History of mathematical notation back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into periods, the distinctions between which are tolerably well marked. Greek mathematics, which originated with the study of geometry, tended from its commencement to be deductive and scientific. Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of
Viviani's theorem Viviani's theorem Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from "any" interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. This proof depends on the readily-proved proposition that the area of a triangle is half its base times its height—that is, half the product of one side with the altitude from that side. Let ABC be an equilateral triangle whose height is "h" and whose side is "a". Let P be any point inside the triangle, and "u, s, t" the distances of P from the sides.