John of Murs's Tables of 1321

Gushee L. , “New sources for the biography of Johannes de Muris”, Journal of the American Musicological Society, xxii (1969), 3–26; Poulle E. , “John of Murs”, in Dictionary of scientific biography, vii (1973), 1973–33; Beaujouan G. , “Observations et calculs astronomiques de Jean de Murs (1321–1344)”, in Proceedings of the XIVth International Congress of the History of Science (Tokyo—Kyoto 1974) (Tokyo, 1975), ii, 27–30, reprinted in idem, Par raison des nombres: L'art du calcul et les savoirs scientifiques médiévaux (Aldershot, 1991), Essay VII; North J. D. , “The Alfonsine Tables in England”, in Maeyama Y. Salzer W. G. (eds), Prismata: Festschrift für Willy Hartner (Wiesbaden, 1977), 269–301; l'Huiller G. , “Aspects nouveaux de la biographie de Jean de Murs”, Archives d'histoire doctrinale et littéraire du Moyen Âge, xlvii (1980), 1980–6; Schabel C. , “John of Murs and Firmin of Beauval's letter and Treatise on the Calendar Reform for Clement VI”, Cahiers de l'Institut du Moyen-âge Grec et Latin, lxvi (1996), 1996–215; Chabás J. Goldstein B. R. , The Alfonsine Tables of Toledo (Dordrecht and Boston, 2003); Lejbowicz M. , “Présentation de Jean de Murs ‘observateur et calculateur sagace et laborieux’”, in Grelland C. (ed.), Méthodes et statut des sciences à la fin du Moyen Âge (Villeneuve d'Ascq, 2004), 159–80; Kremer R. L. , “John of Murs, Wenzel Faber and the computation of true syzygy in the fourteenth and fifteenth centuries”, in Dauben J. W. (eds), Mathematics celestial and terrestrial: Festschrift für Menso Folkerts zum 65. Geburtstag (Halle [Saale], 2008), 147–60.

Chabás Goldstein , Alfonsine Tables of Toledo (ref. 1), 277–81.

See Poulle E. , “Jean de Murs et les tables alphonsines”, Archives d'histoire doctrinale et littéraire du Moyen Âge , xlvii (1980), 241–71, especially pp. 261–65; Chabás Goldstein , Alfonsine Tables of Toledo (ref. 1), 263–4, 279–80.

See Goldstein B. R. Chabás J. , “The maximum solar equation in the Alfonsine Tables”, Journal for the history of astronomy , xxxii (2001), 345–8; Chabás J. Goldstein B. R. , “Early Alfonsine astronomy in Paris: The tables of John Vimond (1320)”, Suhayl, iv (2004), 2004–94.

For a brief account, see North , “Alfonsine Tables in England” (ref. 1), 284–5.

See, e.g., Chabás Goldstein , Alfonsine Tables of Toledo (ref. 1), 266–84; Chabás J. Goldstein B. R. , “John Vimond and the Alfonsine trepidation model”, Journal for the history of astronomy, xxxiv (2003), 163–70; Chabás Goldstein , “John Vimond” (ref. 4).

Goldstein B. R. Chabás J. , and Mancha J. L. , “Planetary and lunar velocities in the Castilian Alfonsine Tables”, Proceedings of the American Philosophical Society, cxxxviii (1994), 61–95.

See Chabás J. , “Were the Alfonsine Tables of Toledo first used by their authors?”, Centaurus, xlv (2003), 142–50.

For the evidence in John of Murs's Expositio, see Goldstein Chabás , “Maximum solar equation” (ref. 4), 347 n. 2. For contrary views, see Poulle E. , “The Alfonsine Tables and Alfonso X of Castille”, Journal for the history of astronomy , xix (1988), 97–113; and idem, “Les astronomes parisiens au XIVe siècle et l'astronomie alphonsine”, Histoire littéraire de la France, xliii (2005), 2005–54.

Porres B. Chabás J. , “John of Murs's Tabulae permanentes for finding true syzygies”, Journal for the history of astronomy, xxxii (2001), 63–72.

For a brief account of their contents, see Poulle , “Les astronomes parisiens” (ref. 9), 24–26, where these tables are dated no earlier than 1325.

Tabule astronomice illustrissimi Alfontij regis castelle, ed. by Ratdolt E. (Venice, 1483), ff. a2r–b8v.

For a transcription of these canons, see Chabás Goldstein , Alfonsine Tables of Toledo (ref. 1), 19–94.

For recomputations according to the editio princeps of the Alfonsine Tables (1483), we have used a spreadsheet provided to us by Richard L. Kremer (Dartmouth College, USA), which was prepared by Lars Gislén (Lund University, Sweden). By the standard Alfonsine Tables we mean the collection of tables found in the editio princeps, ed. by Ratdolt E. (ref. 12) that, by and large, goes back to a compilation made in Paris in about 1327 with canons by John of Saxony. Among many others, it includes: Tables for the differences between the eras, tables to transform dates of various eras, a set of radices for various eras, a table for the movement of the 8th sphere (with a maximum of 9;0°), tables of the mean motions (presented as 60 consecutives multiples of the daily mean motions), equations of the luminaries (with maximum values of 2;10° and 4;56° for the Sun and the Moon), equations of the planets, etc. There is no modern edition of these tables which would have to be based on the vast number of extant manuscripts, but we have examined many manuscripts containing them, and none has exactly the same collection as the first edition. However, for example, Madrid, Biblioteca Nacional, MS 10002, and Vienna, Nationalbibliothek, MS 2288, share most of the characteristics of the editio princeps although, in contrast to it, they do not have a star table.

There were two conventions for dates counted from the Incarnation in the Middle Ages: (1) the number of years that have been completed, and (2) the current year which has not been completed. So for a date as we reckon it in current years, e.g., noon, 15 Feb. 1321, one might say equivalently that 1320 years have been completed plus 1 month (January) plus 14 days.

Chabás Goldstein , “John Vimond” (ref. 4), 213 and 229, Tables 1 and 8.

E.g. Abraham Zacut: See Chabás J. Goldstein B. R. , Astronomy in the Iberian Peninsula: Abraham Zacut and the transition from manuscript to print (Philadelphia, 2000), 60 and 117.

The columns for the arguments, the equation of centre, and the stations of Saturn and Jupiter are displayed on a single page, whereas the latitudes of these two planets are presented separately.

Chabás Goldstein , “John Vimond” (ref. 4), 244.

Chabás Goldstein , “John Vimond” (ref. 4), 242.

Chabás Goldstein , Alfonsine Tables of Toledo (ref. 1), 42–43.

Chabás Goldstein , “John Vimond” (ref. 4), 257–8.

See, e.g., Tabule astronomice illustrissimi Alfontij (ref. 12), ff. g6r–g7r.

See Chabás Goldstein , Abraham Zacut (ref. 17), 108–9.

See Chabás Goldstein , Alfonsine Tables of Toledo (ref. 1), 186.

According to Poulle, this work was probably composed in the late 1320s: cf. Poulle , “Les astronomes parisiens” (ref. 9), 26–27.

See, e.g., Kremer , “John of Murs, Wenzel Faber” (ref. 1), 148.

On L 8r—v there is another table containing much the same information with the title, Tabula medie coniunctionis solis et lune in annis ad meridiem Tholeti secundum radices Alfonsii regis castelle. We are only given entries for the last conjunction of each of the 76 years, but with a higher accuracy, both for time (to seconds of an hour) and for the three other quantities (to seconds of an arc).

Toomer G. J. , Ptolemy's Almagest (New York and Berlin, 1984), 174–6.

See Chabás J. Goldstein B. R. , “Computational astronomy: Five centuries of finding true syzygy”, Journal for the history of astronomy, xxviii (1997), 93–105.

For additional details, see Kremer , “John of Murs, Wenzel Faber” (ref. 1), 148–55.

North , “Alfonsine Tables in England” (ref. 1), 279 and 293; Chabás Goldstein , “Finding true syzygy” (ref. 30), 93 and 104 n. 3.

Lejbowicz , “Présentation de Jean de Murs” (ref. 1), 175.