Commandino's theorem

[1][2][3] The theorem is attributed to Commandino, who stated, in his work De Centro Gravitatis Solidorum (The Center of Gravity of Solids, 1565), that the four medians of the tetrahedron are concurrent.

However, according to the 19th century scholar Guillaume Libri, Francesco Maurolico (1494–1575) claimed to have found the result earlier.

Libri nevertheless thought that it had been known even earlier to Leonardo da Vinci, who seemed to have used it in his work.

Julian Coolidge shared that assessment but pointed out that he couldn't find any explicit description or mathematical treatment of the theorem in da Vinci's works.

It can be used to prove the following theorem about the centroid of a tetrahedron, first described in the Mathematische Unterhaltungen by the German physicist Friedrich Eduard Reusch [de]:[8][9] Since a tetrahedron has six edges in three opposite pairs, one obtains the following corollary:[8] A specific case of Reusch's theorem where all four vertices of a tetrahedron are coplanar and lie on a single plane, thereby degenerating into a quadrilateral, Varignon's theorem, named after Pierre Varignon, states the following:[10][11]