The Significance of the Copernican ORBS

See Garin E. , “Alle origini della polemica anticopernicana”, Studia copernicana, vi (1975), 31–42, p. 35.

Kuhn T. S. , The Copernican revolution (Cambridge, Mass., 1957), 144–5.

Krafft F. , “Physikalische Realität oder mathematisch Hypothese? Andreas Osiander und die physikalische Erneuerung der antiken Astronomie durch Nicolaus Copernicus”, Philosophia naturalis, xiv (1973), 243–75, and articles cited in ref. 80, below.

Westman R. S. , “The astronomer's rôle in the sixteenth century: A preliminary study”, History of science, xviii (1980), 105–47.

Swerdlow N. R. , (i) “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; (ii) “Pseudodoxia copernicana: Or, enquiries into very many received tenents and commonly presumed truths, mostly concerning spheres”, Archives internationales d'histoire des sciences, xxvi (1976), 108–58.

Rosen E. , (i) “Copernicus' spheres and epicycles”, Archives internationales d'histoire des sciences, xxv (1975), 82–92; (ii) “Reply to N. Swerdlow”, ibid., xxvi (1976), 301–4.

Nürnberg , c. 1474. Reproduced by permission of the editor of Beiträge zur Inkunabelkunde, dritte Folge, from Zinner E. , “Die wissenschaftlichen Bestrebungen Regiomontans”, Beiträge zur Inkunabelkunde, n.F., ii (1938), 89–103.

Westman , op. cit. (ref. 4), 114; Aiton E. J. , “Celestial spheres and circles”, History of science, xix (1981), 75–113, pp. 96–97.

Capuano's commentary, first published in 1495, went through at least a dozen editions before 1530; see, Houzeau J. C. and Lancaster A. , General bibliography of astronomy to the year 1880 (Bruxelles, 1887), i: 1, 506–7.

A concise account of the Theorica compromise is given by Grant E. , “Cosmology”, in Science in the middle ages, ed. by Lindberg D. C. (Chicago, 1978), 265–302, pp. 280–4.

See below, Section 5.

On Cusanus's cosmology see Goldammer K. , “Nicolaus von Cues und die Überwindung des geozentrischen Weltbildes”, Beiträge zur Geschichte der Wissenschaft und der Technik, v (1965), 5–24. Pontano's views are stated in the prooemium to the third book of his De rebus coelestibus (Naples, 1512).

Achillini A. , Quatuor libri de orbibus (Bologna, 1498); Nifo A. , Expositio in IV libros de caelo et mundo (Naples, 1517).

Amici G. , De motibus corporum coelestium juxta principia peripatetica sine eccentricis et epicyclis (Venice, 1536); Fracastoro G. , Homocentrica sive de stellis (Venice, 1538).

This is questioned by Birkenmajer A. , Études d'histoire des sciences en Pologne, Studia copernicana, iv (1972), 612–46, p. 623.

Commentariolum super Theoricas novas planetarum Georgii Purbachii in studio generale Cracoviensis per Magistrum Albertum de Brudzewo diligenter corrogatum, a.d. 1482 , ed. by Birkenmajer L. A. (Cracow, 1900), 25. The work was published in a somewhat garbled form: Commentaria utilissima in theoricis planetarum (Milan, 1492). On Wojciech's life and works see Palacz R. , “Wojciech Blar z Brudzewa”, Materiały i Studia Zakładu Historii Filożofii Starozytnej i Średniowiecznej, i (1961), 172–98. Though Wojciech's direct contact with Copernicus is disputed, it is generally agreed that this was a prescribed astronomy text at the time he studied at Cracow. Both Birkenmajer L. A. , Stromata copernicana (Cracow, 1924), 85–96 and Palacz R. , “Nicolas Copernic comme philosophe”, Studia copernicana, xiv (1975), 27–40, p. 35, have claimed that passages in Book 1 of De revolutionibus closely follow passages in Wojciech's commentary. Were this true, it could provide important clues to Copernicus's attitude to natural philosophy. My own reading, however, confirms A. Birkenmajer's view that these echoes are illusory (op. cit., 622).

Wojciech , op. cit., 25–26. This is the position taken by Wojciech's master Jan of Głogów; see, e.g., his Introductorium compendiosum in tractatum sphere materialis (Strasbourg, 1518), sig. Kiii, r-v (first published 1506). On Głogów's works see Senko W. , “Wstep do studium nad Janem z Głogówa”, Materiały i Studia Zakładu Historii Filozofii Starożytnej i Średniowiecznej, i (1961), 9–59; iii (1964), 30–38.

Wojciech , op. cit., 26–27. The passage is from Tractatus Albionis, I: 10: North J. D. , Richard of Wallingford: An edition of his writings with introduction, English translation and commentary (Oxford, 1976), i, 278.

Wojciech , op. cit., 7–9.

Wojciech , op. cit., 17–18.

Duhem P. , ΣΩZEIN TA ΦAINOMENA: Essai sur la notion de théorie physique de Platon à Galilée (Paris, 1908); English translation by Dolland E. and Maschler C. (Chicago, 1969).

Duhem's treatment of classical astronomy is challenged by Lloyd G. E. R. , “Saving the appearances”, Classical quarterly, xxviii (1978), 202–22. Aiton E. J. , op. cit. (ref. 8), 78–81, provides a useful discussion of the issue.

Many mediaeval authors followed Geminus (in Simplicius) and Averroes in maintaining a firm distinction between a natural philosophy of the heavens concerned with essences and a mathematical astronomy concerned with accidents, and in emphasizing that saving of the phenomena is the primary task of the astronomer ( Simplicius , In Aristotelis physicorum libros , 291–2; Averroes , commentaries on De caelo, II, 7 and Metaphysica, I, 8). Further, a number of Averroist natural philosophers, Jean de Jandun for example, conceded that despite their falsity the Ptolemaic hypotheses are properly accepted by mathematical astronomers so long as they are unable to find another way of saving the phenomena ( de Jandun Jean , quoted in Duhem , op. cit., 43). But Duhem is, I think, wrong to conflate this Averroist position with the ‘fictionalist’ position prevalent in the sixteenth century according to which use of false or doubtful hypotheses by mathematical astronomers is not merely excusable faute de mieux but both legitimate and inevitable.

On the prevalence of this stance in the latter part of the sixteenth century see Westman R. S. , “The Melanchthon circle, Rheticus, and the Wittenberg interpretation of the Copernican theory”, Isis, lxvi (1975), 163–93; Aiton E. J. , op. cit., 98–191; and Jardine N. , The birth of history and philosophy of science: Kepler's Defence of Tycho against Ursus (Cambridge, in press), ch. 7.

Reinhold E. , Theoricae novae planetarum ab Erasmo Reinholdo Salveldensi pluribus figuris auctae et illustratae scholiis (first publ. 1543, rev. ed., Paris 1553), sig. aiiii, v and f. 1v–2r. On Reinhold's stance see Gingerich O. , “The rôle of Erasmus Reinhold and the Prutenic Tables in the dissemination of Copernican theory”, Studia copernicana, vi (1973), 43–62.

Pereira B. , De communibus omnium rerum naturalium principiis & affectionibus (first publ. 1562; Rome, 1576), 47D–48B.

Naibod V. , Astronomicarum institutionum libri III (Venice, 1580), f. 20 r-v; Schreckenfuchs E. , Commentaria in sphaeram Ioannis de Sacrobusto (first publ. 1556; Basel, 1569), sig. a2v; Peucer C. , Hypotyposes orbium coelestium (Strasbourg, 1568), 7–10 (on the authorship of this anonymous work see Gingerich O. , “Erasmus Reinhold”, Dictionary of scientific biography, ed. by Gillispie C. C. , xi (New York, 1973), 365–7; in loc. cit. (ref. 24), I discuss Peucer's position in more detail and suggest that a similar position is attributable to Reinhold).

In “The forging of modern realism: Clavius and Kepler against the sceptics”, Studies in the history and philosophy of science, x (1979), 141–73, I argue against attribution of strict instrumentalism to Osiander and others considered by Duhem to be fictionalists. Newton-Smith W. H. , The rationality of science (London, 1981), 29, distinguishes what I have called “strict” and “relaxed” instrumentalism as semantic and epistemological instrumentalism, respectively, attributing the latter to Osiander. It is a moot point which brand of instrumentalism Duhem attributes to, and finds praiseworthy in, the astronomers he identifies as “fictionalists”.

In the paper cited above I suggest that the moderately sceptical Augustinian epistemology of Melanchthon's De anima may underlie the attitude to astronomy adopted by him and certain of his colleagues; and it is tempting to relate Ramus's extreme plea for a predictively adequate “astronomy without hypotheses” to his sympathetic treatment of the scepticism of Cicero's Academica: See Schmitt C. B. , Cicero scepticus (The Hague, 1972), 79–81.

De rev. , I: 10, f. 8v, 34–9r, 3. In translating this and subsequent passages I have been helped by Menzzer's C. L. German version, Nicolaus Coppernicus aus Thorn über die Kreisbewegungen der Weltkörper (Toruń, 1879), and the English version of E. Rosen, Copernicus on the revolutions (Warsaw and London, 1978).

In his Three Copernican treatises (3rd rev. edition, New York, 1971), 11, Rosen claims that Copernicus “avoided taking sides in the controversy over the question whether the spheres were imaginary or real”. However, in his biography of Copernicus, ibid. , 389, and in the notes to his translation of De rev., he appears to attribute belief in real spheres to Copernicus (op. cit., 348–9), and his criticisms of Swerdlow in op. cit. (ref. 6, i), 83–85 imply that Copernican celestial spheres are geometrically solid and hence overlapping.

For a masterly account of the rôle of this postulate in the natural philosophy of the period see Grant E. , “The principle of the impenetrability of bodies in the history of concepts of separate space from the Middle Ages to the seventeenth century”, Isis, lxix (1978), 551–71. It should, however, be noted that postulation of corporeal but overlapping orbs has a classical precedent in Sosigenes: See Schramm M. , Ibn al-Haytham's Weg zur Physik (Wiesbaden, 1963), 36–63 and Aiton E. J. , op. cit. (ref. 8), 81–83.

Maestlin M. , Epitome astronomiae (first publ. 1582; Tübingen, 1597), 28–29; De astronomiae hypothesibus … (Heidelberg, 1582), sig. A2, v. The latter work is a dissertation (respondent, Mathias Mener), but the correspondence in content with the Epitome astronomiae confirms Maestlin's authorship: On the general question of authorship of such dissertations see Evans R. J. W. , “German universities after the 30 years' war”, History of universities, i (1981), 169–90, pp. 175–6.

Observatio et demonstratio cometae aetherae … (Tübingen, 1578), cap. viii. On Kepler's heliocentric model for the comet see Westman R. S. , “The comet and the cosmos: Kepler, Maestlin and the Copernican hypothesis”, Studia copernicana, v (1972), 7–30.

Swerdlow , op. cit. (ref. 5, i).

Reinhold , op. cit. (ref. 25), dedication to Albert, Marquis of Brandenburg, sig. aiiii, v.

I cannot trace a Cremonensis who commented De sphaera. Gerard of Cremona, then thought to have been author of the old Theorica planetarum, and Cremonini Cesare , whose Disputatio de coelo was published at Venice in 1613, are possible referents: The latter seems the more likely, since he deals with the nature and substance of orbs in a manner similar to that to be found in commentaries on De sphaera.

Johannes Kepler gesammelte Werke , ed. by von Dyck W. and Caspar M. (München, 1938–), x, 43 (hereafter cited as K.g.W.). A translation of the preface is to be found in Gingerich O. , “Johannes Kepler and the new astronomy”, Quarterly journal of the Royal Astronomical Society, xiii (1972), 346–73, pp. 360–73.

Wolfson H. A. , (i) “The plurality of immovable movers in Aristotle, Averroes and St Thomas”, Harvard studies in classical philology, lxiii (1958), 233–53, and (ii) “The problem of the souls of the spheres from the Byzantine commentators on Aristotle through the Arabs and St Thomas to Kepler”, Dumbarton Oaks papers, xvi (1962), 69–73; Weisheipl J. , “The celestial movers in mediaeval physics”, The Thomist, xxiv (1961), 286–326; Grant , op. cit. (ref. 10).

A clear, if somewhat schematic summary of the Averroist and Thomist accounts of celestial substance is given by Zabarella J. , De rebus naturalibus libri XXX (first publ. 1590; Frankfurt , 1607), 269–90. On the complexities of Aquinas's position see Litt T. , Les corps célestes dans l'univers de Saint Thomas d'Aquin (Louvain, 1963), 58–90.

Grant , op. cit. (ref. 10), 276–8.

Ibid., 301–2.

Romanus Aegidius , De materia celi quaestio … (Padua, 1495), f. 1r–7r.

Wolfson H. A. , op. cit. (ref. 39, ii).

Cf. De caelo, II: 7, 289a 13–17: “The most logical and consistent hypothesis is to make each star consist of the body in which it moves, since we have maintained that there is a body whose nature it is to move in a circle”, transl. by Guthrie W. K. C. , Aristotle on the heavens (London, 1939), 179.

Weisheipl , op. cit. (ref. 39).

Grosseteste R. , De generatione stellarum , ed. by Baur L. , Beiträge zur Geschichte der Philosophie des Mittelalters, ix (1912), 32–36.

On mediaeval schemes of the arts and sciences see Weisheipl J. , “The nature, scope and classification of the sciences”, Science in the Middle Ages, ed. by Lindberg D. C. (Chicago, 1978), 461–82.

See Schmitt C. , “Astronomy in universities, 1550–1650”, General history of astronomy, ed. by Hoskin M. A. (forthcoming). I thank Dr Schmitt for allowing me to see a draft of his contribution.

An extensive treatment of fifteenth-century discussions of the status of natural philosophy is given by Markowski M. , Burydanizm w Polsce w okresie przedkopernikańskim, Studia copernicana, ii (1971).

Venice , June, 1518. This collation is an expansion of an earlier collation that had already gone through at least six editions. One of these is the Venice , 1508, collection, Nota eorum quae in hoc libro continentur. Oratio de laudibus astrologiae …, on which subsequent references to Pierre d'Ailly's Quaestiones in Sphaeram and Capuano's commentaries on Sacrobosco and Peurbach are based.

Attributed by Birkenmajer L. A. , Stromata copernicana (Cracow, 1924), 320–1; see also Czartoryski P. , “The library of Copernicus”, Studia copernicana, xvi (1978), 355–96, p. 382.

Critical editions of the commentaries of Cecco d'Ascoli and that attributed to Scot Michael are to be found in Thorndike L. , The Sphere of Sacrobosco and its commentators (Chicago, 1949).

D'Ailly discusses the nature and causes of the celestial motions in his first two quaestiones, op. cit. (ref. 51), i, f. 71r–[74r]; Capuano touches on these issues in the prooemium to his commentary on Peurbach, ibid., ii, f. [1r]–2r.

See below, Section 5.

Wojciech , op. cit. (ref. 16), 11–13. His treatment of this issue is closely based on Magnus Albertus , Metaphysica , XI, T2, 25–26, which he cites: Opera omnia, ed. by Geyer B. , xvi/2 (Aschendorff, 1964), 515–16.

Ibid., 15–16.

In a letter of 1605 to von Hohenburg Herwart , Kepler remarks Terram nullj solido orbj innexam, palpamus manibus (K.g.W., xv, 185).

Westman , op. cit. (ref. 4), 115–16, suggests very plausibly that Copernicus's awareness of this difficulty may account for his reticence about the substance of celestial orbs.

Swerdlow , op. cit. (ref. 5, ii), 131–2.

K.g.W. , vii, 291–8. At one point Kepler mentions the traditional doctrine of absence of terrestrial qualities in the heavens, but he does so dismissively (ibid., 29).

Donahue W. H. , The dissolution of the celestial spheres (New York, 1981), chs. 1 and 2.

De rev., I: 4, f. 3r, 1–10.

De caelo , II: 6, 288a288a 28–35, transl. by Guthrie W. K. C. , Aristotle on the heavens (London, 1939), 173.

Here I follow Wallis C. G. , On the revolutions of the heavenly spheres, Great books of the western world, xvi, ed. by Hutchins R. M. (Chicago, 1952), 514, who renders disparitatem reuoluti corporis, “the inequality between it and the moved body”; other translators have considered the disparitas to be in the reuolutum corpus. Disparitas is a rare late classical coinage; by analogy with disparilitas and disparatio one would expect a genitive taken by it to be contrastive: cf. Lexicon mediae et infimae latinitatis Poloniae (Wrocław, 1969–74), iii, 662.

De rev. , I: 4, f. 2v2v, 3–8. I have taken per eadem to mean per eadem loca, a reading which is consistent with the passage from De caelo echoed here: “There is no absolute beginning or end or mid point of it, for in time it is eternal and in length it returns upon itself”: De caelo , II: 6, transl. by Guthrie , op. cit., 171.

Cf. Birkenmajer A. , Études d'histoire des sciences en Pologne, Studia copernicana, iv (1972), 655–6.

De caelo, II: 3, 286a 11–13 and II: 6, 288a 24–28.

De rev., I: 4, f. 2v, 8–9.

Ibid. , f. 2v2v, 28–32. Reinhold makes a similar appeal to this harmonia irregularitatis in the apparent motions to support the postulate of simple or compound uniform circular motion: op. cit. (ref. 25), f. 2r.

My construal of this difficult passage differs from those of Menzzer Wallis Kuhn Duncan and Rosen , all of whom attach Quoniam to the preceding in quo plures motus intelliguntur—“in which several motions are perceived”. I have taken Quoniam to depend on consentaneum est, and the whole of Id enim … ordinatione constituta to be an explanatory parenthesis in which cum uero is concessive. The Latin is ambiguous, and my reading rests largely on the principle of charity of interpretation. Attachment of Quoniam to intelliguntur renders Copernicus's line of thought baffling: The plures motus of the preceding clause are, as the context makes clear, apparent motions of the Sun; and the claim that irregular movement of a planet by a single orb is impossible hardly supports the assertion that the Sun has several apparent motions. Attachment to consentaneum est, on the other hand, yields a coherent argument: Since irregular apparent motion cannot be explained if each planet has but a single orb, an alternative arrangement of orbs must be postulated. A modicum of support for my construal is provided by the autograph: Copernicus originally opened the passage Et idcirco fieri nequit, which suggests that the opening clause is indeed independent of the preceding sentence: The manuscript of Nicholas Copernicus “On the revolutions”: Facsimile , ed. by Czartoryski P. (Warsaw and London, 1972).

Ibid., f. 5v, 17–6r, 10.

Cf. De caelo, II: 4, 287a, 12–14.

De rev., I: 5, f. 3v, 23–26.

Ibid., I: 9, f. 7r, 16–24.

See below, Section 5.

Cf. Swerdlow , op. cit. (ref. 5, i) 425.

Guerlac H. , “Copernicus and Aristotle's cosmos”, Journal of the history of ideas, xxix (1968), 109–13.

Grant E. , “Late mediaeval thought, Copernicus and the scientific revolution”, Journal of the history of ideas, xxiii (1962), 197–220; Markowski , op. cit. (ref. 50), 244–57; Palacz R. , “Z badań nad filozofiα przyrody na Uniwersitecie Krakowskim w XV wieku”, Filozofia polska XV wieku, ed. by Palacz R. (Warsaw, 1972), 312–69. There is an immense Polish literature on fifteenth-century Cracovian developments in natural philosophy, much of it motivated by the assumption that such developments provide an important context for the understanding of Copernicus's work. Palacz R. , “Nicolas Copernic comme philosophe”, Studia copernicana, xiv (1975), 27–40 and Knoll P. W. , “The Arts Faculty at the University of Cracow at the end of the fifteenth century”, in The Copernican achievement, ed. by Westman R. S. (Berkeley, 1975), 137–156, provide useful introductions to this literature.

Krafft , op. cit. (ref. 3); (ii) “Der Mathematikos und der Physikos. Bemerkungen zu den angeblichen Platonischen Aufgabe, die Phänomene zu retten”, Beiträge zur Geschichte der Wissenschaft und der Technik, v (1965), 5–24; (iii) “Copernicus retroversus, I”, Studia copernicana, xiii (1975), 113–28; (iv) “Progressus retrogradus”, Die Struktur wissenschaftlichen Revolutionen und die Geschichte der Wissenschaften, ed. by Diemer A. (Meisenheim am Glan, 1977), 20–48.

Op. cit. (ref. 3) 267.

Op. cit. (ref. 4).

Ibid., 111–12.

See ref. 56, above.

Op. cit. (ref. 51), i, f. 3r; ii, f. 2r, f. 14r, f. 25r-v.

See above, Section 3.

On Bacon's treatment of this issue see Aiton , op. cit. (ref. 8), 88–89; on Aquinas's treatments, and his ambivalent attitude to Ptolemaic astronomy, see Litt , op. cit. (ref. 40), ch. 28.

D'Ailly , op. cit. (ref. 51), i, f. 85v; Capuano , ibid., ii, f. 4v.

Averroes , De caelo, II, comm. 35: Aristotelis Stagiritae omnia quae extant opera … Averrois Cordubensis … commentarii (Venice, 1552), v, f. 55r–v; d'Ailly , op. cit. (ref. 51), i, f. 85v–86r; Capuano , ibid., ii, f. 3r–5r.

D'Ailly , ibid., i, f. 86r; Capuano , ibid., ii, f. 4v.

D'Ailly , ibid., i, f. 85v; Capuano , ibid., ii, f. 4v.

Krafft , op. cit. (ref. 3), 266–7.

Nicolai Copernici de hypothesibus motuum caelestium commentariolus, ed. by Prowe L. , in Nicolaus Coppernicus, ii (Berlin, 1884), 186.

Cf. Rosen E. , “Copernicus' axioms”, Centaurus, xx (1976), 44–49. Giovanni Crestone's Dictionarium graecum (Modena, 1499–1500), f. XXVIv, renders axioma as postulatio, dignitas, as does Calepinus's Dictionarium (Hagenau, 1522), f. LIr. The former was owned by Copernicus: See Czartoryski , op. cit. (ref. 52) 366.

For d'Ailly's and Capuano's justifications of the postulate see ref. 88. Cf., for a Cracovian example, Jan of Głogów, op. cit. (ref. 17), sig. Kiiii, r; whilst Głogów accepts eccentric and epicyclic orbs as real bodies, he anticipates Wojciech in considering the equant, which violates the postulate, as a circulus imaginarius, ibid., sig. Kiiii, v. Krafft , op. cit. (ref. 80, ii) traces the postulate back via Aquinas and Henry Bate to Sosigenes.

Cf. Wojciech , op. cit. (ref. 16), 86 where it is deployed against the equant. On Reinhold's endorsement of the postulate in his copy of De rev., see Gingerich , op. cit. (ref. 25), 53; Peucer , loc. cit. (ref. 28).

Westman , op. cit. (ref. 4), especially p. 111.

De rev., sig. iiii, r, 29–v, 3.

On humanist introductions and prefaces to the mathematical arts see Rose P. L. , The Italian renaissance of mathematics: Studies on humanists and mathematicians from Petrarch to Galileo (Geneva, 1975).

Rheticus clearly recognizes the importance of natural philosophical justification in the section entitled Transitio ad enumerationem nouarum hypothesium totius Astronomiae, but he defers treatment of such issues to “a certain other treatise” (pp. 114–15 in Maestlin's edition of 1596).

Maestlin , De astronomiae principalibus et primis fundamentis disputatio … (Heidelberg, 1582), sig. A2r. The respondent to this dissertation was Jeremiah Jecklin; cf. ref. 30.

Maestlin , loc. cit. (ref. 33).

Maestlin , preface to the edition of Rheticus's Narratio prima which he appended to Kepler's Mysterium cosmographicum, K.g. W., i, 82–85. It should, however, be noted that on the question of the location and substance of comets Maestlin was prepared to wield the “certain demonstrations of geometry” against natural philosophers with considerable aggression: op. cit. (ref. 34), cap. iv.

Clavius , In Sphaeram Ioannis de Sacro Bosco commentarius, nunc tertio ab ipso auctore recognitus … (Rome, 1585), 453 et seq.; in the prooemium the rôles of the astrologus and philosophus in the study of the heavens are sharply distinguished.

Westman , op. cit. (ref. 24), considers this aspect of the reception of Copernicus's work.

Westman , op. cit. (ref. 4), 121–34, argues persuasively for a link between the development of astronomy outside the restrictive framework of the universities and the preparedness of astronomers to venture into natural philosophical territory.

In his Apologia pro Tychone contra Ursum Kepler explicitly rebuts those who regard saving of the phenomena as the sole task of the astronomer and who consider argumenta physica to be irrelevant to astronomy: Joannis Kepleri opera omnia , ed. by Frisch C. , i (Frankfurt, 1858), 238–48. Elsewhere I have discussed the sixteenth-century backgrounds to Kepler's innovative views on the rôle of physics and metaphysics in astronomy: op. cit. (ref. 24), chs. 6 and 7.