# 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.

Proofs: 1

Parts: 1
Persons: 2
Proofs: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Propositions: 32 33 34
Sections: 35
Topics: 36 37

Thank you to the contributors under CC BY-SA 4.0!

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non-Github:
@Calahan
@Casey
@Fitzpatrick

### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

#### Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

#### Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"