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Thābit ibn Qurra

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Thābit ibn Qurra
Born210-211 AH/220-221 AH / 826 or 836 AD
Harran, the Jazira (Upper Mesopotamia) (now in Şanlıurfa Province, Turkey)
DiedWednesday, 26 Safar, 288 AH / February 19, 901 AD
Academic background
InfluencesBanu Musa, Archimedes, Apollonius, Nicomachus, Euclid
Academic work
EraIslamic Golden Age
Main interestsMathematics, Mechanics, Astronomy, Astrology, Translation, Number theory
Notable ideas
Influencedal-Khazini, al-Isfizari, Na'im ibn Musa[1]

Thābit ibn Qurra (full name: Abū al-Ḥasan ibn Zahrūn al-Ḥarrānī al-Ṣābiʾ, Arabic: أبو الحسن ثابت بن قرة بن زهرون الحراني الصابئ, Latin: Thebit/Thebith/Tebit;[2] 826 or 836 – February 19, 901),[3] was a polymath known for his work in mathematics, medicine, astronomy, and translation. He lived in Baghdad in the second half of the ninth century during the time of the Abbasid Caliphate.

Thābit ibn Qurra made important discoveries in algebra, geometry, and astronomy. In astronomy, Thābit is considered one of the first reformers of the Ptolemaic system, and in mechanics he was a founder of statics.[4] Thābit also wrote extensively on medicine and produced philosophical treatises.[5]


al-Jazira region and its subdivisions (Diyar Bakr, Diyar Mudar, and Diyar Rabi'a) during the Abbasid Caliphate

Thābit was born in Harran in Upper Mesopotamia, which at the time was part of the Diyar Mudar subdivision of the al-Jazira region of the Abbasid Caliphate. Thābit belonged to the Sabians of Harran, a Hellenized Semitic polytheistic astral religion that still existed in ninth-century Harran.[6]

As a youth, Thābit worked as money changer in a marketplace in Harran until meeting Muḥammad ibn Mūsā, the oldest of three mathematicians and astronomers known as the Banū Mūsā. Thābit displayed such exceptional linguistic skills that ibn Mūsā chose him to come to Baghdad to be trained in mathematics, astronomy, and philosophy under the tutelage of the Banū Mūsā. Here, Thābit was introduced to not only a community of scholars but also to those who had significant power and influence in Baghdad.[7][8]

Thābit and his pupils lived in the midst of the most intellectually vibrant, and probably the largest, city of the time, Baghdad. Thābit came to Baghdad in the first place to work for the Banū Mūsā becoming a part of their circle and helping them translate Greek mathematical texts.[9] What is unknown is how Banū Mūsā and Thābit occupied himself with mathematics, astronomy, astrology, magic, mechanics, medicine, and philosophy. Later in his life, Thābit's patron was the Abbasid Caliph al-Mu'tadid (reigned 892–902), whom he became a court astronomer for.[9] Thābit became the Caliph's personal friend and courtier. Thābit died in Baghdad in 901. His son, Sinan ibn Thabit and grandson, Ibrahim ibn Sinan would also make contributions to the medicine and science.[10] By the end of his life, Thābit had managed to write 150 works on mathematics, astronomy, and medicine.[11] With all the work done by Thābit, most of his work has not lasted time. There are less than a dozen works by him that have survived.[10]


Pages from Thābit's Arabic translation of Apollonius' Conics

Thābit's native language was Syriac,[12] which was the Middle Aramaic variety from Edessa, and he was fluent in both Medieval Greek and Arabic.[13] He was the author to multiple treaties. Due to him being trilingual, Thābit was able to have a major role during the Graeco-Arabic translation movement.[10] He would also make a school of translation in Baghdad.[11]

Thābit translated from Greek into Arabic works by Apollonius of Perga, Archimedes, Euclid and Ptolemy. He revised the translation of Euclid's Elements of Hunayn ibn Ishaq. He also rewrote Ishaq ibn Hunayn's translation of Ptolemy's Almagest and translated Ptolemy's Geography.Thābit's translation of a work by Archimedes which gave a construction of a regular heptagon was discovered in the 20th century, the original having been lost.[citation needed]



Thābit is believed to have been an astronomer of Caliph al-Mu'tadid.[14] Thābit was able to use his mathematical work on the examination of Ptolemaic astronomy.[10] The medieval astronomical theory of the trepidation of the equinoxes is often attributed to Thābit.[citation needed] But it had already been described by Theon of Alexandria in his comments of the Handy Tables of Ptolemy. According to Copernicus, Thābit determined the length of the sidereal year as 365 days, 6 hours, 9 minutes and 12 seconds (an error of 2 seconds). Copernicus based his claim on the Latin text attributed to Thābit. Thābit published his observations of the Sun.[citation needed] In regards to Ptolemy's Planetary Hypotheses, Thābit examined the problems of the motion of the Sun and Moon, and the theory of sundials.[10] When looking at Ptolemy's Hypotheses, Thābit ibn Qurra found the Sidereal year which is when looking at the Earth and measuring it against the background of fixed stars, it will have a constant value.[15]

Thābit was also an author and wrote De Anno Solis. This book contained and recorded facts about the evolution in astronomy in the ninth century.[14] Thābit mentioned in the book that Ptolemy and Hipparchus believed that the movement of stars is consistent with the movement commonly found in planets. What Thābit believed is that this idea can be broadened to include the Sun and Moon.[14] With that in mind, he also thought that the solar year should be calculated by looking at the Sun's return to a given star.[14]



In mathematics, Thābit derived an equation for determining amicable numbers. His proof of this rule is presented in the Treatise on the Derivation of the Amicable Numbers in an Easy Way.[16] This was done while writing on the theory of numbers, extending their use to describe the ratios between geometrical quantities, a step which the Greeks did not take. Thābit's work on amicable numbers and number theory helped him to invest more heavily into the Geometrical relations of numbers establishing his Transversal (geometry) theorem.[11][16]

Thābit described a generalized proof of the Pythagorean theorem.[17] He provided a strengthened extension[clarification needed] of Pythagoras' proof which included the knowledge of Euclid's fifth postulate.[18] This postulate states that the intersection between two straight line segments combine to create two interior angles which are less than 180 degrees. The method of reduction and composition[clarification needed] used by Thābit resulted in a combination and extension[clarification needed] of contemporary and ancient knowledge on this famous proof. Thābit believed that geometry was tied with the equality and differences of magnitudes of lines and angles,[clarification needed] as well as that ideas of motion (and ideas taken from physics more widely) should be integrated in geometry.[19][clarification needed]

The continued work done on geometric relations and the resulting exponential series allowed Thābit to calculate multiple solutions to chessboard problems. This problem was less to do with the game itself, and more to do with the number of solutions or the nature of solutions possible. In Thābit's case, he worked with combinatorics to work on the permutations needed to win a game of chess.[20]

In addition to Thābit's work on Euclidean geometry there is evidence that he was familiar with the geometry of Archimedes as well. His work with conic sections and the calculation of a paraboloid shape (cupola) show his proficiency as an Archimedean geometer. This is further embossed[clarification needed] by Thābit's use of the Archimedean property in order to produce a rudimentary approximation of the volume of a paraboloid. The use of uneven sections, while relatively simple, does show a critical understanding of both Euclidean and Archimedean geometry.[21] Thābit was also responsible for a commentary on Archimedes' Liber Assumpta.[22]



In physics, Thābit rejected the Peripatetic and Aristotelian notions of a "natural place" for each element. He instead proposed a theory of motion in which both the upward and downward motions are caused by weight, and that the order of the universe is a result of two competing attractions (jadhb): one of these being "between the sublunar and celestial elements", and the other being "between all parts of each element separately".[23] and in mechanics he was a founder of statics.[24] In addition, Thābit's Liber Karatonis contained proof of the law of the lever. This work was the result of combining Aristotelian and Archimedean ideas of dynamics and mechanics.[11]

One of Qurra's most important pieces of text is his work with the Kitab fi 'l-qarastun. This text consists of Arabic mechanical tradition.[25] Another piece of important text is Kitab fi sifat alwazn, which discussed concepts of equal-armed balance. Qurra was reportedly one of the first to write about the concept of equal-armed balance or at least to systematize the treatment.

Qurra sought to establish a relationship between forces of motion and the distance traveled by the mobile.[25]



Thābit was well known as a physician and produced a substantial number of medical treatises and commentaries. His works included general reference books such as al-Dhakhira fī ilm al-tibb ("A Treasury of Medicine"), Kitāb al-Rawda fi l–tibb ("Book of the Garden of Medicine"), and al-Kunnash ("Collection"). He also produced specific works on topics such as gallstones; the treatment of diseases such as smallpox, measles, and conditions of the eye; and discussed veterinary medicine and the anatomy of birds. Thābit wrote commentaries on the works of Galen and others, including such works as On Plants (attributed to Aristotle but likely written by the first-century BC philosopher Nicolaus of Damascus).[5]

One account of Thābit's work as a physician is given in Ibn al-Qiftī's Ta’rikh al-hukamā, where Thābit is credited with healing a butcher who was presumed to be certain to die.[5]



Only a few of Thābit's works are preserved in their original form.

  • On the Sector-Figure which deals with Menelaus' theorem.[26]
  • On the Composition of Ratios[26]
  • Kitab fi 'l-qarastun (Book of the Steelyard) [25]
  • Kitab fi sifat alwazn (Book on the Description of Weight)[25] - Short text on equal-armed balance

Additional works by Thābit include:

  • Kitāb al-Mafrūdāt (Book of Data)
  • Maqāla fīistikhrāj al-a‘dād al-mutahābba bi–suhūlat al-maslak ilā dhālika (Book on the Determination of Amicable Numbers)
  • Kitāb fi Misāhat qat‘ almakhrūt alladhī yusammaā al-mukāfi’ (Book on the Measurement of the Conic Section Called Parabolic)
  • Kitāb fī Sanat al-shams (Book on the Solar Year)
  • Qawl fi’l–Sabab alladhī ju‘ilat lahu miyāh al-bahr māliha (Discourse on the Reason Why Seawater Is Salted)
  • al-Dhakhira fī ilm al-tibb (A Treasury of Medicine)
  • Kitāb fi ‘ilm al-‘ayn . . . (Book on the Science of the Eye…)
  • Kitāb fi’l–jadarī wa’l–hasbā (Book on Smallpox and Measles)
  • Masā’il su’ila ’anhā Thābit ibn Qurra al-Harrānī (Questions Posed to Thābit. . .)[27]

In his epitome of al-Qifṭī's Kitāb ikhbār al-'ulamā' bi akhbār al-ḥukamā, al-Zawzanī lists seven religious works in Syriac by Thābit and says that he also wrote in Syriac on music and geometry. According to Bar Hebraeus, the 13th-century Syriac historian, Thābit wrote some 150 works in Arabic and 16 in Syriac. He claims to have seen most of the Syriac works himself and lists them. The list of Bar Hebraeus is consistent with that of al-Zawzanī. Most of the works concern pagan religion, but there is a work on music and two on geometry as well as a "book of the chronicle of the ancient Syrian kings, who are Chaldeans" and a "book on the renown of his race and his forefathers, from whom they descend".[28]



See also

  • al-Battani, a contemporary Sabian astronomer and mathematician


  1. ^ Panza, Marco (2008). "The Role of Algebraic Inferences in Na'īm Ibn Mūsā's Collection of Geometrical Propositions". Arabic Sciences and Philosophy. 18 (2): 165–191. CiteSeerX doi:10.1017/S0957423908000532. S2CID 73620948.
  2. ^ For the Arabic name, see Rashed & Morelon 1960–2007; for the nisba al-Ṣābiʾ applied as a family name, see De Blois 1960–2007; for the Latin name, see Latham 2003, p. 403.
  3. ^ Rashed 2009d, pp. 23–24; Holme 2010.
  4. ^ Holme 2010.
  5. ^ a b c Rosenfeld & Grigorian 2008, p. 292.
  6. ^ De Blois 1960–2007; Hämeen-Anttila 2006, p. 43, note 112; Van Bladel 2009, p. 65; Rashed 2009b, p. 646; Rashed 2009d, p. 21; Roberts 2017, pp. 253, 261–262. Some scholars have also suggested that he adhered to Mandaeism, a Gnostic baptist sect whose members were likewise called 'Sabians' (see Drower 1960, pp. 111–112; Nasoraia 2012, p. 39).
  7. ^ Gingerich 1986; Rashed & Morelon 1960–2007.
  8. ^ Rashed 2009c, pp. 3–4.
  9. ^ a b "Thābit ibn Qurrah | Arab mathematician, physician, and philosopher". Encyclopedia Britannica. Retrieved 2020-11-20.
  10. ^ a b c d e "Thabit ibn Qurra". islamsci.mcgill.ca. Retrieved 2020-11-26.
  11. ^ a b c d Shloming, Robert (1970). "Thabit Ibn Qurra and the Pythagorean Theorem". The Mathematics Teacher. 63 (6): 519–528. doi:10.5951/MT.63.6.0519. ISSN 0025-5769. JSTOR 27958444.
  12. ^ Rashed & Morelon 1960–2007; "Thabit biography". www-groups.dcs.st-and.ac.uk. The sect, with strong Greek connections, had in earlier times adopted Greek culture, and it was common for members to speak Greek although after the conquest of the Sabians by Islam, they became Arabic speakers. There was another language spoken in southeastern Turkey, namely Syriac, which was based on the East Aramaic dialect of Edessa. This language was Thābit ibn Qurra's native language, but he was fluent in both Greek and Arabic.
  13. ^ Rashed & Morelon 1960–2007.
  14. ^ a b c d Carmody, Francis J. (1955). "Notes on the Astronomical Works of Thabit b. Qurra". Isis. 46 (3): 235–242. doi:10.1086/348408. ISSN 0021-1753. JSTOR 226342. S2CID 143097606.
  15. ^ Cohen, H. Floris (2010). "Greek Nature-Knowledge Transplanted: The Islamic World". How Modern Science Came into the World: Four Civilizations, One 17th-Century Breakthrough. Amsterdam University Press. pp. 53–76. doi:10.2307/j.ctt45kddd.6. ISBN 978-90-8964-239-4. JSTOR j.ctt45kddd.6. Retrieved 2020-11-27.
  16. ^ a b Brentjes, Sonja; Hogendijk, Jan P (1989-11-01). "Notes on Thabit ibn Qurra and his rule for amicable numbers". Historia Mathematica. 16 (4): 373–378. doi:10.1016/0315-0860(89)90084-0. ISSN 0315-0860.
  17. ^ Sayili, Aydin (1960-03-01). "Thâbit ibn Qurra's Generalization of the Pythagorean Theorem". Isis. 51 (1): 35–37. doi:10.1086/348837. ISSN 0021-1753. S2CID 119868978.
  18. ^ "Thabit ibn Qurra". islamsci.mcgill.ca. Retrieved 2022-11-19.
  19. ^ Sabra, A. I. (1968). "Thābit Ibn Qurra on Euclid's Parallels Postulate". Journal of the Warburg and Courtauld Institutes. 31: 12–32. doi:10.2307/750634. JSTOR 750634. S2CID 195056568. Retrieved 2022-11-19.
  20. ^ Masood, Ehsan (2009). Science & Islam : a history. Library Genesis. London : Icon. ISBN 978-1-84831-040-7.
  21. ^ Brentjes, Sonja (April 2021). "Wilbur R. Knorr on Thābit ibn Qurra: A Case-Study in the Historiography of Premodern Science". Aestimatio: Sources and Studies in the History of Science. 1. University of Toronto Libraries - UOTL: 113–172. doi:10.33137/aestimatio.v1i1.37604.
  22. ^ Shloming, Robert (1970-10-01). "Historically Speaking—: Thabit Qurra and the Pythagorean Theorem". The Mathematics Teacher. 63 (6): 519–528. doi:10.5951/MT.63.6.0519. ISSN 0025-5769.
  23. ^ Mohammed Abattouy (2001). "Greek Mechanics in Arabic Context: Thabit ibn Qurra, al-Isfizarı and the Arabic Traditions of Aristotelian and Euclidean Mechanics", Science in Context 14, p. 205-206. Cambridge University Press.
  24. ^ Holme 2010.
  25. ^ a b c d Abattouy, Mohammed (June 2001). "Greek Mechanics in Arabic Context: Thābit ibn Qurra, al-Isfizārī and the Arabic Traditions of Aristotelian and Euclidean Mechanics". Science in Context. 14 (1–2): 179–247. doi:10.1017/s0269889701000084. ISSN 0269-8897. S2CID 145604399.
  26. ^ a b Van Brummelen, Glen (2010-01-26). "Review of "On the Sector-Figure and Related Texts"". MAA Reviews. Retrieved 2017-05-12.
  27. ^ Rosenfeld & Grigorian 2008, pp. 292–295.
  28. ^ Hidemi Takahashi, "Thābit b. Qurra", Gorgias Encyclopedic Dictionary of the Syriac Heritage: Electronic Edition (Beth Mardutho: The Syriac Institute, 2011). Retrieved 21 April 2024.

Sources used


Further reading

  • Rashed, Roshdi, ed. (2009a). Thābit ibn Qurra: Science and Philosophy in Ninth-Century Baghdad. Scientia Graeco-Arabica. Berlin: De Gruyter. doi:10.1515/9783110220797. ISBN 9783110220780.
  • Francis J. Carmody: The astronomical works of Thābit b. Qurra. 262 pp. Berkeley and Los Angeles: University of California Press, 1960.
  • Rashed, Roshdi (1996). Les Mathématiques Infinitésimales du IXe au XIe Siècle 1: Fondateurs et commentateurs: Banū Mūsā, Ibn Qurra, Ibn Sīnān, al-Khāzin, al-Qūhī, Ibn al-Samḥ, Ibn Hūd. London.{{cite book}}: CS1 maint: location missing publisher (link) Reviews: Seyyed Hossein Nasr (1998) in Isis 89 (1) pp. 112-113; Charles Burnett (1998) in Bulletin of the School of Oriental and African Studies, University of London 61 (2) p. 406.
  • Churton, Tobias. The Golden Builders: Alchemists, Rosicrucians, and the First Freemasons. Barnes and Noble Publishing, 2006.
  • Hakim S Ayub Ali. Zakhira-i Thābit ibn Qurra (preface by Hakim Syed Zillur Rahman), Aligarh, India, 1987.