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cAlīqushjī and Regiomontanus: Eccentric Transformations and Copernican Revolutions

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References

1. 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. Good summaries can be found in Swerdlow N. M., Neugebauer O., Mathematical astronomy in Copernicus's De revolutionibus (2 parts, New York and Berlin, 1984), 54–64, and in Shank M. H., “Regiomontanus on Ptolemy, physical orbs, and astronomical fictionalism”, Perspectives on science, x (2002), 179–207, pp. 184–5.
2. Recently Goldstein B. R. (“Copernicus and the origin of his heliocentric system”, Journal for the history of astronomy, xxxiii (2002), 219–35) has argued that Copernicus's motivation for the heliocentric system arose from his insistence upon the distance-period relationship for the planets and a rejection of Ptolemy's nesting hypothesis, since the latter violated the former for the Sun, Venus, and Mercury. If true, this would make Swerdlow's reconstruction problematic since it depends upon Copernicus's reaching his decision in favour of heliocentrism only after rejecting a proto-Tychonic model that resulted in an intersection of orbs (specifically those of Mars and the Sun), something not allowed in most of ancient and medieval cosmology. For Swerdlow, Copernicus's initial motivation for exploring alternative models had to do with Ptolemy's violations of uniform, circular motion, thus placing him firmly within the tradition of Islamic theoretical astronomy (hay'a). Goldstein's position, though plausible, has little, if any, textual support from the Commentariolus, depending instead upon the much later De revolutionibus. A straightforward reading of the introduction to the Commentariolus, as well as consideration of the considerable space Copernicus devotes in that work to his alternative mathematical models, would seem to indicate that the “equant problem” was foremost in his mind around 1510. But whatever the motivation, Goldstein agrees that the mathematical transformation from a geocentric to heliocentric cosmology would still rely, as argued by Swerdlow, upon the propositions found in Book XII of Regiomontanus's Epitome, which is the subject of the current article.
3. Toomer G. J., Ptolemy's Almagest (New York and Berlin, 1984), 555 (n. 2).
4. Though completed in 1463, the Epitome was first printed in 1496 in Venice, after Regiomontanus's death. For details, see Swerdlow, Neugebauer, op. cit. (ref. 1), 51. Swerdlow has translated Book XII. 1–2 in his op. cit. (ref. 1), 472–5.
5. For Copernicus's references to his sources, or lack thereof, see Swerdlow, op. cit. (ref. 1), 437.
6. Swerdlow, op. cit. (ref. 1), 471.
7. Shank, op. cit. (ref. 1), 185.
8. On Bessarion's role in encouraging the writing of the Epitome, see Swerdlow, Neugebauer, op. cit. (ref. 1), 50–51. It is worth noting that Bessarion was originally from the Black Sea town of Trebizond, which fell to the Ottomans in 1461.
9. Whence the name Qushjī: Kuş (Ottoman: Qūsh) is the Turkish word for falcon or hawk; kuşçu (Ottoman: Qūshjī) is falconer.
10. For accounts of the Samarqand school and observatory, see: Sayili A., The observatory in Islam (Ankara, 1960), 260–89: Kennedy E. S., “The heritage of Ulugh Beg”, in idem, Astronomy and astrology in the medieval Islamic world (Aldershot and Brookfield, VT, 1998), XI; l. Fazlioğlu, “Osmanli felsefe-biliminin arkaplani: Semerkand matematik-astronomi okulu”, Dîvân ilmî araştirmalar, xiv/1 (2003), 1–66; and Saliba G., “Reform of Ptolemaic astronomy at the court of Ulugh Beg”, in Studies in the history of the exact sciences in honour of David Pingree, ed. by Burnett C., et al. (Leiden, 2004), 810–24.
11. For an account of Qushjī's life, see Fazlioğlu L., “Ali Kuşçu”, in Yaşamlart ve yapitlariyla Osmanlilar ansiklopedisi, ed. by Çakiroğlu E. (Istanbul, 1999), i, 216–19 and idem, “Qūshjī”, in Biographical encyclopaedia of astronomers, ed. by Hockey T. (Springer/Kluwer, forthcoming).
12. Ragep F. J., “Kāḍī-zāde Rūmī”, The encyclopaedia of Islam (Leiden, 2004), xii, 502.
13. Kennedy E. S., “A letter of Jamshīd al-Kāshī to his father: Scientific research and personalities at a fifteenth century court”, Orientalia, xxix (1960), 191–213; reprinted in Kennedy E. S., et al., Studies in the Islamic exact sciences (Beirut, 1983), 722–44. Cf. Bagheri M., “A newly found letter of Al-Kāshī on scientific life in Samarkand”, Historia mathematica, xxiv (1997), 241–56.
14. Kennedy E. S., “Ulugh Beg as scientist”, in idem, Astronomy and astrology in the medieval Islamic world (ref. 10), X.
15. Ragep F. J., “Freeing astronomy from philosophy: An aspect of Islamic influence on science”, Osiris, xvi (2001), 49–71 (espec. 61–63).
16. Ibid. and Ragep F. J., “Tūsī and Copernicus: The Earth's motion in context”, Science in context, xiv (2001), 145–63 (espec. 156–7).
17. This work has been edited and translated by Saliba G., “Al-Qushjī's reform of the Ptolemaic model for Mercury”, Arabic sciences and philosophy: A historical journal, iii (1993), 161–203.
18. For an overview, 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.
19. Cf. Toomer, op. cit. (ref. 3), ix.5, 442 and n. 38. For an informed discussion of this passage, see Neugebauer O., A history of ancient mathematical astronomy (3 vols, New York, 1975), i, 149–50.
20. Saliba, op. cit. (ref. 17), 172 (English translation), 194 (Arabic text); I have slightly modified Saliba's translation.
21. Saliba, op. cit. (ref. 17), 166.
22. Fazlioğlu, op. cit. (ref. 11).
23. Swerdlow, op. cit. (ref. 1), 472.
24. Ibid., 475–6 (n. 8).
25. In Ragep, op. cit. (ref. 16), I present evidence indicating a possible connection between Copernicus and his Islamic predecessors (including Qushjī) regarding the question of the Earth's rotation.
26. A possible transmission through Italy has been advanced (Swerdlow, Neugebauer, op. cit. (ref. 1), 47–48, 55). But the role of Bessarion in transmitting materials to Peurbach and Regiomontanus cannot be discounted.
27. For an elaboration of this point, see Ragep F. J., “Copernicus and his Islamic predecessors: Some historical remarks”, Filozofski vestnik, xxv (2004), 125–42.
28. Needless to say, the similarity in orientation of the two diagrams is striking. If one accepts that this is a case of borrowing, one might speculate that the additional epicycle and eccentric in the initial positions in Qushjī's diagram have been removed for visual simplification. One caveat: The Latin lettering does not correspond to the Arabic.
29. Hypothesis translates aşl, which in turn was used to translate the Greek . Both in Greek and in Arabic, the meaning is ‘basis’, especially that upon which something else is constructed. There is no implication of the modern sense of hypothesis, i.e. a tentative theory that needs to be verified. Cf. Toomer, op. cit. (ref. 3), 23–24.
30. See xii. 1 of the Almagest (Toomer, op. cit. (ref. 3), 555).
31. The reference is to al-Tuḥhfa al-Shāhiyya (The royal gift) by Quṭb al-Dīn al-Shīrāzī (1236–1311). The passage in question occurs in bk. ii, ch. 8. The work as a whole has not been edited or printed, but this chapter has been edited and translated by Robert Morrison and will appear in a forthcoming issue of the Journal for the history of Arabic science..
32. Qushjī evidently has the following diagram in mind, which is an adaptation of a diagram that one may find, among other places, in al-Tadhkira fi cilm al-hay'a by Naşīr al-Dīn al-Tūsī (1201–74). (See Ragep F. J., Naṣsīr al-Dīn al-Ṭūsī's memoir on astronomy (2 vols, New York, 1993), i, 138–9.) In the Almagest (xii. 1), Ptolemy had used a single diagram for both the epicyclic and the eccentric models, but Ṭūsī has split them into two separate representations.
A: Apogee; E: Centre of epicycle/eccentric; G: Epicyclic perigee/perigee; HT: Retrograde arc; O: Centre of world.
Qushjī speculates that the reason Ptolemy had denied the possibility of an eccentric for the lower planets was because he thought that, like the upper planets, they would thereupon undergo retrograde motion at opposition to the Sun, which is contrary to observation. Looking at the above diagram, one can see that, indeed, at first glance one might think that the epicyclic model would allow for both the middle of direct motion and retrogradation to occur at conjunction whereas the eccentric model would require the two to occur 180′ apart. This would be the case if one were to assign the same motions to the eccentric models of both the upper and lower planets, namely the concentric deferent moving (west to east) with the motion of the mean Sun while the eccentric moves (east to west) with the motion of the epicyclic anomaly. But as Qushjī shows below, one can adjust the motions appropriately so that an eccentric model will work for the lower planets.
33. For the eccentric model of the upper planets, the mean motion (or motion of centre) is sequential, i.e. in the order of the zodiacal signs, and equal to the Sun's mean motion, while the eccentric motion is counter-sequential and equal to the motion of anomaly (see Pedersen O., A survey of the Almagest (Odense, 1974), 339–40). For the eccentric model of the lower planets that Qushjī describes here, the mean motion (or motion of centre) must be sequential and equal to the sum of the Sun's mean motion and the motion of anomaly; as with the upper planets, the eccentric here moves counter-sequentially and its motion is equal to the motion of anomaly. (See below and figure in text).
34. Referring to the text figure, the equation in the epicyclic model is ∠KES; in the eccentric model, ∠QES..
35. Equator translates “minṭaqa”, which can be used for both an equator on the surface of a sphere and also a parallel “inner” equator, as it is here; see Ragep, op. cit. (ref. 32), ii, 414, 437–8.
36. One would normally expect “motion of the centre”, i.e. of the centre of the epicycle. Perhaps Qushjī felt that since he was dealing with both models simultaneously, “mean motion” was more appropriate.
37. This is so since ∠SET = ∠QMT = ∠GSK = motion of anomaly.
38. The accompanying diagram occurs in all three manuscripts with essentially the same lettering and orientation. (MS L, however, is missing line EK.) It is also reproduced a second time in MS H, f. 132a with the following header: “This figure is in the treatise written by master cAlī Qūshjī to prove that the eccentric hypothesis is possible for the lower planets as it is for the others.”.

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F. Jamil Ragep
University of Oklahoma

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