John of Murs Revisited: The Kalendarium Solis Et Lune for 1321

Poulle E. , “John of Murs”, in Dictionary of scientific biography , vii (1973), 128–33; 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), no. VII; North J. D. , “The Alfonsine Tables in England”, in Prismata: Festschrift für Willy Hartner , ed. by Maeyama Y. Salzer W. G. (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), 272–6; 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), 187–215; Poulle E. , “Jean de Murs et les tables alphonsines”, Archives d'histoire doctrinale et littéraire du Moyen Âge , xlvii (1980), 241–71; 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 Méthodes et statut des sciences à la fin du Moyen Âge , ed. by Grelland C. (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 Mathematics celestial and terrestrial: Festschrift für Menso Folkerts zum 65. Geburtstag , ed. by Dauben J. W. (Halle [Saale], 2008), 147–60; Chabás J. Goldstein B. R. , “John of Murs's Tables of 1321”, Journal for the history of astronomy , xl (2009), 297–320.

Poulle , “Jean de Murs” (ref. 1); Chabás and Goldstein, Alfonsine Tables (ref. 1), 277–81.

Chabás Goldstein , “Murs's tables” (ref. 1), 297–320.

Chabás Goldstein , “Murs's tables” (ref. 1), 313–17.

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

Brussels, Bibliothèque royale, MS 1086–1115, paper and parchment, 4°, has 214 folios and contains material from the fourteenth and the fifteenth centuries, mostly on ascetic theology, in Latin and Dutch. For descriptions see Van den Gheyn J. , Catalogue des manuscrits de la Bibliothèque royale de Belgique , iii (Brussels, 1903), 453–7; and Calcoen R. , Inventaire des manuscrits scientifiques de la Bibliothèque royale de Belgique , i (Bruxelles, 1965), 37.

Medieval sets of astronomical tables usually come with instructions that are called the canons for these tables.

Chabás Goldstein , Alfonsine Tables (ref. 1), 267–8.

de Phares Simon , Le recueil des plus célèbres astrologues, ed. by Boudet J.-P. (Paris, 1997), 467.

Chabás J. Goldstein B. R. , “Early Alfonsine astronomy in Paris: The tables of John Vimond (1320)”, Suhayl, iv (2004), 207–94.

See Boudet J.-P. , Entre science et «nigromance»: Astrologie, divination et magie dans l'occident médiéval (XII^e – XV^e siècle) (Paris, 2006), 284, n. 2: “clerc normand”; and 299, n. 47: “clerc originaire du diocèse de Bayeux”.

See, e.g., Robson M. , The Franciscans in the Middle Ages (Woodbridge, UK, 2006).

Poulle , “John of Murs” (ref. 1), 129. The tables of Toulouse are a variant of the Toledan Tables that preceded the Alfonsine Tables: See Poulle E. , “Un témoin de l'astronomie du XIII^e siècle, les tables de Toulouse”, in Comprendre et maîtriser la nature au Moyen Âge: Mélanges d'histoire des sciences offerts à Guy Beaujouan (Geneva and Paris, 1994), 55–81.

Pedersen F. S. , Petri Philomenae de Daciae et Petri de S. Audomaro, Opera quadrivalia (Corpus philosophorum Danicorum medii aevi, 10.1–2; Copenhagen, 1983–84), 336–59.

Chabás Goldstein , “Murs's Tables” (ref. 1), see Table 11.

Chabás Goldstein , “Murs's Tables” (ref. 1), 311–12.

Chabás J. Goldstein B. R. , Astronomy in the Iberian Peninsula: Abraham Zacut and the transition from manuscript to print (Transactions of the American Philosophical Society, xc/2; Philadelphia, 2000), 106ff.

Chabás Goldstein , “Murs's Tables” (ref. 1), 314.

Poulle E. , “Les astronomes parisiens au XIV^e siècle et l'astronomie alphonsine”, Histoire littéraire de la France, xliii (2005), 1–54, pp. 26–7.

In Vimond's tables the excess of solar (or lunar) motion (with respect to the solar apogee) over an integer number of returns in longitude in 7521 lunations (about 608 years) is 20; 6, 6°. Thus, the motion of the Moon in this time period is 2,926,460; 6, 6° which, divided by the number of days in 7521 months (7521 × 29; 31, 50, 7, 44, 35d), amounts to 13; 10, 34, 49, 58°/d. This result, increased by 0; 0, 0, 11, 13, 35°/d (the motion of the solar apogee according to Vimond), yields 13; 10, 35, 1, 12, 0°/d. See Chabás and Goldstein, “John Vimond” (ref. 10), 214, 220–1. See also Tabule astronomice illustrissimi Alfontij regis castelle , ed. by Ratdolt E. (Venice, 1483), d5v, and Pedersen F. S. , The Toledan Tables: A review of the manuscripts and the textual versions with an edition (Copenhagen, 2002), 1149–56.

Samsó J. Millás E. , “The computation of planetary longitudes in the Zīj of Ibn al-Bannā”, Arabic sciences and philosophy , viii (1998), 259–86, pp. 276–8; reprinted in Samsó J. , Astronomy and astrology in al-Andalus and the Maghrib (Aldershot, 2007), no. VIII. For the parameter, 5;1°, see Toomer G. J. , Ptolemy's Almagest (New York, 1984), 210, and Nallino C. A. , Al-Battānī sive Albatenii Opus Astronomicum (2 vols, Milan, 1903–7), ii, 81. The parameter, 4;56°, goes back to the Khwārizmī zij in the Hindu tradition, as preserved in a Latin version by Adelard of Bath. The earliest occurrence of this parameter in a Ptolemaic model is in a work by Ibn Mu^cādh, preserved in Latin: See Samsó J. , Las ciencias de los antiguos en al-Andalus (Madrid, 1993), 156.

Chabás Goldstein , Alfonsine Tables (ref. 1), 252–3.

Chabás Goldstein , “Murs's Tables” (ref. 1), 303. The values for half a mean synodic month derived from John of Murs's Tables of 1321 are: 14d 18; 22, 1, 31h (duration); 14; 33, 12, 6° (mean motion); 6s 12; 54, 33, 15° (mean anomaly); and 6s 15; 20, 6, 54° (mean argument of latitude).

See Nallino , Al-Battānī (ref. 21), ii, 88; Toomer G. J. , “A survey of the Toledan Tables”, Osiris , xv (1968), 5–174, pp. 82–4; and Pedersen , The Toledan Tables (ref. 20), 1410–12.

See Goldstein B. R. , “Solar and lunar velocities in the Alfonsine Tables”, Historia mathematica, vii (1980), 134–40.

This equation depends on the approximation given in Ptolemy's Almagest for the ratio of the solar and lunar velocities at conjunction: V_s/v_m ã 1/13: See. e.g., Chabás J. Goldstein B. R. , “Nicholaus de Heybech and his Table for Finding True Syzygy”, Historia mathematica, xix (1992), 266–8.

Neugebauer O. A history of ancient mathematical astronomy (Berlin, 1975), 736–46; see especially p. 738.

Schaldach K. , “Gli ‘schemi delle ombre’ nel Medio Evo latino”, Gnomonica Italiana, xvi (2008), 9–16.

Chabás Goldstein , “Murs's Tables” (ref. 1), 303–4 and 316–17.

Goldstein B. R. , “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. by Casulleras J. Samsó J. (2 vols, Barcelona, 1996), i, 181–94.

For the tables of al-Khwārizmī, see Suter H. , Die astronomischen Tafeln des Muhammad ibn Mūsā al-Khwārizmī (Copenhagen, 1914), 187–90, 193; for the tables of al-Battānī, see Nallino , Al-Battānī (ref. 21), ii, 90–1; and for the Toledan Tables, see Toomer , “Survey” (ref. 24), 86–96; and Pedersen, Toledan Tables (ref. 20), 1458–78.

For the distinction between the underlying parameters and the “outward form” (i.e., the presentation) that characterize a set of astronomical tables, see North J. D. , “Just whose were the Alfonsine Tables?”, in From Baghdad to Barcelona, ed. by Casulleras Samsó (ref. 30), i, 453–69, p. 455.

See Toomer , Ptolemy's Almagest (ref. 21), 308.

See Stahlman W. D. , “The astronomical tables of Codex Vaticanus Graecus 1291”, Ph.D. dissertation, Brown University, 1959; University Microfilms, no. 62–5761, p. 257.