Abraham Zacut and the Medieval Hebrew Astronomical Tradition

Burgos Cantera F. , Abraham Zacut (Madrid, 1935). F. Cantera Burgos also published a Castilian translation of the Hebrew canons to Zacut's tables made by Juan de Salaya in 1481 with the help of Zacut, as well as a Castilian translation from the extant Hebrew manuscripts made by Cantera himself in: “El judío salmantino Abraham Zacut”, Revista de la Academia de Ciencias de Madrid , xxvii (1931), 63–398. These two studies are fundamental for the investigation of Zacut's astronomical work. See also Chabás J. Goldstein B. R. , “Abraham Zacut and Iberian astronomy in the late 15th century” (in preparation). I am most grateful to José Chabás for care in commenting on drafts of this paper, and for supplying me with information on many specific points. I also thank A. C. Bowen, R. Glasner, Y. T. Langermann, J. L. Mancha, and D. Pingree for assistance in the preparation of this article.

Freimann Aron , “Die hebräischen Inkunabeln der Druckereien in Spanien und Portugal”, in Gutenberg Festschrift zur Feier der 25 Iaehrigen Bestehens des Gutenbergsmuseums in Mainz , ed. by Ruppel A. (Mainz, 1925), 203–6; Roth C. , “Who printed Zacuto's tables?”, Sefarad , xiv (1954), 122–5. Note that ‘Zacut’ is a Hebrew word (zakkut), and Abraham Zacut's name appears in this form in the Hebrew manuscripts. The Latin for ‘Zacut’ is ‘Zacutus’ from which the form ‘Zacuto’ has been derived.

For the Latin version of the Almanach perpetuum (Leiria, 1496), I have consulted a photocopy of Biblioteca Nacional (Madrid), shelf mark I.1077. For a list of Zacut's astronomical works in Hebrew manuscripts, see Goldstein B. R. , “The Hebrew astronomical tradition: New sources”, Isis , lxxii (1981), 237–51, as well as Cantera, Abraham Zacut (ref. 1), 40–73. Although I consulted the Hebrew manuscripts of Zacut's canons to his tables, I will generally cite the Spanish translation in Cantera, “El judío salmantino” (ref. 1), which is more accessible. The introduction, most of chap. 9, and all of chap. 10 of Zacut's canons were published in Hebrew with a German translation by Cohn B. , Der Almanach perpetuum des Abraham Zacuto (Schriften der Wissenschaftlichen Gesellschaft in Strassburg, 32. Heft; Strassburg, 1918).

Regiomontanus , Tabulae directionum (Augsburg, 1490); cf. Cohn B. , review of: “Almanach perpetuum coelestium motuum (radix 1473). … Reproduction facsimilé, Edition 1496, … München 1915”, in Vierteljahrsschrift der Astronomischen Gesellschaft , xxv (1917), 102–23 (espec. p. 106); Zinner E. , Regiomontanus: His life and work , transl. by Brown E. (Amsterdam, 1990), 121.

Goldstein B. R. , “The role of science in the Jewish community in fourteenth century France”, Annals of the New York Academy of Sciences , cccxiv (1978), 39–49; idem, “The survival of Arabic astronomy in Hebrew”, Journal for the history of Arabic science , iii (1979), 31–39; idem, “Scientific traditions in late medieval Jewish communities”, in Les Juifs au regard de l'histoire: Mélanges en l'honneur de M. Bernhard Blumenkranz , ed. by Dahan G. (Paris, 1985), 235–47.

Goldstein B. R. , Levi ben Gerson's astronomical tables (New Haven, 1974); idem, The astronomy of Levi ben Gerson (1288–1344) (New York and Berlin, 1985); idem, “A new set of fourteenth century planetary observations”, Proceedings of the American Philosophical Society , cxxxii (1988), 371–99; idem, “The physical astronomy of Levi ben Gerson”, Perspectives on science , v (1997), 1–30.

Cantera , “El judío salmantino” (ref. 1), 194, 300; the occultation is cited in A. Ricius, De motu octauae sphaerae (Paris, 1521), 29r. There was an earlier edition of Ricius's treatise of which only a few copies seem to survive (e.g., Biblioteca Universidad de Salamanca, shelf mark 32.612 [olim I-27-4-37]): Augustini Ritij de motu octaue sphere (Trino [in oppido Tridini], 1513), and the corresponding passage is on 26v–27r. Zacut does not specify the date of this occultation, but modern computation yields the night of 26/27 May 1474, beginning shortly after 22^h00 UT, for an occultation of Spica by the Moon. I am most grateful to Dr David Dunham, President of the International Occultation Timing Association, and senior staff member at the Applied Physics Laboratory of The Johns Hopkins University, for computing the conditions of this occulation. The eclipse report appears in A. Zacut, Sefer Yuhasin [The book of genealogies], ed. by Hayyim Abraham [= Alfred] Freimann (Frankfurt a. M., 1924), 226a: Few details are given. For the path of totality in Spain of the solar eclipse of 1478, see Schroeter J. Fr. , Spezieller Kanon der zentralen Sonnen- und Mondfinsternisse … in Europa sichtbar waren (Kristiania, 1923), chart 106b.

Poulle E. , Les tables alphonsines avec les canons de Jean de Saxe (Paris, 1984); North J. D. , “Just whose were the Alfonsine Tables?”, in From Baghdad to Barcelona: Studies in the Islamic exact science in honour of Prof. Juan Vernet , ed. by Casulleras J. Samsó J. (2 vols, Barcelona, 1996), i, 453–75. In Journal for the history of astronomy , xxv (1994), 196, ref. 27, I referred this article by J. D. North to Proceedings of the Fifth International Symposium on the History of Arabic Science, Granada 1992 (in press), but publication of that volume was subsequently cancelled. Zacut mentions that Alfonso surrounded himself with Jewish, Christian, and Muslim scholars, and goes on to say that the Tables were composed by Isaac ben Sid: See Cantera, “El judío salmantino”, 243–4.

Almanach perpetuum (ref. 3), 14r.

I consulted the copy in Munich, MS Heb. 126.

Petersburg St , Academy, MS Heb. C–076, ff. 31a–54a.

Zacut , ha-Hibbur ha-gadol , Lyon , MS Heb. 14, f. 23v. In contrast to the Alfonsine Tables, Zacut gives the planetary radices for the epochs in base 30 notation: See refs 33 and 34, below.

This St Petersburg manuscript is now being studied by Langermann Tzvi .

Chabás Goldstein , op. cit. (ref. 1); Chabás J. , “The astronomical tables of Jacob ben David Bonjorn”, Archive for history of exact sciences , xlii (1991), 279–314; idem, L'astronomia de Jacob ben David Bonjorn (Barcelona, 1992). Jacob Poel is mentioned a number of times by Zacut: See, e.g., Cantera , “El judío salmantino”, 241.

Vatican , MS Heb. 384, ff. 347a–359a.

The canons of Ben Verga's tables are preserved in St Petersburg, Academy, MS Heb. C–076, ff. 57a–65a; and the tables in Paris, MS Heb. 1085, ff. 86b–98a, and Oxford, MS Heb. Nb. 2044, ff. 222b–236b. In most of Ben Verga's tables the epoch is 1384, but in some it is 1400. For other works by Ben Verga, see Steinschneider M. , Mathematik bei den Juden 2nd edn (Hildesheim, 1964), 196.

Chabás J. , “Astronomy in Salamanca in the mid-fifteenth century: The Tabulae resolutae”, Journal for the history of astronomy , xxix (1998), 167–75.

Zacut , Sefer Yuhasin (ref. 7), 225b; Steinschneider , op. cit. (ref. 16), 143; Freimann Alfred , “Die Ascheriden (1267–1391)”, Jahrbuch der Jüdisch-Literarischen Gesellschaft , xiii (1920), 142–254, espec. pp. 149–56.

Langermann Y. T. , “Sefer Huqqot Shamayim by R. Judah ben Asher”, Kiryat Sefer , lviii (5743 [= 1983]), 622–3 [in Hebrew].

Vatican , MS Heb. 384, f. 285b, gives the date as year 1401 of the Safar Era (= a.d. 1364); Burgos is mentioned on ff. 291a, 292a (“If you wish to find the radices of the planets for a city other than Burgos, …”), etc.

Freimann , “Die Ascheriden” (ref. 18), 152ff.

The planetary apogees for a.d. 1400 in Vatican, MS Heb. 384, f. 263b, are all either 2;47,24° or 2;47,54° greater than those in the zij of Ibn al-Kammād. From a.d. 622, the epoch of Ibn al-Kammād's zij, to 1400, is 778 years. The accumulated progress in 778 years at the rate of 1° in 279 Julian years is about 2;47,24° (accurately, 2;47,19°). This parameter is the value for the motion of the solar apogee according to al-Zarqāllu that the author here has also inappropriately applied to the planetary apogees (cf. Chabás J. Goldstein B. R. , “Andalusian astronomy: al-Zīj al-Muqtabis of Ibn al-Kammād”, Archive for history of exact sciences , xlviii (1994), 1–41, espec. pp. 28, 33).

Vatican, f. 263b Apogee Ibn al-Kammād Diff.

Saturn 241;25,54° 238;38,30° 2;47,24°.

Jupiter 161; 8,54* 158;21, 0 2;47,54.

Mars 122;28,54* 119;41, 0 2;47,54.

Sun 79;32,45 76;45,21 2;47,24.

Venus 79;32,45 76;45,21 2;47,24.

Mercury 201; 8,54* 198;21, 0 2;47,54.

*The ending, 54 seconds, may be a copyist's error for 24 seconds: They look very much alike in Hebrew MSS, and the ending for the apogee of Saturn is 54 seconds.

Chabás J. , “Astronomia andalusí en Cataluña: Las tablas de Barcelona”, in Casulleras Samsó (eds), From Baghdad to Barcelona (ref. 8), i, 477–525, espec. pp. 489–94.

Goldstein B. R. Chabás J. Mancha J. L. , “Planetary and lunar velocities in the Castilian Alfonsine Tables”, Proceedings of the American Philosophical Society , cxxxviii (1994), 61–95. In the Vatican copy of this planetary velocity table only one column (of two) for each planet is valid; the entries in the column for the motion in anomaly were computed by an incorrect rule. In the case of the outer planets, the entries in that column are simply the differences between the adjacent entries in the column for the motion of centre and the daily mean motion of the Sun, 0;59,8°/d; in the case of the inner planets, the entries in the column for the motion in anomaly are the differences between either 4;5,32°/d for Mercury, or 1;35,59°/d for Venus (the sum of the daily mean motion in anomaly of the planet and the daily mean motion of the Sun, approximately), and the adjacent entries in the column for the motion of centre. In the case of Mars, the entries in the Vatican Hebrew manuscript for the motion of centre agree with the thirteenth-century Latin manuscript (against all other manuscripts) for arguments 120°, 138°, and 180°.

There has just come to my attention additional support for the origin of this planetary velocity table in Islamic Spain. J. Samsó has published an article on the zij of Ibn ‘Azzūz that contains both columns of this table for each planet (“Andalusian astronomy in 14th century Fez: al-zīj al-muwāfiq of Ibn al-'Azzūz al-Qusantān”, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften , xi (1997), 73–110, see espec. pp. 88–90, 104–5). In a number of significant instances the variants for this table in the zij agree with the thirteenth-century Latin manuscript as well as with the text of Judah ben Asher (against all other manuscripts). So we have yet another witness to this table that is independent of John of Lignères.

For examples of different double argument tables, see North J. D. , “The Alfonsine Tables in England”, in Prismata , ed by Maeyama Y. Saltzer W. G. (Wiesbaden, 1977), 269–301.

Almanach perpetuum (ref. 3), 149r–151v; Zacut , ha-Hibbur ha-gadol , Lyon , MS Heb. 14, ff. 41r–38v; idem, Munich, MS Heb. 109, ff. 151b–154a. Note that the folio numbers in the Lyon manuscript follow the Latin order rather than the Hebrew order: The text begins on f. 215v.

The double argument table for the daily velocity of Mercury is found in Vatican, MS Heb. 384, ff. 372a–374a, and the double argument tables for the daily velocities of the other planets begin on f. 364a. The names of the planets here are unusual in an astronomical context, but they do occur in astrological treatises: Saturn is called “old man” (zaqen), Jupiter is called “judge” (shofet), Mars is called “killer” (horeg), Venus is called “woman” (ishshah), and Mercury is called “scribe” (sofer).

Vatican , MS Heb. 384, ff. 375a–384b.

Among the Parisians who produced lunar velocity tables in the 1330s was John of Genoa: Goldstein B. R. , “Lunar velocity in the Ptolemaic tradition”, in The investigation of difficult things: Essays on Newton and the history of the exact sciences , ed. by Harman P. M. Shapiro A. E. (Cambridge, 1992), 3–17 (the entries in al-Battān's lunar velocity table are compared here with the entries in the Parisian lunar velocity tables); see also idem, “Solar and lunar velocity in the Alfonsine Tables”, Historia mathematica , vii (1980), 134–40; idem, “Lunar velocity in the Middle Ages: A comparative study”, in Casulleras Samsó (eds), From Baghdad to Barcelona (ref. 8), i, 181–94.

Cf. Poulle E. , “The Alfonsine Tables and Alfonso X of Castille”, Journal for the history of astronomy , xix (1988), 97–113. Poulle lists six criteria for the Parisian Alfonsine Tables; only one of them (signs of 60°) is satisfied by the text and tables of Judah ben Asher.

Cantera , “El judío salmantino” (ref. 1), 152: 11,325 days = 12,17,15 days (base 30).

See Lyon , MS Heb. 14, ff. 31r–29v, 25r–21r. The mean motion tables, base 30, are described in the canons to Zacut's Great composition, chap. 19: See Cantera , “El judío salmantino” (ref. 1), 234ff, 357ff. There is no comparable discussion in the canons to the Almanach perpetuum.

Lyon , MS Heb. 14, f. 23r: 0;29,17,2,13,17,14,8,0 (base 30), whereas in the Parisian version of the Alfonsine Tables the daily motion of the Sun is 0;59,8,19,37,19,13,56 (base 60): Poulle , op. cit. (ref. 8), 134. This conversion is correct to 7 places, base 30.

Lyon , MS Heb. 14, ff. 31r–29v; Munich, MS Heb. 109, ff. 161b–163a. The principles of this decimal place-value system and of base 30 notation are explained in Zacut's Great composition, chap. 18: See Cantera , “El judío salmantino” (ref. 1), 225ff. There is no comparable discussion in the Almanach perpetuum. For the introduction of decimal place-value notation in Hebrew, see Abraham Ibn Ezra's Sefer ha-mispar , ed. and transl. by Silberberg M. (Frankfurt a. M., 1895); cf. Sarfatti G. B. , Mathematical terminology in Hebrew scientific literature of the Middle Ages (Jerusalem, 1968), 131ff.

Vatican , MS Heb. 384, ff. 347a–359a.

Lyon , MS Heb. 14, f. 23v; Poulle , op. cit. (ref. 8), 107–8.

Goldstein B. R. Chabás J. , “Ibn al-Kammād's star list”, Centaurus , xxxviii (1996), 317–34.

Lyon , MS Heb. 14, ff. 114v–114r.

Beit-Arié M. Idel M. , “Treatise on eschatology and astrology by R. Abraham Zacut”, Kiryat Sefer , liv (5739 [= 1979]), 174–94 [in Hebrew]. For another text by Zacut where astrology and eschatology are discussed, see Roth C. , “The last years of Abraham Zacut”, Sefarad , ix (1949), 445–54.

There has been much controversy concerning the date of Zacut's death, but Roth , op. cit. (ref. 39), presents a persuasive argument in support of the date originally proposed by Steinschneider.

Goldstein , op. cit. (ref. 3).

Ricius , op. cit. , ed. 1521 (ref. 7), 6v [= Ritius , op. cit. , ed. 1513 (ref. 7), 5r]: “Habraham Zacuth, astronomiae nostra tempestate peritissimus in sua magna editione affirmat, nobisque eum legentem in Africa apud Carthaginem audientibus …”; ed. 1521, 29r [= ed. 1513, 26v–27r]: “Abraham Zacuth, quem praeceptorem in astronomia habuimus …” (minor variants in spelling and punctuation have not been noted).