¹ See, e.g., Donahue, W. H., The Dissolution of the Celestial Spheres, New York, 1981Google Scholar; Rosen, E., ‘The dissolution of the solid celestial spheres’, Journal of the History of Ideas (1985), 46, 13–31CrossRefGoogle Scholar; 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.CrossRefGoogle Scholar

² Rosen, , op. cit. (1)Google Scholar, 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)Google Scholar. 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 n6CrossRefGoogle Scholar; Moran, B., ‘Christoph Rothmann, the Copernican theory, and institutional and technical influences on the criticism of Aristotelian cosmology’, Sixteenth Century Journal (1982), 13, 85–108, on 85.CrossRefGoogle Scholar

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

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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)CrossRefGoogle Scholar. 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, 158.29–39Google Scholar (hereafter cited as TBOO).Google Scholar

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

¹² See Neugebauer, O., ‘On the planetary theory of Copernicus’, Vistas in Astronomy (1968), 10, 89–103, on 92.CrossRefGoogle Scholar

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, 130CrossRefGoogle Scholar; and Ursus, (1588)Google Scholar, and Roeslin, (1597)Google Scholar, 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, 33–44, on 34 and 36.Google Scholar

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, 461–82Google Scholar; 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.Google Scholar

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

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

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

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

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.Google Scholar

²⁰ Alhazen, (Optics, vii. 55Google Scholar, in Risner, F., Opticae thesaurus Alhazeni Arabis… item Vitellonis…, Basel, 1572Google Scholar, repr. New York, 1972, 280–2), and Witelo, (Optics, x. 54Google Scholar, 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, 69–156, on 109CrossRefGoogle Scholar, where these passages are cited (presumably Rothmann was using Risner's edition, but he does not indicate it); and Lerner, , op. cit. (1), 270Google Scholar. Neither Alhazen nor Witelo mentions the relevant passage from the Almagest.

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

²² Pena, J., Euclidis optica… Paris, 1557, aa iii r–bb i vGoogle Scholar; translated in Barker, P., ‘Jean Pena (1528–58) and Stoic physics in the sixteenth century’, The Southern Journal of Philosophy (1985), 23 (Supplement), 93–107, on 97.CrossRefGoogle Scholar

²³ Barker, P., ‘The optical theory of comets from Apian to Kepler’, Physis (1993), 30, 1–25Google Scholar; Barker, P. and Goldstein, B. R., ‘The role of comets in the Copernican revolution’, Studies in the History and Philosophy of Science (1988), 19, 299–319.CrossRefGoogle Scholar

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

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

²⁶ Rothmann related the cause of atmospheric refraction to that of twilight and, according to Kepler, (Ad Vitellionem Paralipomena, Frankfurt, 1604, 78)Google Scholar, 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 n8Google Scholar; and Goldstein, B. R., ‘Refraction, twilight and the height of the atmosphere’, Vistas in Astronomy (1976), 20, 105–7).CrossRefGoogle Scholar

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

²⁸ Rothman, , op. cit. (20), 110Google Scholar: ‘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.Google Scholar

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

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, 21–46Google Scholar. 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.CrossRefGoogle Scholar

³² TBOO, vii, 186–7.Google Scholar

³³ For example, in Thoren, V., The Lord of Uraniborg: A Biography of Tycho Brahe, Cambridge, 1990, 274Google Scholar, 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, 34Google Scholar; See also Rosner, F., The Existence and Unity of God: Three Treatises Attributed to Moses Maimonides, Northvale, NJ, and London, 1990, 48)Google Scholar. 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)Google Scholar 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 fGoogle Scholar. 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).Google Scholar

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

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

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

³⁸ Cf. Josephus, , Antiquities, i. 1Google Scholar (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, 1987Google Scholar. Despite Josephus, in Genesis 1 the firmament is not called ‘crystalline’.

³⁹ Grant, , op. cit. (29), 324–70.Google Scholar

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

⁴¹ Brahe, to Peucer, , 13 09 1588Google Scholar, in TBOO, vii, 133–4Google Scholar. 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 ffGoogle Scholar; and Zanier, G., Medicina e filosofia tra '500 e'600, Milan, 1983, 20–38Google Scholar. 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, 1587Google Scholar; 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 polykhalypsGoogle Scholar, 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, 395Google Scholar; TBOO, vii, 134.7.Google Scholar

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

⁴⁴ TBOO, vi, 93.21.Google Scholar

⁴⁵ TBOO, iv, 222–3Google Scholar, passim.

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

⁴⁷ TBOO, vii, 80.Google Scholar

⁴⁸ As Thoren, , op. cit. (33), 258Google Scholar, 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. 11Google Scholar, translated in Donahue, W. H., Johannes Kepler: New Astronomy, Cambridge, 1992, 203.Google Scholar

⁴⁹ Dreyer, J. L. E., Tycho Brahe: A Picture of Scientific Life and Work in the Sixteenth Century, 1890, repr. New York, 1963, 178–9Google Scholar: ‘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.Google Scholar

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

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

⁵³ TBOO, iv, 399 ff.Google Scholar

⁵⁴ TBOO, vi, 159–60.Google Scholar

⁵⁵ TBOO, vi, 181.30–1.Google Scholar

⁵⁶ TBOO, vii, 134–5.Google Scholar

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

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

⁵⁹ Hooykaas, , op. cit. (57) 66–9.Google Scholar

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

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

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

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

⁶⁴ TBOO, vi, 217.Google Scholar

⁶⁵ TBOO, vi, 222–3.Google Scholar

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.Google Scholar

⁶⁸ TBOO, vi, 118.Google Scholar

⁶⁹ TBOO, vi, 144Google Scholar, translated in Shackelford, J., ‘Paracelsianism in Denmark and Norway in the 16th and 17th Centuries’, Ph.D. thesis, University of Wisconsin-Madison, 1989, 190Google Scholar. 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.Google Scholar

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

⁷¹ As Thoren, , op. cit. (33), 363Google Scholar, 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, 231Google Scholar, 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).Google Scholar

⁷² TBOO, vi 214–15.Google Scholar

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

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

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⁷⁸ TBOO, x, 283–8.Google Scholar

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

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