Copernicus's Path to His Cosmology: An Attempted Reconstruction

Swerdlow Noel 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), 423–511, on p. 437.

Kennedy E. S. Roberts Victor , “The planetary theories of Ibn al-Shatir”, Isis 1 (1959), 227–35.

Wilson Curtis , “Rheticus, Ravetz, and the ‘necessity’ of Copernicus's innovation”, in The Copernican achievement , ed. by Westman R. S. (Berkeley, 1975), 17–39, p. 32.

See for example footnote P. 177:12 that appears on page 400 of Nicholas Copernicus, On the revolutions, translation and commentary by Edward Rosen (Baltimore, 1992).

The papers in which this controversy erupted are: Rosen Edward , “Copernicus' spheres and epicycles”, Archives internationales d'histoire des sciences , xxv (1975), 82–92; Swerdlow Noel M. , “Pseudodoxia Copernicana: Or, enquiries into the very many received tenets and commonly received truths, mostly concerning spheres”, ibid. , xxvi (1976), 108–58; and Rosen , “Reply to N. Swerdlow”, ibid. , xxvi (1976), 301–4.

Swerdlow , “Commentariolus” (ref. 1), first on p. 426 and then in many other places.

The notes are reproduced on p. 428 and transcribed on p. 429 of Swerdlow, “Commentariolus” (ref. 1).

It might conceivably signify the 60th part, as “M” does in the second half of the notes.

I find it convenient to use the word ‘heliocentric’ to apply to any system in which the planets revolve around the Sun, whether the system is geostatic (Tychonic) or heliostatic (Copernican).

Goldstein Bernard R. , “Copernicus and the origin of his heliocentric system”, Journal for the history of astronomy , xxxiii (2002), 219–35.

Rheticus's Narratio prima (in Rosen Edward , Three Copernican treatises (New York, 1959), 136–7.

Gingerich Owen , “The search for a plenum universe”, Selection 8 of The eye of heaven (New York, 1993), 145. This article was reprinted from Great ideas today 1979, edited by Adler M. J. van Doren J. (Chicago, 1979).

“Copernicus' translation of Theophylactus Simocatta”, in Copernicus Nicholas , Minor works , translation and commentary by Edward Rosen with the assistance of Erna Hilfstein (Baltimore and London, 1992), 27.

Copernicus , Minor works (ref. 13), 24. It is conceivable that the alternating movements of brother Sun might refer to the seasonal changes in declination, but I think this is unlikely since these changes in declination are perfectly well explained by the Ptolemaic system.

Margolis Howard , “Tycho's illusion”, Nature , cccxcii (1998), 857, pointed out how curious it was that Tycho did not see the possibility.

Goldstein , “Origin” (ref. 10), 222.

Quoted in Dreyer J. L. E. , A history of astronomy from Thales to Kepler (New York, 1953), 127.

Rosen , Three Copernican treatises (ref. 11), 136.

This and all following quotations from On the revolutions are from Edward Rosen's translation (Baltimore and London, 1992).

See Swerdlow N. M. Neugebauer O. , Mathematical astronomy in Copernicus's De revolutionibus (New York, 1984), 300, 356ff, 384ff.

Reinhold wrote at the bottom of the title page of his copy of On the revolutions , “The axiom of astronomy: Celestial motion is uniform and circular, or composed of uniform and circular motions”. See Gingerich Owen , An annotated census of Copernicus' De revolutionibus (Nuremburg, 1543 and Basel, 1566) (Leiden, 2002), Fig. 45 on p. 269.

See Gingerich Owen , “Heliocentrism as model and as reality”, Selection 16 of Eye of heaven (ref. 12), 291–4. This paper was reprinted from Proceedings of the American Philosophical Society , cxvii (1973), 513–22.

For example, as Gingerich points out in “The search for a plenum universe” (ref. 12), 146, Tycho Brahe complained that “Copernicus's theory … gives to the Earth, this lazy, sluggish body unfit for motion, a movement as fast as the aetherial torches”. The Earth is “unfit for motion” because heavy things naturally fall to the centre, so it is natural for the heavy Earth to remain stationary at the centre of the universe. For a translation of the relevant chapter in Tycho Brahe, De mundi aetherei recentioribus phaenomenis, see Boas M. Hall Rupert A. , Occasional notes of the Royal Astronomical Society , iii (1959), 253–63.

When Mephistopheles says in Marlowe's Doctor Faustus, “Why, this is hell, nor am I out of it”, Marlowe was giving voice to the ubiquitarian doctrine which had been condemned by the Catholic church. Even today, according to the article on hell in the online version of the Catholic encyclopedia, “theologians generally accept the opinion that hell is really within the Earth”.

See Gingerich Owen , “‘Crisis’ versus aesthetic in the Copernican revolution”, Selection 11 of Eye of heaven (ref. 12), 200. This paper was reprinted from Vistas in astronomy , xvii (1975), 85–95.

Heller Henry , “Copernican ideas in sixteenth century France”, Renaissance and Reformation , xx (1996), 5–26.

Howard Margolis has suggested that the discovery of a continent on the backside of the Earth induced a change from two separate spheres of earth and water to a single terraqueous sphere, and this was a “shock to entrenched intuition”. See chap. 3 of It started with Copernicus (New York, 2002), and the more detailed account in chaps. 10 and 11 of Patterns, thinking and cognition (Chicago, 1987).

See Colie Rosalie L. , Paradoxia epidemica: The Renaissance tradition of paradox (Princeton, 1966).

For a good summary of Hermetism, see chap. 5 of Shumaker Wayne , The occult sciences in the Renaissance: A study in intellectual patterns (Berkeley, 1972).

See Eisenstein Elizabeth , The printing revolution of modern Europe (Cambridge, 1983), especially chap. 7, or the unabridged account in The printing press as an agent of change (Cambridge, 1979).

“Merit would from now on be measured very largely by one's inventiveness; or rather inventiveness was beginning to become a condition sine qua non of merit”, Bramley Serge , Leonardo: The artist and the man (London, 1994), 77.

The portrait of Copernicus by Tobias Stimmer on the astronomical clock in Strasbourg cathedral was, according to the inscription, “a true likeness from his own self-portrait”. This has led scholars to conjecture that the portrait in Torun city hall may be the actual self-portrait by Copernicus himself, or else another copy of that self-portrait. See Gingerich Owen , The book nobody read (New York, 2004), which reproduces Tobias Stimmer's portrait and the Torun portrait side by side as Plates 2 and 3. The Torun portrait not only shows great technical skill, but also displays a sensitivity to the inner psychology of the sitter that is reminiscent of portraits by Giovanni Bellini, for example his The Doge Loredano (National Gallery, London), which as it happens was painted at about the same time as Copernicus was in Padua. If the Torun portrait is really by Copernicus himself, then he showed a brilliant mastery of the art of portraiture. Another “portrait, which Copernicus is said to have painted with his own hand” was used by Tycho Brahe for his image in The instruments of awakened astronomy (Wandsbeck, 1598). See pp. 331–2 of the third edn of Rosen, Three Copernican treatises (New York, 1971). In addition, the portrait of Copernicus now in Lidzbark castle is sometimes said to be a copy of a self-portrait.

Swerdlow , “Commentariolus” (ref. 1), 434–5.

On p. 123 of the illuminating if polemical essay on circles, orbs, and spheres in the long footnote 326 of Copernicus, Minor works (ref. 13).

This was, however, true only of Copernicus's longitude mechanisms; his latitude mechanisms did not even preserve uniform motions. The problem of the origin of Copernicus's latitude mechanisms deserves a detailed study.

Gingerich , Census (ref. 21), 154.

Gingerich , Census (ref. 21), 136.

Kennedy Roberts , “Planetary theories of Ibn al-Shatir” (ref. 2).

Grant Edward , Planets, stars, and orbs: The medieval cosmos, 1200–1687 (Cambridge, 1994), in chap. 14, “Are the heavens composed of hard orbs or a fluid substance?”.

Elementary astronomy textbooks explain the redshifts of receding galaxies as Doppler shifts, despite its being obvious to anyone who has gone through the general relativistic derivation that cosmic redshifts are not determined by the velocity of the galaxies and have nothing to do with the Doppler effect. Instead, they are a direct measure of the expansion factor of the universe: The space between us and a galaxy of redshift z has expanded by a factor 1 + z between the time the galaxy's light was emitted and the time it arrives at our telescope. It is possible to imagine a universe which is not expanding either at the time of emission or at the time of arrival, but expands by a factor of three between these times; the Doppler shift would be zero but the cosmic redshift would be 3 – 1 = 2.

Monographs on orthogonal polynomials and texts on special functions derive recurrence relations connecting orthogonal polynomials of degrees n + 1, n, and n — 1. But few explain that orthogonal polynomials should be generated using recurrence relations; this is too ‘obvious’ to be worth mentioning. I have seen an eminent astrophysicist generate Legendre polynomials in a FORTRAN program by the clumsy process of expanding them as a series of powers which, because powers are highly ill-conditioned, results in the loss of many significant digits.

Rosen , “Copernicus' spheres and epicycles” (ref. 5), 85. Ironically, this quotation appears two pages after Rosen has castigated Swerdlow for making the distinction between a geometrical circle and the corresponding solid sphere. Rosen reproduces of Swerdlow's Figure 12 in “Commentariolus” (ref. 1) which demonstrates the distinction, and calls it a “highly constipated conception”. Swerdlow's figure is not only admirably clear, it also fulfils exactly the condition that Pedro Nunes demanded of Copernicus's lunar epicycles.

Copernicus , Minor works (ref. 13), note 169 on p. 107.