Thābit ibn Qurra

Abstract

Abū’l‐Ḥasan Thābit ibn Qurra ibn Marwān al‐Ḥarrānī al‐Ṣābi˒ (836–901) was a Syrian mathematician, astronomer, physicist, physician, geographer, philosopher, historian, and translator fromGreek and Syriac into Arabic. His scientific treatises were written primarily in Arabic and partly in Syriac. He was born in Kafartūtha nearḤarrān (nowAltinbasak in Southern Turkey) and was a student inḤarrān.Ḥarrānians, the descendants of the ancient nation Mitanni in the Hellenistic age, were Hellenized, and their ancient religion of star worship was deeply connected to Greek philosophy. In the Arab caliphate, Ḥarrānians called themselves Ṣābians since the Ṣābian religion was one permitted by the Qur˒ān. Ḥarrān University was founded in the fifth century in Alexandria as a school of philosophy and medicine. After the Arab conquest, it was moved to Antiochia and later to Ḥarrān where, under the influence of Ḥarrānian traditions, astronomy and mathematics were taught, and it became a university. At first Thābit ibn Qurra worked in Kafartūtha as a money changer. Here the Baghdad mathematician Muḥammad ibn Mūsā ibn Shākir met him and invited him to Baghdad, where Muḥammad and his brothers Aḥmad and al‐Ḥasan, the Banū Mūsā, became his teachers. Later he worked at the court of the caliphs in Baghdad and in Surra man ra’a (Samarra) as a physician and astronomer. His position as the caliph’s physician allowed him to keep his heathen religion. His son Sinān ibn Thābit and grandson Ibrāhīm ibn Sinān also were mathematicians, astronomers, and physicians in Baghdad. Thābit ibn Qurra’s contributions to science covered many different disciplines, from mathematics to philosophy. In mathematics, he was a translator or editor of translations of many works of Euclid, Archimedes, Apollonius, Theodosius, and Menelaus. Many of these are extant only in these translations. These translations, together with the geometric treatise of Thābit’s teachers, the brothers BanūMūsa, and his Kitāb al‐mafrūḍāt (Book of Assumptions), constituted the so‐called middle books which were studied between Euclid’s Elements and Ptolemy’s Almagest. Two of Thābit’s treatises on parallel lines were first written in Syriac, the first under the title Ktovo al‐ hay da‐tren surte trishe kad mettapkin al bshir men tarten gonowoto dag˓in bahdode (Book [in which is proved] that Two Lines Produced Under Angles Which are Less Than Two Right Angles Will Meet). The second is called “the second book on the same topic.” Both these treatises are extant only in the Arabic translations made by Thābit himself. The ideas of these treatises were further developed by Ibn al‐ Haytham (965–ca. 1050), ˓Umar al‐Khayyām (1048–1131), and Naṣīr al‐Dīn al‐Ṭūsī (1201–1274) and later led to the discovery of non‐Euclidean geometry. Thābit’s Kitāb fī ta˓lī f al‐nusub (Book on Composition of Ratios) was devoted to the theory of compound ratios. This theory later led to the notion of real numbers and to the discovery of differential calculus. Other works covered such subjects as a simple proof of the Menelaus theorem (the first theorem of spherical trigonometry), mensuration of plane and solid figures, and solutions of different problems of integral calculus. His books contained some proofs of the Pythagorean theorem and its generalization and dealt with the subject of amicable numbers, in which each number is equal to the sum of the divisors of the other. In the field of astronomy, Thābit was the editor of the translation of Ptolemy’s Almagest and the author of many treatises on the movement of the sun and moon, sundials, visibility of the newmoon, and celestial