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The role of Rothmann in the dissolution of the celestial spheres

  • Bernard R. Goldstein (a1) and Peter Barker (a2)

At the end of the sixteenth century astronomers and others felt compelled to choose among different cosmologies. For Tycho Brahe, who played a central role in these debates, the intersection of the spheres of Mars and the Sun was an outstanding problem that had to be resolved before he made his choice. His ultimate solution was to eliminate celestial spheres in favour of fluid heavens, a crucial step in the abandonment of the Ptolemaic system and the demise of Aristotelian celestial physics. These debates involved issues that had not previously been part of astronomy, and had the effect of undermining the traditional hierarchy of the sciences. While this complicated story involves many scientific personalities of the sixteenth and seventeenth centuries, in the present paper we will concentrate on one figure who has been assigned an unnecessarily minor role in most histories of science: Christoph Rothmann. In the present paper we show that ‘the dissolution of the celestial spheres’ depends on arguments about the substance of the heavens, following a mistaken argument of Gemma Frisius, elaborated by Joannes Pena and appropriated by Rothmann. We next consider the status and origin of the doctrine, as presented by Brahe, that the heavenly spheres are solid, and the impact on Brahe of Rothmann's treatise on the comet of 1585. Rothmann provided several key ideas that enabled Brahe to develop his system, and we suggest in passing that Rothmann may also have precipitated Brahe's re-evaluation of his attempt to detect the parallax of Mars during the opposition of 1582–83. We offer a new account of this central piece of evidence for the Tychonic system.

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1 See, e.g., Donahue, W. H., The Dissolution of the Celestial Spheres, New York, 1981; Rosen, E., ‘The dissolution of the solid celestial spheres’, Journal of the History of Ideas (1985), 46, 1331; and Lerner, M.-P., ‘Le problème de la matière céleste après 1550: aspects de la bataille des cieux fluides’, Revue d'Histoire des Sciences (1989), 42, 255–80.

2 Rosen, , op. cit. (1), is an exception; however, as we will argue, he errs in giving Rothmann priority for views that Pena had already held.

3 We begin by adhering to the common expression, ‘celestial sphere’, but later we will generally use the technical term, ‘orb’. For the definition of ‘orb’, see item (3) on p. 387, below. The terms, ‘sphere’, ‘orb’ and ‘heaven’, have often been used interchangeably, and it is not easy to be entirely consistent. Further, it would be more accurate to talk about the demise of the doctrines concerning celestial spheres, rather than the dissolution of the spheres themselves.

4 The latest document by Rothmann we have found is a letter he wrote in 1597 concerning his work on the fixed stars: see Philippi, H., Politische Akten nach Philipp d. Gr., 1567–1821, Abteilung a: Landgräfliche Personalien, in Repertorien des hessischen Staatsarchivs Marburg, Bestand 4, Marburg, 1973, 23 (MS 39, 24). We are most grateful to K. Manders for bringing this reference to our attention.

5 Westman, R., ‘The astronomer's role in the sixteenth century: a preliminary study’, History of Science (1980), 18, 105–47, on 106 and 136 n6; Moran, B., ‘Christoph Rothmann, the Copernican theory, and institutional and technical influences on the criticism of Aristotelian cosmology’, Sixteenth Century Journal (1982), 13, 85108, on 85.

6 Moran, , op. cit. (5), 88; Westman, R., ‘The Melanchthon circle, Rheticus, and the Wittenberg interpretation of the Copernican theory’, Isis (1975), 66, 165–93.

7 Moesgaard, K. P., ‘The Copernican influence on Tycho Brahe’, in Studia Copernicana 5 [Colloquia Copernicana 1], Warsaw, 1972, 3155, on 48.

8 Ptolemy specified that the ratio of maximum to minimum distance of a planet from the Earth in the model (where the mean distance is 60), is the same as the ratio of its true maximum to minimum distance from the Earth (measured in terrestrial radii).

9 See Goldstein, B. R., ‘The Arabic Version of Ptolemy's Planetary Hypotheses’, Transactions of the American Philosophical Society (1967), 57 (4). A further assumption made by Ptolemy, but not by many of his successors, is that the spherical shells may be replaced by ‘sawn pieces’, whose breadth for each planet is fixed by its maximum latitude to the north and south of the ecliptic.

10 Tychonis Brahe opera omnia (ed. Dreyer, J. L. E.), 15 vols., Copenhagen, 1913, vi, 158.29–39 (hereafter cited as TBOO).

11 Grant, E., ‘Celestial orbs in the Latin Middle Ages’, Isis (1987), 78, 153–73.

12 See Neugebauer, O., ‘On the planetary theory of Copernicus’, Vistas in Astronomy (1968), 10, 89103, on 92.

13 In addition to the figure in Rothmann's manuscript displayed here, see, for example, the diagrams by Wittich (1578), in Gingerich, O. and Westman, R. S., ‘The Wittich Connection: Conflict and Priority in Late Sixteenth-Century Cosmology’, Transactions of the American Philosophical Society (1988), 78, (7), 48, 130; and Ursus, (1588), and Roeslin, (1597), in Schofield, C., ‘The Tychonic and semi-Tychonic world systems’, in The General History of Astronomy, vol. 2A, Planetary Astronomy from the Renaissance to the Rise of Astrophysics: Tycho Brahe to Newton (ed. Taton, R. and Wilson, C.), Cambridge, 1989, 3344, on 34 and 36.

14 See, e.g., Weisheipl, J., ‘The nature, scope, and classification of the sciences’, in Science in the Middle Ages (ed. Lindberg, D. C.), Chicago, 1978, 461–82; and Donahue, W. H., ‘The solid planetary spheres in post-Copernican natural philosophy’, in The Copernican Achievement (ed. Westman, R. S.), Berkeley and Los Angeles, 1975, 244–75, on 245.

15 See, for example, Maestlin, M., De astronomiae principalibus et primis fundamentis disputatio, Heidelberg, 1582, theses 8, 28, 36, 53, 61.

16 See, for example, Georgii Joachimi Rhetici narratio prima (ed. Hugonnard-Roche, H. et al. ,) Wroclaw, 1982, 56 (translated in Rosen, E., Three Copernican Treatises, 1939, repr. New York, 1959, 139); and Rothmann, , in TBOO, vii, 158.35.

17 Moran, , op. cit. (5), 86.

18 Toomer, G. J., Ptolemy's Almagest, New York, 1984, 421.

19 Goldstein, B. R., ‘Remarks on Gemma Frisius's De radio astronomico et geometrico’, in From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe (ed. Berggren, J. L. and Goldstein, B. R.), Copenhagen, 1987, 167–79, on 173.

20 Alhazen, (Optics, vii. 55, in Risner, F., Opticae thesaurus Alhazeni Arabis… item Vitellonis…, Basel, 1572, repr. New York, 1972, 280–2), and Witelo, (Optics, x. 54, in Risner, ibid., 448–9) both accepted atmospheric refraction, and interpreted the difference in the distance between two stars near the horizon in contrast to their distance near mid-heaven as resulting from it. See also Rothmann, C., Descriptio accurata cometae anni 1585 [composed in 1586], in Willebrordi Snellii descriptio cometae anno 1618…, Louvain, 1619, 69156, on 109, where these passages are cited (presumably Rothmann was using Risner's edition, but he does not indicate it); and Lerner, , op. cit. (1), 270. Neither Alhazen nor Witelo mentions the relevant passage from the Almagest.

21 See, e.g., Ptolemy, 's Optics, translated in Cohen, M. R. and Drabkin, I. E., A Source Book in Creek Science, Cambridge, MA, 1958, 281.

22 Pena, J., Euclidis opticaParis, 1557, aa iii r–bb i v; translated in Barker, P., ‘Jean Pena (1528–58) and Stoic physics in the sixteenth century’, The Southern Journal of Philosophy (1985), 23 (Supplement), 93107, on 97.

23 Barker, P., ‘The optical theory of comets from Apian to Kepler’, Physis (1993), 30, 125; Barker, P. and Goldstein, B. R., ‘The role of comets in the Copernican revolution’, Studies in the History and Philosophy of Science (1988), 19, 299319.

24 Jervis, J. L., Cometary Theory in Fifteenth-Century Europe, Warsaw, 1985, 118–19.

25 Barker, , op. cit. (22), and Barker, , op. cit. (23).

26 Rothmann related the cause of atmospheric refraction to that of twilight and, according to Kepler, (Ad Vitellionem Paralipomena, Frankfurt, 1604, 78), physicists, using arguments based on twilight, considered the height of the air to be 12 German miles (= 89km: see Chevalley, C., Kepler: Les fondements de l’optique moderne, Paris, 1980, 441 n8; and Goldstein, B. R., ‘Refraction, twilight and the height of the atmosphere’, Vistas in Astronomy (1976), 20, 105–7).

27 Rothmann, , op. cit. (20), 98.

28 Rothman, , op. cit. (20), 110: ‘Sive igitur dixerimus, sole quiescente terram moven, in qua sententia non adeo, ut creditur, absurda fuerunt olim nobiles illi Pythagorei, itemque Platonis Timaeus, Seleucus, Aristarchius Samius, Archimedes etc. et hac tempestate divinus Copernicus, Rheticus et alij praestantissimi Mathematici, quorum aliqui adhuc sunt in vivis: sive quiescente terra solem moveri dixerimus, nihilominus Planetas in aëre pendere dixerimus’.

29 See Grant, E., Planets, Stars, and Orbs: The Medieval Cosmos, 1200–1687, Cambridge, 1994.

30 Translated in Grant, , op. cit. (29), 334 n30.

31 The Astronomy of Levi ben Gerson (Leo de Balneolis) was translated by Petrus of Alexandria during the author's lifetime, and the Latin version survives in a number of manuscripts: see Mancha, J. L., ‘The Latin translation of Levi ben Gerson's Astronomy’, in Studies on Gersonides: A Fourteenth-Century Jewish Philosopher-Scientist (ed. Freudenthal, G.), Leiden, 1992, 2146. The expression cited appears in Vatican MS 3098, fol. 7rb, and Lyon MS 326, fol. 21r; cf. Goldstein, B. R., The Astronomy of Levi ben Gerson (1288–1344), New York and Berlin, 1985, 51.

32 TBOO, vii, 186–7.

33 For example, in Thoren, V., The Lord of Uraniborg: A Biography of Tycho Brahe, Cambridge, 1990, 274, we read: ‘the next question was how the planets actually made their rounds of the heavens if there were no crystalline spheres to carry them’.

34 The only possible exception we have found (after an extensive search of many early sources, aided by J. L. Mancha) is in the Hebrew text of the Mishneh Torah by Maimonides (d. 1204), Yesodei ha-Torah 3.1: ‘You see all the stars [i.e., the planets and the fixed stars] as if they are all on one orb (galgal), even though one is above the other, because the orbs are pure and transparent (zakkim) like glass (zekukit) or sapphire (sappir)’(Praizler, T. H., Sefer Mishneh Torah le-rabbenu Mosheh ben Maimon, Jerusalem, 1985, 34; See also Rosner, F., The Existence and Unity of God: Three Treatises Attributed to Moses Maimonides, Northvale, NJ, and London, 1990, 48). Maimonides may have understood sappir to refer to ‘crystal’: cf. Guide of the Perplexed, i.28 (Kafah, Y., Moreh nevukhim le-rabbenu Mosheh ben Maimon, 3 vols., Jerusalem, 1972, i, 63) where the Arabic ballúr (meaning ‘crystal’) is used to translate the Hebrew sappir in Exodus 24:10. See also T. Langermann, ‘The “True Perplexity”: The Guide of the Perplexed, Part II, Chapter 24’, in Perspectives on Maimonides (ed. Kraemer, J. L.), Oxford, 1991, 159–74, on 162 f. Note that even here the relevant property of ‘crystal’ is transparency, not hardness. The earliest text we have found in which the hardness of crystalline planetary orbs is assumed to be the prevalent view before Brahe is in a work by Fontenelle that appeared in 1687: ‘Mais on a vu des comètes qui, étant plus élevées qu'on ne croyait autrefois, briseraient tout le cristal des cieux par où elles passent’ (Schackleton, R., Fontenelle: Entretiens sur la pluralité des mondes, Oxford, 1955, 68).

35 Benjamin, F. S. Jr and Toomer, G. J., Campanus of Novara and Medieval Planetary Theory, Madison, 1971, 182.

36 Li livres dou tresor de Brunetto Latini (ed. Carmody, F. J.), Berkeley and Los Angeles, 1948, 93; translated in Barrette, P. and Baldwin, S., Brunetto Latini: The Book of the Treasure, New York, 1993, 71.

37 This figure also appears in Grant, , op. cit. (11), 152.

38 Cf. Josephus, , Antiquities, i. 1 (concerning the creation), ‘After this, on the second day, he [God] placed the heaven over the whole world, and separated it from the other parts; and determined it should stand by itself. He also placed a crystalline [firmament] round it, and put it together in a manner agreeable to the earth’, translated in Whiston, W., The Works of Josephus, 1736, repr. Peabody, MA, 1987. Despite Josephus, in Genesis 1 the firmament is not called ‘crystalline’.

39 Grant, , op. cit. (29), 324–70.

40 Grant, , op. cit. (11), 173; cf. Grant, , op. cit. (29), 347.

41 Brahe, to Peucer, , 13 09 1588, in TBOO, vii, 133–4. On Vallés, who served as physician to the Spanish king, Philip II, see Thorndike, L., A History of Magic and Experimental Science, 8 vols., New York, 1941, vi, 355 ff; and Zanier, G., Medicina e filosofia tra '500 e'600, Milan, 1983, 2038. Vallés, 's book was first published 1587: Francisci Vallesii de Us quae scripta sunt physice in libris sacris, sive de sacra philosophia liber singularis…, Turin, 1587; but Brahe referred to the Lyon edition of 1588. We have depended on the Lyon edition of 1595 that J. L. Mancha checked for us; the relevant passage appears on pp. 395–6 of that edition: Caput quinquagesimum primum. Ex capite trigesimoseptimo lob: Tu forsiran cum eo fabricatus es coelos, qui solidissimi quasi aere fusi sunt. De substantia coeli… dubitatum est plurimum a Philosophis: siquidem nonnullis veterum visum est rationi consonum, earn mundi partem, vt est suprema, ita esse tenuissimam, siquidem & in aliis omnibus, de quibus vtpote vicinioribus, possumus iudicare, ita fieri conspicimus, vt quo superius est aliquid, eo sit & tenuius. Itaque esse regionem quandam, substantia alia, aere longe puriori & tenuiori plenam, per eamque ferri astra omnia per sese, quasi volantia. Plerisque tamen atque adeo optimis (nam Phythagorae, Parmenidi, Platoni, & Aristoteli) visum est, coelum substantia quadam constare firmissima & solidissima, adeo vt penitus neque diuisionem, neque distractionem recipere possit, & astra partes esse ipsorum orbium, a? cum illis ferri haudquaquam proprio concitata impetu. Ex eo vero quod de motu astrorum quis sentiat, pendei, & quod de coeli soliditate sit consentanueum. Si enim astra feruntur per se per coelum, illud certe est tenuissimum, & facillime cedens: non enim tanta posset esse astrorum celeritas medio resistente. Si autem illa feruntur cum orbibus, constat orbes tanto solidiores esse adamante, vt penitus diuidi non possint… igitur ij orbes cum quibus feruntur, nullam partium distractionem accipiunt vnquam, sed feruntur toti simul firmissime. Neque hoc aliter fieri potest: quapropter eorum substantia neque diuidi, neque distrahi possit, sit igitur solidissima… at vero Aristoteles multis argumentis probat secundo de coelo motum coelestium corporum esse regularem: non igitur mouentur per se astra, sed cum coelo, quod est mundi murus, vt dixit Parmenides, solidissimum. Cui sententia plurimum attestantur praescripta verba lob: Solidissimi quasi aere fusi. Quibus consonant & haec Homeri ouranos polykhalyps [in Greek letters], id est, multis aeris coelum. The expression ascribed to Homer, , ouranos polykhalyps, does not appear in his works; rather, the expression is ouranon es polychalchon [Iliad 5.504; Odyssey 3.2). It would seem that Vallés was relying on his memory.

42 Vallés, , op. cit. (41), ed. Lyon, 1595, 395; TBOO, vii, 134.7.

43 Rothmann, , op. cit. (20), 102; Brahe, , De mundi, in TBOO, iv, 222.

44 TBOO, vi, 93.21.

45 TBOO, iv, 222–3, passim.

46 See, e.g. Brahe, , De mundi, in TBOO, iv, 223.

47 TBOO, vii, 80.

48 As Thoren, , op. cit. (33), 258, put it: ‘Tycho registered, in letters written in mid-January 1587, his first doubts concerning the existence of solid spheres… Perhaps he made at this time the confused calculations [of the parallax of Mars] that so mystified Kepler and various later commentators’. See Kepler, Johannes, Astronomia nova, ch. 11, translated in Donahue, W. H., Johannes Kepler: New Astronomy, Cambridge, 1992, 203.

49 Dreyer, J. L. E., Tycho Brahe: A Picture of Scientific Life and Work in the Sixteenth Century, 1890, repr. New York, 1963, 178–9: ‘the horizontal parallax of Mars can at most reach 23″, a quantity that Brahe's instruments could not possibly measure’.

50 See Hugonnard-Roche, et al. , op. cit. (16), 107.

51 Rothmann, , op. cit. (20), 99.

52 Cf. Thoren, , op. cit. (33), 258.

53 TBOO, iv, 399 ff.

54 TBOO, vi, 159–60.

55 TBOO, vi, 181.30–1.

56 TBOO, vii, 134–5.

57 See, for example, Hooykaas, R., G. J. Rheticus' Treatise on Holy Scripture and the Motion of the Earth, Amsterdam, 1984, 31.

58 Mersenne, M., Questiones… in Genesim, Paris, 1623.

59 Hooykaas, , op. cit. (57) 66–9.

60 Hooykaas, , op. cit. (57), 73.

61 TBOO, vi, 218. See also Moesgaard, , op. cit. (7), 52; and Gassendi, P., ‘De Tychonis Braheis vita’, in Opera omnia, 6 vols., Lyon, 1658, repr. Cannstatt, Stuttgart-Bad, 1964, v, 434.

62 TBOO, vi, 314–15; cf. Thoren, , op. cit. (33), 363.

63 TBOO, vi, 160; cf. Moesgaard, , op. cit. (7), 49.

64 TBOO, vi, 217.

65 TBOO, vi, 222–3.

66 We intended to treat this correspondence more extensively in our book, Kepler's Unification of Physics and Cosmology (in preparation).

67 Thoren, , op. cit. (33), 213.

68 TBOO, vi, 118.

69 TBOO, vi, 144, translated in Shackelford, J., ‘Paracelsianism in Denmark and Norway in the 16th and 17th Centuries’, Ph.D. thesis, University of Wisconsin-Madison, 1989, 190. See also Segonds, A., ‘Tycho Brahe et l'alchimie’, in Alchimie et philosophie à la Renaissance (ed. Margolin, J.-C. and Matton, S.), Paris, 1993, 365–78, on 368.

70 Shackelford, , op. cit. (69), ch. 4.

71 As Thoren, , op. cit. (33), 363, noted, Brahe received a letter (unbeknownst to Rothmann) from Rothmann's patron, the Landgrave of Hesse-Cassel, in which the Landgrave had referred to Rothmann's suffering from ‘Morbum Gallicum’ (syphilis); but Tycho altered the phrase to the less indelicate, ‘a serious and harmful disease’. Thoren referred to TBOO, vi, 231, a letter of 15 May 1591 from the Landgrave to Brahe, which indeed contains the phrase ‘ein schwere und schedliche Kranckheit’. In a note to this passage Dreyer remarked, ‘For the words “ein schwere und schedliche Kranckheit” the hand written letter shows “Morbum Gallicum”. The correction seems to be Tycho's’ (TBOO, vi, 366).

72 TBOO, vi 214–15.

73 TBOO, vi, 314.20–1, and vi, 316.5–10. See also Gassendi, , op. cit. (61), 434.

74 Moran, , op. cit. (5); Rosen, , op. cit. (1).

75 See Barker, and Goldstein, , op. cit. (23).

76 TBOO, vii, 129; translated in Hugonnard-Roche, et al. , op. cit. (16), 186.

77 See Gingerich, and Westman, , op. cit. (13), 69 ff.

78 TBOO, x, 283–8.

79 TBOO, x, 286; cf. Kepler, , Astronomia nova, chs. 15, 64, translated in Donahue, , op. cit. (48), 239, 620–1.

80 For Brahe's tables of refraction, see Moesgaard, K. P., ‘Refraction in Tycho Brahe's small universe’, in Mapping the Sky (ed. Débarbat, S. et al. ), Dordrecht and Boston, 1988, 8793.

81 Gingerich, and Westman, , op. cit. (13), 71.

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