Ancestors of Physics

By Rosenfeld L. in Centaurus, x (1964–65), 60.

Preface, unnumbered page.

ibid.

See ref. 1.

We remember that for Aristotle the rational soul received the forms of objects. De anima, III. 4, 429a10–430a9.

Dürr K. , The propositional logic of Boethius (Amsterdam, 1951), 19–20; Spengler O. , The decline of the West , tr. Atkinson C. F. (New York, 1945), i, 60–61. Most of Spengler's chapter “The meaning of numbers” is reprinted in The world of mathematics, ed. Newman J. R. (London, 2nd imp., 1961), iv, 2312–47 Our quotation is at 2319–20.

Bradwardine Thomas , Tractatus de proportionibus, ed. Crosby H. L. (Madison, 1955), 110.

On the mathematical interpretation of Bradwardine's law see also A. Molland G. , “The geometrical background to the ‘Merton School’”, British journal for the history of science, iv (1968–69), 108–25.

For the importance of ‘devices' leading to concepts see Wilder R. L. , Evolution of mathematical concepts (Transworld Student Library edn, London, 1974), 110 et passim.

I have used this policy in “Richard Swineshead and continuously varying quantities”, Actes du XII^e Congrès International d'Histoire des Sciences (Paris 1970–71), iv, 127–30.

See, for instance, Robinson A. , “The metaphysics of the calculus”, Problems in the philosophy of mathematics. Proceedings of the International Colloquium in the Philosophy of Science, London, 1965, vol. i, ed. Lakatos I. (Amsterdam, 1967), 28–40, reprinted in The philosophy of mathematics, ed. Hintikka J. (London, 1969), 153–63.

On the methods and concerns of Aristotle's Physics see the very illuminating article by Owen G. E. L. , “”, Aristote et les problèmes de la méthode (Louvain, 1961), 83–103, reprinted in Aristotle, ed. Moravcsik J. M. E. (London, 1968), 167–90.

Physica, II. 2, 194a6–11.

Ibid ., and see Anal. post., I. 7, 75b14–16, I. 9, 76a22–25, I. 12, 77a40–b2, I. 13, 78b35–79a13.

Pedersen O. , “Du quadrivium à la physique: Quelques aperçus de l‘évolution scientifique au Moyen Age”, Artes liberales: Von der Antiken Bildung zur Wissenschaft des Mittelalters, ed. Koch J. (Leiden and Cologne, 1959), 107–23.

ibid., 123.

Meno, 81E–86A.

Mach E. , The science of mechanics , tr. McCormack T. J. (4th edn, Chicago and London, 1919), 8–20. Cf. Dijksterhuis E. J. , Archimedes, tr. Dikshoorn C. (Copenhagen, 1956), 291–304.

Cf. Düring I. , Ptolemaios und Porphyries über die Musik (Göteborg, 1934), 23–24; Boethius , De institutione musica , V. 3 (ed. Friedlein G. (Leipzig, 1867, reprinted Frankfurt, 1966), 354–5); Dickreiter M. , Der Musiktheoretiker Johannes Kepler (Berne and Munich, 1973), 61–68.

See particularly Anal. post., I. 13, 78b31–79a16.

Physica, II. 2, 193b22–194a11.

Gagné J. , “Du quadrivium aux scientiae mediae”, Actes du Quatrième Congrès International de Philosophie Médiévale (Montreal and Paris, 1969), 975–86.

Cf. Sambursky S. , “Philoponus' interpretation of Aristotle's theory of light”, Osiris, xiii (1958), 114–26, and Molland A. G. , “John Dumbleton and the status of geometrical optics”, Actes du XIII^e Congrès International d'Histoire des Sciences (Moscow, 1974), iii–iv, 125–30.

Ed. with German translation by Ritzenfeld A. (Leipzig, 1912). The partial twelfth century Latin translation is edited by H. Boese, Die mittelalterliche Übersetzung der des Proclus (Berlin, 1958).

Cf. Molland A. G. , “Nicole Oresme and scientific progress”, Miscellanea mediaevalia, ix (1974), 206–20, at 208–13.

Gagné , op. cit. (ref. 22), 986.

Snow C. P. , “The case of Leavis and the serious case”, Times literary supplement (1970), 737–40. Cf. Medawar P. B. , The hope of progress (London, 1972), 107: “Science … in some sense comprehends its history within itself“; but Medawar insists that he is speaking of “scientific endeavours and accomplishments” and not of the “history of scientific ideas”.

See also Goldstein B. R. , “On the theory of trepidation according to Thābit b. Qurra and al-Zarqāllu and its implications for homocentric planetary theory”, Centaurus, x (1964–65), 232–47.

Prowe L. , Nicolaus Coppernicus (Berlin, 1883–84; reprinted Osnabrück, 1967), ii, 177. Translation from Rosen E. , Three Copernican treatises (2nd edn, New York, 1959), 99.

See, for example, Goldstein B. R. , “Evidence for a supernova of a.d. 1006”, The astronomical journal, lxx (1965), 105–14.

They do not discuss the question of influence. On this see Hartner W. , “Copernicus, the man, the work, and its history”, Proceedings of the American Philosophical Society, cxvii (1973), 413–22, at 420–1.

Neugebauer O. , “On the planetary theory of Copernicus”, Vistas in astronomy, x (1968), 89–103.

Swerdlow N. M. , “The derivation and first draft of Copernicus's planetary theory. A translation of the Commentariolus with commentary”, Proceedings of the American Philosophical Society, cxvii (1973), 423–512. A gentle protest against Swerdlow's attitude in this regard is entered by Hartner , op. cit. (ref. 31), 416, n. 7.

Cohen M. R. and Drabkin I. E. , A source book in Greek science (Cambridge, Mass., 1948), 91. On the relation of Copernicus to ‘saving the phenomena’ see Mittelstrass J. , Die Rettung der Phänomene (Berlin, 1962), 197–206.

See especially De revolutionibus, I. 8. Oresme had made similar moves in discussing the possibility of the rotation of the Earth while commenting on Aristotle's De coelo. See Oresme Nicole , Le livre du del et du monde, ed. Menut A. D. and Denomy A. J. (Madison, 1968), 526–28.

Archimedes , Opera omnia cum commentariis Eutocii, ed. Heiberg J. L. (2nd edn, Leipzig, 1910–15), vol. iii, p. xcviii.

Clagett M. , “The De curvis superficiebus Archimenidis: A medieval commentary of Johannes de Tinemue on Book I of the De sphaera et cylindro of Archimedes”, Osiris, xi (1954), 295–346, at 295–9.

Clagett M. , Archimedes in the middle ages (Madison, 1964–), i, 440–2.

ibid., 441, n. 8.

Speculum, xlii (1967), 362–5.

Clagett , op. cit. (ref. 37), 296; op. cit. (ref. 38), 440.

Clagett , op. cit. (ref. 38), Addenda and Corrigenda.

Emden A. B. , A biographical register of the University of Oxford to A.D. 1500 (Oxford, 1957–59), iii, 1923. Cf. Cheney C. R. , Hubert Walter (London, 1967), 164–6.

Jordani Nemorarii Geometria vel de triangulis , ed. Curtze M. (Torun, 1887), 21; MS Edinburgh, Royal Observatory, Crawford Library, no. 1, [f. 6v]. The manuscript is unfoliated; the numbers that I give assume that the text starts on f. 1r. The version of the De triangulis in the manuscript is substantially different from that in Curtze's edition, and is probably a more accurate reflection of the original work. Clagett M. , “The Liber de motu of Gerard of Brussels and the origin of kinematics in the West”, Osiris, xii (1956) 73–175, at 121. For the dating of the works of Jordanus and Gerard see below.

Edited by Clagett , op. cit. (ref. 44). Some important new points of interpretation are made in Sylla E. D. , “The Oxford calculators and the mathematics of Motion, 1320–1350. Physics and measurement by latitudes” (Unpublished Ph.D. thesis, Harvard University, 1970), Appendix B, B1-B14. Sylla's exegeses are on the whole very convincing, but I cannot altogether agree with her general characterization that “What Gerard does is to find average or mean velocities” (B1). This seems to introduce concepts that were not in his mind.

Clagett , op. cit. (ref. 44), 104; MS cit. (ref. 44), [f. 52v].

Clagett , op. cit. (ref. 44), 106.

Grosseteste Robert , Epistolae , ed. Luard H. R. (London, 1861), 131–3.

Trivet Nicholas , Annales sex regum Angliae qui a comitibus Andegavensibus originem traxerunt, ed. Hog Thomas (London, 1845), 211; “Hoc anno, in capitulo fratrum Praedicatorum generali tertio, quod Parisiis celebratum est, successor beati Dominici in magisterio ordinis fratrum Praedicatorum factus est frater Jordanus, natione Teutonicus, dioecesis Maguntinae; qui cum Parisiis in scientiis saecularibus et praecipue in mathematicis magnus haberetur, libros duos admodum utiles, unum de Ponderibus, et alium de Lineis datis, dicitur edidisse”.

Cf. Jamison E. , Admiral Eugenius of Sicily, (London, 1957), 158.

Materials for the life of Thomas Becket Archbishop of Canterbury, ed. Robertson J. C. (London, 1875–85), iii, 526; Knowles D. , The episcopal colleagues of Archbishop Thomas Becket (Cambridge, 1951), 26.

Cheney , op. cit. (ref. 43), 163; Cartulary of the Priory of St Gregory, Canterbury, ed. Woodcock A. M. , Camden 3rd Series vol. lxxxviii (London, 1956), 5.

For discussions of the identification of the two Jordanus's see: Jordanus, ed. cit. (ref. 44), iv–vi; Duhem P. , Les origines de la statique (Paris, 1905–6), i, 104–5; Moody E. A. and Clagett M. , The medieval science of weights (2nd printing, Madison, 1960), 121–2; Hofmann J. E. , “Ueber eine Euklid-Bearbeitung, die dem Albertus Magnus zugeschrieben wird”, Proceedings of the International Congress of Mathematicians, 1958 (Cambridge, 1960), 554–66, at 561–2; Clagett M. , “Jordanus de Nemore”, New Catholic encyclopedia (New York, 1967), vii, 1103–4; Grant E. , “Jordanus de Nemore”, Dictionary of scientific biography, vii (New York, 1973), 171–9, at 172; Thomson R. B. , “Jordanus de Nemore and the University of Toulouse”, British journal for the history of science, vii (1974), 163–5.

Richard of Fournival's library contained several works from the corpus, and Richard died before 1260. See Items 43, 45, 47, 48, 59 of his Biblionomia (or library catalogue) as given in Birkenmajer A. , Études d'histoire des sciences et de la philosophie du moyen âge (Wroclaw, 1970), 166–73. As Clagett has noted in Isis, lxiv, (1973), 392, Item 43 can be identified with the Edinburgh manuscript cited in ref. 44 above. Murdoch J. E. , “The medieval language of proportions”, Scientific change, ed. Crombie A. C. (London, 1963), 237–71, at 258, has shown how Campanus of Novara took over some definitions from Jordanus's Arithmetica in his version of the Elements, and Murdoch has also been able to fix a terminus ante quem of 1259 for this version: “The medieval Euclid: Salient aspects of the translations of the Elements by Adelard of Bath and Campanus of Novara”, Revue de synthèse, lxxxix (1968), 67–94, at 73, n. 18.

MS Oxford, Bodleian, Savile 21 has a probable date of 1215–16 and contains two algorithmic works from the corpus, quite possibly copied by Grosseteste. See Thomson S. H. , The writings of Robert Grosseteste (Cambridge, 1940), 32, and Hunt R. W. , “The library of Robert Grosseteste”, Robert Grosseteste, ed. Callus D. A. (Oxford, 1955), 121–45, at 133–4.

Jordanus , ed. cit. (ref. 44), 21; MS cit. (ref. 44), [ff, 6v, 7v, 8v]. An Arabic and a Latin version of the Liber de similibus arcubus are edited by Busard H. L. L. , and van Koningsveld P. S. , “Der Liber de arcubus similibus des Ahmed ibn Jusuf”, Annals of science, xxx (1973), 381–406. Another (probably derivative) Latin version is edited in Jordanus , ed. cit. (ref. 44), 48–50.

All these are edited in Moody and Clagett , op. cit. (ref. 53).

Duhem , op. cit. (ref. 53), i, 128–30; Moody, in Moody and Clagett, op. cit. (ref. 53), 145–6; Clagett M. , The science of mechanics in the middle ages (Madison, 1959), 73, 84; Maier's review of Moody's and Claggett's work in Isis, xlvi, (1955), reprinted in Maier A. , Ausgehendes Mittelalter (Rome, 1964–67), ii, 453–8.

Thurot C. , “Recherches historiques sur le principe d'Archimède”, Revue archéologique, 2nd series, xix, (1869), 42–49, 111–23, 294–9, 354–60, at 117.

Duhem , op. cit. (ref. 53), i, 134–6. Cf. Sarton G. , Introduction to the history of science (Baltimore, 1927–48), ii, 614.

Duhem's later thesis is expounded in Duhem P. , Études sur Léonard de Vinci (Paris, 1906–13), i, 311–16; Duhem , op. cit. (ref. 53), ii, 318–23; Duhem P. , Le système du monde (Paris, 1913–59), i, 388–93.

Moody and Clagett , op. cit. (ref. 53), 171–2.

Clagett , op. cit. (ref. 58), 73–74, 80.

We may note two recent editions: Hughes B. B. , The De numeris datis of Jordanus de Nemore: A critical edition, analysis, evaluation and translation (Ph.D. thesis, Stanford University, 1970); Thomson R. B. , Thirteenth century mathematical astronomy: De plana spere Iordani (D. Phil. thesis, Oxford University, 1974). Thomson's thesis contains a valuable bibliography of Jordanus's writings.

For the phrase cf. Whewell W. , History of the inductive sciences (3rd edn, London, 1857), i, 203–14.

See ref. 56 above.

MS cit. (ref. 44), [ff. 1v, 7r]. On the translation of the work see Björnbo A. A. , “Die mittelalterlichen lateinische Übersetzungen aus dem Griechischen auf dem Gebiet der mathematischen Wissenschaften”, Archiv für die Geschichte der Naturwissenschaften und der Technik, i (1909), 385–94, at 393.

Clagett , op. cit. (ref. 58), 439, n. 35.

McVaugh M. , “Arnald of Villanova and Bradwardine's law”, Isis, lviii (1967), 56–64.

Skabelund D. and Thomas P. , “Walter of Odington's mathematical treatment of the primary qualities”, Isis, lx (1969), 331–50.

Drake S. , “Medieval radio theory vs compound medicines in the origins of Bradwardine's Rule”, Isis, lxiv (1973), 67–77. A fuller discussion of Drake's views on this and related matters must await another occasion.

See especially Physica, IV.8, 215a33–216a7, VII.5, 249b30–250a15; De coelo, I.6, 273b31–274a10.

Physica, VII, comm. 35 (Opera Aristotelis Stagiritae (Venice, 1560), vol. iv, f.266v): “… velocitas propria unicuique motui sequitur excessum potentiae motoris super potentiam moti …”.

De coelo, II, comm. 36 (ed. cit., vol. v, f 125v): “velocitas … et tarditas non sunt nisi secundum proportionem potentiae motoris ad potentiam moti”.

Bradwardine, ed. cit. (ref. 7), 86, 110.

Ed. cit., 110. Latin given at ref. 7 above.

Ed. cit., 112.

Ed. cit., 98.

Ed. cit., 104.

Ed. cit., 106.

See for instance Boethius, De inst. musica, II. 11 (ed. cit. in ref. 19, p. 241), and other parts of that work.

Cf. Cohen and Drabkin , op. cit. (ref. 34), 294–9, and Boethius , De inst. mus., I.4, I. 10–11, IV.1, IV.18 (ed. cit., 188–91, 196–8, 301–2, 348–9).

Bradwardine , ed. cit. (ref. 7), 106–10.

Nicole Oresme and the medieval geometry of qualities and motions. A treatise on the uniformity and difformity of intensities, known as Tractatus de configurationibus qualitatum et motuum, ed. Clagett M. (Madison, 1968), 404.

On the tensions in Oresme cf. Molland , op. cit. (ref. 25), and my essay review of Grant's edition of the De commensurabilitate vel incommensurabilitate motuum celi in British journal for the history of science, vi (1972–73), 311–13.

Cf. Hesse Hermann , The glass bead game (Magister ludi) , tr. Winston R. Winston C. (Harmondsworth, 1972). Originally Das Glasperlenspiel (1943).