¹ For a collection of such works see, Kennedy, E. S. et al. , Studies in the Islamic Exact Sciences (Beirut, 1983),pp. 50–107Google Scholar, and Saliba, G., The Astronomical Work of Mu'ayyad al-Dīn al-'Urḍī (d. 1266): A Thirteenth Century Reform of Ptolemaic Astronomy, a critical edition of, with an introduction to, ʽUrḍīʼs Kitāb al-Hay'ah, based on all extant manuscripts (Beirut, 1990)Google Scholar; idem, The Final Quest in Astronomical Principles, a critical edition of Ibn al-Shātir's Nihāyat al-sūl fi taşḥīḥ al-uşūl, based on all the extant manuscripts (forthcoming); idem, “The original source of Quṭb al-Dīn al-Shīrāzī's planetary model,” Journal for the History of Arabic Science, 3 (1979): 3–18; idem, “The first non-Ptolemaic astronomy at the Maraghah school,” Isis, 70 (1979): 571–6; idem, “A Damascene astronomer proposes a non-Ptolemaic astronomy,” [Arabic with English summary], Journal for the History of Arabic Science, 4 (1980): 3–17; idem, “Ibn Sīnā and Abū ‘Ubayd al-Jūzjānī: The problem of the Ptolemaic equant,” Journal for the History of Arabic Science, 4 (1980): 376–403; idem, “Arabic astronomy and Copernicus,” Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften, 1 (1984): 73–87; idem, “Theory and observation in Islamic astronomy: the work of Ibn al-Shāṭir of Damascus (d. 1375),” Journal for the History of Astronomy, 18 (1987): 35–43; idem, “The role of the Almagest commentaries in medieval Arabic astronomy: A Preliminary survey of Tūsī's redaction of Ptolemy's Almagest,” Archives Internationales d'Histoire des Sciences, 37 (1987): 3–20; idem, “The role of Maragha in the development of Islamic astronomy: A Scientific revolution before the Renaissance,” Revue de Synthèse, 108 (1987): 361–73; idem, “A medieval Arabic reform of the Ptolemaic lunar model,” Journal for the History of Astronomy, 20 (1989): 157–64.

² The work of Ibn al-Shāṭir's contemporary, Ṣadr al-Sharī'a of Bukhārā (1347) has been the subject of an as yet unpublished dissertation by al-Dallāl, Aḥmad, The Astronomical Work of Ṣadr al-Sharī‛a: An Islamic Response to Greek Astronomy, Columbia University, Department of Middle East Languages and Cultures (New York, 1990),Google Scholar and “A non-Ptolemaic lunar model fromfourteenth-century Central Asia,” Arabic Sciences and Philosophy, 2 (1992): 237–97.

³ For a short biography of Qushjī see, Ṭaşköprülü-Zāde (TZ), Eş-Şeḳā'iḳu N-Nu'mānīye fi 'Ulamā'i D-Devleti L-'Oşmānīye, ed. Furat, Ahmed Subhi (Istanbul, 1985), pp. 159–62.Google Scholar In this biography we are told that Qushjī had written two astronomical works: 1) On the Solution of the Problem of the Moon (for Ulugh Beg), and 2) al-Fatḥiyya (for Muḥammad al-Fātih 1451–1481). Besides, the treatise studied here, Brokelmann and Suter attribute to Qushjī yet a third astronomical work, namely a commentary upon Shīrāzī's astronomical work al-Tuḥfa al-shāhiyya, Brockelmann, C., Geschichte der arabischen Literatur (Weimar, 1898), vol. II, p. 212, Sup. II (Leiden, 1937), pp. 235, 330;Google ScholarSuter, Heinrich, Die Mathematiker und Astronomen der Araber und Ihre Werke (Leipzig, 1900), p. 179.Google Scholar Moreover, MS Marsh 396, fols. 190^r–374 at the Bodleain Library, Oxford, has the title of Sullam al-samā' and is attributed to Qushjī. The text itself is a commentary on Ulugh Beg's Zīj, and begins with the first treatise, thus avoiding the prolegomena which could have shed some light on the identity of the author. Neither Brockelmann nor Suter mention the subject of this study, i.e. the treatise on the solution of the problem of Mercury.

⁴ Suter, Die Mathematiker und Astronomen, pp. 178–9.Google Scholar

⁵ TZ, p. 160.

⁶ TZ, p. 159, and Suter, Die Mathematiker und Astronomen, p. 179.Google Scholar

⁷ The author is grateful to Professor Abd al-Ḥamīd Sabra of Harvard University who supplied him, in 1981, with a copy of his notes covering parts of the manuscript Cārullāh 2060, but not the complete treatise. I am also grateful to the Librarian of the Asiatic Society of Calcutta who first allowed me to have a full copy of Qushjī's text despite the fact that at the time the manuscript was not identified as such. Thanks to the cooperation of the librarians at the Süleymaniye and the Bāyazid libraries the other copies were made available to the author – my heartfelt gratitude for that cooperation.

⁸ I have elsewhere referred to this manuscript in a survey article on “Arabic planetary theories after the eleventh century,” in Rashe, R.(ed), Arabic Science (forthcoming), where the attribution is made to ananonymous student of Ulugh Beg.Google Scholar

⁹ Note the similar language used by Qushjī's contemporary al-Kāshī, Jamshīd b. Ghiyāth al-Dīn in the shorter introduction to his Miftāḥ al-ḥisāb, ed. al-Nābulsī, Nādir (Damascus, 1977), pp. 36–9.Google Scholar

¹⁰ TZ, p. 159.

¹¹ Sayili, Aydin, Ghiyāth al-Dīn al-Kāshī's Letter on Ulugh Bey and the Scientific Activity in Samarqand (Ankara, 1985).Google Scholar

¹² Ibid., and Suter, Die Mathematiker und Astronomen, p. 173.

¹³ Suter, Die Mathematiker und Astronomen, p. 174.Google Scholar

¹⁴ al-Khafrī, Muḥammad b. Aḥmad, al-Takmila fi sharḥ al-Tadhkira, Ẓāhiriyya MS Arabic 6782, fols. 199^r–199^v.Google Scholar

¹⁵ TZ, p. 159.

¹⁶ See the introduction to Zīj, Ulugh Beg's, in Prolégomènes des tables astronomiques d'Ouloug-Beg, tr. comm. par M.L.P.E.A. Sédillot (Paris, 1853), pp. 290 (text), 5 (tr.).Google Scholar

¹⁷ 'Urḍī's Lemma, here called the Principle of the Encompassing (sphere) as it was called by Quṭb al-Dīn al-Shīrāzī at various places in his Nihāyat al-idrāk fī dirāyat al-aflāk, and al-Tuḥfa al-shāhiyya, stipulates that if two equal lines, such as NH, BD, are attached to the extremity of one line such as HB, and are made to move at the same speed, such that angles NHB, and DBH are always equal, then line DN will always be parallel to line HB. For the text of this Lemma and a more detailed description, see Saliba, “The Original Source.”