Section 2
Whose Science is Arabic Science in Renaissance Europe?
© 1999
George Saliba
Columbia University
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Arabic/Islamic Science and the Renaissance Science in Italy
Between the years 1957 and 1984, Otto Neugebauer, Edward Kennedy, Willy Hartner, Noel Swerdlow, and the present author, as well as others, have managed to determine that the mathematical edifice of Copernican astronomy could not have been built, as it was finally built, by just using the mathematical information available in such classical Greek mathematical and astronomical works as Euclid’s Elements and Ptolemy’s Almagest.2 What was needed, and was in fact deployed by Copernicus (1473-1543) himself, was the addition of two new mathematical theorems. Both of those theorems were first produced some three centuries before Copernicus and were used by astronomers working in the Islamic world for the express purpose to reform Greek astronomy.3
In other words, the research that has accumulated over the last forty odd years has  now established that the mathematical basis of Copernican astronomy was mainly inherited from the Greek sources -- mostly from Euclid and Ptolemy -- except for two important theorems that were added later on by astronomers working within the Islamic world and writing mainly in Arabic. Furthermore, the same recent findings have now demonstrated the context within which these theorems first appeared in the Arabic astronomical sources, namely, the context of criticizing and reformulating the Greek astronomical tradition.  We also know that the works containing such theorems were mostly produced during the thirteenth century and thereafter.  Accounts of such works have been detailed in various publications.4
As far as we know, none of the Arabic works containing these theorems had ever been translated into Latin, at least not translated in the same fashion we know of other Arabic scientific sources that were translated during the earlier Middle Ages. Hence there is no easy explanation of direct transmission in the same fashion one could account for the transmission of Avicenna’s medical works into Latin or Averroes’s philosophical works or the hundreds of other Arabic texts that could be easily documented as having been "translated" into Latin during the great well known (but least studied) translation period of Arabic texts during the early Middle Ages.  Moreover, we also know that those same theorems, once produced, they continued to be extensively used, in various shapes and forms, in Arabic astronomical texts well before the time of Copernicus, contemporaneously with him and even after his time.5
Finally, it is now better understood that the Arabic astronomical texts that deployed these theorems formed part of a rather well established tradition in Arabic astronomy whose purpose was to criticize, object to, and create alternatives to the inherited Greek astronomy rather than preserve it, tinker with it, and deliver it to Europe during the Arabic Latin translations of the Middle Ages as is so often repeated. That much is already well known and has been relatively well established by the research of the last forty years or so.



Now, when we remember that Copernican astronomy itself gave us such concepts as the "Copernican Revolution", a concept that was so brilliantly expounded by Thomas Kuhn in his book with the same title,6 and that the "Copernican Revolution" crystallized in itself the spirit of science during the Renaissance, then it is not difficult to imagine why this overlapping between the mathematical astronomy of Copernicus and the mathematical astronomy of the Arabic-writing astronomers who preceded him, or rather that blurring of the borders between Arabic and Copernican astronomies, would become extremely interesting. But before pursuing the implications of that intersection any further it is very important to devote a few words to the very core of this intersection, namely, the two theorems in question in order to demonstrate the level of sophistication involved, the level of integration these theorems enjoyed within Copernican astronomy itself, and the level to which such evidence can indeed blur the borders as was stated above.


The first theorem is now called the Tusi Couple (slides 1&2). It takes its name from the famous astronomer and polymath, Nasir al-Din al-Tusi (d. 1274) who first proposed it in 1247,7 (slides 3&4) and later formalized and proved it in 1259/60 (slide 5). In essence the theorem simply stipulates that if we take two spheres, one of them twice the size of the other, and place them in such a way that the smaller sphere is inner tangent at one point to the larger sphere, then if we allow the larger sphere to move in place at any speed and allow the smaller sphere to move also in place, but in the opposite direction, at twice that speed, then the original point of tangency on the circumference of the smaller sphere would oscillate back and forth along the diameter of the larger sphere. In much more general and philosophical terms, the theorem states that linear motion could be derived from circular uniform motion and vice versa, with all that this new formulation implies for the general framework of Aristotelian categorization of celestial versus sublunar motion.
As it is now evident, the same theorem appears again in the works of Copernicus, in the sixteenth century, and is deployed to solve the same problems that it was used to solve in the Arabic sources where it was first conceived.
(6&7) In a seminal article, written in the early seventies, the late German historian of science Willy Hartner pushed the discussion yet another step further. He drew attention to the fact that even the geometric points employed in the diagram (slides 6&7) preserved in the Copernican works were phonetically identical to the same geometric points used in the diagram employed by Tusi three centuries earlier. In effect, he noticed that where the Arabic diagram has a geometric point designated with the alphabetic letter "Alef" the Copernican diagram would have the corresponding point marked with the phonetically equivalent letter "A", where the Arabic has "Ba’" the Copernican diagram would have "B", and so on. That much about the Tusi Couple has been already known since the early seventies.
(8&9) The second theorem is slightly more subtle, but just as simple. I have so far dubbed it as the ‘Urdi Lemma (slides 8&9), also after the name of Mu’ayyad al-Din al-‘Urdi (d. 1266) who first proposed it sometime before 1250, as I have established somewhere else.8 The same theorem appears once more in the works of Copernicus to serve, in his astronomical construction, again exactly the same purposes it had served in the works of ‘Urdi about three centuries earlier. The only difference is that in the work of ‘Urdi, the theorem is consciously introduced as a new theorem and provided with a full formal mathematical proof, while in the works of Copernicus it was taken for granted and thus left without any such proof.
(10&11) Because of its relative neglect in the works of Copernicus it later became the subject of a correspondence between Kepler and his teacher Maestlin, where Kepler asked his teacher specifically about this theorem in Copernicus’s astronomy and the reason why it was not proven. In a 1973 article (slides 10&11), Anthony Grafton, of Princeton University, has elegantly demonstrated how Maestlin supplied the proof to the theorem in his answer to his student Kepler.9
For the purposes of highlighting the contours of the blurred borders between the world of Islam and Renaissance Europe, it should be emphasized at this point that those two theorems leave no doubt about their functionality within Copernican astronomy. They are organically embedded within that astronomy, so much so, that it would be inconceivable to extract them and still leave the mathematical edifice of Copernican astronomy intact. It has also been demonstrated in the technical literature dealing with Copernican and Arabic astronomy that those two theorems which were employed by Copernicus were not only technically the same as the ones which were first proposed and proven in the Arabic astronomical works some three centuries earlier, but that they had served the same astronomical and mathematical functions in building the greater edifice of both Islamic and Copernican astronomy. Furthermore, they were both used in the context of creating alternatives to Greek astronomy.
Such similarities could not go unnoticed. And by themselves they cry out for explanation. If seen only as manifestations of transmission of scientific ideas across cultural lines, they constitute indisputable facts that give rise to all sorts of problems that have to do with the nature of creativity in science, cultural and social settings that produce a certain kind of science and not another, and most importantly point to a possible direction of motion of scientific ideas from the lands of Islam to Europe at the surprisingly late date of the European Renaissance.  All such issues go way beyond the commonly accepted "narrative" of the history of science, and the history of western science in particular. Furthermore, they indicate very clearly the futility of cultural borders, and invite the consideration of the blurred borders at least in as far as the production of such science was concerned.
One should quickly point out that we are talking here on the level of technical mathematical theorems, used to construct mathematical models that would have predictive powers in accounting for the position of planets in both the Copernican "system" as well as the Arabic/Islamic/Ptolemaic "system". There is no talk at this point of heliocentrism, the concept commonly stressed in Copernican astronomy. But one should also equally hasten to say that Copernican heliocentrism is itself stressed (in a hindsight fashion) at the expense of the mathematical foundations of Copernican astronomy, foundations that Copernicus developed and used before he took the last step of displacing the center of the universe from the earth to the sun. One should also add at this point that in mathematical terms heliocentrism can be accomplished just by reversing the direction of the last vector connecting the earth to the sun. The rest of the mathematics involved in both types of astronomical systems could then remain the same.  That fact was well known to pre-Copernican astronomers, and notably to someone like the polymath Biruni (d. c. 1049), and was dismissed as a philosophical problem and not an astronomical / mathematical one per se.
It may be useful to stress here as well that this shift in the Copernican system from the earth to the sun makes no cosmological sense at the time of Copernicus, particularly because there was no theory of universal gravitation to account for the cosmological viability of such a system. There are several works discussing the issue of heliocentrism in Copernican astronomy and the reason it was formulated the way it was, but as far as I know there is no bold attempt to confront the issue of its cosmological non-viability in light of the unavailability of a theory of universal gravitation to hold it together.10
With the same mathematics, the same observations, more or less, astronomers working within the Islamic world could account for the planetary positions just as well as Copernicus could do, or even Ptolemy for that matter, despite the fact that the astronomers of the Islamic world continued to work within the cosmologically earth-centered Aristotelian system which was perfectly defensible for their time. The central problem for them had nothing to do with the issue of heliocentrism, rather it had to do with issues related to the lack of the inner consistency of Greek astronomy. By that I mean that they were seeking mathematical constructions that did not exhibit by their very definition a contradiction with the physical realities they were supposed to represent, as was clearly done in the defunct Ptolemaic astronomy.
(12) Neither the astronomers working in the Islamic domain, nor Copernicus himself, as it seems from his introduction to his earliest astronomical work the Commentariolus (slide 12), would lay great emphasis on the issue of heliocentrism.11 Instead, the context and the problems within which such discussions were shaped had very much to do with the adequacy of the Ptolemaic system to represent the coherent Aristotelian cosmological universe. The discussion of heliocentrism would become important later on. At this stage, i.e. before the sixteenth century, the problem was that of physical and mathematical inconsistencies just mentioned that were embedded within the inherited Ptolemaic astronomy. Both Copernicus and his predecessors in the Islamic world were attempting to remove those inconsistencies, which included among other things such famous problems as the equant circles that became the subject of complaint by astronomers working on both sides of the Mediterranean. It is those equant circles that were clearly underlined in the Copernican introduction to the Commentariolus. It is those circles that also implied that the Ptolemaic system indeed harbored a physical world view that was not consistent with the mathematical models that were used to describe that world as was just said. The problem was then: How else to represent the real physical celestial world surrounding us?
The discovery that such solutions to the Ptolemaic predicament were being vigorously pursued in both the Islamic world first and then in the works of Copernicus ignited some sparks over the last forty years or so, and framed the question in terms of contacts between the world of Islam and Europe or in terms of the influence of one on the other as the most commonly used terminology would put it. The possibility of the permeability of borders, or the blurring just mentioned, has not yet been directly raised. 
Indeed, when one looks at this issue from the perspective of blurred borders, then the possibility of the mobility of ideas similar to the ones expressed in these two theorems becomes in itself very intriguing. For it clearly has serious implications for the autonomy of the Renaissance scientific tradition or the Arabic/Islamic scientific tradition, and even has further implications for the concept of "local" versus "world" or "universal" science as these terms are currently used to delineate cultural boundaries in some instances and to obliterate them in others.12
When framed in terms of transmission of Arabic science to the west or the influence of the Arabic science on western science, it becomes easy to imagine why the most important research that is currently pursued in the history of Arabic and Renaissance astronomy has to do with the route through which those two theorems could have reached Copernicus. For the question is no longer raised as to whether or not Copernicus was aware of the works of his Islamic predecessors, but "when, where and in what form" he learned of them, as was most recently put by Swerdlow and Neugebauer in their now-classic work on the mathematical astronomy of Copernicus.13
(13&14) In that pursuit, and during the seventies, O. Neugebauer had already established one possible route for one of those theorems.14 He had found in a Greek Byzantine manuscript (slides 13-14), the first of the two theorems, the one now known as the Tusi Couple, and had determined that the Greek manuscript containing that theorem was brought to Italy after the fall of Constantinople in the year 1453. The obvious implication is that, once in Italy, this very same Greek manuscript or an account of its contents could have come to the attention of Copernicus who was a frequent visitor and a resident in northern Italy towards the end of the fifteenth and beginning of the sixteenth centuries.
The problematic implied in the approach of the transmission of scientific ideas from the Islamic world to Europe, when raised at this point with respect to those two theorems, leads one to realize that it plays havoc with the commonly accepted assumptions that governed the discussion for the last forty years or so. First, there is no concrete evidence that Copernicus himself could read Arabic in order to benefit directly from the research that was still going on in the Islamic civilization, nor to benefit from the Arabic texts that were produced by that civilization and contained such theorems. Second, there is no concrete evidence either that such Arabic works were ever translated into Latin, the language that is well known that Copernicus could read and write. Furthermore, it is known that Copernicus could read Greek, for he was in every respect a well educated "Renaissance" scientist, and it is well known that he lived, on and off, and studied in northern Italy for a period of about ten years. Then the likelihood of his coming across the specific Greek manuscript uncovered by Neugebauer which also contained among other things the Tusi Couple was at least thought to be plausible, or so was implied by Neugebauer then and later stated slightly more forcefully by Swerdlow and Neugebauer. In fact, Swerdlow and Neugebauer made the bold statement in their joint work that such Arabic theorems were indeed circulating in Italy around the year 1500 and thus implying that Copernicus could have learned about them from his contacts in Italy.15
In the interest of illustrating once more the futility of cultural science studies one should focus on the problems raised by the very same Greek Byzantine manuscript which was uncovered by Neugebauer and wonder whether it should be thought of as part of the "Greek" science that contained no such theorem in its history or as part of "Islamic/Arabic" science where the theorem, that was "translated" back into Greek and copied in this manuscript, was first formulated. The author of the Byzantine Greek manuscript is supposed to have gone to the lands of Islam towards the beginning of the fourteenth century for the express purpose of learning specifically the latest findings in Islamic/Arabic astronomy and to report back into Greek the results of his fact-finding mission. Among those results was the Tusi Couple under discussion. In this context it is perfectly legitimate to ask: whose science is the science contained in that late Greek Byzantine manuscript?
On the level of documenting the transmission of ideas through written texts, the discovery of the Tusi Couple in a Greek manuscript that could have been accessible to Copernicus accounts fairly well for the possible transmission of that theorem through the Greek route. The second theorem, however, has not yet had the similar fortune, as it has not yet been documented in a similar Greek source, and its possible transmission from Arabic to Copernicus still awaits further verification.
2. Full references to these works can now be found in the bibliography appended to George Saliba’s A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam, NYU Press, 1994, pp. 307-317.

3. One of those theorems was the subject of an article by Willy Hartner, "Copernicus, the Man, the Work, and its History," Proceedings of the American Philosophical Society, vol. 117 (1973), pp. 413-422, and the second was discussed in George Saliba, "Arabic Astronomy and Copernicus," Zeitschrift fur Geschichte der Arabisch-Islamischen Wissenschaften, Vol. 1 (1984), pp. 73-87, now reprinted in Saliba, A History of Arabic Astronomy, pp. 291-305.

4. A good number of those publications are now listed in the bibliography appended to Saliba, A History of Arabic Astronomy.

5. Most of the astronomical works that were completed between the eleventh and the fifteenth centuries that were surveyed in Saliba, A History of Arabic Astronomy use one or both of these theorems. To those one should add the works of Khafri (d. 1550) in which both theorems were used. See G. Saliba, "A Sixteenth-Century Arabic Critique of Ptolemaic Astronomy: The Work of Shams al-Din al-Khafri," Journal for the History of Astronomy, vol. 25 (1994), pp. 15-38; idem, "A Redeployment of Mathematics in a Sixteenth-Century Arabic Critique of Ptolemaic Astronomy," in Perspectives arabes et médiévales sur la tradition scientifique et philosophique grecque. Actes du Colloque de la S.I.H.S.P.A.I. (Société internationale d’histoire des sciences et de la philosophie arabe et islamique). Paris, 31 mars-3 avril 1993, A. Hasnawi, A. Elamrani-Jamal, M. Aouad (éd.), Peeters, 1997, pp. 105-122.

6. Thomas Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, with Foreword by James Conant, originally published by Harvard University Press, Cambridge, 1957, and then by Vintage Book, NY, 1957.

7. George Saliba, "The Role of the Almagest Commentaries in Mediæval Arabic Astronomy: A Preliminary Survey of Tusi’s Redaction of Ptolemy’s Almagest," Archives internationales  d’histoire des sciences, vol. 37 (1987), p.3-20, now reprinted in Saliba, A History of Arabic Astronomy, pp. 143-160, esp. 152-154.

8. See George Saliba The Astronomical Work of Mu’ayyad al-Din al-‘Urdi: A Thirteenth-Century Reform of Ptolemaic Astronomy, Center for Arab Unity Studies, Beirut, 1990, English introduction, pp. 31-36.

9. See Anthony Grafton, "Michael Maestlin’s Account of Copernican Planetary Theory," Proceedings of the American Philosophical Society, vol. 117 (1973), pp. 523-552.

10. The beginnings of such an attempt to analyze the relationship between Copernican astronomy and Ptolemaic astronomy from that perspective were already tentatively advanced by the late Derek J. de S. Price, "Contra-Copernicus: A Critical Re-estimation of the Mathematical Planetary Theory of Ptolemy, Copernicus and Kepler," in Critical Problems in the History of Science, ed. Marshal Clagett, University of Wisconsin Press, Madison, 1969, pp. 197-216. But that attempt still did not confront the issue raised here, namely, how could Copernicus have hoped to convince his contemporaries that his system had any cosmological validity when he did not have a theory of universal gravitation to account for the centrality of the sun. See also, Owen Gingerich, "From Copernicus to Kepler: Heliocentrism as Model and as Reality," Proceedings of the American Philosophical Society, vol. 117 (1973), pp. 513-522.

11. For the Introduction of the Commentariolus, see, Noel Swerdlow, "The Derivation and First Draft of Copernicus’s Planetary Theory: A Translation of the Commentariolus with Commentary," Proceedings of the American Philosophical Society, vol., 117 (1973) 423-512, [Herafter Commentariolus].  Here Copernicus says: "Nevertheless, the theories concerning these matters that have been put forth far and wide by Ptolemy and most others, although they correspond numerically [with the apparent motions], also seemed quite doubtful, for these theories were inadequate unless they also envisioned certain equant circles, on account of which it appeared that the planet never moves with uniform velocity either in its deferent sphere or with respect to its proper center.  Therefore a theory of this kind seemed neither perfect enough nor sufficiently in accordance with reason." p. 434.  For the discussion of the concerns of Copernicus regarding this point in particular, see Noel Swerdlow and Otto Neugebauer in Mathematical Astronomy in Copernicus’s De Revolutionibus, Springer, NY, 1984, pp. 55ff.

12. The issue of locality versus essence as applied to the characterization of Arabic science has been treated most recently by Sabra, A.I., "Situating Arabic Science: Locality versus Essence," Isis, vol. 87 (1996), pp. 645-670. And more recently the Princeton workshop of March 1999 was subtitled "Local Science in World Context."

13. Swerdlow and Neugebauer, Mathematical Astronomy, p. 47.

14. See Otto Neugebauer, A History of Ancient Mathematical Astronomy [HAMA], Springer, NY, 1975, p. 1035 and plate IX.

15. Swerdlow and Neugebauer, Mathematical Astronomy, pp. 41-54.

Section 3: Role of Arabic Scientific Manuscripts in European Libraries
Section 4: Travelers in Search of Science (Large file)
Section 5: Conclusion
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