Pythagoras triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"—that is, formula_1. According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole "hecatomb", to the gods. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough. The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, but it is possible that he
Geometric mean theorem to complete it, the other a rectangle of area "pq". Since both arrangements yield the same triangle, the areas of the square and the rectangle must be identical. The square of the altitude can be transformed into an rectangle of equal area with sides "p" and "q" with the help of three shear mappings (shear mappings preserve the area): Geometric mean theorem The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the lengths of the altitude on the hypotenuse in a right triangle and the two line segments it