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

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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.

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Notes

  1. 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. 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. 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. 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. 5.

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

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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

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