Bīrūnī's Four-Point Method for Determining the Eccentricity and the Direction of the Apsidal Lines of the Superior Planets

Cf. Toomer G. J. , Ptolemy's Almagest (Princeton, 1998), 484–98, 507–19, 525–37; Pedersen O. , A survey of the Almagest (Odense, 1974), with annotation and new commentary by A. Jones (New York, 2010), 271–83; Neugebauer O. , A history of ancient mathematical astronomy (3 vols, Berlin, 1975), 172–9; Duke D. , “Ptolemy's treatment of the outer planets”, Archives for history of exact sciences, lix (2005), 169–87, esp. pp. 179–82.

Swerdlow N. M. , “Jābir ibn Aflaḥ's interesting method for finding the eccentricities and direction of the apsidal line of a superior planet”, in King D. A. Saliba G. (eds), From deferent to equant: A volume of studies on the history of science of the ancient and medieval Near East in honor of E. S. Kennedy (New York, 1987), 501–12. On the astronomy of Jābir and his critical remarks concerning Ptolemy's Almagest, cf. e.g., Lorch R. P. , Arabic mathematical sciences: Instruments, text, transmission (Aldershot, 1995), chaps. VI, VIII, XVI; Samsó J. , “Ibn al-Haytham and Jābir b. Aflaḥ's criticism of Ptolemy's determination of the parameters of Mercury”, Suhayl, ii (2001), 199–225; Bellver J. , “Jābir b. Aflaḥ on the four-eclipse method for finding the lunar period in anomaly”, Suhayl, vi (2006), 159–248; and Bellver J. , “Jābir b. Aflaḥ on lunar eclipses”, Suhayl, viii (2008), 47–91.

Al-Bīrūnī , al-Qānūnal-mas'ūdī (3 vols, Hyderabad, 1954–56), iii, 1183–4. Its contents are introduced in Kennedy E. S. , “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.

Kennedy E. S. , “Transcription of Arabic letters in geometric figures”, Zeitschrift fur Geschichte der Arabisch-Islamischen Wissenschaften, vii (1991/92), 21–2.

Al-Bīrūnī , al-Qānūn (ref. 3), ii, 665–7; cf. Hartner Willy Schramm Matthias , “Al-Bīrūnī and the theory of the solar apogee: An example of originality in Arabic science”, in Crombie A. C. (ed.), Scientific change (London, 1961), 206–18, pp. 212–14.

Samsó J. , “Al-Bīrūnī in al-Andalus”, in Casulleras J. Samsó J. (eds), From Baghdad to Barcelona (Barcelona, 1996), reprinted in Samsó, Astronomy and astrology in al-Andalus and the Maghrib (Aldershot, 2007) chap. VI.