Work C.1.12
Abū l-Ḥasan al-Nasawī
الإشباع في شرح الشكل القطّاع
al-Ishbāʿ fī sharḥ al-shakl al-qaṭṭāʿ
A treatise on the sector figure (shakl al-qaṭṭāʿ, the Arabic term for the Theorem of Menelaos, also called ‘secant figure’ or ‘quadrilateral figure’ and ‘Transversalensatz’ in German), written in 1036-7, which repeatedly quotes from, and comments on, Book I of the Almagest. It consists of three sections (fuṣul): Section 1 deals with trigonometry, Ptolemy’s calculation of chords and the determination of the obliquity of the ecliptic; Section 2 discusses the sector figure in the plane and on the sphere and propositions that Ptolemy proofs using it; and Section 3 considers ratios and introduces other problems that can be solved by means of the sector figure. Lorch pointed out the close correspondence of al-Nasawī’s formulations with what he, at the time, considered to be a Latin commentary on the Almagest in the manuscript Dresden, SLUB, Db. 87. Grupe (‘The “Thābit Version”’, The Latin Reception) claimed that al-Nasawī made a direct use of Thābit b. Qurra’s translation of the Almagest (A.1.3), which he corroborated by an inspection of the sole surviving Jaipur manuscript of that work (‘Manuscript Jaipur 20’).
Note Iranian scholars have established al-Nasawī’s lifetime (cf. Ghorbani, BEA): in the preface of his book on falconry (Bāz-nama), finished in the month Shahrīwar of the Yazdigird year 449 (473/1080), al-Nasawī states that he was born in Rayy in the Yazdigird year 371 (392-3/1002-3); al-Bayhaqī in fact suggests that he became nearly 100 years old. In his K. al-Lāmiʿ fī amthilat al-Zīj al-Jāmiʿ, al-Nasawī mentions that he was a student of Kūshyār ibn Labbān, who still made a copy of his zīj in 1025 (Zamani). Al-Nasawī wrote a Persian treatise on Indian arithmetic for the young Buyid ruler Madj al-Dīn (d. 1029), of which he later also made an Arabic version. His commentary on Euclid’s Elements was written for the famous shiʿite scholar al-Sharīf al-Murtaḍā (965–1044) in Baghdad. The present work is likewise dedicated to al-Murtaḍā and can be dated to
Text: [Istanbul, Topkapı, Ahmet III 3464]
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Bibl.: al-Bayhaqī, Tatimma (ed. ShafīʿMuḥammad Shafīʿ, Tatimma Ṣiwān al-ḥikma of ʿAlī b. Zaid al-Baihaḳī. Fasc. 1: Arabic text, Lahore: Ishwar Das, 1935 (1352 AH), pp. 109–110; English tr. MeyerhofMax Meyerhof, ‘ʿAlī al-Bayhaqī’s Tatimmat Ṣiwān al-ḥikma. A Biographical Work on Learned Men of the Islam’, Osiris 8 (1948), pp. 122–217, p. 170 (no. 64)). — SuterHeinrich Suter, Die Mathematiker und Astronomen der Araber und ihre Werke, Leipzig: Teubner, 1900, pp. 96–97 (no. 214); GAS VFuat Sezgin, Geschichte des arabischen Schrifttums. Vol. V: Mathematik bis ca. 430 H., Leiden: Brill, 1974, pp. 345–348, esp. p. 347; DSBCharles C. Gillispie (ed.), Dictionary of Scientific Biography, 14 vols plus 2 supplementary vols, New York: Scribner’s Sons, 1970–1990 article ‘al-Nasawī’ by A. S. Saidan; GhorbaniAbolghasem Ghorbani, Zindagīnāma-yi rīyāḍīdānān-i dawra-yi Islāmī. Az sada-yi siwum tā sada-yi yāzdahum-i Hijrī, Tehran: Markaz-i Nashr-i Dānishgāhī, 1986–1987, pp. 477–484 (no. 159), esp. p. 481; BEAThomas Hockey (ed.), The Biographical Encyclopedia of Astronomers, 2 vols, Dordrecht: Springer, 2007 article ‘Nasawī’ by Hamid-Reza Giahi Yazdi; Islamic Scientific Manuscript Initiative: https://ismi.mpiwg-berlin.mpg.de/text/139268. — Axel Björnbo and Heinrich Suter, Thabits Werk über den Transversalensatz (liber de figura sectore), Erlangen: Mencke, 1924, pp. 53–55; Oskar Schirmer, ‘Studien zur Astronomie der Araber’, Sitzungsberichte der Physikalisch-Medizinischen Sozietät zu Erlangen 58 (1926), pp. 33–88, here pp. 43, 46–49, and 80–85 (Anhang II, by Eilhard Wiedemann); Richard P. Lorch, Thābit ibn Qurra. On the Sector-Figure and Related Texts, Frankfurt am Main: Institut für Geschichte der Arabisch-Islamischen Wissenschaften, 2001, pp. 16–17, 343, 348, 355–357, and 362–375; Dirk Grupe, ‘The ‘Thābit-Version’ of Ptolemy’s Almagest in MS Dresden Db.87’, Suhayl 11 (2012), pp. 147–153, here p. 149; Dirk Grupe, The Latin Reception of Arabic Astronomy and Cosmology in Mid-Twelfth-Century Antioch. The Liber Mamonis and the Dresden Almagest, PhD dissertation, The Warburg Institute, 2013, pp. 79, 117–125, and 395–407 (Appendix C); Maryam Zamani, Wīrāyish, tarjama wa-sharḥ-i chahār faṣl-i awwal az risāla-yi al-Lāmiʿ fī amthilat al-Zīj al-Jāmiʿ, taʾlīf-i ʿAlī ibn Aḥmad-i Nasawī, MSc thesis, Institute for the History of Science, Tehran University, 2014, pp. 12 and 13; Dirk Grupe, ‘Thābit ibn Qurra’s Version of the Almagest and Its Reception in Arabic Astronomical Commentaries (based on the presentation held at the Warburg Institute, London, 5th November 2015)’, in David Juste, Benno van Dalen, Dag Nikolaus Hasse and Charles Burnett (eds), Ptolemy’s Science of the Stars in the Middle Ages, Turnhout: Brepols, 2020, pp. 139–157, here pp. 145–147 and 153; Dirk Grupe, ‘Manuscript Jaipur 20 and the Arabic Translation of Ptolemy’s Almagest by Thābit ibn Qurra’, in Fahameddin Başar, Mustafa Kaçar, M. Cüneyt Kaya and A. Zişan Furat (eds), The 1st International Prof. Dr. Fuat Sezgin Symposium on History of Science in Islam Proceedings Book. June 13-15, 2019, Istanbul: Istanbul University Press, 2020, pp. 139–149, esp. p. 145.
Ed.: Schirmer includes a German translation of the preface by Eilhard Wiedemann. Several sections from al-Nasawī’s treatise are quoted and translated into English in Lorch; Grupe, The Latin Reception; and Grupe, ‘Thābit ibn Qurra’s Version’.
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