Thabit ibn Qurra's theorem generalizes the Pythagorean theorem to an arbitrary triangle similar
triangles give
(1)
and
(2)
Adding the two identities yields
(3)
When right angle , the construction reduces to the
usual Pythagorean theorem . Thabit ibn Qurra
gave this result in a ninth-century treatise on the proof attributed to Socrates
(Sayili 1960, Maor 2007).
See also Law of Cosines ,
Pythagorean
Theorem ,
Similar Triangles
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References History of Mathematics Project. "Ibn Qurra's Pythagorean Theorem Proofs." https://www.history-of-mathematics.org/artifacts/ibn-qurras-pythagorean-theorem-proofs . Maor,
E. The
Pythagorean Theorem: A 4,000-Year History. Sayili, A. "Thabit ibn Qurra's Generalization
of the Pythagorean Theorem." Isis 51 , 35-37, 1960.
Cite this as:
Weisstein, Eric W. "Thabit ibn Qurra's Theorem."
From MathWorld https://mathworld.wolfram.com/ThabitibnQurrasTheorem.html
Subject classifications
. Choose points 
and 
on the line 
so that 
. The resulting similar
triangles give
is a right angle, the construction reduces to the
usual Pythagorean theorem. Thabit ibn Qurra
gave this result in a ninth-century treatise on the proof attributed to Socrates
(Sayili 1960, Maor 2007).
