The Medieval Moon in a Matrix: Double Argument Tables for Lunar Motion *

Résumé En

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. Keywords Ibn al-Kammād, Jacob ben Makhir, Parisian Alfonsine Tables, John Vimond, Bonfils Beginning at the end of the thirteenth century, double argument tables-both in Latin and Hebrew-became a powerful tool for presenting astronomical information to determine the positions of the Moon and the planets. They were put in the format of what is now called a matrix with its columns and rows, very convenient for dealing simultaneously with two quantities, or variables as they are presently known. In this respect, it seems that European astronomers followed the lead of astronomers in the Muslim world, and already in the late tenth century Ibn Yūnus (Egypt, d. 1009) had compiled an extensive double argument table for the lunar equation (This paper deals with the application of double argument tables to lunar motion, for which we have identified seven categories: (i) tables for the lunar equation, or the equivalent; (ii) tables for the true lunar position; (iii) tables for lunar velocity at any time; (iv) tables for the time from mean to true syzygy; (v) tables for the distance in longitude from mean to true syzygy; (vi) tables to determine the position of the Moon between syzygies; and (vii) table for solar eclipses. Since double argument tables in (iv) have previously been addressed systematically by the authors of the present paper (Chabás and Goldstein 1997), here we focus on the other categories. Double argument tables were not only used to describe the lunar motions; they were also applied to the planets, a subject that will be addressed in a subsequent paper. I. Double argument tables for the lunar equation *