几何原本
Today, we know of the Pythagorean theorem because of Euclid's Elements, a set of 13 books on mathematics—from around 300 BCE—and the knowledge it contained has been used for more than 2000 years. Euclid's proof is described in book 1, proposition 47 and uses the idea of equal areas along with shearing and rotating triangles. In the "dissection proof", the square of the hypotenuse is cut into pieces to fit into the other two squares. Proposition 31 in book 6 of Euclid's Elements describes the similarity proof, which states that the squares of each side can be replaced by shapes that are similar to each other and the proof still works.