◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--1-plane-geometry / Proposition: 1.47: Pythagorean Theorem

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.

Table of Contents

Proofs: 1

Mentioned in:

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"