Namely, Ya'qūb ibn Tāriq (fl. Baghdad, c. 760) in Kennedy, 157–63, now supplemented by Hogendijk 1; Thābit ibn Qurra (fl. Baghdad, c. 900) in Kennedy, 140–3, and Morelon, pp. xciii–cxviii, 93–117, and 230–59; al-Battānî (fl. Raqqa, c. 910) in Nallino, i, 85–92 (Latin trans.) and 265–72 (comm.), and iii, 129–38 (Arabic text), and a new, English translation and commentary in Bruin; Maimonides (fl. Cordova then Cairo, c. 1175) in Neugebauer 1, 349–60, and 2; and various early tables for determining lunar crescent visibility examined in my contribution to the Kennedy Festschrift, now supplemented by Hogendijk 2.
2.
I am currently preparing for publication surveys of lunar crescent visibility in later Egyptian / Syrian and Yemeni sources. An investigation of the legal texts on the subject is a formidable task for the future.
3.
On Ibn Yūnus and his works see my article in DSB, xiv, 574–80, to which add the sources listed in Cairo survey, no. B59. The listings in Sezgin, v, 342–3, vi, 228–31, and vii, 173, confuse the Ḥākimī Zīj with the Cairo corpus of tables for timekeeping and include a spurious astrological text. On Ibn Yūnus's milieu see the articles “Fāṭimids”, “Fusṭāṭ”, “al-Ḥākim”, and “al-Ḳāhira” in EI2.
4.
A detailed analysis of the spherical astronomy in the Ḥākimī Zīj is contained in King 1. In addition I have prepared a new translation of the observation accounts first published in Caussin as well as an analysis of the planetary astronomy in this work.
5.
On astronomy in medieval Egypt and Yemen see King 3/III, and 2 (also 3/IV), respectively.
6.
The titles of the 81 chapters of the Ḥākimī Zīj are listed in the introduction published in Caussin, 67–79. There was no chapter devoted entirely to lunar cresent visibility, but this topic was probably discussed in Chap. 76 entitled Fī ẓuhūr al-kawākib wa-khtifā'ihā, “On the first and last visibility of the planets [including the moon?]”.
7.
On the Muṣṭalaḥ Zīj (Kennedy, no. 47) see King 3/III, 535, and V, 135, and also Cairo survey, no. C12.
8.
de Slane, 446.
9.
Cairo survey, no. C12, p. 57asub 2.1.15(c).
10.
Ibid., no. B59, p. 43bsub 2.1.6.
11.
On Abu l-'Uqūl and his works see King 2, Section II.9 (pp. 30–32) and also 3/IV, 63. The Mukhtār Zīj is listed as Kennedy, no. 57.
12.
Rieu, 525–6.
13.
See Kennedy, 141–2, on planetary longitude determinations, and al-Bîrūnî, Section 321 on pp. 186–91 for an example of a medieval Islamic ephemeris.
14.
See Kennedy, 143b, and as-Saleh in Kennedy.
15.
Kennedy, 140b–141a.
16.
Ibid., 142b.
17.
On the ‘arc of light’ see Kennedy, 128. In Hogendijk 2 it is shown that the earliest Muslim astronomers used a more complicated formula than (2) in order to tabulate L(Δλ,β).
18.
On the shadow functions see Schoy and also Kennedy, 140a.
19.
See King 1, passim.
20.
See Kennedy, 140b, and the article “Maṭāli” in EI2.
21.
Kennedy, 170b, and King 1, Part II, Section 14.
22.
See Ilyas for a recent study of the problem of lunar crescent visibility by a modern astronomer.
23.
See the references to Neugebauer's studies in ref. 1 above.
24.
Ibid.
25.
Ibid.
26.
On al-Khalîlî see Suter, no. 418; Cairo survey, no. C37; and my article in DSB.
27.
al-Bîrūnî: WrightR. R., trans., The book of instruction in the elements of the art of astrology by … al-Bīrūnī (London, 1934).
28.
Bruin: BruinF., “The first visibility of the lunar crescent”, Vistas in astronomy, xxi (1979), 331–58.
29.
Cairo catalogue and survey: KingD. A., A catalogue of the scientific manuscripts in the Egyptian National Library, 2 vols (Cairo, 1981–87), and idem, A survey of the scientific manuscripts in the Egyptian National Library (Publications of the American Research Center in Egypt) (Winona Lake, Indiana, 1987).
30.
Caussin: de PercevalCaussin, “Le livre de la grande table Hakémite, observée par le Sheikh … ebn Iounis …”, Notices et extraits des manuscrits de la Bibliothèque Nationale, 7 (An XII = 1804), 16–240. [The pagination in the separatum runs from 1 to 224.].
31.
DSB: Dictionary of scientific biography, 14 vols and 3 supp. vols (New York, 1970–80).
32.
EI2: Encyclopaedia of Islam, 2nd ed., 5 vols to date (Leiden, 1960–).
33.
Hogendijk 1: HogendijkJ. P., “New light on the lunar crescent visibility table of Ya'qūb ibn Ṭāriq”, to appear in Journal of Near Eastern studies.
34.
Hogendijk 2: HogendijkJ. P., “Three Islamic lunar crescent visibility tables”, Journal for the history of astronomy, xix (1988), 29–44.
35.
Ilyas: IlyasM., A modern guide to the astronomical calculations of Islamic calendar, times & qibla (Kuala Lumpur, 1984).
36.
Kennedy: KennedyE. S., “A survey of Islamic astronomical tables”, Transactions of the American Philosophical Society, n.s., xlvi: 2 (1956), 123–77.
37.
Kennedy: KennedyE. S., Colleagues and Former Students, Studies in the Islamic exact sciences (Beirut, 1983). Includes reprints of: KennedyE. S., “The crescent visibility theory of Thābit bin Qurra”, Proceedings of the Mathematical and Physical Society of the United Arab Republic, 1960, 71–74, repr. on pp. 140–3; KennedyE. S. and JanjanianM., “The crescent visibility table in Al-Khwārizmî's Zîj”, Centaurus, xi (1965), 73–78, repr. on pp. 151–6; KennedyE. S., “The lunar visibility theory of Ya'qūb ibn Ṭāriq”, Journal of Near Eastern studies, xxvii (1968), 126–32, repr. on pp. 157–63; and as-SalehJ. A., “Solar and lunar distances and apparent velocities in the astronomical tables of Ḥabash al-Ḥāsib”, al-Abhath, xxiii (1970), 129–77, repr. on pp. 204–52.
38.
Kennedy Festschrift: KingD. A. and SalibaG. (eds), From deferent to equant: Studies in the history of science in the ancient and medieval Near East in honor of E. S. Kennedy. Annals of the New York Academy of Science, d (= 500) (1983). Includes: KingD. A., “Some early Islamic tables for lunar crescent visibility”, on pp. 185–225.
39.
King 1: KingD. A., Spherical astronomy in medieval Islam: The Ḥākimī Zīj of Ibn Yūnus, to appear (Frankfurt-am-Main?).
40.
King 2: KingD. A., Mathematical astronomy in medieval Yemen: A bio-bibliographical survey (Publications of the American Research Center in Egypt) (Malibu, California, 1983).
41.
King 3: KingD. A., Islamic mathematical astronomy (London, 1986). Includes reprints of: III, “The astronomy of the Mamluks”, Isis, lxxiv (1983), 531–55; IV, “Mathematical astronomy in medieval Yemen”, Arabian studies, v (1979), 61–65; and V, “A double-argument table for the lunar equation attributed to Ibn Yūnus”, Centaurus, xviii (1974), 129–46.
42.
Morelon: MorelonR., Thābit ibn Qurra: Oeuvres d'astronomie (Paris, 1987).
43.
Nallino: NallinoC. A., al-Battani sive Albatenii opus astronomicum (Pubblicazioni del Reale Osservatorio de Brera in Milano, xl), 3 vols (Milan and Rome, 1899–1907; reprinted Frankfurt, 1969).
44.
Neugebauer 1: NeugebauerO., “The astronomy of Maimonides and its sources”, Hebrew Union College annual, xxii (1949), 321–63, reprinted in his Astronomy and history: Selected essays (New York, 1983), 381–423.
45.
Neugebauer 2: NeugebauerO., “Astronomical commentary”, in GandzS.ObermannJ. and NeugebauerO., The Code of Maimonides, Book 3, Treatise 8, Sanctification of the New Moon (New Haven, Connecticut, 1956).
46.
Renaud: RenaudH. P. J., “Additions et corrections à Suter ‘Die Mathematiker und Astronomen der Araber’”, Isis, xviii (1932), 166–83.
47.
Rieu: RieuC., Supplement to the Catalogue of the Arabic manuscripts in the British Museum (London, 1894).
48.
Schoy: SchoyC., Über den Gnomonschatten und die Schattentafeln der arabischen Astronomie (Hanover, 1923).
49.
Sezgin: SezginF., Geschichte des arabischen Schrifttums, 10 vols to date (Leiden, 1967–).
50.
de Slane: le Baron de SlaneM., Catalogue des manuscrits arabes (Paris, 1883–95).
51.
Suter: SuterH., “Die Mathematiker und Astronomen der Araber und ihre Werke”, Abhandlungen zur Geschichte der mathematischen Wissenschaften, x (1900), and “Nachträge und Berichtigungen”, ibid., xiv (1902), 157–85 (repr. Amsterdam, 1982, and again in his Beiträge zur Geschichte der Mathematik und Astronomie im Islam, 2 vols (Frankfurt, 1986)).
