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
Euclidean geometry knowledge of geometry. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost. There are 13 books in the "Elements": Books I–IV and VI discuss plane geometry. Many results about plane figures are proved, for example "In any triangle two angles taken together in any manner are less than two right angles." (Book 1 proposition 17 ) and the Pythagorean theorem "In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides