IBN AL-Zarqālluh on Mercury

For a good survey of medieval and Renaissance equatoria see Poulle Emmanuel , Les instruments de la théorie des planètes selon Ptolémée: Equatoires et horlogerie planétaire du XIIIe au XVIe siècle (2 vols, Geneva and Paris, 1980).

Rico y Sinobas Manuel , Libros del saber de astronomia del rey D. Alfonso X de Castilla, iii (Madrid, 1864), 241–84. On these two astronomers see Samsó Julio , Las ciencias de los antiguos en al-Andalus (Madrid, 1992), 80–84, 105–10, 147–52, 166–240.

Comes Mercè , Ecuatorios andalusíes: Ihn al-Samḥ, al-Zarqālluh y Abū-l-Ṣalt (Barcelona, 1991). On the basis of this study the two instruments were reconstructed by M. Comes and H. Mielgo for the exhibition “El legado cientifico andalusf” held in Madrid (Museo Arqueológico National) in April-May 1992. Photographs of these reconstructions appear in Vernet J. and Samsó J. (eds), El legado cientifico andalusi (Madrid, 1992), 77, 211, 212. Two sets of copies of both instruments were made and they are kept in the Museo Nacional de la Ciencia y de la Técnica (Madrid) and in the Arabie Department of the University of Barcelona.

Rico , Libros, iii, 278–80. The method used to draw the curve was described by Willy Hartner in “The Mercury horoscope of Marcantonio Michiel of Venice: A study in the history of Renaissance astrology and astronomy”, Oriens-occidens (Hildesheim, 1968), 440–95, pp. 476–7; see also Comes , Ecuatorios, 117–23.

On Ptolemy's model for Mercury see Neugebauer Otto , A history of ancient mathematical astronomy (Berlin, 1975), 158–82; Olaf Pedersen, A survey of the Almagest (Odense, 1974), 309–28.

On Ibn al-Zarqālluh's eccentricity see Willy Hartner's two papers reprinted in the volume Oriens-occidens II (Hildesheim, 1984): “Ptolemy, Azarquiel, Ibn al-Shāṭir and Copernicus on Mercury: A study of parameters” (pp. 292–312); “The Islamic astronomical background to Nicholas Copernicus” (pp. 316–25); see also Comes , Ecuatorios, 119–20.

Comes , Ecuatorios, 117; Rico , Libros, iii, 279. The Italian fourteenth-century translation states: “e sarae il cerco del leuatore figura di talliatura iscemata ouer[o] tracta delle tagliature che ue(n)gono nella figura [blank in the manuscript]” ( Comes , Ecuatorios, 198).

Hartner , “Trepidation and planetary theories: Common features in late Islamic and early Renaissance astronomy”, in Oriens-occidens II, 267–87, pp. 282, 287.

Comes , Ecuatorios, 117, 207 (“^calā shakl al-bayḍa wa huwa al-shakl al-ma^crūf bi-l-bayḍī ^cinda-l^−cārifīn bi^−cilm al-hay'a”, “with the shape of an egg, which is the shape called oval by those who know astronomy”). See Millás J. M. , Estudios sobre Azarquiel (Madrid and Granada, 1943–50), 459.

Souissi Mohammed , La langue des mathématiques en arabe (Tunis, 1968), 221. This Arabic equivalent was communicated to W. Hartner, before 1969, by M. Schramm: See Hartner , “Trepidation and planetary theories”, 287, n. 19.

Samsó J. , “El original árabe y la versión alfonsi del Kitāb fī hay'at al^−cālam de Ibn al-Hayṭam”, in Comes M. Mielgo H. and Samsó J. (eds), “Ochava espera” y “Astrofisica”: Textos y estudios sobre las fuentes árabes de la astronomía de Alfonso X (Barcelona, 1990), 115–31, pp. 124–5. The Arabic edition of Ibn al-Haytham's book has been published by Langermann Tzvi Y. , Ibn al-Haytham's On the configuration of the world (New York and London, 1990). The Latin Alfonsine translation has been Edited by Mancha Luis José , “La version alfonsi del Fī hay'at al^−cālam (De configuratione mundi) de Ibn al-Hayṭam (Oxford, Canon, misc. 45, ff. lr-56r)” in “Ochava Espera” y “Astrofisica”, 133–207.

See Souissi , La langue des mathématiques en arabe, 286; Hogendijk J. P. , Ibn al-Haytham's Completion of the conies (New York, 1985), 399; Toomer G. J. , Apollonius Conies: Books V to VII. The Arabic translation of the lost Greek original in the version of the Bonū Mūsā (New York, 1990), ii, 875. Our friend and colleague, Dr Roser Puig, told us that the semi-ellipses that appear in the orthographic projection of the back of the ṣafīḥa [saphea/açafeha] zarqāliyya are called, in the Alfonsine text, linnas [= lines] de taias minguadas. See Puig R. , Los tratados de construcción y uso de la azafea de Azarquiel (Madrid, 1987), 20–22, and “La proyección ortográfica en el Libro de la açafeha alfonsí”, in Cornes M. Puig R. and Samsó J. (eds), De astronomia Alphonsi Regis (Barcelona, 1987), 127.

Hartner , “Mercury horoscope”, 465–78.

Hartner , “The Islamic astronomical background to Nicholas Copernicus”, 319–20.

We have revised the Toledan Tables (Madrid National Library manuscript 9271 and Escorial ms. O-II-10), those of Ibn al-Kammād (Madrid National Library Latin ms. 10023) and the two zījes of Ibn al-Raqqām (mss. Istanbul Kandilli 249, Rabat General Library 260). On Ibn al-Kammād (fl. 1125) and Ibn al-Raqqām (d. 1315) see Samsó , Ciencias de los antiguos, 320–4, 414–15, 421–7.

Alfonsine Tables in the edition of Poulle Emmanuel (Les tables alphonsines avec les canons de Jean de Saxe (Paris, 1984)); Tables of Barcelona in the edition of J.M. Millás Vallicrosa (Las tablas astronómicas del Rey Don Pedro el Ceremonioso (Madrid and Barcelona, 1962)).

Zījes of Ibn Isḥāq (fl. 1200) (Hyderabad Andra Pradesh State Library ms. 298) and Ibn al-Bannā' al-Marrākushī (1256–1321) (ms. without number in the Madrid Museo Naval).

Neugebauer , op. cit. (ref. 5), 1003.

We have checked the editions by Abbé Halma (Paris, 1822–25) and by William D. Stahlman (“The astronomical tables of Codex Vaticanus Graecus 1291”, Ph.D. dissertation, Brown University, 1959, available through University Microfilms).

Samsó , Ciencias de los antiguos, 330–60.

Uṣaybica Abī Ibn , ^cUyūn al-anbā ‘fī ṭabaqāt al-aṭibbā’, ed. by al-Fikr Dār (Beirut, 1957), iii, 82–84 and 103. The identification has already been made by al-cAlawī al-Dī Jamāl, Rasā 'il falsafiyya li-Abī Bakr b. Bājja (Beirut and Casablanca, 1983), 77 n. 1; Pines S. , “La dynamique d'Ibn Bajija”, in L'aventure de la science: Mélanges Alexandre Koyré I (Paris, 1964), 442–68, p. 444, notes 7 and 8.

The text has been edited by al^−cAlawī, Rasā 'il, 77–78.

He quotes in particular Ibn al-Haytham's criticism of the Ptolemaic method to determine the eccentricity of Venus and Mercury: See Ibn al-Haytham's Shukūk in the edition by Sabra A. I. and Shehaby N. (Cairo, 1971), 29ff. This is, incidentally and to the best of our knowledge, the first instance of an allusion to Ibn al-Haytham's Shukūk in al-Andalus.

“Maqāla fī ibṭāl al-ṭarīq allatī salaka-hā Baṭlīmūs fī istikhrāj al-bu^cd al-ab^cad li^−cUṭārid”: ^cAlawī's edition, 78.

Owen Gingerich states that Ptolemy erred by about 30°: See his paper “Mercury theory from Antiquity to Kepler”, first published in 1971 and reprinted in the volume by the same author, The eye of heaven: Ptolemy, Copernicus, Kepler (New York, 1993), 379–87. Newton Robert R. (The crime of Claudius Ptolemy (Baltimore and London, 1977), 278–9) reaches a similar conclusion when he says that the longitude of Mercury's apogee should be about 219° in Ptolemy's time instead of the 190° we find in Almagest IX, 7.

See Boutelle Marion , “The almanac of Azarquiel”, reprinted in Kennedy E.S. , Studies in the Islamic exact sciences (Beirut, 1983), 502–10. This paper should be read together with the important remarks by Noel Swerdlow in Mathematical reviews, xli (1971), no. 5149. For a general survey of this source see Samsó , Ciencias de los antiguos, 166–71.

According to Bernardus de Virduno: See Toomer G. J. , “The solar theory of az-Zarqāl: An epilogue”, in King D. A. and Saliba G. (eds), From deferent to equant: A volume of studies in the history of science in the ancient and medieval Near East in honor of E. S. Kennedy (New York, 1987), 513–23. This value (like many others) has been confirmed by Ibn al-Hā'im (fl. in Seville at the beginning of the 13th century) in his al-Zīj al-Kāmil fī-l-Ta^cālīm extant in the manuscript Bodleian Library Marsh ms. 618, fol. 5v: cf. Samsó , Ciencias de los antiguos, 211; see also Samsó J. and Millás E. , “Ibn al-Bannā', Ibn Isḥāq and Ibn al-Zarqālluh's solar theory”, reprinted in Samsó J. , Islamic astronomy and medieval Spain (Aldershot, 1994), no. X, p. 9.

Goldstein Bernard R. , “Remarks on Ptolemy's equant model”, in Prismata: Festschrift für Willy Hartner (Wiesbaden, 1977), 165–81.

A further incongruity would be raised in the case of the Sun: Toomer G. J. (“The solar theory of az-Zarqal: A history of errors”, in Centaurus, xiv (1969), 306–36, pp. 320–1) has calculated that Ibn al-Zarqālluh uses a sidereal solar apogee in the Almanac the longitude of which is 79;30°: The apogee longitude 85;49° mentioned by Ibn al-Hā'im and Bernardus de Virduno is, obviously, tropical.

Neugebauer O. , The astronomical tables of al-Khwārizmī: Translation with commentaries of the Latin version edited by H. Suter supplemented by Corpus Christi College MS 283 (Copenhagen, 1962), 41, 99. Mercier Raymond (“Astronomical tables in the twelfth century” in Burnett Charles (ed.), Adelard of Bath: An English scientist and Arabist of the early twelfth century (London, 1987), 87–118, pp. 91–92) has proved the origin of this apogee longitude: With parameters of the Brahmasphutasiddhanta he obtains 224;53,13° for the beginning of the Hijra.