Let A', B', C' be the points in which the Euler line of a triangle ABC meet the sidelines BC, CA, AB, respectively. Then the Euler lines of the triangles AB'C', BC'A', CA'B' form the Gossard triangle, which is congruent to ABC, has the same Euler line as ABC, and is homothetic to ABC about a point named the Gossard perspector by John Conway in 1998.
Gossard received his Ph. D. from Johns Hopkins University in 1912. Prior to that he had taught in high schools. From 1912 to 1916, he was a member of the mathematics department at the University of Oklahoma. During two years of World War I, he taught at the U. S. Naval Academy. Thereafter, he was a professor at University of Oklahoma (1918-19), University of Wyoming (1921-25), and Nebraska Wesleyan University (1926-31).
From 1931 to 1939, Gossard served as President of New Mexico Normal University (now Highlands University), and from 1939 to 1950, as Dean of Eastern New Mexico College (now University). During his last four years, he was employed by the U. S. State Department in Stuttgart, Germany.
The earliest published record of the Gossard theorem is the first of three publications in his name:
1. "Note on the Euler line," Bulletin of the American Mathematical Society 22 (1916) 218-219.
2. "On the relations between the faces and edges of a tetrahedron," Bulletin of the American Mathematical Society 23 (1917) 212.
3. "On a special elliptic ruled surface of the ninth order," American Journal of Mathematics 38 (1916) 431-445.
The photograph of H. C. Gossard was kindly supplied by Gene Bundy, Archivist, Eastern New Mexico University.