An extensive commentary on the Almagest written mainly for didactical purposes, with a focus on the mathematical proofs. Brief characterisations of the contents are given, in particular, by Sabra and Rashed in their arguments in favour of, and against, the existence of one or two Ibn al-Haythams (Muḥammad and al-Ḥasan; the unique manuscript Istanbul, Topkapı, Ahmet III 3329 repeatedly refers to the author as ‘Muḥammad’). Ibn al-Haytham shortens Ptolemy’s discussions, adds proofs for the determination of quantities usually explained in Islamic astronomical handbooks with tables (zījes), but omits most of the practical calculations in order to make the Almagest more accessible for students. He quotes numerous Greek and Arabic predecessors, e.g., besides Ptolemy, Euclid, Theodosius and Menelaos and Thābit ibn Qurra, the Banū Mūsā and Ibrahīm ibn Sinān (Sabra, ‘One Ibn al-Haytham’, p. 37). Furthermore, he presents the Almagest in such a way that it can be used for practical calculations in Islamic lands, by giving spherical-astronomical tables for localities in the second to fourth climates (latitudes 24 to 36°) and basing the planetary mean motion tables on the Persian Yazdigird calendar. Ibn al-Haytham’s commentary cannot be identified with absolute certainty in his extant autobibliographies preserved by Ibn Abī Uṣaybiʿa, but the third item in his list of mathematical works composed up to February 1027, ‘Commentary and Epitome of the Almagest’, covers the contents quite well. Alternative titles: Tahdhīb al-Majisṭī (? Ibn al-Qifṭī), Kitāb fī istrikhrāj al-juzʾ al-ʿamalī min Kitāb al-Majisṭī (? Ibn Abī Uṣaybiʿa, work no. 19 in the supplementary autobibliography).
Content: According to the preface, Ibn al-Haytham’s commentary would follow the structure of the Almagest itself in 13 sections (faṣls). However, the surviving nearly five sections do not run exactly parallel to Books I–V of the Almagest. The work contains:
- Section I: On Ptolemy’s seven cosmological principles (the heavens, the planets and the Earth are spherical; the Earth is at the centre of the heavens, is imperceptibly small in comparison to it, and does not have a locomotion (ḥarakat intiqāl); heavenly motions have varying velocities).
- Section II: On chords, but adding a discussion of sines and tangents and a sine table.
- Section III: On the sector figure (qaṭṭāʿ Baṭlamyūs).
- Section IV: Spherical astronomy, with an explanation of one of Ptolemy’s instruments and solar observations, proofs for calculations of numerous quantities on the sphere, and a huge geographical table.
- Section V: Solar and lunar motion (mean motions, equations, and syzygies; end missing).
Tables The Topkapı manuscript includes frames for 13 tables. In none of these were the tabular values filled in, but in several the title and column headers were written and in some the arguments. The layout of the frames together with the descriptions of the tables and their use in the text make it possible to identify and characterise the intended tables. The tables of chords, the solar declination, right and oblique ascensions, zenith distances and ecliptic angles, the solar equation for eccentricity 2;30, and the equation of the first lunar anomaly were taken directly from Ptolemy’s Almagest. Ibn al-Haytham added: a sine table (for 1, 2, 3, … 90°, with interpolation coefficients); a table for easier calculation of compound ratios needed in the application of the sector figure; a geographical table with coordinates for 432 cities taken from al-Khwārizmī’s Kitāb al-Maʿmūra; a table for the solar altitude and the shadow of a gnomon of 12 digits at noon at the beginning of the twelve zodiacal signs, for latitudes 24, 30, 33 and 36°; solar and lunar mean motion tables; and a table for syzygies. The mean motion tables were set up for the Persian Yazdigird calendar, with instructions for how to use them also with Byzantine-Julian dates, but the yielded positions are explicitly indicated to be Ptolemy’s.
Text: [Istanbul, Topkapı, Ahmet III 3329]
Bibl.: Ibn al-Qifṭī, Taʾrīkh al-ḥukamā (ed. LippertJulius Lippert, Ibn al-Qifṭī’s Taʾrīḫ al-ḥukamā, Leipzig: Dieterich, 1903, pp. 165–168); Ibn Abī Uṣaybiʿa, Uyūn al-anbāʾ (ed. MüllerAugust Müller, ʿUyūn al-anbāʾ fī l-ṭabaqāt al-aṭibbāʾ li-ibn Abī Uṣaybiʿa, 2 vols, Cairo: al-Maṭbaʿa al-Wahbiyya, 1882, pp. 90–98, esp. p. 93 (no. 3) and p. 97, line −13; German tr. WiedemannEilhard Wiedemann, ‘Ibn al Haiṯam, ein arabischer Gelehrter’, in Festschrift J. Rosenthal zur Vollendung seines siebzigsten Lebensjahres gewidmet, Leipzig: Georg Thieme, 1906, Teil I, pp. 147–178, esp. pp. 161 and 170; ed./tr.Savage-Smithetal., no. 14.22, esp. 18.104.22.168/3 and 22.214.171.124/19). — Moritz Steinschneider, ‘Die arabischen Bearbeiter des Almagest’, Bibliotheca mathematica Neue Folge 6 (1892), pp. 53–62, here p. 56; DSBCharles C. Gillispie (ed.), Dictionary of Scientific Biography, 14 vols plus 2 supplementary vols, New York: Scribner’s Sons, 1970–1990 article ‘Ibn al-Haytham’ by Abdelhamid I. Sabra, esp. pp. 199 and 208; GAS VIFuat Sezgin, Geschichte des arabischen Schrifttums. Vol. VI: Astronomie bis ca. 430 H., Leiden: Brill, 1978, p. 259 (no. 15); MAOSICBoris A. Rosenfeld and Ekmeleddin İhsanoğlu, Mathematicians, Astronomers, and other Scholars of Islamic Civilization and their Works (7th–19th c.), Istanbul: Research Centre for Islamic History, Art and Culture (IRCICA), 2003, pp. 130–138 (no. 327, A1); BEAThomas Hockey (ed.), The Biographical Encyclopedia of Astronomers, 2 vols, Dordrecht: Springer, 2007 article ‘Ibn al-Haytham’ by Y. Tzvi Langermann. — Fehmi Edhem Karatay and O. Rešer, Topkapı Saraı Müzesi Kütüphanesi. Arapça yazmalar kataloğu, 4 vols, İstanbul: Topkapı Sarayı Müzesi, 1962–1969, vol. III, p. 783 (no. 7140); Matthias Schramm, ‘Ibn al-Haythams Stellung in der Geschichte der Wissenschaften’, Fikrun wa fann 6 (1965), pp. 85–65, here pp. 78–77; Abdelhamid I. Sabra, N. Shehaby and I. Madkour, Ibn al-Haytham: al-Shukūk ʿalā Batlamyūs (Dubitationes in Ptolemaeum), Cairo: The National Library Press, 1971, pp. 74–77; Abdelhamid I. Sabra, The Optics of Ibn al-Haytham. Books I-III. On Direct Vision, 2 vols, London: Warburg Institute, 1989, part II, pp. xxxiv–xxxvii and xlviii; Roshdi Rashed, Les mathématiques infinitésimales du IXe aux XIe siècle. Vol. II: Ibn al-Haytham, London: Al-Furqān Islamic Heritage Foundation, 1993, pp. 16–18 (English tr. Roshdi Rashed, Ibn al-Haytham and Analytical Mathematics. A History of Arabic Sciences and Mathematics. Vol. 2, New York: Routledge, 2013, pp. 21–24); Abdelhamid I. Sabra, ‘One Ibn al-Haytham or Two? An Exercise in Reading the Bio-bibliographical Sources’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 12 (1998), pp. 1–50, here pp. 33–39 and 48–49; Richard P. Lorch, Thābit ibn Qurra. On the Sector-Figure and Related Texts, Frankfurt am Main: Institut für Geschichte der Arabisch-Islamischen Wissenschaften, 2001, p. 353; Abdelhamid I. Sabra, ‘One Ibn al-Haytham or Two? Conclusion’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 15 (2002–2003), pp. 95–108, here pp. 104–106; Johannes Thomann, ‘The Second Revival of Astronomy in the Tenth Century and the Establishment of Astronomy as an Element of Encyclopedic Education’, Asiatische Studien 71 (2017), pp. 907–957, here pp. 928–929; Y. Tzvi Langermann, ‘Revamping Ptolemy’s Proof for the Sphericity of the Heavens: Three Arabic Commentaries on Almagest I.3’, 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. 159–180, here pp. 160 and 161–167; Roshdi Rashed, Lʼhydrostatique de Ménélaüs. Introduction, édition et traduction, Berlin / Boston: De Gruyter, 2020, pp. 95–96; Paul Hullmeine, Ptolemaic Astronomy in the Cosmological Debates in Classical Arabic Thought. With an Edition of the Arabic Text of Ptolemy’s Planetary Hypotheses, PhD dissertation, München: Ludwig Maximilian University, 2021, pp. 246–247. A second manuscript of this work was sold at Christie’s in 2008: https://www.christies.com/en/lot/lot-5057480.
Ed.: English translation of part of the preface in Sabra, ‘One Ibn al-Haytham’, p. 35, as well as in Langermann, pp. 161–162. French translation of part of the preface in Rashed, L’hydrostatique. Edition of the untitled section on optics on ff. 42v–43v of the Topkapı manuscript in Sabra & Shehaby.