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arXiv · 2403.19670

The altitudes of a triangle

Mark Mandelkern
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Abstract

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.

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Mark Mandelkern. 2024-02-15. The altitudes of a triangle. https://doi.org/10.1080/00029890.2023.2276635

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