An Occultation of Venus Observed by Abraham Zacut in 1476

See Sachs A. J. Hunger H. , Astronomical diaries and related texts from Babylonia (3 vols, Vienna, 1988–96), i, 327, where, for example, there is a report of an occultation of Jupiter, dated 7 Oct. −277.

Aristotle , On the heavens , transl. by Guthrie W. K. C. (Cambridge, Mass., 1939), 205.

Although we can hardly pretend to have exhausted all medieval sources, we have looked at several modern discussions of such medieval observational reports. See, e.g., King D. A. Gingerich O. , “Some astronomical observations from thirteenth-century Egypt”, Journal for the history of astronomy , xiii (1982), 121–8, espec. pp. 123f. These observations are in a zij by a thirteenth-century Yemenite astronomer, al-Kawāshī. In particular he reports that:

i. “The Moon was in conjunction with Mercury and occulted it [as seen] at the town of Qus [on the Nile in Egypt: Lat. 25;55° N, long. 32;44° E]. The planet remained occulted for about half an hour.” The date given, 2 Muharram 672 a.h., is equivalent to 17 July 1273.

ii. “The Moon occulted Venus on the night of Saturday, 4 Muharram, in the year 682 [2 April 1283]. The beginning of the occultation was at the end of the second hour of that night … at Alexandria [lat. 31;12° N, long. 29;54° E].”.

Ibn Yūnus (d. 1009) reports occultations of one planet by another (cf. Delambre J. B. , Histoire de l'astronomie du Moyen Age (Paris 1819), 87ff), and King and Gingerich (p. 121) claim that the list by al-Kawāshī is the only set of observed planetary conjunctions in a medieval Arabic source to have come to light since the early nineteenth century. Other reports in Arabic of planetary observations in the thirteenth century are mentioned in Saliba G. , A history of Arabic astronomy (New York, 1994), 175–6, but they do not concern occultations. A list of planetary obervations by Levi ben Gerson (d. 1344) is found in Goldstein B. R. , “A new set of fourteenth century planetary observations”, Proceedings of the American Philosophical Society , cxxxii (1988), 371–99, and a (near) occultation of Jupiter by Venus on 28 Sept. 1339 is reported in it (p. 397).

The most extensive list of planetary observations before the middle of the sixteenth century is found in Schoener J. , Scripta clarissima mathematici (Nuremberg, 1544): See Kremer R. , “Bernard Walther's astronomical observations”, Journal for the history of astronomy , xi (1980), 174–91. We are most grateful to Dr Kremer who called our attention to two occultations observed by Walther in Nuremberg (lat. 49;27°N, long. 11;5°E): An occultation of Saturn on 12 Jan. 1482 (Schoener, op. cit., ff. 49v–50r); and of Mars on 28 Nov. 1484 (Schoener, op. cit., f. 50v). The description of the occultation of Mars is very brief (only the time of night is given), whereas that of Saturn is more extensive (giving times and positions in the course of the occultation).

In De revolutionibus, v.23, Copernicus describes his only observation of Venus, an occultation on 12 March 1529, which he then used to determine the mean motion of Venus; see Swerdlow N. M. Neugebauer O. , Mathematical astronomy in Copernicus's De revolutionibus (New York and Berlin, 1984), 392–403. This observation was made a few years after the death of Abraham Zacut.

Almagest vii.3; Toomer G. J. , Ptolemy's Almagest (New York, 1984), 334–8.

See, e.g., Almagest xi.3; Toomer , op. cit. (ref. 4), 522.

The basic studies of Zacut are Burgos Cantera F. , “El judío salmantino Abraham Zacut”, Revista de la Academia de Ciencias de Madrid , xxvii (1931), 63–398 (hereafter Revista); and idem, Abraham Zacut (Madrid, 1935). Zacut is known to have made only two other astronomical observations: The first was of the Moon occulting Spica in 1474, and the second was of a total solar eclipse on 29 July 1478: See Goldstein B. R. , “Abraham Zacut and the medieval Hebrew astronomical tradition”, Journal for the history of astronomy , xxix (1998), 177–86. But he gives no details in either case.

The same title is given to a Hebrew translation of the Almagest by Anatoli Jacob , c. 1335. On Anatoli, see Lay J. , “L'Abrégé de l'Almageste: Un inédit d'Averroès en version hébraïque”, Arabic sciences and philosophy , vi (1996), 23–61; for the Hebrew title, see Steinschneider M. , Die hebraeischen Übersetzungen (Berlin, 1893), 523; and for the Almagest in Hebrew, see Zonta M. , “La tradizione ebraica dell'Almagesto di Tolomeo”, Henoch , xv (1993), 325–50.

The title page of the Leiria edition of 1496 has: Tabule tabularum celestium motuum astronomi zacuti … but, following customary usage, we will refer to it as Zacut's Almanach perpetuum, edn 1496.

MS S: Salamanca, sign. 2–163 (in Castilian), transcribed in Cantera, Revista (ref. 6), 151–236.

We have consulted the following Hebrew manuscripts for Zacut's ha-Hibbur ha-gadol: B. Oxford, Bodleian, MS Opp. Add. 8° 42;.

Lyon L. , MS Heb. 14;.

Munich M. , MS Heb. 109;.

Warsaw W. , ZIH, MS 245.

The copyist of MS B was al-Gazi Joseph , a contemporary of Zacut, who completed this work in March 1489 (MS B, 54b). The other Hebrew copies are undated, but they were made long after the death of Zacut and there are considerable differences among them.

We are most grateful to Herald D. Dr of Woden, Australia, for sending us information on the circumstances of this occultation. He calculated the time when the occultation began, that it took 39 seconds for the Moon to cover the full disk of Venus, and that the angular distance of the event from the north cusp of the Moon was 65°. For modern recomputations of planetary positions, we have depended on a computer program made available to us by Huber P. Dr , for which we are also grateful.

See Chabás J. , “Astronomy in Salamanca in the mid-fifteenth century: The Tabulae resolutae”, Journal for the history of astronomy , xxix (1998), 167–75. It is also possible that Zacut had access to a copy of the Alfonsine Tables in Hebrew characters: See Goldstein, op. cit. (ref. 6). For our computations according to the Alfonsine Tables we have consulted the editio princeps, Tabularum astronomicarum Alfontii regis castelle (hereafter Alfonsine Tables) (Venice, 1483); and Poulle E. , Les tables alphonsines avec les canons de Jean de Saxe (Paris, 1984).

In his table for finding the longitude of Venus, Ptolemy consistently used an eccentricity of 1;15 but, in the Alfonsine Tables, 1;15 is used for finding the equation of argument and 1;8 for finding the equation of centre: See North J. D. , Richard of Wallingford (3 vols, Oxford, 1976), iii, 196–7.

Alfonsine Tables (ref. 12), hlr. Note that the maximum lunar latitude here is 5°.

MS B, 15b:5ff; cf. MS S, 14r–14v. A maximum lunar latitude of 4;29° is found in Ibn al-Kammād's zij: 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. p. 22; and in the tables of Barcelona: Vallicrosa Millás J. M. , Las Tablas Astronómicas del Rey Don Pedro el Ceremonioso (Madrid and Barcelona, 1962), 234; and Chabás J. “Astronomía andalusí en Cataluña: Las Tablas de Barcelona”, 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), 477–525, espec. p. 504.

On Bonjorn , see 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).

We are grateful to Langermann Y. T. for identifying this manuscript, and calling it to our attention. Note that there is another Judah ben Asher (d. 1349) with whom the author of these tables is sometimes confused.

‘Zij’ is a word borrowed from Arabic for a set of astronomical tables and their canons, and it is a very useful term. For al-Khwārizmīs zij, see Suter H. , Die astronomischen Tafeln des Muhammad ibn Mūsā al-Khwārizmī (Copenhagen, 1914). Ibn al-Kammād's zij has a variant of this table with a maximum of 0;48,32° (see Chabás and Goldstein, op. cit. (ref. 15), 19ff), and it is also found in the Tables of Barcelona (Millás, op. cit. (ref. 15), 235; Chabás , op. cit. (ref. 15), 509).

Neugebauer O. , The Astronomical Tables of al-Khwārizmī (Copenhagen, 1962), 121.

Neugebauer , op. cit. (ref. 19), 122.

Almagest v. 17; Toomer , op. cit. (ref. 4), 259.

Vatican, MS. Heb. 384, espec. ff. 326a–327a.

Suter , op. cit. (ref. 18), 191–2.

Poulle E. , “John of Lignères”, in Dictionary of scientific biography , vii, 122–8.

Manuscripts of John of Lignères's tables are listed in Poulle, op. cit. (ref. 24), 127; and in Rosińska G. , Scientific writings and astronomical tables in Cracow (XIVth-XVIth centuries) (Studia Copernicana, xxii; Wrocław, 1984), 488–98. Rosińska lists two sets of planetary latitude tables, one set that follows the Almagest (p. 489), and one set that follows al-Khwārizmī (p. 498), but only one manuscript has both sets. Manuscripts of the Toledan Tables also have one or both sets of tables ( Toomer G. J. , “A survey of the Toledan Tables”, Osiris , xv (1968), 5–174, espec. pp. 69–72). See Kennedy E. S. Ukashah W. , “al-Khwūrizm's Planetary Latitude Tables”, Centaurus , xiv (1969), 86–96, where the computation of these tables is explained.

For the procedure to compute the latitude of Venus, see Neugebauer O. , A history of ancient mathematical astronomy (Berlin, Heidelberg and New York, 1975), 222ff.

Almanach perpetuum (ret. 8), 121v ff. We are aware of only one other set of double argument planetary latitude tables, John of Gmunden's tables dated 1437: See, e.g., Vienna, National Library, MS 5268, 18v–25v. A copy of these tables, with many errors, was published by Henri Baers (or Vekenstyl) in Les tables astronomiques de Louvain de 1528, facsimile edition with introduction by Poulle E. De Smet A. (Brussels, 1976). On the other hand, there are quite a few medieval double argument tables for planetary longitudes: See, e.g., North J. D. , “The Alfonsine Tables in England”, in Prismata , ed. by Maeyama Y. Salzer W. G. (Wiesbaden, 1977), 269–301.

Although there are latitude tables for Venus ascribed to John of Lignères that follow the Hindu tradition, the canons of his Priores astrologi motus corporum… (1322) describe only computations based on Almagest xiii.5. In canon 22 the relevant passage on the latitude of Venus is:

Postea centro Veneris 60 gradus adde quod si post additionem provenerint ultra 360 gradibus abjice 360 et cum residuo vel cum eo quod fuerit minus 360 ingredere easdem lineas numeri. … Deinde cum simplici centro Veneris prius servato, scilicet antequam sibi fieret additio 60 gradus [sic. read: Graduum] lineas numeri tabule ingredere et quod in ejus directo fuerit de minutis proportionalibus in duobus locis seorsum scribe. ( Saby M.-M. , “Les canons de Jean de Lignères sur les tables astronomiques de 1321”, thèse pour l'obtention du diplôme d'archiviste paléographe, École Nationale des Chartes, Paris, 1987, 207–8).

(Then add 60 degrees to the centre of Venus, and if the result exceeds 360 degrees, subtract 360 from them, and enter with the remainder, or the quantity less than 360 degrees, into the same argument. … After that, use the uncorrected centre of Venus you kept, i.e., before the addition of 60 degrees, to enter into the argument of the table, and write down in two separate places what you find opposite it in the column of the minutes of proportion.).

The edition by Saby is based on six MSS: Erfurt F 377; Cracow 551; Catania 85; Erfurt Q 366; Paris, BNF, lat. 7281; and Paris, BNF, lat. 7295A. In the critical apparatus for these two sentences no variant readings are registered but we have been informed by Mancha J. L. that, in the copy of these canons in Paris, BNF, MS lat. 7281, 190v–191r, the “60 degrees” in the text has been corrected in the margin to “90 degrees” (both times). We are grateful to Mancha J. L. for this reference. It is also noteworthy that there is no known Hebrew translation of Lignères's text, whereas all other texts cited explicitly by Zacut in The great composition were either composed in Hebrew or available in Hebrew translation.

In the Latin version of the Almanach perpetuum (ref. 8), 14r, we find:

Scito quod hanc latitudinem veneris principaliter fecimus secundum mentem ptholomei in almagesto et albategni et alfragani et avenrois et non secundum ordinem tabularum iohanis de linerijs. Eo quod mihi illa opinio primorum videtur verior.

(Know that we calculated this latitude of Venus mainly according to the opinion (mens) of Ptolemy in the Almagest and al-Battānī and al-Farghānī and Averroes, and not according to the canons to the tables of John of Lignères, because the opinion (opinio) of the former [scholars] seems to me [to agree] better with the truth [than the opinion of John of Lignères].).

In the Hebrew text of the canons to The great composition, Chapter 14, Zacut says (B, 39a; cf. S, 45v–46r): “To find the latitude of Venus … and we depended on the Almagest by Ptolemy and Ben Rushd [i.e., Averroes] and on al-Farghān….”.

John of Lignères is not mentioned in Chapter 14 of these canons until the gloss that is preserved only in MS B. On al-Battānī (d. 929), see Nallino C. A. , al-Battānī sive Albatenii Opus astronomicum (3 vols, Milan, 1899–1907); on al-Farghānī (ninth century), see Sezgin F. , Geschichte des arabischen Schrifttums (9 vols, Leiden, 1967–95), vi, 149–51; on Averroes (d. 1198), see Lay , op. cit. (ref. 7).

For a French translation of this passage in Averroes's chapter on the order of the planets, see Lay J. , “L'Abrégé de l'Almageste , attribué à Averroès, dans sa version hébraïque”, thèse de doctorat, École Pratique des Hautes Études: Section des Sciences Religieuses, Paris, 1991, iii, 140. For the discussion of Venus's parallax by Jābir (twelfth century, Spain) as preserved in Latin, see Lorch R. , “The Astronomy of Jābir ibn Aflah”, Centaurus , xix (1975), 85–107, espec. pp. 97–98. We are most grateful to J. Samsó for calling this article to our attention, and for his comments on the passage in Book 7 of Jābir's Astronomy in Arabic. The relevant passage is found in Escurial, MS Ar. 910, 78b–79a, and in the Hebrew version it is found in Paris, BNF, MS Heb. 1024, 76b–77a.

The parallax of Venus is not often discussed in medieval astronomical texts, but we found a brief remark by Levi ben Gerson (d. 1344) where the value 0;18° is given without specifying whether it is for Venus or Mercury. See Levi ben Gerson's Astronomy: Paris, BNF, MS Heb. 724, 252b:23; and Paris, BNF, MS Heb. 725, 223a:25.

See Goldstein B. R. , The Arabic version of Ptolemy's Planetary Hypotheses ( Transactions of the American Philosophical Society , n.s., lvii/4; Philadelphia, 1967), 7.

See Toomer , op. cit. (ref. 4), 652–3, for a worked example of a parallax computation. Toomer's results differ noticeably from those that Ptolemy obtained.

See, e.g., Chabás J. Tihon A. , “Verification of parallax in Ptolemy's Handy Tables”, Journal for the history of astronomy , xxiv (1993), 123–41; Kennedy E. S. , A survey of Islamic astronomical tables (Transactions of the American Philosophical Society, n.s., xlvi/2; Philadelphia, 1956), 143, 155, et passim.

Goldstein B. R. , “Medieval observations of solar and lunar eclipses”, Archives internationales d'histoire des sciences , xxix (1979), 101–56, espec. pp. 149–50.

Note that the reports of Walther's observations of occultations (see ref. 3, above) do not mention lunar parallax. Kremer , op. cit. (ref. 3), 186, adds that Walther occasionally compared his observations with positions computed from “tables” but, in checking these reports, we find that lunar parallax was not invoked in any of them.

See Goldstein B. R. , Levi ben Gerson's Astronomical Tables (New Haven, 1974), 65.

See Swerdlow Neugebauer , op. cit. (ref. 3), 193. Note that Copernicus's lunar model was anticipated by Ibn al-Shātir (d. 1375): See Roberts V. , “The solar and lunar theory of Ibn ash-Shātir”, Isis , xlviii (1957), 428–32. Copernicus's reduction in the variation of lunar distance attracted the support of some of his contemporaries, e.g., Gemma Frisius (d. 1555) who noticed that Copernicus's lunar theory produced better agreement with his observations than did Ptolemy's lunar theory: See Goldstein B. R. , “Remarks on Gemma Frisius's De radio astronomico et geometrico”, in From ancient omens to statistical mechanics: Essays on the exact sciences presented to Asger Aaboe , ed. by Berggren J. L. Goldstein B. R. (Copenhagen, 1987), 167–79.

The difficulty in the latitude theory for Venus is mentioned in Regiomontanus's letter (c. 1464) to Bianchini concerning various problems in Ptolemaic astronomy. Regiomontanus says: “Finally I have seen Venus slower in the heaven than the computation had predicted by about three-quarters of a degree, and it is also extremely difficult to avoid falsehood in computing its latitudes” ( Swerdlow N. M. , “Regiomontanus on the critical problems of astronomy”, in Nature, experiment, and the sciences , ed. by Levere T. H. Shea W. R. (Dordrecht, 1990), 165–95, espec. p. 173).

There are, in general, many uncertainties in interpreting this letter and, in this case, it is not at all clear whether Regiomontanus was referring to the complicated instructions for computing the latitude of Venus, or suggesting that the theory was faulty in some way. He did not elaborate on this brief comment, and it was not pursued by his immediate successors, as far as we know. For example, in Copernicus's De revolutionibus, the table for Venus's latitude is essentially the same as in the Almagest: See Swerdlow Neugebauer , op. cit. (ref. 3), 505ff, 530ff.

Earlier, Ibn al-Haytham (d. 1040) had offered philosophical objections to Ptolemy's treatment of the latitude of Venus, but no alternative was presented. See Ibn al-Haytham's al-Shukūk ^calā Batlamyūs [Doubts concerning Ptolemy], ed. by Sabra A. I. Shehaby N. (Cairo, 1971), 36–37; translated in Langermann Y. T. , Ibn al-Haytham's On the Configuration of the World (New York, 1990), 9. For a discussion of Ibn al-Haytham's model for the latitude of Venus, and the response by Nasīr al-Dīn al-Tūsī (d. 1274), see Ragep F. J. , Nasīr al-Dīn al-Tūs's Memoir on Astronomy (New York, 1993), 68ff (and the references cited there); and Saliba , op. cit. (ref. 3), 151ff. For possible echoes of this discussion in Latin sources, see Mancha J. L. , “Ibn al-Haytham's homocentric epicycles in Latin astronomical texts of the XIVth and XVth centuries”, Centaurus , xxxiii (1990), 70–89.

Levi ben Gerson reports observations of the latitude of Venus, and remarks that they do not agree with computations based on Ptolemy's model: See Goldstein , op. cit. (ref. 3), 396–7.