De Gua's theorem

The set of de Gua is a spatial analogue of the theorem of Pythagoras and according to Jean Paul de Gua de Malves (1713-1785) appointed who published it in 1783.

When a tetrahedron, a right-angled corner (such as a cube corner ) has, then the sum of squares of the areas of the surfaces adjacent to the right angle corner is equal to the squared surface area of ​​the side opposite to the right angle surface.

The Pythagorean theorem and the theorem of de Gua are special cases ( n = 2.3 ) of a general theorem on n- simplexes with a " right-angled " corner.

The set was released at the same time in a somewhat more general form by the French mathematician Tinseau d' Amondans (1746-1818) and was even much earlier René Descartes (1596-1650) and John Faulhaber (1580-1635) was known.