 The Pythagorean theorem and de Gua's theorem are special cases ("n" = 2, 3) of a general theorem about "n"-simplices with a right-angle corner.This, in turn, is a special case of a yet more general theorem by Donald R. Conant and William A. Beyer, which can be stated as follows.Let "U" be a measurable subset of a "k"-dimensional affine subspace of formula_2 (so formula_3).