A Proof of the Pythagorean Theorem by Thabit ibn Qurra

Thabit Ibn Qurra Ibn Marwan al-Sabi al-Harrani was born in the year 836 C.E. at Harran (present Turkey). As the name indicates he was basically a member of the Sabian sect, but the great Muslim mathematician Muhammad Ibn Musa Ibn Shakir, impressed by his knowledge of languages, and realising his potential for a scientific career, selected him to join the scientific group at Baghdad that was being patronised by the Abbasid Caliphs. There, he studied under the famous Banu Musa brothers. It was in this setting that Thabit contributed to several branches of science, notably mathematics, astronomy and mechanics, in addition to translating a large number of works from Greek to Arabic. Later, he was patronised by the Abbasid Caliph al-M'utadid. After a long career of scholarship, Thabit died at Baghdad in 901 C.E.

Thabit's major contribution lies in mathematics and astronomy. He was instrumental in extending the concept of traditional geometry to geometrical algebra and proposed several theories that led to the development of non-Euclidean geometry, spherical trigonometry, integral calculus and real numbers. He criticised a number of theorems of Euclid's elements and proposed important improvements. He applied arithmetical terminology to geometrical quantities, and studied several aspects of conic sections, notably those of parabola and ellipse. A number of his computations aimed at determining the surfaces and volumes of different types of bodies and constitute, in fact, the processes of integral calculus, as developed later.

In astronomy he was one of the early reformers of Ptolemic views. He analysed several. problems related to the movements of sun and moon and wrote treatises on sun-dials.

In the fields of mechanics and physics he may be recognised as the founder of statics. He examined conditions of equilibrium of bodies, beams and levers.

In addition to translating a large number of books himself, he founded a school of translation and supervised the translation of a further large number of books from Greek to Arabic.

Among Thabit's writings a large number have survived, while several are not extant. Most of the books are on mathematics, followed by astronomy and medicine. The books have been written in Arabic but some are in Syriac. In the Middle Ages, some of his books were translated into Latin by Gherard of Cremona. In recent centuries, a number of his books have been translated into European languages and published.

He carried further the work of the Banu Musa brothers and later his son and grandson continued in this tradition, together with the other members of the group. His original books as well as his translations accomplished in the 9th century exerted a positive influence on the development of subsequent scientific research.

References

Abattouy, Mohammed (2001): "Greek Mechanics in Arabic Context: Thābit Ibn Qurra, al-Isfizārī and the Arabic Traditions of Aristotelian and Euclidean Mechanics," Science in Context, vol. 14: 179-247.

Dold Samplonius, Yvonne (1996): "The Book of Assumptions by Thābit Ibn Qurra (836-901)." In: History of Mathematics: The States of the Art. Edited by J. Dauben et al. San Diego/Boston: Academic Press, 207-222.

Lorch, Richard (2001): Thābit Ibn Qurra: On the Sector-Figure and Related Texts. Edited with Translation and Commentary. Frankfurt, 2001.

Morelon, Régis (1994). "Thābit b. Qurra and Arab Astronomy in the 9th Century." Arabic Sciences and Philosophy, vol. 4: 111–139.

Rosenfeld, B. A. and A. T. Grigorian (1976): "Thābit ibn Qurra." In Dictionary of Scientific Biography, edited by Charles Coulson Gillispie. New York: C. Scribner's Sons, vol. 13, 288-295.

Thābit ibn Qurra (1987): Oeuvres d'astronomie. Texte établi et traduit par R. Morélon. Paris: Les Belles Lettres.