Planetary Velocities and the Astrological Month

Goldstein B. R. Chabás J. , and Mancha J. L. , “Planetary and lunar velocities in the Castilian Alfonsine Tables”, Proceedings of the American Philosophical Society, cxxxviii (1994), 61–95.

Chabás J. Goldstein B. R. The Alfonsine Tables of Toledo [henceforth ATT] (Archimedes: New Studies in the History and Philosophy of Science and Technology, 8; Dordrecht and Boston, 2003), 170–82. See also Kennedy E. S. , “The Astronomical Tables of Ibn al-Raqqām, a scientist of Granada”, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, xi (1997), 1997–72, p. 66: “A peculiar table claims to have as argument n = 1, 2, 3, …, 13 ‘months’ …. It takes a solar year and splits into thirteenths …. “This “peculiar” table can now be understood as presenting the astrological months (see Table 1).

Chabás J. Goldstein B. R. , A survey of European astronomical tables in the late Middle Ages (Leiden, 2012), 221–3.

The term hyleg derives from the Arabic haylāj: Latin: hylech, and variants of it; English: hyleg, and variants of it. In the Oxford English dictionary (online version), sub hyleg, William Lilly (1647) is quoted: “Of the Prorogator of Life, called Hylech, or Hyleg, or Apheta” and, sub prorogator, he is quoted: “If such a Planet be in an Apheticall place, he shall be Prorogator.” Apheta is the Greek term that corresponds to the Arabic haylāj: See al-Bīrūnī, Book of instruction in the elements of the art of astrology, ed. and transl. by Wright R. R. (London, 1934), 323 n. 2. See also Section 5.

The lot of fortune is defined as a point on the ecliptic whose distance from the ascendant in the direction of signs is equal to the distance of the Moon from the Sun in the opposite direction: cf. al-Bīrūnī, op. cit. (ref. 4), 279.

For Ptolemy ( Tetrabiblos IV.10; ed. and transl. by Robbins F. E. (London and Cambridge, MA, 1940), 447–9), the horoscope (i.e., the ascendant) was associated with “events relating to the body and the journeys abroad”, the lot of fortune with “matters of property”, the Moon with “affections of the soul and marriage”, the Sun with “dignities and glory”, and the midheaven with “other details of the conduct of life, such as actions, friendships, and the begetting of children”.

Ptolemy , op. cit. (ref. 6), 449–53.

Ptolemy , op. cit. (ref. 6), 453.

Bouché-Leclercq A. , L'astrologie grecque (Paris, 1899), 505.

The astrological month, m, is of the tropical year. y. and corresponds to 390°. To find t, the time in days that corresponds to 30°, one forms the proportion m/390 = t/30, or t = m/13, where m = y/13. Thus, t = y/(13 · 13). With Ptolemy's tropical year, t = 2;9,40d.

On ^cAlī Ibn Abī l-Rijāl, see Sezgin F. , Geschichte des arabischen Schrifttums (15 vols, Leiden, 1967–2010 [henceforth GAS]), vii (1979), 186–8. Sezgin lists many copies in Arabic of Kitāb al-bāri^c with their dates; there is no edition of this text. See also Pingree D. , “Ibn Abī l-Ridjāl”, Encyclopaedia of Islam, 2nd edn (13 vols, Leiden, 1954–2008), iii (1971), 688. We are most grateful to Julio Samsó for providing us with copies of several Arabic manuscripts of Book 6, chapter 15, with these tables, notably London, British Library, MS Add. 23399 (dated 1758–59); and Heidelberg, Universitätsbibliothek, MS Arabic 172 (dated 1732–33). The conventions for sexagesimal digits in Arabic astronomical tables have not always been followed in the manuscripts with these tables: See Irani R. A. K. , “Arabic numeral forms”, Centaurus, iv (1955), 1955–12; reprinted in Studies in the Islamic exact sciences by Kennedy E. S. , ed. by King D. A. Kennedy M. H. (Beirut, 1983), 710–21.

See Chabás Goldstein , ATT (ref. 2), 230–1. We have consulted two editions: Albohazen Hali filius Abenragel, Liber conpletus in iudiciis stellarum (Venice, 1485), and Albohazen Haly filius Abenragel, Liber de iudiciis astrorum (Basel, 1551).

For the tables in this version we have consulted Hilty G. , El Libro Conplido en los Iudizios de las Estrellas: Partes 6 a 8 (Zaragoza, 2005), 83–4, as well as a copy of Book 6, chapter 15, in the unique manuscript written in Hebrew characters, Oxford, Bodleian Library, MS Laud Or. 310, graciously sent to us by Gerold Hilty. For a description of this manuscript, see Hilty , op. cit., pp. xxxiv-xxxvi.

Vienna, Österreichische Nationalbibliothek, MS Heb. 198/52. In this Hebrew translation the relevant chapter in Book 6 is numbered 14 (rather than 15 as it is in the Latin version). Ruth Glasner kindly provided us with a scanned copy of the tables in this manuscript, based on film no. 1329 at the Institute for Microfilmed Hebrew Manuscripts in Jerusalem. A detailed description of this manuscript can be found in Krafft A. Deutsch S. , Die handschriftlichen hebräischen Werke der k. k. Hofbibliothek zu Wien (Vienna, 1847), 184–5. Another copy of this translation, Paris, Bibliothèque nationale de France, MS Heb. 1067, has the relevant chapter (ff. 209b-210a), but without the tables. On Solomon Davin, see Steinschneider M. , Mathematik bei den Juden, 2nd edn (Hildesheim, 1964), 166–7; and Chabás J. Goldstein B. R. , Astronomy in the Iberian Peninsula: Abraham Zacut and the transition from manuscript to print (Transactions of the American Philosophical Society, xc/2; Philadelphia, 2000), 22.

Chabás Goldstein , ATT (ref. 2), 182. For example, for day 15 some MSS read 208;14, others read 204;14 and 308;14, and for day 22 some MSS read 305;24, others read 315;24.

Tabule astronomice illustrissimi Alfontij regis castelle, ed. by Ratdolt E. (Venice, 1483), d3r. The entry for 1 month is 28d 2;17,38,9,11,51h.

Tabule astronomice Alfonsi Regis, ed. by Santritter J. L. (Venice, 1492), k5v. The entry for 1 month is 28d 2;17,38,9,12h.

Santritter , op. cit. (ref. 17), D6v–D7r; cf. Liber conpletus (ref. 12), 109v. There are minor textual variants between Santritter's discussion and the one found in the Liber conpletus.

Schöner J. , De iudiciis nativitatum, libri tres (Nuremberg, 1545), 109v, and Gaurico L. , Tractatus iudicandi conversiones sive revolutiones nativitatum (Rome, 1560), 18v, 19v. The version of Table 1 in Schöner, op. cit., 109v, and the corresponding table in Gaurico, op cit., 18v, are not displayed in the Appendix.

For this zij, see Mestres A. , “Maghribī astronomy in the 13th century: A description of manuscript Hyderabad Andra Pradesh State Library 298”, in From Baghdad to Barcelona: Studies in the Islamic exact sciences in honour of Prof. Juan Vernet , ed. by Casulleras J. Samsó J. (2 vols, Barcelona, 1996), i, 383–443, p. 424. Julio Samsó kindly provided us with a facsimile of the relevant table in this Arabic manuscript as well as several pages from Mestres's unpublished edition of the Arabic text. Some tables in this zij related to Table 1 are displayed in Abdulrahman M. , “Ibn al-Hā'im's zīj did have numerical tables”, in Casulleras and Samsó, op. cit., 365–81, pp. 376–7 (in Arabic). On Ibn al-Kammād, see Chabās J. Goldstein B. R. , “Andalusian astronomy: al-Zīj al-Muqtabis of Ibn al-Kammād”, Archive for history of exact sciences, xlviii (1994), 1994–41.

Sela S. , “A newly identified essay on anniversary horoscopy embedded in Abraham Bar Hiyya's Astronomical Tables: Hebrew edition, translation and commentary”, Aleph, xiii (2013), 27–76. The tables are uniquely preserved in Paris, Bibliothèque nationale de France, MS Heb. 1058, f. 118v; Sela presents a facsimile of this page without transcribing the tables on it.

Gaurico L. Alfonsis hispaniarum regis tabule (Venice, 1524), and idem, op. cit. (ref. 19).

Lemay R. , “Origin and success of the Kitāb Thamara of Abū Ja^cfar ibn Yūsuf ibn Ibrāhīm”, Proceedings of the First International Symposium for the History of Arabic Science (2 vols, Aleppo, 1978), ii, 91–107; cf. Savage-Smith E. , “Review of Proceedings of the First International Symposium for the History of Arabic Science”, Isis, lxxi (1980), 1980–3, and Sezgin , GAS (ref. 11), vii, 157. Note that Ibn al-Dāya has several names, including Abu Ja^cfar ibn Yūsuf ibn Ibrāhīm. In a private communication, Maria Mavroudi informed one of us (BRG) that she is preparing an article in which she will argue that the extant Greek version of Karpos (i.e., Centiloquium) was composed no later than the fifth century, and that the Arabic version is a translation from a Greek archetype.

Liber Ptholomei quattuor tractatuum: Cum Centiloquio euisdem Ptholomei: Et commento Haly (Venice, 1484), h9r. The last quire in this volume has six signatures, h[1] to h6, rather than the usual 4 signatures. The colophon to the edition of 1484 ascribes the commentaries on the Quadripartitum and on the Centiloquium to Haly, that is, ^cAlī ibn Riḍwān (Cairo, d. c. 1061). However, while ^cAlī ibn Riḍwān wrote the commentary on the Quadripartitum, it is not the case for the Centiloquium for, according to Sezgin, this Latin version is a translation from Arabic of the commentary by Ibn al-Dāya: See Sezgin , GAS (ref. 11), vii, 157. See also Lemay , op. cit. (ref. 23), 103–4; Millás J. M. , Las traducciones orientales en los manuscritos de la Biblioteca Catedral de Toledo (Madrid, 1942), 154.

Wright , op. cit. (ref. 4), 325–6: 365/13 = 28d 1;51h, and 365/(13 · 13) = 2d 3;50h.

Hali , Liber conpletus (ref. 12), 109v, col. 1: 50; Haly , Liber de iudiciis astrorum (ref. 12), 295, col. 1:30; London, British Library, MS Add. 23399, 274b:20.

Sela , op. cit. (ref. 21), 58–60.

Sela S. , “Sefer ha-Tequfah: An unknown treatise on anniversary horoscopy by Abraham Ibn Ezra”, Aleph, ix (2009), 241–54, p. 252.

We are most grateful to Shlomo Sela for emphasizing this point in a private communication.

Dorothei Sidonii Carmen astrologicum: Interpretationem Arabicam in linguam Anglicam versam una cum Dorothei fragmentis et Graecis et Latinis, ed. and transl. by Pingree D. (Leipzig, 1976), 242.

Ptolemy , Tetrabiblos, op. cit. (ref. 6), 271.

Wright , op. cit. (ref. 4), 323 n. 6.

Al-Qabīṣī (Alcabitius): The Introduction to Astrology, editions of the Arabic and Latin texts and an English translation by Burnett Ch. Yamamoto K. , and Yano M. (London and Turin, 2004), 200–1.

Al-Qabisi , op. cit. (ref. 33), 111–17 (English translation of the Arabic); 319–23 (Latin).