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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")

Edit or AddNotationAxiomatic Method

This work was contributed under CC BY-SA 4.0 by:

This work is a derivative of:

CC BY-SA 4.0

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

CC BY-SA 4.0

Freely downloadable

[6419] Fitzpatrick, Richard: “Euclid’s Elements of Geometry”, http://farside.ph.utexas.edu/Books/Euclid/Euclid.html, 2007

Public domain

[628] Casey, John: “The First Six Books of the Elements of Euclid”, http://www.gutenberg.org/ebooks/21076, 2007

Bibliography (further reading)

(none)