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According to historical documents, it is challenging to establish whether a proof of Th¯abit’s theorem exists based exclusively on equidecomposibility, as in the case of the Pythagorean and Pappus theorems. This article presents the corresponding proof. Key Words: Euclidean geometry, generalization of Pythagorean theorem, equide-
THABIT IBN QURRA AND THE PYTHAGOREAN THEOREM By Robert Shloming, Brooklyn College, Brooklyn, New York DURING the Dark Ages of Western Europe, Islam was very much mathemati cally alive. The Arabs were able to solve the most difficult problems of Archimedes and Apollonius at a time when Latin mathematical knowledge was at a level
The proof of Thabit’s generalization is identical to one of the standard ways of proving the theorem of Pythagoras using similar triangles, and provides a very accessible generalisation with which to challenge learners.
Proof of Thabit ibn Qurra’s Theorem. It will be helpful to translate everything into algebra by introducing the following notation: |∠∠∠B′′′′AB| = δδδδ111 |∠∠∠∠C′′′′AX| = δδδδ2222 We then have the following equations, the first of which is true by the additivity properties of
His original contributions include proofs of the Pythagorean theorem, a proof of Menelaus's theorem, proofs of Euclid's fifth postulate, and work on composite ratios. Thābit's achievements in astronomy are closely linked to his work in mathematics.
Request PDF | On a Proof of the Thābit Ibn Qurra's Generalization of the Pythagorean Theorem | One of the most interesting generalizations of the Pythagorean theorem was stated by Thābit...
15 Δεκ 2009 · Thabit ibn Qurra (826–901) was one of history’s most original thinkers and displayed expertise in the most difficult disciplines of this time: geometry, number theory, and astronomy as well as ontology, physics, and metaphysics.
