cropped up frequently in some papers just after that time.
The only reference I located is:
Deaux, R.: Quadrilateres de Zeeman.
Mathesis 69 (1961) 399-405
> I never looked this up either, but my guess is that it's the type
> of quadrilateral abcd described in the following theorem, which
> follows trivially from Gossard's.
>
> Take four lines a,b,c,d with the property that d is parallel
> to the Euler line of abc. Then symmetrically the four Euler lines
>
> a' of bcd, b' of cda, c' of dab, d' of abc
>
> are respectively parallel to a,b,c,d. Moreover the two
> quadrilaterals are in perspective from a point P, and I think
> congruent by reflection in P.
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
Antreas