Proposition: 1.47: Pythagorean Theorem 

(Proposition 47 from Book 1 of Euclid’s “Elements”)

In right-angled triangles, the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle.

• Let $ABC$ be a right-angled triangle having the angle $BAC$ a right angle.
• I say that the square on $BC$ is equal to the (sum of the) squares on $BA$ and $AC$.

Modern Formulation

In a right triangle (\(\triangle{ABC}\)), the square on the hypotenuse (\(\overline{BC}\)) is equal to the sum of the squares on the other two sides (\(\overline{AB}\), \(\overline{CA}\)).

This theorem is also known as the theorem of Pythagoras.

| | | | | created: 2014-10-05 18:25:43 | modified: 2019-03-24 08:10:46 | by: bookofproofs | references: [626], [628], [6419]

1.Proof: (related to "1.47: Pythagorean Theorem")