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## 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.

### 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")

### CC BY-SA 4.0

[626] Callahan, Daniel: “Euclid’s ‘Elements’ Redux”, http://starrhorse.com/euclid/, 2014