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Published online by Cambridge University Press: 17 February 2016
Since the appearance of the studies of Pierre Duhem at the beginning of this century, much research has been done on natural philosophy at Oxford and Paris in the mid-fourteenth century. In the last decades of what Anneliese Maier has called the ‘classical century of natural philosophy’ both universities seem to have been chiefly influenced by two major schools of thought. In Paris, John Buridan was followed by Nicole Oresme, Albert of Saxony, Themo Judaicus, and Marsilius of Inghen; in Oxford, Thomas Bradwardine led a group of philosophers, which roughly included William Heytesbury, Richard Swineshead, John Dumbleton, and Richard Kilvington. (It is, however, to be noted that both in Oxford and in Paris it is difficult to determine the degrees of dependance.) It has been shown that these two schools influenced one another, in particular concerning the teachings of Thomas Bradwardine.
I wish to thank Professor Dr. D. Kurze for his permanent support, and Privatdozent Dr. S. Jenks for correcting the English version of this paper. The faults that remain are mine.
1 For a survey of the problems and the literature see Lindberg, D., ed. Science in the Middle Ages, (Chicago-London 1978)Google Scholar esp. Murdoch, J. E./Sylla, E. D., ‘The science of motion’, pp. 206–64; The Cambridge History of Later Medieval Philosophy, ed. Kretzmann, N., Kenny, A., Pinborg, J. (Cambridge 1982)Google Scholar esp. Weisheipl, J. A., ‘The Interpretation of Aristotle’s Physics and the Science of Motion’, pp. 521–36Google Scholar; Grant, E., ‘The Effect of the Condemnation of 1277’, pp. 537–9CrossRefGoogle Scholar; Sylla, E. D., ‘The Oxford Calculators’, pp. 540–63CrossRefGoogle Scholar; Murdoch, J. E., ‘Infinity and Continuity’, pp. 564–91Google Scholar; and Bottin, F., La scienza degli Occamisti (Rimini 1982).Google Scholar
2 Maier, A., Studien zur Naturphilosophie der Spätscholastik 5 (Rome 1958) p. 382.Google Scholar (Maier refers to the century between 1277 (the date of Aegidius Romanus’s commentary on the Physics of Aristotle) and 1377 (the date of Nicole Oresme’s Livre du ciel et du monde).
3 For biographies of the philosophers see the various articles in: The Dictionary of Scientific Biography, ed. C. C. Gillispie, 16 vols. (New York 1970-1980); Emden (O), 3 vols. (Oxford 1957-9).
4 On Bradwardine’s rule of motion and its influence see Murdoch, /Sylla, , ‘Science’ (n. 1), pp. 224–31Google Scholar; Wallace, W. A., ‘Mechanics from Bradwardine to Galileo’, JHI 32 (1971) pp. 15–28CrossRefGoogle Scholar; Maier, A., Studien (n. 2) 1 (Rome 1966, 2nd ed.) pp. 81–110Google Scholar; Clagett, M., The Science of Mechanics in the Middle Ages Publications in Medieval Science 4 (Madison, Wisc., 1959) pp. 199–253Google Scholar; and others. On other lines of influence see Murdoch, J. E., ‘“Subtilitates Anglicanae” in Fourteenth-Century Paris: John of Mirecourt and Peter Ceffons’, in Machaut’s World, Science and Art in the Fourteenth Century (= Annals of the New York Academy of Science 114 1978), ed. Cosman, M. P./Chandler, B., pp. 51–86Google Scholar; Wilson, C., William Heytesbury, Medieval Logic and the Rise of Mathematical Physics Publications in Medieval Science 3 (Madison, Wisc., 1960, 2nd pr), pp. 25–8, 94–112.Google Scholar
5 See the list of MSS in: Thomas of Bradwardine, His Tractatus de proportionibus, ed. and transl. H. L. Crosby, Publications in Medieval Science 2 (Madison, Wisc. 1961 2nd ed.) pp. 59-61. For other MSS see Thorndike, L. and Kibre, P., A Catalogue oflncipits of Mediaeval Scientific Writings in Latin (Cambridge, Mass. 1963)Google Scholar cols. 794, 1001; further MSS (either in the long or in the short version) are: Berlin Staatsbibl. Preuss. Kulturbes. MS Lat. fol. 852, fols. 71ra-75va; Cologne Hist. Archiv. MSW415, fols. 1r-20v; Paris BN MS Lat. 15105; Pommersfelden Gráflich-Schönbornsche Bibl. MS 236 (2858); Vienna Dominikanerbibl. MS 192/158.
6 For lists of MSS see Wilson, , Heytesbury (n. 4) p. 207Google Scholar; Thorndike, and Kibre, , Catalogue (n. 5)Google Scholar cols. 82, 129, 1254, 1406,1587, 1596; Mohan, G. E., ‘Incipits of Logical Writings of the XIIIth to XVth Centuries’, Franc Stud 12 (1952) pp. 349–489CrossRefGoogle Scholar, here p. 457; Ch. Lohr, ‘Mediaeval Latin Aristotle Commentaries’, ‘Authors G-I’, Traditio 24 (1968) pp. 149-245, here p. 200.
7 See Thorndike, and Kibre, , Catalogue (n. 5)Google Scholar cols. 725, 1055; Mohan, , ‘incipits’ (n. 6) p. 428Google Scholar; Lohr, , ‘Commentaries’ (n. 6)Google Scholar ‘Authors: Jacobus-Johannes Juff’, Traditio 26 (1970) pp. 135-216, here p. 189.
8 See Botrin, F., ‘Un testo fondomentale nell’ambito della “nuova fisica” di Oxford: 1 sophismata di Richard Kilmington’, “Antiqui” und “Moderni” Miscellanea Mediaevalia 9, ed. Zimmermann, A. (Berlin-New York 1974) pp. 201–5, here p. 202Google Scholar; Mohan, , ‘Incipits’ (n. 6) pp. 355, 467Google Scholar; another (fragmentary) MS is Berlin Staatsbibl. Preuss. Kulturbes. MS Lat. qu. 932, 7 fols.
9 See Hoskin, M. A. and Molland, A. G., ‘Swineshead on Falling Bodies’, The British Journal for the History of Science 3 (1966) pp. 150–82, here p. 155CrossRefGoogle Scholar; Thorndike, and Kibre, , Catalogue (n. 5)Google Scholar col. 1030.
10 On the different approach of Oxford philosophers to natural philosophy see Sylla, , ‘Calculators’ (n. 1) pp. 541–53Google Scholar; Murdoch, J. E., ‘Mathesis in Philosophiam Scholasticam Introducta’, Arts Libéraux et Philosophie au Moyen Åge, Actes du quatrième congrès internationale de philosophie médiévale (Montreal-Paris 1969) pp. 215–49, here pp. 224–38.Google Scholar
11 See Lohr, , ‘Commentaries’ (n. 12) p. 396Google Scholar; Maier, , Studien (n. 2) vol. 3 (Rome 1952, 2nd ed.) p. 269, n. 34Google Scholar. On the commentaries on the Aristotelian Physics see the remarks of Walsh, K., A Fourteenth-Century Scholar and Primate, Richard Fitzralph in Oxford, Avignon, and Armagh, (Oxford 1981) pp. 18–9Google Scholar; Weisheipl, , ‘Interpretation’(n. 1) pp. 522–4, 533–6Google Scholar; Sylla, , ‘Calculators’ (n. 1) p. 543, n. 9Google Scholar; Sylla, E. D., ‘The “A Posteriori” Foundations of Natural Science’, Synthese 40 (1979) pp. 147–187CrossRefGoogle Scholar (for bk. 1, caps. 1-2).
12 Lohr, Cf., ‘Commentaries’ (n. 6), ‘Authors: Narcissus-Richardus’, Traditio 28 (1972) pp. 281–396, here p. 393CrossRefGoogle Scholar; Maier, , Studien, 1 (n. 4) p. 97.Google Scholar
13 See Emden (O) (n. 3) 3 p. 1680.
14 See Lohr, , ‘Commentaries’ (n. 6), ‘Authors Johannes de Kanthi-Myngodus’, Traditio 27 (1971) pp. 251–351, here p. 279CrossRefGoogle Scholar; Thoradike, and Kibre, , Catalogue (n. 5)Google Scholar cols. 347, 1200, 1676.
15 See Lohr, , ‘Commentaries’(n. 12) p. 392Google Scholar; Walsh, , Scholar (n. 11) pp. 55–6.Google Scholar
16 See, for instance, Sylla, , ‘Calculators’ (n. 1) p. 540.Google Scholar
17 On the dates of composition of Buridan’s third and fourth versions (the only surviving ones), see Maier, , Studien (n. 2) 2 (Rome 1968, 3rd ed.) pp. 366–70Google Scholar. For a list of MSS see Lohr, , ‘Commentaries’ (n. 7), here pp. 167–9Google Scholar. Our quotations from the earlier version are from the MS Vatican Bibl. Apost. Vat. Chigi E.VI.199. This text will be cited as ‘Buridan, Physics (III)’. For the ultima lectura see the text in the only printed edition: John Buridan, Subtilissime questiones super octophisicorum libros Aristotelis (Paris in edibus dionisii roce 1509, repr. Frankfurt a.M. 1964) (cited as ‘Buridan, Physics (IV)’).
18 Only one surviving MS of Oresme’s commentary is known: MS Sevilla Bibl. Capitolar Colombina 07-06-30 (for a description see Lohr, Ch., ‘Aristotelica Hispalensia’, Theologie una Philosophie 50 (1975) pp. 547–64, here pp. 554–7)Google Scholar. On the basis of internal evidence, Maier has come to the conclusion that this text is an early version, read in about 1346/47, see her Studien (n. 4) pp. 307-14. She thought that there also must have been a later commentary on the Physics (now lost) which Oresme cited in his Livre du ciel et du monde, ed. A. D. Menut and A. J. Denomy, Publications in Medieval Science (Madison, Wisc, 1968), bk. 1, cap. 18, p. 144. On the other hand, Menut viewed the self-citation as a reference to the text in Sevilla. In a recent article, Markowski, M., ‘Les Quaestiones super I—VIII libros “Physicorum” Aristotelis de Nicolas Oresme retrouvees?’, MPP 26 (1982) pp. 19–41Google Scholar, has raised doubts about Oresme’s authorship in the case of the Sevillian manuscript and attributed to him the text which I will cite as ‘Buridan, Physics (III)’. In my doctoral dissertation, ‘Die aristotelisch-scholastische Theorie der Bewegung, Studien zum Kommentar Alberts von Sachsen zur Physik des Aristoteles’ (Diss. phil. masch., Freie Universität Berlin, 1985) I have compared the two commentaries attributed to Buridan with the texts in Sevilla and of Albert of Saxony. I have come to the conclusion that there is a striking similarity between Buridan’s printed commentary and the text in the Vatican and Erfurt manuscripts (though there are some characteristic differences), while the originality of (and the ascription in) the Sevillian text makes it quite probable that it was delivered by Nicole Oresme, despite the problems raised by the fact that it has survived only in the form of a reportation. Therefore I will refer to the Sevillian MS for Oresme’s Physics.
19 For the influential earlier commentary of Albert see the extensive treatment in my doctoral dissertation (n. 18). In my opinion the text was written shordy after 1351. For the MSS and the early editions of this text see Lohr, , ‘Commentaries’ (n. 6), ‘Authors A-F’ Traditio 23 (1967) pp. 313–413CrossRefGoogle Scholar, here pp. 349/50. As I was able to show for the first time, it is very likely that there exists a later version of his commentary (possibly delivered in the later part of his Paris years) in a London MS, see my doctoral dissertation (n. 18), Anhang III. But there Albert deals only with the first five bks (the text of bks six to eight is identical with the earlier version), and consequendy I refer only to his first treatment of the theory of motion. I quote ‘Albert, Physics’ from a good early edition: Albert of Saxony, Acutissime Questiones super libros de Physica auscultatione (Venice sumptibus heredum Octaviani Scoti 1516).
20 Marsilius at least wrote a summary commentary in Aristotle’s Physics, the Abhreviationes super ocio libros physicorum Aristotelis (ed. Venice heredum Octaviani Scoti 1521) (for the MSS see Lohr, , ‘Commentaries’ (n. 14), pp. 328–9)Google Scholar, and longer questions on the Physics which have recently been discovered by M. Markowski, ‘1st Marsilius von Inghen der Verfasser der in Hs. 5437 der Osterreichischen Nationalbibliothek sich befindenden Quaestiones in I—III libros “De anima” Aristotelis und Quaestiones in I-VI libros “Physicorum” Aristotelis?’, MPP 18 (1973) pp. 35-50, and Bos, E. P., ‘A Note of an Unknown Manuscript Bearing upon Marsilius of Inghen’s Philosophy of Nature: Ms. Cuyk en S. Agatha (The Netherlands) Kruisherenklooster C12’, Vivarium 17 (1979) pp. 61–8CrossRefGoogle Scholar. Another text, the Questiones subtilissime super octo libros phisycorum secundum nominalium viam, (ed. Lyons per Johannem Marion 1518, repr. Frankfurt a.M. 1964), which has usually been ascribed to Marsilius (though the title bears the name Johannes Marsilius Inguen), was probably not compiled by this philosopher, though the question deserves further attention. On Marsilius, who achieved his ‘magisterium’ at Paris in 1362 and became the first rector of the university of Heidelberg in 13 86, see G. Ritter, Studien zur Spätscholastik, vol. 1, Marsilius von Inghen und die okkamistische Schule in Deutschland Sitzungsber.d.Heidelberger Akad.d.Wiss., 1921, 4, (Heidelberg 1921). In the following considerations I quote from the Venice edition of the Abbreviationes.
21 Albert, , Physics (n. 19)Google Scholar bk. 6, qu. 6, art. 1, conci. 2, fol. 67va. The problem Albert is concerned with is the measure of velocities in augmentations.
22 On Heytesbury’s and Swineshead’s position see Wilson, , Heytesbury (n. 4) pp. 128–39Google Scholar; as for the ambiguity of Heytesbury’s statement see ibid., p. 200, n. 59.
23 See the literature cited in n. 4 above. The final formulation of Bradwardine’s ‘law’ runs as follows: ‘Proportio velocitatum in motibus sequitur proportionem potentiarum movencium ad potentias resistivas, et edam econtrario. Vel sic sub aliis verbis, eadem sententia remanente: Proporciones potentiarum movenrium ad potentias resistivas, eodem ordine proportionales existunt, et similiter econtrario. Et hoc de geometrica proportionalitate intellegas …’ ( Bradwardine, , Tractatus (n. 5) cap. 3, th. I, p. 112).Google Scholar
24 On the Aristotelian rules cf.Heath, T., Mathematics in Aristotle (Oxford 1949, repr. 1970 pp. 142–6).Google Scholar
25 ‘Supponenda est ad presens quod velocitas motus sequitur proportionem maioris inequalitatis ipsius motoris ad resistentiam, unde quanto est maior proportio, tanto est maior velocitas…’ (Buridan, Physics (III) (n. 17) bk. 7, qu. 8, supp., fol. 87rb.)
26 See Buridan, , Physics (IV) (n. 17)Google Scholar bk. 7, qu. 7, concl. 5-6, fol. 107vb; Bradwardine, cf., Tractatus (n. 5) cap. 2, pt. 3 and 4, pp. 94 and 104.Google Scholar
27 ‘Et ita proportio velocitatum motuum attendenda est penes proportionem proportionum moventium ad suas resistentias …’ ( Buridan, , Physics (IV) (n. 17)Google Scholar bk. 7, qu. 7, concl. 7, fol. 108ra.)
28 ‘Velocitas sequitur proportionem potencie motoris ad potentiam sive resistentiam rei mote, sive quod velocitas augetur et diminuetur proportionaliter secundum augmentum et detrimentum talis proportionis. Et est proportio velocitatum sicut proportio talium proporrionum. Et intellego proportionem maioris inequalitatis …’ (Oresme, Physics (n. 18) bk. 7, qu. 9, art. I, affirm, concl., fol. 78rb.)
29 Albert, Physics (n. 19) bk. 7, qu. 8, art. 2, concl. 1-2, fol. 75rb–va; see also Buridan, , Physics (III) (n. 17)Google Scholar bk. 7, qu. 8, ex hoc, 87va; Buridan, , Physics (IV) (n. 17)Google Scholar bk. 7, qu. 7, concl. 8, fol. 108ra. The mistake in the Aristotelian rules is explained by a mistake in translation, see Oresme, , Physics (n. 18)Google Scholar bk. 7, qu. 10, ad auct., fol. 79vb; Albert, Phpics (a 19) bk. 7, qu. 8, ad. rat., fol. 75vb.
30 See Clagett, , Science (n. 4) pp. 207–9Google Scholar; Wallace, , ‘Mechanics’ (n. 4), pp. 20–2Google Scholar. According to Emden (O) (n. 3) vol. 3, pp. 1836-7, who refers to Weisheipl’s dissertation on Merton natural philosophy, the De motu (from which Clagett quotes) belongs to Roger Swineshead, the Liber calculationum to Richard Swineshead. The problem of authorship deserves further consideration. For the few MSS of De motu see Thorndike, and Kibre, , Catalogue (n. 5)Google Scholar cols. 325-6, 836.
31 See Oresme, Physics (n. 18) bk. 6, qu. 5-6, fol. 68rb-70va.
32 ‘Velocitas potest attendi vel cognosci penes aliquid tanquam penes causam vel tanquam penes effectum. Penes causam sicut penes proporcionem potenrie moventis ad suam resistentiam… Modo autem nolo dicere penes quid attendatur tanquam penes causam, sed de hoc dicerur in septimo. Sed modo volo dicere penes quid attenditur tanquam penes effectum, et primo quo ad motum localem, quorum unus est rectus et alius circularis…’ (Albert, Physics (n. 19) bk. 6, qu. 4, art. 1, not. 3, fol. 66va.)
33 See Heath, , Mathematics (n. 24) pp. 128–30.Google Scholar
34 So Albert follows Bradwardine and Heytesbury in measuring circular motion by the fastest point of the moving body and refers to Oxford solutions in the case of the velocity in augmentations, see Albert, Physics (n. 19) bk. 6, qu. 5, art. 1, op. 2, fol. 67rb, and qu. 6, art. 1, concl. 2-3, fol. 67va-vb; see also n. 21-2 above.
35 ‘In velocitate sunt duo consideranda, scil. unum penes quid mensuratur, ut sparium pertransitum. Secundum id a quo procedit, scil. causa propter quam est tantum vel tantum gradus. Sic enim sequitur velocitas suam causam, ut effectum id a quo est…’ ( Marsilius, , Abbreviations (n. 20)Google Scholar bk. 7, not. 2, qu. 5, fol. (32)vb.)
36 ‘Utrum omnis velocitas motus attendatur penes sparium in tanto vel tanto tempore pertransitum …’ (Marsilius, ibid., bk. 6, not. 1, qu. 4, fol. 26rb; for the solution see ibid., prop. 4, fol. 27rb.)
37 Marsilius, ibid., prop. 4, fol. 27rb; see Bradwardine, , Tractatus (n. 5) cap. 4, pt. 2, th. 4, p. 130Google Scholar; Heytesbury, William, Regule solvendi sophismata, De Motu locali (ed. Venice per Bonetum Locatellum sumpribus Octaviani Scoti 1494)Google Scholar fol. 38vb; Oresme, , Physics (n. 18)Google Scholar bk. 6, qu. 5, concl. 2-4, fol. 68va-vb; Albert, , Physics (n. 19)Google Scholar bk. 6, qu. 4, art. 2, concl. 5-7, fol. 66vb.
38 See Sylla, E. D., ‘Medieval Logic and the Infinite’, Proceedings of the XIVth International Congress of the History of Science (1974) 2 (Tokyo 1975) pp. 87–90Google Scholar; Murdoch, , ‘Infinity’ (n. 1) pp. 567–8.Google Scholar
39 See Grant, E., Much Ado about Nothing, Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution (Cambridge 1981) pp. 57–60CrossRefGoogle Scholar, and other articles.
40 See the editions of Grant, E., Oresme, Nicole, De proportionibus proportionum and Ad pauca respicientes, ed. and tr.Grant, E., Publications in Medieval Science, (Madison, Wisc., 1966)Google Scholar and Busard, H. L. L., ‘Albert of Saxony, Tractatus proportionum’, ed. Busard, H. L. L., Denkschriften d. Osterr. Akad. d. Wiss., mathemat.-naturwiss. Kl., 116, 2 (Vienna 1971) pp. 43–72.Google Scholar
41 The MSS are: Oxford Bodl. Libr. Can. misc. 219, 423, 462 (Albert’s De Caelo); Can. misc. 393, 506 (his Tractatus proportionum); Can. misc. 508 (his Physics); Oxford Balliol Coll. 97, Oxford Bodl. Libr. Lat. misc.e. in (Buridan’s Physics); Can. misc. 6562B (Oresme’s Ad pauca respicientes); Oxford St. John’s Coll. 188 (Oresme’s Algorismus proportionum); besides others.
42 See Duhem, P., Les systeme du monde 8, (Paris 1958) pp. 225–6.Google Scholar
43 See. Sylla, E. D., ‘Medieval Quantifications of Qualities: The Merton School’, Archive for the History of the Exact Sciences 8 (1971/72) pp. 9–39, here p. 9–10.CrossRefGoogle Scholar
44 See above, n. 16-20.
45 On Chilmark see Emden (O) (n. 3) 1, p. 416; Clagett, , Science (n. 4) pp. 631/32Google Scholar; Thorndike, /Kibre, , Catalogue (n. 5)Google Scholar cols. 53, 470, 690, 878, 932, 1134.