Skip to main content
Log in

The medieval Moon in a matrix: double argument tables for lunar motion

  • Published:
Archive for History of Exact Sciences Aims and scope Submit manuscript

Abstract

Astronomers have always considered the motion of the Moon as highly complicated, and this motion is decisive in determining the circumstances of such critical celestial phenomena as eclipses. Table-makers devoted much ingenuity in trying to find ways to present it in tabular form. In the late Middle Ages, double argument tables provided a smart and compact solution to address this problem satisfactorily, and many tables of this kind were compiled by both Christian and Jewish astronomers. This paper presents multiple examples of the diversity of approaches adopted by compilers of tables who used this powerful tool, and brings to light intellectual interactions among them that are otherwise hidden from view.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. The order of the columns in Almagest V.8 was not followed in the tables for the lunar equation compiled by subsequent astronomers. Moreover, al-Battānī added a column for the solar equation. For the correspondence of the various columns in this table in the Almagest, the zij of al-Battānī, the Toledan Tables, and the Parisian Alfonsine Tables, see Chabás and Goldstein (2012b, p. 71).

  2. Elongation is the difference between the mean position of the Moon and that of the Sun, and double elongation is twice this difference. Strictly speaking, this angular distance should be called “mean elongation” in contrast to “true elongation,” understood as the difference between the true positions of the Moon and the Sun. Unless otherwise specified, in this paper “elongation” refers to “mean elongation.” In Sect. 2.4, below, we refer to an unusual expression found in a medieval text, namely “true” elongation, which does not fit either of the two definitions above, for it represents the difference between the mean Sun and the true Moon.

  3. See Kennedy (1977) and Samsó (2003) on displaced tables in Islamic astronomy and Chabás and Goldstein (2013) for those in Latin, and the references therein.

  4. Among them are Erfurt, Universitäts- und Forschungsbibliothek, MS Amplon. F 377, 46r; Bernkastel-Kues, Cusanusstiftsbibliothek, MS 212, 91r; Paris, BnF, MS lat. 7286C, 53v; Paris, BnF, MS lat. 7295A, 162r. For the Tables of John of Lignères for 1322, see Chabás (2019), forthcoming.

  5. We have been informed that R. L. Kremer is about to publish a paper on the mathematical aspects of this table.

References

  • Boudet, J.-P. 1994. Lire dans le ciel. Brussels: Centre d’Études des Manuscrits.

    Google Scholar 

  • Castells, M. 1996. Una tabla de posiciones medias planetarias en el Zīŷ de Ibn Waqār (Toledo, ca. 1357). In From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet, ed. J. Casulleras and J. Samsó, 445–452. Barcelona: Instituto Millás Vallicrosa.

    Google Scholar 

  • Chabás, J. 1996. Astronomía andalusí en Cataluña: Las Tablas de Barcelona. In From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet, ed. J. Casulleras and J. Samsó, 477–525. Barcelona: Instituto Millás Vallicrosa.

    Google Scholar 

  • Chabás, J. 2019. Computational astronomy in the Middle Ages: Sets of astronomical tables in Latin. Barcelona: CSIC.

    Google Scholar 

  • Chabás, J., and B.R. Goldstein. 1994. Andalusian astronomy: al-Zīj al-muqtabis of Ibn al-Kammād. Archive for History of Exact Sciences 48: 1–41.

    Article  MathSciNet  MATH  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 1997. Computational astronomy: Five centuries of finding true syzygy. Journal for the History of Astronomy 47: 93–105; reprinted in Chabás and Goldstein 2015b, pp. 40–56.

  • Chabás, J., and B.R. Goldstein. 2000. Astronomy in the Iberian Peninsula: Abraham Zacut and the transition from manuscript to print. Transactions of the American Philosophical Society, vol. 90, no. 2. Philadelphia.

  • Chabás, J., and B.R. Goldstein. 2004. Early Alfonsine astronomy in Paris: The tables of John Vimond (1320). Suhayl 4: 207–294; reprinted in Chabás and Goldstein 2015b, pp. 227–307.

  • Chabás, J., and B.R. Goldstein. 2009. The Astronomical Tables of Giovanni Bianchini. Leiden: Brill.

    Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2012a. John of Murs revisited: The Kalendarium solis et lune for 1321. Journal for the History of Astronomy 43: 411–437.

    Article  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2012b. A Survey of European astronomical tables in the late Middle Ages. Leiden: Brill.

    Book  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2013. Displaced tables in Latin: The Tables for the Seven Planets for 1340. Archive for History of Exact Sciences 67: 1–42.

    Article  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2015a. Ibn al-Kammād’s Muqtabis zij and the astronomical tradition of Indian origin in the Iberian Peninsula. Archive for History of Exact Sciences 69: 577–650.

    Article  MathSciNet  MATH  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2015b. Essays on medieval computational astronomy. Leiden: Brill.

    MATH  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2016. The Moon in the Oxford Tables of 1348. Journal for the History of Astronomy 47: 159–167.

    Article  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2018. Adaptations of the Oxford Tables to Paris, Mantua, and Louvain. Journal for the History of Astronomy 49(1): 99–115.

    Article  Google Scholar 

  • Chabás, J., and B.R. Goldstein. 2019. The Almanac of Jacob ben Makhir. In Editing and analysing historical astronomical tables, ed. M. Husson, B. van Dalen, and C. Montelle. Turnhout: Brepols.

  • Goldstein, B.R. 1974. The Astronomical Tables of Levi ben Gerson. Transactions of the Connecticut Academy of Arts and Sciences, vol. 45. New Haven.

  • Goldstein, B.R. 1992. Lunar velocity in the Ptolemaic tradition. In The investigation of difficult things: Essays on Newton and the history of the exact sciences, ed. P.M. Harman and A.E. Shapiro, 3–17. Cambridge: Cambridge University Press.

    Google Scholar 

  • Goldstein, B.R. 1996. Lunar velocity in the Middle Ages: A comparative study. In From Baghdad to Barcelona: Studies in the Islamic exact sciences in honour of Prof. Juan Vernet, ed. J. Casulleras and J. Samsó, 181–194. Barcelona: Instituto Millás Vallicrosa.

    Google Scholar 

  • Goldstein, B.R. 1998. Abraham Zacut and the medieval Hebrew astronomical tradition. Journal for the History of Astronomy 29: 177–186.

    Article  MathSciNet  Google Scholar 

  • Goldstein, B.R. 2001. The astronomical tables of Judah ben Verga. Suhayl 2: 227–289.

    MathSciNet  MATH  Google Scholar 

  • Goldstein, B.R. 2003. An anonymous zij in Hebrew for 1400 A.D.: A Preliminary Report. Archive for History of Exact Sciences 57: 151–171.

    Article  MathSciNet  MATH  Google Scholar 

  • Goldstein, B.R. 2013. Preliminary remarks on the astronomical tables of Solomon Franco. Aleph 13: 175–184.

    Article  Google Scholar 

  • Goldstein, B.R., and J. Chabás. 2016–2017. The astronomical tables of Moses Farissol Botarel, Suhayl 15: 29–65.

  • Goldstein, B.R., and J. Chabás. 2017. Analysis of the astronomical tables for 1340 compiled by Immanuel ben Jacob Bonfils. Archive for History of Exact Sciences 71: 71–108.

    Article  MathSciNet  MATH  Google Scholar 

  • Kennedy, E.S. 1977. The astronomical tables of Ibn al-Aclam. Journal for the History of Arabic Science 1: 13–23.

    MathSciNet  Google Scholar 

  • Kennedy, E.S., and N. Faris. 1970. The Solar Eclipse Technique of Yaḥyā b. Abī Manṣūr. Journal for the History of Astronomy 1: 20–38; reprinted in Kennedy 1983, Studies in the Islamic Exact Sciences. Beirut, pp. 185–203.

  • King, D.A. 1974. A double-argument table for the lunar equation attributed to Ibn Yūnus. Centaurus 18: 129–146.

    Article  MATH  Google Scholar 

  • King, D.A., J. Samsó, and B.R. Goldstein. 2001. Astronomical Handbooks and Tables from the Islamic World (750–1900): An Interim Report. Suhayl 2: 9–105.

    MathSciNet  MATH  Google Scholar 

  • Mancha, J.L. 1998. The Provençal version of Levi ben Gerson’s tables for eclipses. Archives Internationales d'Histoire des Sciences 48: 269–353.

    MathSciNet  MATH  Google Scholar 

  • Nallino, C.A. 1903–1907. Al-Battānī sive Albatenii Opus Astronomicum, vol. 2. Milan.

  • North, J.D. 1977. The Alfonsine Tables in England. In Prismata. Naturwissenschaftsgeschichtliche Studien, ed. Y. Maeyama and W. G. Saltzer, pp. 269–301. Festschrift für Willy Hartner. Wiesbaden. Reprinted in idem 1989. Stars, minds and fate. Essays in ancient and medieval cosmology. London, pp. 327–359.

  • Pedersen, F.S. 2002. The Toledan Tables: A review of the manuscripts and the textual versions with an edition. Copenhagen: Kongelige Danske Videnskabernes Selskab.

    Google Scholar 

  • Porres, B., and J. Chabás. 2001. John of Murs’s Tabulae permanentes for finding true syzygies. Journal for the History of Astronomy 32: 63–72.

    Article  MathSciNet  Google Scholar 

  • Richler, B. et al. 2008. Hebrew manuscripts in the Vatican Library. Studi e Testi 438. Vatican City.

  • Saliba, G. 1976. The double-argument lunar tables of Cyriacus. Journal for the history of astronomy 7: 41–46.

    Article  MathSciNet  Google Scholar 

  • Samsó, J. 2003. On the Lunar Tables in Sanjaq Dār’s Zīj al-Sharīf. In The Enterprise of Science in Islam, ed. J. Hogendijk and A.I. Sabra. Cambridge, MA: MIT Press.

    Google Scholar 

  • Schuba, L. 1992. Die Quadrivium-Handschriften der Codices Palatini Latini in der Vatikanischen Bibliothek. Wiesbaden: Reichert.

    Google Scholar 

  • Solon, P. 1968. The ‘Hexapterygon’ of Michael Chrysokokkes. Brown University. Ph.D. dissertation (unpublished: ProQuest, UMI, AAT 6910019).

  • Solon, P. 1970. The Six Wings of Immanuel Bonfils and Michael Chrysokokkes. Centaurus 15: 1–20.

    Article  MathSciNet  MATH  Google Scholar 

  • Steinschneider, M. 1964. Mathematik bei den Juden. Hildesheim: Georg Olms.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to José Chabás.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Communicated by Robert Morrison.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chabás, J., Goldstein, B.R. The medieval Moon in a matrix: double argument tables for lunar motion. Arch. Hist. Exact Sci. 73, 335–359 (2019). https://doi.org/10.1007/s00407-019-00226-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00407-019-00226-y

Navigation