Pythagorean theorem four elementary lemmata: Next, each top square is related to a triangle congruent with another triangle related in turn to one of two rectangles making up the lower square. The proof is as follows: This proof, which appears in Euclid's "Elements" as that of Proposition 47 in Book 1, demonstrates that the area of the square on the hypotenuse is the sum of the areas of the other two squares. This is quite distinct from the proof by similarity of triangles, which is conjectured to be the proof that Pythagoras used. We have already discussed the Pythagorean proof, which was
Hypotenuse is the square root of 25, that is, 5. The word "hypotenuse" is derived from Greek (sc. or ), meaning "[side] subtending the right angle" (Apollodorus), The Greek term was loaned into Late Latin, as "hypotēnūsa". Adoption as a learned Latinism used in modern languages dates to the 16th century. The spelling in "-e", as "hypotenuse", is French in origin (Estienne de La Roche 1520). The length of the hypotenuse is calculated using the square root function implied by the Pythagorean theorem. Using the common notation that the length of the two legs of the triangle (the sides perpendicular to