  A long-standing, unanswered question regarding Euclid's Elements concerns the
absence of a theorem for the concurrence of the altitudes of a triangle, and
the possible reasons for this omission. In the centuries following Euclid, a
remarkable number of proofs have been put forward; this suggests a search for
the most elementary and direct proof. This paper provides a simple, direct,
elementary proof of the theorem; it is based solely on the Elements.
