A Critique of the Arguments for Maragha Influence on Copernicus

According to Swerdlow, for example, “the relation between the models is so close that independent discovery by Copernicus is all but impossible” (Noel M. Swerdlow, “Copernicus, Nicolaus (1473–1543)”, in Wilbur Applebaum (ed.), Encyclopedia of the Scientific Revolution (New York and London, 2005), 254–63, p. 259), so that “the question therefore is not whether, but when, where, and in what form he learned of Maragha theory” (Noel M. Swerdlow and Otto Neugebauer, Mathematical astronomy in Copernicus's De revolutionibus (New York and Berlin, 1984), 47). See the latter reference also for a brief census of the similarities. Swerdlow's position is embraced by influential scholars such as Ragep and Saliba, relying in large part on the technical work of Swerdlow. Swerdlow's account is now considered near-definitive, but the argument did not originate with him. Kennedy, to take another example, also surveys the similarities and concludes in the same way: “In the face of this array of similarities, the conclusion seems inescapable that, somehow or other, Copernicus was strongly influenced by the work of these people” (E. S. Kennedy, “Late medieval planetary theory”, Isis, lvii (1966), 365–78, p. 377).

Swerdlow and Neugebauer, op. cit. (ref. 1), 41–3. This concerns works that were available in Latin translation. All parties agree that Copernicus most likely could not read Arabic.

The only substantial exception is the existence of a manuscript translation into Greek of a treatise containing the so-called Tusi couple, which in itself is only a small part of the corpus Copernicus supposedly copied. See Swerdlow and Neugebauer, op. cit. (ref. 1), pp. 48–9. The Tusi couple also appears in two works by Italian contemporaries of Copernicus, though without evidence of a link to either Islamic sources or to Copernicus. See Mario di Bono, “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 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), 423–512, pp. 434–5.

Almagest, IX.2, Toomer's translation.

Ragep F. J. , “Copernicus and his Islamic predecessors: Some historical remarks”, History of science, xlv (2007), 65–81, p. 70.

Ragep , op. cit. (ref. 6), 71. This is effectively a stronger formulation of an argument suggested more tentatively by George Saliba, “Arabic astronomy and Copernicus”, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, i (1984), 73–87, p. 86.

Swerdlow Noel M. , “Copernicus and astrology, with an appendix of translations of primary sources”, Perspectives on science, xx (2012), 352–78, p. 372.

Hartner Willy , “Copernicus, the man, the work, and its history”, Proceedings of the American Philosophical Society, cxvii (1973), 413–22, p. 421.

Ragep , op. cit. (ref. 6), 68.

Saliba George , Islamic science and the making of the European Renaissance (Cambridge, MA, 2007), 200–1.

Saliba George , “Greek astronomy and the medieval Arabic tradition”, American scientist, xc (2002), 360–7, p. 367.

Saliba , op. cit. (ref. 11), 205.

Saliba , op. cit. (ref. 11), 196.

See Roberts Victor , “The solar and lunar theory of Ibn ash-Shatir: A pre-Copernican Copernican model”, Isis, xlviii (1957), 428–32, p. 431, and Swerdlow and Neugebauer, op. cit. (ref. 1), 544, and, for the Commentariolus, Swerdlow, op. cit. (ref. 4), 454–61.

Swerdlow , op. cit. (ref. 4), 461.

Swerdlow and Neugebauer, op. cit. (ref. 1), 63. See this work as well as Swerdlow, op. cit. (ref. 4), and Otto Neugebauer, “On the planetary theory of Copernicus”, Vistas in astronomy, x (1968), 89–103, for demonstrations of the equivalences and near-equivalences of the various models.

Swerdlow , op. cit. (ref. 4), 504.

Saliba , op. cit. (ref. 11), 207.

Swerdlow , op. cit. (ref. 4), 503.

Swerdlow , op. cit. (ref. 4), 504. Italics in the original.

For these computations we have implemented Copernicus's Mercury model ( Swerdlow , op. cit. (ref. 4), 499–500, 503) in complex polar form by the formula ( 9.4 − 29 60 cos ( 2 α ) ) e 2 π i t / 88 + ( 1 + 41 60 ) e 2 π i t / 88 e − 2 π i t / 88 + ( 34 60 ) e 2 π i t / 88 e − 2 π i t / 88 e 4 π i α where α is the angular distance of the Earth from Mercury's apsis, and t is a time variable counted in days. This gives the position of Mercury as a complex number in a coordinate system where the Earth moves on a circle of radius 25 centred at the origin, and the apsis line of Mercury is the positive real axis. The products of multiple complex exponentials in the latter terms capture the fact that epicycles rotate along with the major circles they are attached to, in addition to their own rotation. The cosine term is the radius correction; discarding it gives the uncorrected model. Figure 6 plots the orbit for a fixed α and all possible values of t.

Almagest, IX.8–9. Cf. Swerdlow, op. cit. (ref. 4), 505–9, Swerdlow and Neugebauer, op. cit. (ref. 1), 422, Willy Hartner, “Ptolemy, Azarquiel, Ibn al-Shatir, and Copernicus on Mercury: A study of parameters”, Archives internationales d'histoire des sciences, xxiv (1974), 5–25.

Swerdlow , op. cit. (ref. 4), 504. Italics in the original.