Copernicus and the Critics of Ptolemy

The classic statement of this position is of course: Pierre Duhem ,: Essai sur la notion de théorie physique de Platon d Galilée (Paris, 1908). See also: Peter Barker Bernard R. Goldstein , “Realism and instrumentalism in sixteenth century astronomy: A reappraisal”, Perspectives on science , vi (1998), 232–58.

Goldstein B. R. , The Arabic version of Ptolemy's Planetary Hypotheses, Transactions of the American Philosophical Society , lvii/4 (1967); A. Van Helden , Measuring the universe (Chicago, 1985); Georg Peurbach , Theoricae novae planetarum (Nuremberg, 1472); Aiton E. J. , “Peurbach's Theoricae novae planetarum: A translation with commentary”, Osiris , 2nd ser., iii (1987), 5–43.

Weisheipl J. A. , “Classification of the sciences in medieval thought”, in Nature and motion in the Middle Ages , ed. by Weisheipl J. A. (Washington, D.C., 1985), 203–37.

Sabra A. I. , “The Andalusian revolt against Ptolemaic astronomy: Averroes and al-Biṭtrūjī”, in Transformation and tradition in the sciences , ed. by Mendelsohn E. (Cambridge, 1984), 133–53.

Barker Goldstein , “Realism and instrumentalism” (ref. 1); Lattis J. , Between Copernicus and Galileo: Christopher Clavius and the collapse of Ptolemaic astronomy (Chicago, 1994).

Barker Goldstein , “Realism and instrumentalism” (ref. 1).

The term ‘Averroist’ has long been disputed by Renaissance historians. Like the term ‘Aristotelian’, it would be improper to regard it as designating a single homogeneous school of thought ( Schmitt C. B. , “Towards a reassessment of Renaissance Aristotelialism”, History of science , xi (1973), 159–93). For the purposes of this paper I use the term to apply only to people who explicitly defer to Averroes in matters of natural philosophy, especially the nature of the heavens, the critique of Ptolemaic astronomy and support for homocentric models.

My translation of Copernicus N. , De revolutionibus orbium coelestium (Nuremberg, 1543), iiiR.

de Albertus Brudzewo's Commentariolum super theoricas novas planetarum Georgii Purbachii was based on material presented in courses at Cracow beginning in 1482, and appears to have been completed by 1488. See: Aleksander Birkenmajer , Études d'histoire des sciences en Pologne (Studia copernicana , iv; Warsaw , 1972), 478. For a modern edition see: de Albertus Brudzewo , Commentariolum super theoricas novas planetarum Georgii Purbachii, denuo edendum , ed. by Birkenmajer L. A. (Cracow, 1900). On de Brudzewo's curricular innovations see ibid. , 487–8.

Birkenmajer L. A. (ed.), Albertus de Brudzewo: Commenlariolum super theoricas novas planetarum (ref. 9). For Averroes on the ninth sphere, see pp. 5–6; against eccentrics pp. 25–26. See also Birkenmajer , Études (ref. 9), 622.

Birkemajer L. A. (ed.), Albertus de Brudzewo: Commentariolum super theoricas novas planetarum (ref. 9), 28: “[Huius oppositum COMMENTATOR putabat destruens eccentricos, verum in hoc sentiens] tanquam philosophus, cuius non est nisi motum totius sphaerae considerare, non autem partialis orbis, quod Astronomiae proprium est.”.

De Brudzewo L. A. quotes Richard of Wallingford on the indispensability of epicycles and eccentrics for the treatment of celestial motions by mathematicians, Birkemajer L. A. (ed.), Albertus de Brudzewo: Commentariolum super theoricas novas planetarum (ref. 9), 27: “… sine huiusmodi [cum epicyclis et eccentricis] imaginationibus mathematicis, de stellarum motibus regularis ars tradi non potest….”.

Birkenmajer A. , Studia copernicana , iv (ref. 9), 489.

Brozek Z. P. , “Wojciech de Brudzewo”, in The Cracow Circle of Nicholas Copernicus , ed. by Markowski M. (Cracow, 1973), 61–75, esp. p. 67. Birkenmajer A. , Studia copernicana , iv (ref. 9), 623, dates the De caelo lectures to “Summer semester 1493”.

Birkenmajer L. A. , Albertus de Brudzewo: Commentariolum super theoricas (ref. 9), 55, suggests a further possible connection between de Brudzewo and Copernicus in the parallel wording of passages in the Commentariolum super theoricas (p. 55, text to n. 6, in his edition) and De revolutionibus , Book 4, Chap. 2.I am inclined to accept Birkenmajer's claim that this establishes a direct intellectual link between the two figures, although it does not establish the date.

Leopold Prowe , Nicolaus Coppernicus (Berlin, 1883), i, 236–46; Rose P. L. , The Italian renaissance of mathematics (Geneva, 1975), 119–20.

Michael H. Shank , “Regiomontanus and homocentric astronomy”, Journal for the history of astronomy , xxix (1998), 157–66; Noel M. Swerdlow , “Regiomontanus's concentric sphere models for the Sun and Moon”, Journal for the history of astronomy , xxx (1999), 1–23.

Ernst Zinner , Regiomontanus: His life and work , transl. by Ezra Brown (Amsterdam, 1990), 153–4. Cf. Rose , Italian renaissance of mathematics (ref. 16), 120.

For a detailed discussion see Swerdlow , “Regiomontanus's concentric sphere models for the Sun and Moon” (ref. 17). On al-Biṭrūjī see Bernard R. Goldstein , Al-Biṭrūjī: On the principles of astronomy (2 vols, New Haven, 1971).

Michael H. Shank , abstract of “Regiomontanus and homocentric astronomy”, Bulletin of the American Astronomical Society , xiv (1982), 897.

Shank , however, points out that the Epitome, Book 5, Proposition 22, states the objection to Ptolemy's lunar model that it requires an apparent size four times larger at perigee than at apogee. This argument could be used in favour of a homocentric model. It was also used by Copernicus to support his own lunar model, in which he greatly decreased the variation in distance: Swerdlow N. M. Neugebauer O. , Mathematical astronomy in Copernicus's De revolutionibus (2 vols, Berlin, 1984), 240ff. Copernicus's reduction in the variation in lunar distance was cited in 1545 by Gemma Frisius as a reason to prefer Copernicus's model over that of Ptolemy: Bernard R. Goldstein , “Remarks on Gemma Frisius's De radio astronomico et geometrico”, in From ancient omens to statistical mechanics , ed. by Berggren J.L. Goldstein B. R. (Copenhagen, 1987), 167–79, p. 172. Copernicus's lunar model was also singled out for special praise by Melanchthon . See below and Barker P. , “Religion and natural philosophy in the Lutheran response to Copernicus”, in Rethinking the Scientific Revolution , ed. by Osler M. J. (Cambridge, in press).

On the Defence of Theon against George of Trebizond see especially Shank , “Regiomontanus and homocentric astronomy” (ref. 17), 161–3. Swerdlow , “Regiomontanus's concentric sphere models for the Sun and Moon” (ref. 17), pp. 2 & 5, sounds a note of caution on the solar and lunar models of 1460: Regiomontanus removed what may have been references to them from the Tabulae primi mobilis completed no later than 1471.

Alessandro Achillini , De orbibus libri quatuor (Bologna, 1498), cited below in the Opera omnia edition of 1545. For the epithet “second Aristotle” see e.g. “Achillini, Alessandro” in Encyclopedia Britannica , 11th edition (Cambridge, 1910), i, 144.

Alessandro Achillini , Opera omnia in unum collecta: De intelligentia, De orbibus, etc. (Venice, 1545), f. 29r, col. 2–f. 29v, col. 2.

Ibid. , f. 29r: Motus quos ponit Ptolomaeus fundantur super duo fundamenta quae non conveniunt scientiae naturali exce[n]tricum et epiciclum, quorum utrumque est falsum…. Contra quos ponitur haec conclusio. Nullam corpus caeleste est excentricum, et est conclusio Averrois 12 Metaphysics, co. 45. excentricum autem et epiciclum dicere est extra naturam. Epiciclum autem est impossibile ut sit omnino, et 2 De Caelo co. 32. Ex hoc apparet quod dicunt mathematici de excentricis est impossibile. idem co. 35. et in suo libro Almagesti….

Ibid. , f. 29v, cols 1–2.

Ibid. , f. 30v, col. 1, theorica for fixed stars; f. 31v, col. 2, theorica for Saturn; f. 32r, col. 2, theoricae for Jupiter, Mars, Sun, Venus; f. 32v, col. 1, theorica for Mercury, col. 2, Moon —eclipses, etc.

di Bono M. , La sfere omocentriche di Giovan Battista Amico nell'astronomia del Cinquencento (Genoa, 1990), 62–65, and idem, “Copernicus, Amico, Fracastoro and Tusi's device: Observations on the use and transmission of a model”, Journal for the history of astronomy , xxvi (1995), 133–54, n. 72.

Franceschini P. , “Alessandro Achillini”, in Dictionary of scientific biography , i, 46–47.

On Novara's treatise De mora nati, see Zinner , Regiomontanus (ref. 18), 153–4.

Rashdall H. , The universities of Europe in the Middle Ages (3 vols, ed. by Powicke F. M. Emden A. B. , Oxford, 1936): “By the Bologna statutes the doctor is required to read the ‘glosses’ immediately after the text” (i, 218). “[T]he new Aristotle — the study of physics, metaphysics and moral philosophy — was in no way an essential or usual preliminary for a legal education…”, but medical students were expected to study astrology, and the university supported a chair in that field (i, 234). Note that the legal faculty was completely separate from the faculties of Arts and Medicine in Italian universities (i, 241), making Copernicus's straddling of subjects even more surprising.

Jacopo Zabarella , De rebus naturalibus libri XXX (Venice, 1590), quoted in Randall J. H. The School of Padua and the emergence of modem science (Padua, 1961), 77, n. 12 & text: Fuit Averrois sententia … animam rationalem, quae ab Averroe vocatur intellectus possibilis, … est intelligentia omnium infima, cui assignata sit tota humana species tanquam proprius, et ille aequator orbis….

Randall , School of Padua (ref. 32), 89, makes a persuasive case that Pomponazzi was trained by the de Francesco Thomist Neritone , and not by the Averroist Nicholas Vernia, as suggested by Pine M. , “Pietro Pomponazzi”, in Dictionary of scientific biography , xi, 71–74, p. 71.

Randall , The School of Padua (ref. 32); Lohr C. , “The sixteenth century transformation of Aristotelian natural philosophy”, in Aristotelismus und Renaissance , ed. by Kessler E. (Weisbaden, 1988), 89–99, pp. 90–91.

Thorndike L. , “The education of Joachim Cureus at Wittenberg, Padua and Bologna 1554–1558”, in Thorndike L. , University records and life in the Middle Ages (New York, 1944), 373–6, esp. pp. 374, 375. Thorndike translates an original from 1601. Evidence elsewhere in the same book supports the idea that this may give us an indication of university life in Copernicus's time: The curriculum in Italian universities seems to have changed very slowly during the early modern period. Bologna was still using the Almagest, the Epitome of the Almagest and Peurbach's Theoricae novae as late as the 1640s ( ibid. , 396).

Randall , School of Padua (ref. 32), 90 & n. 35.

Giovanni Battista Amico , De motibus corporum coelestium (Venice, 1536); Swerdlow N. M. , “Aristotelian planetary theory in the Renaissance: Giovanni Battista Amico's homocentric spheres”, Journal for the history of astronomy , iii (1972), 36–48; Girolamo Fracastoro , Homocentrica (Venice, 1538). On Tusi couples see especially Ragep F. J. , “Two versions of the Tusi couple”, in From the deferent to the equant , ed. by King D. A. Saliba G. (New York, 1987), 329–56. Compare di Bono M. ,“Copernicus, Amico, Fracastoro and Tusi's device: Observations on the use and transmission of a model”, Journal for the history of astronomy , xxvi (1995), 133–54.

Swerdlow , “Aristotelian planetary theory in the Renaissance” (ref. 37), 431.

Ragep , “Two versions of the Tusi couple”, and di Bono , “Copernicus, Amico, Fracastoro and Tusi's device” (ref. 37).

On Tusi couples in the Commentariolus see Swerdlow N. 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), 423–512, and di Bono , “Copernicus, Amico, Fracastoro and Tusi's device” (ref. 37), 95. Compare Copernicus, De revolutionibus , Book 3, Chap. 4. Although Copernicus demonstrates that the difference between arcs (in the spherical versions) and chords (in the planar circular version) is negligible (Book 3, Chap. 5), in di Bono's opinion ( op. cit , 141), only the planar form appears in De revolutionibus.

The possible independence of Amico Fracastoro is discussed in di Bono , “Copernicus, Amico, Fracastoro and Tusi's device” (ref. 37), 148–9.

Swerdlow Neugebauer , Mathematical astronomy in Copernicus's De Revolutionibus (ref. 21), 41–48, esp. p. 47, suggest transmission by means of a Byzantine version of an Arabic original. A new possibility has recently been suggested by Jerzy Dobrzycki Richard L. Kremer (“Peurbach and Maragha astronomy? The ephemerides of Johannes Angelus and their implications”, Journal for the history of astronomy , xxvii (1996), 187–237), who propose that Maragha models may have reached Johannes Angelus, and perhaps Copernicus, through Vienna, and specifically through the work of Peurbach. Given the close association of Peurbach with Regiomontanus, further evidence in support of this suggestion would also tend to strengthen support for a line of transmission for other astronomical information from Regiomontanus, through Novara to Copernicus.

Melanchthon P. , Initia doctrina physicae (Wittenberg, 1549); in Melanchthon P. , Corpus Reformatorum, ed. by Bretschneider C. G. , xiii (Halle, 1846; reprinted New York, 1963). For Melanchthon's views on orbs see Barker Goldstein , “Realism and instrumentalism in sixteenth century astronomy” (ref. 1). On Melanchthon , Reinhold and their successors see Barker , “The role of religion in the Lutheran response to Copernicus” (ref. 21).

Lattis , Between Copernicus and Galileo (ref. 5). On Clavius's response to the Averroists see pp. 79ff. and pp. 91–94. On Copernicus see esp. chap. 5.

I would like to thank Bernard R. Goldstein , and also Ronald Schleifer Renzo Baldasso Maureen McCormick and the other members of the Spring 1999 Professional Writing seminar at the University of Oklahoma, for helpful suggestions.