Bīrūnī's Examination of the Path of the Centre of the Epicycle in Ptolemy's Lunar Model

Cf. Toomer G. J. , Ptolemy's Almagest (Princeton, 1998), 220f; Pedersen O. , A survey of the Almagest (Odense, 1974), with annotation and new commentary by A. Jones (New York, 2010), chap. 6; Neugebauer O. , A history of ancient mathematical astronomy (3 Parts, Berlin, Heidelberg and New York, 1975), 53f.

He gives his dated systematic observations, performed in the Maragha Observatory from 7 March 1262 A.D. (lunar eclipse) to 12 August 1274 A.D. (Jupiter), and explained his computations of the Ptolemaic planetary orbital elements in a treatise named Talkhīṣ al-majsṭī (“The compendium of the Almagest”, MS. Leiden, Or. 110). The contents of the treatise are listed in G. Saliba, “An observational notebook of a thirteenth-century astronomer”, Isis, lxxiv (1983), 388–401, and its two parts treated in his “Solar observations at Maragha observatory”, Journal for the history of astronomy, xvi (1985), 113–22 and “The determination of new planetary parameters at the Maragha observatory”, Centaurus, xxix (1986), 249–71. The three articles are reprinted in G. Saliba, A history of Arabic astronomy: Planetary theories during the golden age of Islam (New York and London, 1994). Al-Māghribā's lunar measurements will be discussed in a forthcoming paper: S. M. Mozaffari, “Muḥyā al-Dān al-Maghribā's lunar measurements at the Maragha Observatory”, Archive for history of exact sciences, DOI 10.1007/s00407-013-130-4.

Pedersen, op. cit. (ref. 1), 188.

A. al-Bīrūnī, al-Qānūn al-mas'ūdī (3 vols, Hyderabad, 1954), 794–5. The contents of this work are introduced in E. S. Kennedy, “Al-Bīrūnī's Masudic Canon”, Al-Abhath, xxiv (1971), 59–78; reprinted in E. S. Kennedy, colleagues, and former students, Studies in the Islamic exact sciences (Beirut, 1983), 573–92.

The published text (hereafter: PB) reads “the apogee of the Moon's orb”, which makes no sense here.

The original lettering is transcribed according to the standard proposed by Kennedy E. S. , “Transcription of Arabic letters in geometric figures”, Zeitschrift fur Geschichte der Arabisch-Islamischen Wissenschaften, vii (1991–92), 21–2.

PB: E, A, L, and H.

PB: TE.

PB: ZA.

Hartner W. , “The Mercury horoscope of Marcantonio Michiel of Venice”, Vistas in astronomy , i (1955), 84–138, pp. 109–22; reprinted with additions in W. Hartner, Oriens-Occidens (Hildesheim, 968), 440–95. Following Hartner's study, cf. Pedersen, op. cit. (ref. 1), 320–4; Neugebauer, op. cit. (ref. 1), i, 168–9.

Kennedy E. S. , “A fifteenth-century planetary computer: Al-Kīshī's ‘Ṭabaq al-Manāṭeq’ II. Longitudes, distances, and equations of the planets”, Isis, xliii (1952), 42–50, pp. 46–7 and 49–50 (reprinted in idem, Studies (ref. 4), 472–80, pp. 476–7 and 479–80); Samsó J. Mielgo H. , “Ibn al-Zarqālluh on Mercury”, Journal for the history of astronomy , xxv (1994), 289–96. Neither Ibn al-Zarqālluh nor al-Kāshī considered the path of the centre of the lunar epicycle as an ellipse; cf. Puig R. , “Al-Zarqālluh's graphical method for finding lunar distances”, Centaurus , xxxii (1989), 294–309; Kennedy E. S. , “A fifteenth-century planetary computer: Al-Kāshī's ‘Ṭabaq al-Manāṭeq' I. Motion of the Sun and the Moon in longitude”, Isis, xli (1950), 180–3, pp. 182–3 (reprinted in idem, Studies (ref. 4), 452–5, pp. 454–5).

There are many editions of Reinhold's commentary. In the Paris, 1553 edition, the figure for the Moon is between ff. 38 and 39 and for Mercury between ff. 68 and 69.