The Maximum Solar Equation in the Alfonsine Tables

See Samsó J. , “On the solar model and the precession of the equinoxes in the Alphonsine zij and its Arabic sources”, History of oriental astronomy: Proceedings of an International Astronomical Union Colloquium no. 91, held in New Dehli, India (13–16 November 1985), ed. by Swarup G. Bag A. K. , and Shukla K. S. (Cambridge, 1987), 174–83, espec. p. 176 (reprinted in Samsó J. , Islamic astronomy and medieval Spain (Aldershot, 1994), Essay XIX); Suter H. , Die astronomischen Tafeln des Muhammad ihn Mūsā al-Khwārizmī (Copenhagen, 1914), 134; for Ibn Mu^cādh, see Samsó J. , Las ciencias de los antiguos en al-Andalus (Madrid, 1992), 157; Nallino C. A. , Al-Battānī sive Albatenii Opus astronomicum (3 vols, Milan, 1899–1907), ii, 81; Toomer G. J. , “A survey of the Toledan Tables”, Osiris, xv (1968), 5–174 (espec. p. 56); Richter-Bernburg L. , “Ṣā^cid, the Toledan Tables, and Andalusī science”, Annals of the New York Academy of Sciences, vol. 500 (1987), 373–401.

Poulle E. , “Jean de Murs et les tables alphonsines”, Archives d'histoire doctrinale et littêraire du moyen âge, xlvii (1980), 241–71. In the Expositio John of Murs refers to the Alfonsine Tables (see, e.g., p. 253: “Alfonsius … in capite tabule motus solis”) as well as to the canons (p. 256: “ut invenit Alfonsius causa introductionis tabularum ejus …”). The original version of the Alfonsine Tables does not survive, but the canons, preserved in Castilian in a unique manuscript, have been published: M. Rico y Sinobas, Libros del Saber de Astronomía del Rey D. Alfonso X de Castillo (5 vols, Madrid, 1863–67), iv, 111–83. In the course of preparing a new edition of this important text, we have noticed many errors in Rico's transcription.

Poulle , op. cit. (ref. 2), 250–6.

Neugebauer O. , “Thābit Ben Qurra ‘On the solar year’ and ‘On the motion of the eighth sphere’”, Proceedings of the American Philosophical Society, cvi (1962), 264–99 (espec. p. 285); Morelon R. , Thābit ibn Qurra: Oeuvres d'astronomie (Paris, 1987), pp. lii, 60. In the treatise on calendar reform addressed to Pope Clement VI in 1345, the year length according to Alfonso is given as 365^d 5;49,16^h (= 365;14,33,10^d): Schabel C. , “John of Murs and Firmin of Beauval's Letter and Treatise on the Calendar for Clement VI”, Cahiers de l'Institut du Moyen-Âge Grec et Latin, no. 66 (1996), 187–215 (espec. p. 197).

Poulle , op. cit. (ref. 2), 251. For other examples of the convention for expressing the length of the year as a unit fraction less than (or more than) 365 ¼^d, see Toomer G. J. , “The solar theory of az-Zarqāl: A history of errors”, Centaurus, xiv (1969), 306–36 (espec. pp. 318–19).

Poulle , op. cit. (ref. 2), 255.

Ratdolt E. , Tabule astronomice illustrissimi Alfontij regis castelle (Venice, 1483), d5r.

Ptolemy's determination of the solar eccentricity depends on observations of two equinoxes and one solstice (Almagest, III.4, transl. in Toomer G. J. , Ptolemy's Almagest (New York and Berlin, 1984), 153–5). In the work by Banū Mūsā (often attributed to Thābit), On the solar year, solar observations at the octant points serve the same purpose (Neugebauer, op. cit. (ref. 4), 274—-5); and al-Bīrūnī (d. 1048) correctly noted that, in the general case, three solar observations at arbitrary times are sufficient, ascribing this discovery to his predecessor, Abū Na⋅r Man⋅ūr b. ^cAlī b. ^cIrāq (see al-Bīrūnī, The chronology of ancient nations, transl. by Sachau C. E. (London, 1879), 167).

Poulle , op. cit. (ref. 2), 263; North J. D. , “Just whose were the Alfonsine Tables?”, in From Baghdad to Barcelona: Studies in the Islamic exact sciences in honour of Prof. Juan Vernet, ed. by Casulleras J. and Samsó J. (Barcelona, 1996), 453–75 (espec. p. 461).

For planetary positions and apogees according to the Toledan Tables we use a computer program prepared by Kennedy E. S. and Mielgo H. . See also Israeli Isaac , Yesod ^cOlam, V.9, in idem, Liber Jesod Olam seu Fundamentum mundi , ed. by Goldberg B. and Rosenkranz L. (2 vols, Berlin, 1846–48), ii, 40b. Azarquiel took the tropical longitude of the solar apogee to be about 86° in 1074–75: See Samsó , Las ciencias (ref. 1), 211.

Almagest , III.7, transl. in Toomer , op. cit. (ref. 8), 168.