Copernicus and the Origin of his Heliocentric System

As Neugebauer demonstrated, Copernicus and his Muslim predecessors did not ‘abandon’ the equant; on the contrary, it was preserved and, with a secondary epicycle and uniform circular motions, very nearly the same results are produced as those that follow from Ptolemy's equant models: See Neugebauer O. , “On the planetary theory of Copernicus”, Vistas in astronomy, x (1968), 89–103 (espec. pp. 92–96), reprinted in idem, Astronomy and history: Selected essays (New York and Berlin, 1983). See also Swerdlow N. M. , “The Commentariolus of Copernicus”, Proceedings of the American Philosophical Society, cxvii (1973), 423–512 (espec. pp. 434–5); and Swerdlow N. M. and Neugebauer O. , Mathematical astronomy in Copernicus's De revolutionibus (New York and Berlin, 1984), 43–48, 294–5. For a comparison of Copernicus's planetary models with those of Ibn al-Shāṭir (d. 1375), see Saliba G. , “Arabic planetary theories after the eleventh century AD”, in Encyclopedia of the history of Arabic science, ed. by Rashed R. (3 vols, London and New York, 1996), i, 58–127 (espec. pp. 108–14).

See Toomer G. J. , Ptolemy's Almagest (New York and Berlin, 1984), 419–20; Goldstein B. R. , The Arabic version of Ptolemy's Planetary Hypotheses, Transactions of the American Philosophical Society, lvii/4 (1967); and Aaboe A. , Episodes from the early history of astronomy (New York and Berlin, 2001), 114–34. In the Mysterium cosmographicum, Kepler revived the nesting hypothesis in a heliocentric system such that the dimensions of the five regular solids fit the spaces between the six planets: See Kepler Johannes , Mysterium cosmographicum (Tübingen, 1596), chap. 14, translated by Duncan A. M. with introduction and commentary by E. J. Alton (New York, 1981), 155–9; see also Barker P. and Goldstein B. R. , “Theological foundations of Kepler's astronomy”, Osiris, xvi (2001), 88–113 (espec. pp. 99–103).

Swerdlow, op. cit. (ref. 1), 436. The locus classicus for the heliocentric theory in Antiquity is Archimedes's Arenarius (Sandreckoner) concerning Aristarchus: Heath T. L. , The works of Archimedes (Cambridge, 1897; reprinted New York, 1953), 221–2. But there is no evidence that Copernicus knew the passage and it was not published until after his death: cf. Nicholas Copernicus, On the revolutions, transl. and commentary by E. Rosen (Baltimore, 1992), 361. Copernicus mentioned Aristarchus in the autograph manuscript of De revolutionibus, but the passage was crossed out and not included in the editio princeps: Cf. P. L. Rose, The Italian renaissance of mathematics (Geneva, 1975), 125; and Rosen, op. cit., 25. Although not cited by Copernicus, his source was likely to have been Plutarch, On the faces of the Moon, 923A: Thereupon Lucius laughed and said: “Oh, sir, just don't bring suit against us for impiety as Cleanthes thought that the Greeks ought to lay an action against Aristarchus the Samian on the ground that he was disturbing the hearth of the universe because he sought to save the phenomena by assuming that the Heaven is at rest while the Earth is revolving along the ecliptic and at the same time rotating about its own axis” (Plutarch, Moralia: Concerning the face that appears in the orb of the Moon, ed. and transl. by H. Cherniss (Cambridge, Mass., 1957), 55; and, according to Rosen, op. cit., 360, Plutarchi opuscula LXXXXII: Index moralium omnium, & eorum quae in ipsis tractantur, habetur hoc quaternione: Numerus autem arithmeticus remittit lectorem ad semipagina[m], ubi tractantur singula (Venice, 1509), 932). On the other hand, Copernicus does quote a passage from Pseudo-Plutarch in Greek that was included in the edition of Plutarch in 1509, cited above (N. Copernicus, De revolutionibus orbium coelestium (Nuremberg, 1543; facsimile reproduction, Brussels, 1966), Dedication to the Pope, f. iiij r; cf. chap. 5, f. 3v): Some think that the Earth remains at rest. But Philolaus the Pythagorean believes that, like the Sun and Moon, it revolves around the fire in an oblique circle. Heraclides of Pontus and Ecphantus the Pythagorean make the Earth move, not in a progressive motion, but like a wheel in a rotation from west to east about its own centre (transl. Rosen, op. cit., 5 and, according to Rosen, this passage is found in Plutarch, op. cit. (ed. 1509), 328). There is also a confused remark about Aristarchus in G. Valla, De expetendis et fugiendis rebus … (2 vols, Venice, 1501): cf. Rose, op. cit., 125; and Rosen, op. cit., 360–1. A similar passage is found in Cicero's Academica (ii.39.123) that was available in manuscript in Frauenburg and, according to Rosen (op. cit., 341), Copernicus transcribed this passage in his copy of Pliny's Natural history (Venice, 1487; cf. Rose, op. cit., 125; and Czartoryski P. , “The library of Copernicus”, Studia Copernicana, xvi (1978), 355–96 (espec. p. 372)): The Syracusan Hicetas, as Theophrastus asserts, holds the view that the heaven, Sun, Moon, stars, and in short all of the things on high are stationary, and that nothing in the world is in motion except the Earth, which by revolving and twisting round its axis with its extreme velocity produces all the same results as would be produced if the Earth were stationary and the heaven in motion (Cicero, De natura deorum; Academica, ed. and transl. by H. Rackham (Cambridge, Mass., 1951), 627). This passage is cited by Copernicus, op. cit., Dedication to the Pope, f. iiij r, and in chap. 5, f. 3v; in both places “Hicetas” appears as “Nicetas”.

Copernicus , op. cit. (ref. 3), 10r.

Swerdlow , op. cit. (ref. 1), 471–8.

Swerdlow and Neugebauer , op. cit. (ref. 1), 56–60.

See Swerdlow, op. cit. (ref. 1), 478; cf. Goldstein B. R. and Barker P. , “The role of Rothmann in the dissolution of the celestial spheres”, The British journal for history of science, xxviii (1995), 385–403.

Copernicus , op. cit. (ref. 3), 8v–9v; Copernicus , On the revolutions of the heavenly spheres, transl. by Duncan A. M. (London and New York, 1976), 47–50.

For the Greek text, see Aristotle , On the heavens, ed. and transl. by Guthrie W. K. C. (Cambridge, Mass., 1939), 198; transl. in A. C. Bowen, Simplicius' Commentary on Aristotle, De caelo ii 10–12: An annotated translation (in preparation). Guthrie's translation of this passage is faulty; a better translation is available in S. Leggatt, Aristotle: On the heavens, I and II (Warminster, 1995), 143.

For Scot's translation, see Aristotelis opera cum Averrois commentariis (Venice, 1495–96), 212va-b; Aristotelis opera cum Averrois commentariis: Quintum volumen Aristotelis De caelo,… (Venice, 1562; reprinted Frankfurt/M. 1962), 136I-L. I am most grateful to José Chabás for checking the copy of the edition of 1495–96 at the library of the University of Barcelona (shelf mark: Inc 612–1). In Moerbeke's translation the expression in ibid. (ed. 1495–96), 212va, is secundum rationem… elongationibus, whereas in ibid. (ed. 1562), 136G, it is secundum rationem… ipsis spatijs; there are other differences between the two editions of Moerbeke's translation, but they do not affect the argument here. Gerhard Endress kindly made available to me a critical edition of Scot's Latin translation of Averroes's Comment 58 on De caelo, ii. 10, prepared by F. J. Carmody (to be published with a critical apparatus edited by R. Arnzen in a volume under the general supervision of G. Endress in the series Averrois opera). I am also grateful to G. Endress for informing me that Ibn al-Bitriq's Arabic version of De caelo (which is quoted by Averroes) has calā na&hdotwi bucdihi (Aristotle, Kitāb al-samā wa-l-cālam, ed. by cAbd al-Ra&hdotmán Badawi (Cairo, 1961), 267), and Michael Scot (correctly) translated it as secundum suam remotionem.

Endress G. , “Averroes' De caelo, Ibn Rushd's cosmology in his Commentaries on Aristotle's On the heavens”, Arabic sciences and philosophy, v (1995), 9–49 (espec. p. 43). See Averroes, long commentary on De caelo, Comment 58, in Aristotle and Averroes, op. cit. (ref. 10), ed. 1495–96, 212vb–213ra; and ed. 1562, 136M–137H. The original Arabic of Averroes's Comment 58 on De caelo does not survive. Oresme (fourteenth century) translated De caelo into French and commented on it. In the case of the passage in De caelo, ii. 10, he translates the words “in proportion” but comments that With this theory, it is not necessary to assume that the planets' being lower than, or farther from, the sovereign heaven causes their proper movement to be fast proportionally or in a precise proportion (proporcionelment ou selonc proporcionalité precise), for, in addition, we must consider and compensate for the force (la puissance) and will or desire of the motive power (N. Oresme, Le livre du ciel et du monde, ed. by A. D. Menut and A. J. Denomy; transl. with an introd. by A. D. Menut (Madison, 1968), 491). In this context Oresme noticed another problem with Aristotle's version of the distance-period relationship, namely, the Sun, Venus, and Mercury all have the same period of revolution around the Earth. He suggested that the astronomers in Aristotle's time may have placed all three of them in the same heaven (ciel), but he did not cite any ancient source for this view (see Comment [4]). I have no reason to believe that Copernicus was aware of this passage; it is cited to indicate that scholars in the late Middle Ages were concerned with the interpretation of De caelo, ii. 10, and it seems likely that Oresme was familiar with the Latin version of Averroes's commentary (see ref. 24, below).

On Copernicus in Italy, see Rose, op. cit. (ref. 3), 118–42.

Achillini A. , De orbibus (Bologna, 1498; reprinted Venice, 1545); idem, Opera omnia … (Venice, 1545), 34vb and 35ra: I am most grateful to Peter Barker for finding these passages and translating them. See also Barker P. , “Copernicus and the critics of Ptolemy”, Journal for the history of astronomy, xxx (1999), 343–58 (espec. p. 349).

Genequand C. , Ibn Rushd's Metaphysics: A translation with introduction of Ibn Rushd's Commentary on Aristotle's Metaphysics, Book Lām (Leiden, 1986), 172.

For the Greek text, see Heiberg J. L. , Simplicii in Aristotelis De caelo Commentaria (Berlin, 1894), 471; transl. in Bowen, op. cit. (ref. 9).

Swerdlow , op. cit. (ref. 1), 440.

Swerdlow , op. cit. (ref. 1), 465.

Swerdlow , op. cit. (ref. 1), 466.

Duncan , op. cit. (ref. 2), 197 (slightly modified).

Rosen , op. cit. (ref. 3), 355, claims that Copernicus depended on B. Zamberti's Latin translation of Euclid (Venice, 1505); cf. Ver Eecke P. , Euclide: L'optique et la catoptrique (Paris, 1959), p. xxxvii.

Neugebauer , op. cit. (ref. 1), 92; cf. Van Helden A. , Measuring the universe (Chicago, 1985), 42–44.

These periods of Saturn and Jupiter are given in Copernicus, op. cit. (ref. 3), i.10, f. 9r.

According to Rosen, op. cit. (ref. 3), 355–6, information on Proclus's treatise was available to Copernicus in Valla, op. cit. (ref. 3), Book XVIII, chap. 23, sig. gg 6v; cf. Swerdlow and Neugebauer, op. cit. (ref. 1), 475.

Copernicus , op. cit. (ref. 3), 7v-8r; cf. Endress, op. cit. (ref. 11), 43: “Ibn Rushd [Averroes] declares that the conditions underlying Aristotle's exposition [in De caelo, ii.10] are reconciliable only with ‘the opinion of those who say that the Sun is below Mercury and Venus, and not above …’” (Sed hoc non currit secundum ordinem nisi secundum opinionem dicentis quod sol est sub Mercurio et Venere et non supra). The quotation is from Averroes's Comment 58 on De caelo, ii.10, in Aristotle and Averroes, op. cit. (ref. 10), ed. 1495–96, 212vb; ed. 1562, 136M. Averroes seems to think that the velocity of the Sun is greater than the velocities of Venus and Mercury but, even so, the Sun may lie above them, for its power may surpass theirs (Et secundum hoc non est inconveniens quod motus Solis sit velocior motu Mercurij et Veneris, quamvis sit supra; et hoc erit propter abundantiam suae potentiae supra potentiam earum: Ibid., ed. 1495–96, 213ra; ed. 1562, 137G). To be sure, his remark is based on a false assumption (where ‘velocity’ refers to mean angular velocity, i.e., 360° divided by the period), for the geocentric periods of the Sun, Venus, and Mercury are exactly the same. Later in De revolutionibus, i.10, Copernicus cited an observation, reported by Averroes in his “Paraphrase of Ptolemy”, of Venus and Mercury being seen as spots on the Sun, from which it had been concluded that their orbs are both closer to the Earth than the orb of the Sun. This text, Averroes's Epitome of the Almagest, is only extant in an unpublished Hebrew translation, and Copernicus probably depended on a citation of it by G. Pico della Mirandola in his Disputationes in astrologiam (Bologna, 1495), x.4: See Goldstein B. R. , “Some medieval reports of Venus and Mercury transits”, Centaurus, xiv (1969), 49–59 (espec. pp. 53–58); and Lay J. , ”L'Abrégé de l'Almageste, un inédit d'Averroès en version hébraïque”, Arabie sciences and philosophy, vi (1996), 23–61. The view of al-Biṭrūjī would have been available to Copernicus in Regiomontanus's Epytoma Joannis de monte regio In almagestum Ptolemaei (Venice, 1496), ix.l: See Shank M. , “The ‘Notes on al-Biṭrūjī’ attributed to Regiomontanus: Second thoughts”, Journal for the history of astronomy, xxiii (1992), 15–30 (espec. pp. 17 and 27 n. 17). The earliest Latin edition of al-Biṭrūjī's Astronomy was published in Venice in 1531, and it was a translation from the Hebrew version, rather than from the original Arabic: See Goldstein B. R. , Al-Biṭrūjī: On the principles of astronomy (2 vols, New Haven, 1971), i, 3.

On these gaps, see Rheticus G. J. , Narratio prima (Gdansk, 1540); for a modern edition, see Georgii Joachimi Rhetici Narratio prima, ed. and transl. by Hugonnard-Roche H. (Wroclaw and Warsaw, 1982), p. 60, line 101 (Latin), p. 113 (French). In contrast to Rheticus's passing remark, Kepler described these gaps in detail and recognised that they were significant: See Kepler, transl. by Duncan, op. cit. (ref. 2), 63–65. Cf. Van Helden, op. cit. (ref. 21), 44.

This passage is quoted in Latin in Eastwood B. S. , “Kepler as historian of science: Precursors of Copernican heliocentrism according to De revolutionibus, I, 10”, Proceedings of the American Philosophical Society, cxxvi (1982), 367–94 (espec. p. 369). The translation, however, is mine. Cf. Martianus Capella, De nuptiis Philologiae et Mercurii (Vicenza, 1499). For a nuanced approach to the heliocentrism of Martianus Capella and its reception in the ninth century, see now Eastwood B. S. , “Johannes Scottus Eriugena, Sun-centred planets, and Carolingian astronomy”, Journal for the history of astronomy, xxxii (2001), 281–324 (espec. p. 295).

For the Latin text, see Vitruvius , On architecture, ed. by Granger F. (2 vols, Cambridge, Mass., 1934), 216; transl. by Barker P. .

See Eastwood , op. cit. (ref. 26), 383ff.

Rheticus , ed. by Hugonnard-Roche H. , op. cit. (ref. 25), 55.

Eastwood , op. cit. (ref. 26), 394.

Jardine N. , The birth of history and philosophy of science: Kepler's A defence of Tycho against Ursus (Cambridge, 1984), 197–207.

According to Almagest, ix.3; Toomer, op. cit. (ref. 2), 424: For Venus, 5 returns take place in about 8 years. Then 8 · 365;15d/5 ≈ 584d.

Kepler , op. cit. (ref. 2), Plate 1, after f. 18; transl. by Duncan, 227 (Annotations to the plates); cf. Smart W. M. , Text-book on spherical astronomy, 5th edn (Cambridge, 1962), 422.

Swerdlow , op. cit. (ref. 1), 440, 490; Copernicus, op. cit. (ref. 3), 9v. Rheticus repeated the value that appears in De revolutionibus, but Maestlin corrected it to 7 ½ months in his edition of Rheticus's Narratio prima (1596): See Rheticus, ed. and transl. by Hugonnard-Roche H. op. cit. (ref. 25), 113, 169.

According to Almagest, ix.3; Toomer, op. cit. (ref. 2), 424: For Mercury, 145 returns take place in about 46 years. Then 46–365; 15d= 16801;30d; and 16801;30d/145 ≈ 115;52 days or about 116days.

Kepler , op. cit. (ref. 2), Plate 1, after f. 18; transl. by Duncan, 227 (Annotations to the plates); cf. Smart, op. cit. (ref. 33), 422.

Swerdlow , op. cit. (ref. 1), 499; Copernicus, op. cit. (ref. 3), 9v.

Vitruvius , Ten books on architecture, transl. by Rowland Ingrid D. , commentary and illustrations by Thomas Noble Howe, with additional commentary by Ingrid D. Rowland and Michael J. Dewar (New York, 1999), 111 (slightly modified). Cf. L. Victruvii Pollionis ad Cesarem Augustum De architectura liber primus[-decimus] (Rome, 1482).

Cf. Swerdlow and Neugebauer, op. cit. (ref. 1), 572–3, and the discussion on p. 58.