The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other three faces. This theorem was presented to the Paris Academy of Sciences in 1783 by J. P. de Gua de Malves (1712-1785), although it was known to Descartes (1859) and to Faulhaber (Altshiller-Court 1979, p. 300). It is a special case of a general theorem presented by Tinseau to the Paris Academy in 1774 (Osgood and Graustein 1930, p. 517; Altshiller-Court 1979).
de Gua's Theorem
See also
Pythagorean Theorem, Trirectangular TetrahedronExplore with Wolfram|Alpha
References
Altshiller-Court, N. Modern Pure Solid Geometry. New York: Chelsea, pp. 92 and 300, 1979.Descartes, R. Oeuvres inédites de Descartes. Paris, 1859.Kheyfits, A. "The Theorem of Cosines for Pyramids." College Math. J. 35, 385-388, 2004.Osgood, W. F. and Graustein, W. C. Plane and Solid Analytic Geometry. New York: Macmillan, Th. 2, p. 517, 1930.Referenced on Wolfram|Alpha
de Gua's TheoremCite this as:
Weisstein, Eric W. "de Gua's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deGuasTheorem.html