John of Murs

(fl. France half of the fourteenth century)

mathematics, astronomy, music.

Originally from the diocese of Lisieux in Normandy, John of Murs was active in science from 1317 until at least 1345. He wrote most of his works in Paris, at the Sorbonne, where he was already a master of arts in 1321. Between 1338 and 1342 he was among the clerks of Philippe III d’sé vreux, king of Navarre, and in 1344 he was canon of Mé zié res- en- Brenne, in the diocese of Bourges.¹ The date of his death is not known. His letter to Clement VI on the conjunctions of 1357 and 1365 must have been sent before the pope’s death in 1352; on the other hand, the chronicler Jean de Venette prefaced his account of the year 1340 with two prophecies, one for the year 1315 and the other, no date given, attributed to John of Murs, of whom he speaks in the past tense.² But this prophecy is probably not by John of Murs.³ Moreover, Jean de Venette, whose information is not necessarily firsthand, wrote his chronicle at different times and probably made corrections and additions which do not permit the assignment of a definite year to the composition of the account of the year 1340.⁴ There has been an attempt to argue that John of Murs’s life extended beyond the accession of Philipped de Vitry to the see of Meaux in 1351, but there is no ground for accepting this assertion.

John of Murs wrote a great deal, but certain of his works appear not to have been preserved. Among the missing are one on squaring the circle and a “genealogia astronomie,” both cited at the end of the Canones tabule tabularum as composed in 1321. The other writings are devoted to music, mathematics, and astronomy.

John of Murs’s musical works include Ars nove musice, composed in 1319, according to the explicit of one of the manuscripts; Musica speculativa secundum Boetium, dating from 1323 and written at the Sorbonne; Libellus cantus mensurabilis; and Questiones super partes musice, which takesup again, in theform of questions and answer, the material of the Libellus. We do not know whether to this list should be added the Artis musice noticia cited by the Canones tabule tabularum among the works composed in 1321, or whether this text is the same as the Ars nove musice mentioned above. The other treatises bear witness to a scientific conception of music, new at the beginning of the fourteenth century: it is as a mathematician that John of Murs views musical problems. In addition to its fundamental originality, his work reveals the pedagogic qualities that assured his musical writings a wide diffusion until the end of the Middle Ages.

It was in mathematics that John of Murs’s learned work received its greatest development. The Canones tabule tabularum mentions a squaring of the circle which does not seem to have been preserved; it is therefore not known whether he was acquainted at that time with Archimedes’ De mensura circuli in the translation of William of Moerbeke, which he mentions knowing twenty years later. This quadrature aside, the earliest mathematical work of John of Murs is the Tabula tabularum proportionis. . .” It is a table giving, for the numbers one to sixty inscribed as both abscissas and ordinates, the product of their multiplication expressed directly in sexagesimal notation. They year of this table, 1321, and its title clearly reveal the preoccupations which led John of Murs to construct it, since he was associated at that time with the project of recasting the astronomical tables of Alfonso X of Castile in a strictly sexagesimal presentation. This systematic conversion of the chronological elements into the number of days expressed in sexagesimal numeration presupposed great suppleness in the mental gymnastics involved in such a conversion.

In addition to calculations in sexagesimal numeration, knowledge of trigonometry was necessary in astronomy. Hence it is not surprising to find, under the name of John of Murs, a short treatise on trigonometry entitled Figura inveniendi sinus kardagarum(“Omnes sinus recti incipiunt a dyametro orthogonaliter. . .”), which concerns the construction of a table of sines.

Yet it would be wholly incorrect to concider John of Murs’s mathematical work as only a sort of handmaiden to astronomy. About 1344⁵ he completed De arte mensurandi (“Quamvis plures de arte mensurandi inveniantur tractatus . . .”), in twelve chaptersof which the first four chapters and the beginning of the fifth had already been written by another author and deal precisely with the mathematical knowledge necessary for astronomy (operations on sexagesimal fractions and trigonometry). Going beyond these elementary notions, John of Murs utilized Archimedes’ treatises on spirals, on the measurement of the circle, on the sphere and the cylinder, and on the conoids and spheroids, which he knew in the translation of William of Moerbeke. Moreover, he inserted in this work, as the eighth chapter, a squaring of the circle which is sometimes found seperately (“Circulo dato possible est accipere. . .”) and which is dated 1340. The propositions of the De arte mensurandi appeared, without the demonstrations, under the title Commensurator or as Problemata geometrica omnimoda, long attributed to Regiomontanus.⁶

John of Murs’s most famous mathematical work is his Quadripartitum numerorum (“Sapiens ubique sua intelligit. . .”), which takes its name from its division into four books. They are preceded by a section in verse (“Ante boves aratrum res intendens. . .”) and completed by a semiliber interpolated between books III and IV. The arithmetical portions of this treatise derive from al-Khwārizmī, with no evidence of any great advance over the original. Yet the appearance, in book III, of the use of decimal fraction in a particular case, that of the extraction of square roots, is noteworthy; but reference to their use is almost accidental and is not developed. The sections on algebra, both in the versified portion and in book III, draw on the Flos super solutionibus of Leonardo Fibonacci. Since book IV is devoted to practical applications of arithmetic, John of Murs uses this occasion to introduce a discussion on music (De sonis musicis) and two treatises on mechanics (De movimentis et motis and De ponderibus), the second of which reproduces long extracts from the Liber Archimedis de incidentibus in humidum.⁷

The Quadripartitum is dated 13 November 1343, and the versified part is addressed to philippe de Vitry. Since the Paris manuscripts of this text note that this celebrated poet and musician was also the bishop of Meaux,⁸ it has been claimed that the versified part cannot be prior to 1351, the year in which Philippe de Vitry assumed his episcopal functions; in fact, the part in verse was indeed written after the prose part, but the date of the former is certainly not much later than that of the latter (see note 5). The reference to the bishopric of Meaux is made by the copyist of the Paris manuscript, not by John of Murs.

In astronomy John of Murs’s name is associated, as is that of John of Lingnè res, with the introduction of the Alfonsine tables into medieval science. Yet his first astronomical writing, a critique of the ecclesiastical computation of the calender (“Autores calendarii nostri duo principaliter tractaverunt. . .”), in 1317, is that of a convinced partisan of the Toulouse tables, which he declares to be the best. The attribution of this text to John is proposed only by a fifteenth- century manuscript, but there is no reason to contest it; moreover, the author’s style, very critical and impassioned, is definitely that of John of Murs when, later on, he attacked the defects of the calender. The reference to the Toulouse tables would then demonstrate that, whatever P. Duhem may have believed, the introduction of the Alfonsine tables among the Paris astronomers was not yet complete in 1317.

Nor is that introduction established for 1318. In fact, we possess the report of the observation of the equinox and of the calculation of the hour of the entry of the sun into Aries, both made in that year at é vreux by John of Murs. Since the report invokes the authority of Alfonso X and his tables, Duhem saw in it proof that those tables were then in current use; but his account rests on an erroneous subdivision of a poorly identified text, the Expositio intentionis regis Alfonsii circa tabulas ejus, preserved in the manuscript Paris lat. 7281 (“Alfonsius Castelle rex illustris florens. . .”). Duhem made two different texts from it, dating the first 1301 and proposing to attribute it to William of Saint- Cloud, and assigning to John of Murs only the second, reduced to the account of the observation of 1318. In truth, the references to 1300 (anno perfecto, that is to say 1301) are found in both texts, and therefore cannot signify the year in which the texts were composed, for they accompany the results of the observation of 1318; the latter, moreover, is not described as a very recent event but as evidence invoked a posteriori to confirm the excellence of the Alfonsine tables This Expositio,including the account of 1318, must correspond to the Expositio, including the account of 1318, must correspond to the Expositio tabularum Alfonsie regis Castelle mentioned in John’s Canones tabule tabularum as being among the works that he composed in 1321. It must, consequently, have been between 1317 and 1321 that John learned of the Alfonsine tables. These dates may be compared with those of the first two tables of John of Lidnè res: those from around 1320, which appear to be independent of the Alfonsine tables, and those from 1322, which present the Alfonsine tables in a first draft. This Expositio is presented as a technical study of the values given by the Alfonsine tables for the composite movement of the apogees of the planets and for mean the movement of the sun; as the copyist of manuscript Paris lat. 7281 remarks in a final note, nothing appears about the eccentricities of the planets.10 It was not untill 1339 that John of Murs composed, after John of Lingé res and John of Saxony, canons of the Alfonsine tables in their definitive version: “Prima tabula docet differentiam unius ere. . .” ¹¹

We have seen that John of Murs had observed the sun at Eé vreux in 1318, on the occasion of the vernal equinox. This was not his only observation: a manuscript in the Escorial preserves abundant autograph notes by him dealing with his observations at Bernay, Fontevrault, é vreux, Paris, and Méziéresen-Brenne between 1321 and 1344, notably at the time of the solar eclipse of 3 March 1337.12 They attest to the scientific character of an outstanding mind, for the records of medieval astronomical observations are quite exceptional.

An informed practitioner very closely associated with the diffusion of the Alfonsine tables, John of Murs was not unaware of the extent to which astronomical tables based on the calculation of the mean movements and mean arguments of the planets, and on the corresponding equations, however satisfying they might be theoretically, contained snares and difficulties when put to practical use. An important part of his work was therefore devoted to perfecting the tables and the calculating procedures in order to lighten the task of determining planetary positions on a given date.

Thus the tables of 1321, bearing the canons “Si vera loca planetarum per presentes tabulas invenire..” represent one of the most original productions of medieval astronomy. They are based on the generalization to all the planets of the principle ordinarily applied in calculating solar and lunar conjunctions and oppositions. This calculation rests on the determination of a mean conjunction or opposition, a unique moment in which the two bodies have the same mean movement and, consequently, the equation of the center of the moon is null. Likewise, John of Murs provided, for the sixty years beginning on 1 January 1321, the list of dates on which the sun and each of the planets have the same mean movement; the argument of the planet and the equation of the argument are then null. Next, a contratahula gives directly the equation to be added to the mean movement in order to obtain the true position, partly as a function of the difference between the date for which the true position of the planet and that of its “mean conjunction” with the sun are sought and partly as a function of the mean center of the planet at the moment of the “mean conjunction.”

For the particular case of the sun and the moon, John of Murs proposed to simplify further the calculation of their conjunctions and oppositions by means of new tables, termed tabule permanentes, and of their cannon “Omnis utriusque sexus armoniam celestem . . .” : knowing the date of a mean conjunction or opposition of the two bodies (it is determined very easily with the aid of the table of mean elongation of the sun and the moon, which is included among the tables of mean movements and mean arguments of the planets), John of Murs presented directly the difference in time which separates the mean conjuction or opposition from the true conjunction of opposition in a double- entry table, where the sun’ argument is given as the abscissa and that of the moon as the ordinate.

Maintaining the goal of a rapid determination of the conjunctions and oppositions of the sun and the moon, the Patefit (so designated after the first word of its canon: “Patefit ex Ptolomei disciplinis in libro suo. . .”) offers a complete solution that is limited to the period 1321- 1396.13 A series of tables gives, without the necessity of calculation, the dates of the mean conjunctions and oppositions, the true positions of the two bodies at the times of the mean conjunctions, and the data needed to calculate rapidly, from this information, their actual positions at the times of the true conjunctions. Other tables deal with the determination of those conjunctions and oppositions which eclipse one of the two bodies and also with the calculation of the duration of the eclipse. All these tables form an annex to a calendar of which the originality consists in providing, in addition to the true daily position of the sun during the years of a bissextile cycle, the correction to be employed after the years 1321- 1324 of the first cycle. Here John of Murs’s concern to replace the ecclesiastical calendar, frozen in a nonscientific conservatism (the faults of which already were revealed in 1317), by a chronological instrument conforming to astronomical reality becomes fully apparent.

John of Murs expressed that concern again on two occasions in texts on the calendar and on the reforms that should be made in it. One of these (“De regulis computistarum quia cognite sunt a multis. . .”), by the violence of its style, almost seems to be a pamphlet against the traditional computus and the computists; 14 it nevertheless offers some constructive solutions, such as suppressing, for forty years; the intercalation of the bissextile or shortening eleven months of any given year by one day each, so that at the end of the period thus treated the calendar will have lost the eleven-day advance that it then would have recorded over the astronomical phenomena whose rhythm it should have reproduced. Another of its suggestions was to adopt a lunar cycle of four times nineteen years, a better one than the ordinary cycle of nineteen years. One of the manuscripts of the De regulis computistarum preserved at Erfurt assigns to the text the date of 1337.¹⁵

The other text on the calendar has a more official character; in fact, in 1344, John of Murs and Firmin de Belleval were called to Avignon by Pope Clement VI to give their opinion on calendar reform.¹⁶ The result of this consultation was, in 1345, a memoir (“Sanctissimo in Christo patri ac domino. . .”) in which the experts proposed two arrangements: the suppression of a bissextile year every 134 years to correct the solar calendar (after applying a suitable correction to compensate for the gap of eleven days between the date of the equinox of the computists and the true date), and the adoption of a new table of golden numbers to correct the lunar calendar.¹⁷ It was suggested that the reform being in 1349, which offered the advantage of being the first year after a bissextile and of having “1” for its golden number according to the ancient computus. This advice was not followed, and the Julian calendar retained its errors for more than two centuries.¹⁸

It was perhaps to follow up on these matters that John of Murs again sent to Clement VI, at an unknown date but necessarily before the pope’s death in 1352, an opinion concerning the anticipated conjunction of Saturn and Jupiter on 30 October 1365 and of Saturn and Mars on 8 June 1357 (“Sanctissimo et reverendissimo patri et domino . . .”). In it he informed the pope of the particularly favorable conditions which were to conjoin in 1365 for the success of a crusade against the Muslims, but he beseeched him at the same time to use the weight of his authority to prevent the wars between the Christian states inscribed in the very unfavorable conjunction of 1357. Analogous astrological concern had elicited, at the time of the triple conjunction of 1345, parallel commentaries by Leo of Balneolis (his commentary was translated into Latin by Peter of Alexandria), by Firmin de Belleval, and by John of Murs (“Ex doctrina mirabili sapientium qui circa noticiam. . .”); the conjunctions were predicted for 1 March between Jupiter and Mars, for 4 March between Saturn and Mars, and for 20 March between Saturn and Jupiter, all in the sign of Aquarius. An autograph note by John of Murs on the same conjunction is found in one of the manuscripts of De arte mensurandi.¹⁹

NOTES

1. L. Gushee, “New Sources for the Biography of Johannes de Muris,” in Journal of the American Musicological Society, 22 (1969), 3–26, esp. 19, 26.

2. “Quam, ut fertur, fecit magister Johannes de Muris qui temporibus suis fuit magnus astronomus,” in H. Géraud, Charonique latine de Guillaume de Nangis de 1113 à 1300 avec les continuations de cette chronique de 1300 á 1368, II (Paris, 1843; Société de I’histoire de France), 181. This prophecy is completely independent of the texts on the conjunction of 1345 and the conjunctions of 1357 and 1365.

3. This prophecy appears elsewhere than in Jean de Venette’s chronicle: see H. L. D. Ward, Catalogue of Romances in the Department of Manuscripts in the British Museum, I (London, 1883), 302, 314, 316- 319, 321. It is taken up again by the fifteenth-century historian Thedericus Pauly, in Speculum historiale, edited by W. Focke in his inaugural dissertation, Theodericus Pauli ein Geschichtsschreiber des XV.Jahrhunderts (Halle, 1892), pp. 47- 48, but only Jean de Venette attributes it to John of Murs; it is generally given under the name of Hemerus, the equivalent of Merlin.

4. A. Coville, “La chronique de 1340 á 1368 dite de Jean de Venette,” in Histoire litté raire de la France,38 (1949), 33– 354, esp. 344– 346.

5. The De arte mensurandi was completed after the prose part of the Quadripartitum numerorum, to which it alludes in several places, but before the epistle in verse which accompanies the Quadripartitum and in which there is an allusion to the De arte mensurandi.

6. M. Clagett, “A Note on the Commensurator Falsely Attributed to Regiomontanus,” in Isis,60 9169), 383– 384.

7. E. A. Moody and M. Clagett, The Medieval Science of Weights (Madison, Wis., 1960), pp. 35- 53. It was published by Clagett in The Science of Mechanics in the Middle Ages, pp. 126- 135.

8. The allusion to the bishopric of Meaux is not found in either of the two Vienna MSS.

9. The announcement of the observation is made in a quite solemn and perhaps parodic manner, according to a formulation borrowed from the charters: “Noverint preterea presentes et futuri . . .”; similary at the end there is a prohibitive clause against the ignorant and the jealous.

10. Paris lat. 7281, fol. 160: after the explicit of the Expositio the copyist has added: “Per Joh. de Muris credo; mirum videtur quod iste non determinavit de quantitate eccentricitatum deferentis solis et aliorum planetarum et de quantitate epiciclorum, consequenter de quantitate equationum argumenti solis, centri et argumenti etc. ceteris planetis convenientium secundum intentionem regis Alfonsii quia alias et differentes posuit ab antiquis, prospecto quod de istis fuit semper diversitas inter consideratore.”

11. These canons are not very frequently found in the MSS and often appear only in a fragmentary state, which explains why John of Murs is constantly credited with canons on the eclipses that Duhem assigned to the year 1339, distinguishing them from the canons of the Alfonsine tables that he thought dated from 1321, having confused them with the Canones tabule tabularum that he had not read; in fact, the canons on the eclipses form the last part of the canons of the Alfonsine tables. MS Oxford Hertford Coll. 4, fols. 140– 147, appears to preserve the totality of these canons, but its text is constantly interrupted by explicits, anonymous or referring to John of Murs.

12. G. Beaujouan (who is preparing an ed. of these notes), in é cole pratique des hautes é tudes, IV^esection, Sciences Historiques et Philologiques, Annuaire, 1964- 1965, pp. 259- 260; these notes were partially used by L. Gushee (see note 1).

13. In the London MS, the Patefit is designated as Calendarium Beccense and includes a long explicit in which the author, who does not identify himself, dedicates his work to Geoffroy, abbot of Bec-Hellouin. A problem results from the fact that the abbot of Becin 1321 was Gilbert de St.- é tienne; Geoffroy Fare did not become abbot until 1327. It is perhaps for this reason that an annotator of the Metz MS, in which the tables are attributed to John of Murs, has corrected them thus: “Falsum, et quidam dicunt quia fuit cujusdam monachi Beccensis.”

14. The computists were reproached in particular for never stating whether their dates were “completo” or “incompleto anno” and for calculating the life of Christ in solar years rather than in lunar years.

15. Erfurt 4° 371, fol. 45. It is this MS, which is undoubtedly the source of the information on John of Murs’s calendrical work before 1345, on which Duhem relied—Le systé me du monde, IV (Paris, 1916), 51- following a work by Schubring (1883) cited by M. Cantor, Vorlesungen uiber die Geschichte der Mathematik, II, 2nd ed. (Leipzig, 1900), 125, which no one has been able to locate.

16. The papal letters addressed to John of Murs and Firmin de Belleval were published in E. Deprez, “Une tentative de reforme du calendrier sous Clé ment VI: Jean de Murs et de chronique de Jean de Venette,” in é cole francaise de Rome, Mé langes d’ archẹ ologie et d’ histoire, 19 (1889), 131- 143, republished in Clement VI, lettres closes, patentes et curiales se rapportant ā la France, E. Deprez, ed., I (Paris, 1901- 1925), nos. 1134, 1139, 1140.

17. The summary found at the end of the text is an integral part of it and is in all the MSS.

18. A London MS—Sloane 3124, fols. 2- 8v—preserves a calendar whose brief canon (“Canon autem tabule ita scripte ut supra apparet est de renovatione lune . . .”) attributes it to John of Murs and to the other experts who composed it at the request of Clement VI; but this calendar was established for a classical cycle of nineteen years beginning in 1356.

19. Paris lat. 7380, fol. 38v.

BIBLIOGRAPHY

I. Orginal Works. Almost all of John of Murs’s musical work has been published: The Ars nove musice was included by M. Gerbert in his Scriptores ecclesiastici de musica sacra, III (St.– Blaise, 1784), but it was fragmented under various titles (pp. 256– 258, 312– 315, 292– 301), as were the Musica speculativa (ibid., pp. 249– 255, 258– 283; also printed in Cologne, ca. 1500, in a collection entitled Epitoma quadrivii practica [Klebs 554.1]) and the Questiones super partes musice (ibid., pp.301– 308). The Questioners was reproduced, under the title of Accidentia musice, by E. De Coussemaker in Scriptorum de musica medii aevi nova series, III (Paris, 1869), 102– 106; Coussemaker also published the Libellus cantus mensurabilis (ibid., pp. 4658). U. Michels, “Die Musiktraktate des Johannes de Muris,” in Beihefte zum Archiv fū Musikwissenschaft, 8 (1970). The Summa musice, published under the name of John of Murs by Gerbert (op. cit., pp.190– 248), and the Speculum musice, published in part by Coussemaker (op. cit., II [Paris, 1867], 193– 433), although long attributed to John, are not by him.

Of John of Murs’s mathematical works, the only ones which have been published are an abridgment of Boethius’ Arithmetica (Vienna, 1515; Mainz, 1538), dealt with in A. Favaro, “Intorno alla vita ed alle opere di Prosdocimo de’ Beldomandi,” in Bullettino di bibliografia e di storia delle scienze matematiche e fisiche,12 (1879), 231, D. E. Smith, Rara arithmetica (Boston, 1908), pp. 117– 119, and H. L. L. Busard, “Die ‘ Arithmetica speculativa’ des Johannes de Muris,” in Scientiarum historia,13 (1971), 103– 132; and the short treatise on trigonometry, M. Curtze, ed., “Urkunden zur Geschichte der Trigonometrie imchristlichen Mittelater,” in Bibliotheca mathematica, 3rd ser., 1 (1900), 321– 416, no.8, pp. 413– 416: “Die Sinusrechnung des Johannes de Muris.” A partial ed. of De arte mensurandi is in preparation: M. Clagett, Archimedes in the Middle Ages, III; it will be based on MS Paris lat. 7380, of which the parts composed by John of Murs are autograph—see S. Victor, “Johannes de Muris’ Autograph of the De Arte Mensurandi,” in Isis, 61 (1970), 389-394. Other MSS are Florence, Magliab. XI–2, fols. 1– 89, and XI– 44, fols. 2– 26v.

The Canones tabule tabularumare in the following MSS: Berlin F.246, fols. 79v– 81; Brussels 1022– 47, fols.41– 43v, 154v– 158v; Erfurt F.377, fols. 37– 38; Paris lat. 7401, pp. 115– 124v; Vienna 5268, fols. 35– 39. Of the MSS cited, only those of Paris and Vienna contain the table itself.

Extracts of bk. II of the Quadripartitum were published in A. Nagl, “Das Quadripartitum des Johnannes de Muris,” in Abhandlungen zur Geschichte der Mathematik, 5 (1890), 135– 146; and extracts of the versified portion and of bk. III were published in L. C. Karpinski, “The Quadripartitum numerorum of John of Meurs,” In Bibliotheca mathematica, 3rd ser., ¹³ (1912– 1913), 99– 114. The second tract of bk. IV was published in M. Clagett, The Science of Mechanics in the Middle Ages (Madison, Wis., 1959; 1961), pp. 126– 135. The Quadripartitum is preserved in four MSS: Paris lat. 7190, fols. 21– 100v; Paris lat. 14736, fols. 23– 108; Vinna 4770, fols. 174– 324v; Vienna 10954, fols. 4– 167. MS Paris lat. 14736, which begins with bk. II and has a lacuna in bk. IV, was completed by its copyist with the De elementis mathematicis of Wigandus Durnheimer, which replaces bk. 1, and with the text of the versified portion, inserted in the middle of bk. IV. This MS served as the model for MS paris lat. 7190; but since Durnheimer’s text was incomplete in it, it was completed, in the sixteenth century, by the MS now cited as Paris lat. 7191, where it was wrongly baptized “Residuum primi libri Quadripartiti numerorum Johannis de Muris.” In MS Vienna 10954, the epistle in verse appears after bk. IV.

The only text of John of Murs’s astronomical oeuvre which has been published is that on the triple conjunction of 1345: H. Pruckner, Studien zu den astrologischen Schriften des Heinrich von Langenstein (Leipzig, 1933), pp. 222-226. The letter to the pope on the conjunctions of 1357 and 1365 is translated in P. Duhem, Le systeme du monde, IV (Paris, 1916), 35– 37; the original text can be found in MS Paris lat. 7443, fols.33– 34v.

The criticism of the computus of 1317 is in MSS Vienna 5273, fols. 91– 102; and Vienna 5292, fols. 199– 209v. The treatise on the calendar, De regulis computistarum, is in MSS Brussels 1022– 47, fols. 40– 40v, 203– 204v; Erfurt 4° 360, fols. 51v– 52; Erfurt 4° 371, fols. 44v– 45. The letter to Clement VI on calendar reform is in Paris lat. 15104, fols. 114v – 121v (formerly fols. 50v– 58v, or fols. 208v– 215v, the MS having three simultaneous foliations); Vienna 5226, fols. 73– 77v; Vienna 5273, fols. 111– 122; and Vienna 5292, fols. 221– 230.

The Expositio tabularum Alfonsii is preserved in only one MS, Paris lat. 7281, fols. 156v– 160.

The tables of 1321 and their canons are in MSS Lisbon, Ajuda 52– VI– 25, fols. 24– 66; Oxford, Canon. misc. 501, fols. 54– 106v. The Canones tabularum permanentium are in MSS Munich lat. 14783, fols. 198v– 200v; London, Add. 24070, fols. 55, 57v; Vatican, Palat. lat. 1354, fols. 60– 60v; Vienna 5268, fols. 45v– 48v. None of the MSS cited in L. Thorndike and P. Kibre, A Catalogue of Incipits, 2nd ed. (London, 1963), col. 1004, appears to contain the tables, which are found only in the Vienna MS. The Alfonsine canons of 1339 are in MSS Erfurt 4° 366, fols. 52– 52v; Oxford, Hertford Coll. 4, fols. 140– 147; Paris lat. 18504, fols. 209– 209v.

The Patefit is in MSS Erfurt 4° 360, fols. 35– 51, 52– 55; Erfurt 4° 371, fols. 2– 42v; London, Royal 12. C.XVII, fols. 145v– 190, 203– 210; Metz 285. In MS Lisbon, Ajuda 52– VI– 25, fols. 1– 14v, is an extract of the Patefit: the list of mean and true conjunctions and oppositions for 1321– 1396, with the canon “In canone hujus operis continentur medie et vere conjonctiones . . . Deus dat bona hominibus qui sit benedictus. . .” This extract seems to have been printed in 1484; see O. Mazal, “Ein unbekannter astronomischer Wiegendruck,” in Gutenberg Jahrbuch, 1969, 89– 90.

Duhem, op. cit., p. 33, has called attention to a MS of Fractiones or Arbor Boetii, written in 1324; and L. Thorndike, A History of Magic and Experimental Science, III (New York, 1934), 301, mentions a Figura maris aenei Salomonis, also of 1324, the nature of which is uncertain.

A Cambridge MS attributes to John of Murs a short memoir refuting the Alfonsine tables in 1347– 1348, “Bonum mihi quidem videtur omnibus nobis. . .,” in Cambridge, Trinity Coll. 1418, fols. 55– 57v; this attribution, which contradicts John of Murs’s actions during the same period, cannot be upheld. This text is sometimes also attributed to Henri Bate, despite the chronological improbability. Duhem (op. cit., pp. 22– 24) resolved this difficulty by very subtle but unconvincing artifices. Also geomancy according to a Venetian MS—see Thorndike, op. cit., III, 323– 324—and of a poem in French on the philosophers’stone, the “Pratique de maistre Jean de Murs parisiensis” —Florence, Laurenz. Acq. e Doni 380, fols. 83– 86v.

II. Secondary Literature. John of Murs’s work has interested historians of music. The article in Grove’s Dictionary of Music and Musicians, 5th ed., V (London, 1954), 1005– 1008, is now completely outdated; that by H. Besseler, Die Musik in Geschichte und Gegenwart, VII (Kassel, 1958), cols. 105– 115, is excellent and contains an abundant bibliography. For John of Murs’s astronomical work, however, it is dependent on Duhem, op. cit., pp. 30– 38, 51– 60; and Thorndike, op. cit., pp. 268– 270, 294– 324, which should be used—especially the former—with caution. L. Gushee, “New Sources for the Biography of Johannes de Muris,” in Journal of the American Musicological Society,22 (1969), 3– 26, is presented as a restatement, with new documentation, of Besseler’s article but likewise remains tied to Duhem’s information.

Emmanuel Poulle