Three Islamic Lunar Crescent Visibility Tables

For a modern discussion see Ilyas M. , A modern guide to astronomical calculations of Islamic calendar, times and qibla (Kuala Lumpur, 1984).

See King D. A. , “Some early Islamic tables for determining lunar crescent visibility”, in: King D. A. and Saliba G. (eds), From deferent to equant: Studies in the history of science in the Near East in honor of E. S. Kennedy (Annals of the New York Academy of Science, d (= 500); New York, 1987), 185–225.

See Pedersen O. , A survey of the Almagest (Odense, 1974), 386–90.

In this paper we use a semicolon for separating the integral part from the fractional part of a sexagesimal number. Sexagesimal places will be separated by commas. Thus 23°51′20″ will be written as 23;51,20°. The degree symbol (°) will be omitted in all tables.

See Suter H. , Die astronomischen Tafeln des Muhammad ibn Mūsā al-Khwārizmī in der Bearbeitung des Maslama ibn Ahmed al-Madjrītī und der lateinischen Übersetzung des Athelard von Bath auf Grund der Vorarbeiten von A. Bjørnbo und R. Besthorn herausgegeben und kommentiert (Copenhagen, 1914), 168. The entries 21;17 for the third face of Virgo and the first face of Libra are corrections made by O. Neugebauer to Suter's values 21;57, see Neugebauer O. , The astronomical tables of al-Khwārizmī (Copenhagen, 1962) 103. Suter's edition has now been reprinted in Suter H. , Beiträge zur Geschichte der Mathematik und Astronomie im Islam: Nachdruck seiner Schriften aus den Jahren 1892–1922 (Veröffentlichungen des Instituts für Geschichte der Arabisch-Islamischen Wissenschaften, Frankfurt, 1986), i, 473–751.

See King , op. cit., 192–7.

Suter , op. cit. (1914), 16–17, 66–68; Neugebauer , op. cit., 42–44.

Kennedy E. S. and Janjanian M. , “The crescent visibility table in Al-Khwārizmīs Zīj”, Centaurus, xi (1965), 73–78, esp. p. 77. The article of Kennedy and Janjanian has been reprinted in Kennedy E. S. , colleagues and former students, Studies in the Islamic exact sciences (Beirut, 1983), 151–6.

King , op. cit., 194.

Suter , op. cit. (1914), 19, lines 7–8; Neugebauer , op. cit., 47, line 2, 96.

Toomer G. J. , “A survey of the Toledan Tables”, Osiris, xv (1968), 5–174, esp. p. 142.

A perfectly symmetrical table based on the Indian criterion can be obtained in the following way: For the first six signs, compute for the situation where the sun is at the beginning of each face, and for the last six signs, compute for the situation where the moon is at the end of each face.

For an explanation of the concept of oblique ascension see Pedersen , op. cit., 99–101, 110–15.

Toomer , op. cit., 146.

North J. , Horoscopes and history (London, 1986), 17.

Kennedy E. S. and Kennedy M. H. , Geographical coordinates of localities from Islamic sources (Veröffentlichungen des Instituts für Geschichte der Arabisch-Islamischen Wissenschaften A 2, Frankfurt, 1987), 701.

Kennedy and Kennedy , op. cit., 227.

Kennedy and Kennedy , op. cit., p. xliv.

Kennedy and Kennedy , op. cit., 305; the actual latitude of Saragossa is 41;39°.

See for references Hogendijk J. P. , “Discovery of an 11th-century geometrical compilation: The Istikmāl of Yūsuf al-Mu'taman ibn Hūd, King of Saragossa”, Historia mathematica, xiii (1986), 43–52.

Kennedy and Kennedy , op. cit., 701.

The Mufrad Zīj is listed as no. 65 in Kennedy E. S. , “A survey of Islamic astronomical tables”, Transactions of the American Philosophical Society, n.s., xlvi: 2 (1956), 123–77. The work is extant in Ms. Cambridge, Browne 0.1. On al-Tabarī see Sezgin F. , Geschichte des arabischen Schrifttums, vi (Leiden, 1978), 385–6.

King , op. cit. (ref. 2), 208. The lunar visibility table is on f. 129a–129b of the manuscript in ref. 22.

Kennedy and Kennedy , op. cit., 688.

For solutions to this problem cf. Sédillot J.-J. and Sédillot L.-A. , Traité des instruments astronomiques des Arabes (Paris; 1834, reprinted Frankfurt, 1986, as Veröffentlichungen des Instituts für Geschichte der Arabisch-Islamischen Wissenschaften B 2), 258–64, and Kennedy E. S. , “Spherical astronomy in Kāshī's Khāqānī Zīj”, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, ii (1985), 1–46.

See King D. A. , “Ibn Yūnus' Very useful tables for reckoning time by the sun”, Archive for history of exact sciences, x (1973), 342–94, reprinted in King D. A. , Islamic mathematical astronomy (London, 1986).

See Pedersen , op. cit. (ref. 3), 386–90.

On Abū Ja°far al-Khāzin, see Sezgin , op. cit., v (Leiden, 1974), 298–9, 305–7, and vi, 189–90.

See King , op. cit. (ref. 2), 207. The lunar visibility table is in Ms. Paris, Bibliothèque Nationale, Fonds Arabe 5968, f. 157b-158a. On the Dustūr al-Munajjimīn see Sezgin , op. cit., vi, 63–64.

On f. 76b of the manuscript cited in ref. 29.

See King , op. cit. (ref 2), 207. On al-Abharī and his Zīj see Suter H. , Die Mathematiker und Astronomen der Araber und ihre Werke (Leipzig, 1900), 145, and Kennedy , op. cit. (ref. 22), no. 56. The lunar visibility table is in Ms. Dublin, Chester Beatty 4076, f. 16b–17a. Suter's book has been reprinted in Suter , Beiträge (ref. 5), 1–285.

See refs 29 and 31.