Commentators who came after Shīrāzī continued to draw attention to those consequences, but mostly focused on denying the moment of rest between the two contrary motions, rather than the production of linear motion as a result of circular motion. In the same vein, Galileo does the same thing and uses the very same Ṭūsī Couple, that he had learned from Copernicus's De Revolutionibus, III,4, to disprove the Aristotelian notion of a moment of rest between two opposite motions.[284]
Only Khafrī tried to raise the issue once more from a slightly different perspective. While he agreed with Shīrāzī and others that the circular motion of the Ṭūsī Couple did in fact produce linear motion, nevertheless that linear motion itself was not as uniform as the circular motion. His concern was that the point of tangency, which moved linearly along the diameter of the larger sphere of the Ṭūsī Couple, did not in fact move at constant speed as the circular motion that caused it did. In his usual mathematical acumen and insight, his analysis came very close to defining the concepts of limits and of acceleration, but did not do so in the strict sense. He simply said that the linear motion was not the same at all points, and thus wondered if this is the same motion that Aristotle was talking about so that now it was being refuted by the Ṭūsī Couple. In his opinion it was not the same. Thus all that one could say is that the circular motion did indeed produce linear motion, but cannot say that uniform circular motion would produce uniform linear motion.
With the status of the literature that we now have from medieval Islamic times, it is hard to determine if this last aspect of the theorem, which was mainly picked up by Ṭūsī's commentators, had itself initiated any discussions among the astronomers themselves, or whether this discussion crossed over to the philosophers. What seems to be certain is that examples given by one group, such as the example that was given by Abū al-Barakāt al-Baghdādī could easily cross over to the astronomers, with some variation of course.
The variation that was offered by Shīrāzī, however, is of some significance for it seems to connect both aspects of the theorem: its implication for the moment of rest between two contrary motions and its implication for circular motion producing linear motion. By introducing a semi-spherical bowl, rather than the ruler of Baghdādī, Shīrāzī introduced the circular rim, although at varying heights from the base of the inverted bowl. And by allowing the hand to move along the circular rim, it was that motion that produced the linear oscillation of the heavy object.
Although Abū al-Barakāt's example seems to have been the direct ancestor of this problem, all the later astronomers, that I know of, who cited this continuous oscillatory motion, would use a variation on Ṭūsī's Couple to illustrate it, i.e. always staying in the context of the theorem that secured the generation of linear motion from circular motion as the Couple stipulates. And as we just said, it is hard to trace the lines of intersection between the philosophers and the astronomers in this respect so that one can determine who owes what to whom. But what seems to be certain is that the very discussion itself, as it moved from philosophical circles to astronomical ones, and back, demonstrates very clearly the shared interest the two disciplines had in such philosophical issues.
At this point I return to the issue that was raised by Ibn al-Shāṭir again, in order to illustrate once more the direct relationship between astronomy and philosophy. I have already cited the words of Averroes who objected very vehemently to the concepts of epicycles and eccentrics. I also said above that Ibn al-Shāṭir was the only astronomer I knew of who rose to the challenge. By arguing for the permissibility of the epicycles, Ibn al-Shāṭir moved away from arguing about the nature of their motions and focused on the very nature of the Aristotelian celestial world that produced the problem in the first place.
In Ibn al-Shāṭir's view, to assume that the spheres that carried the stars and the planets were all, together with the stars that they carried, made of the same simple element ether, whose very nature exhibited circular motion only, presented a very serious problem when one considered that some of the fixed stars, which were huge indeed, and some were larger than the largest planetary epicycle, emitted light while the sphere that carried them did not. To put it simply, the visible fixed stars were obviously not the same as the invisible sphere that carried them, and thus could not be made of the same element. And if they were, then that element could not be simple. In Ibn al-Shāṭir's words, Aristotle must admit that there is "some composition" (tarkībun mā) in the celestial element. And if this composition is allowed in the celestial realm, as it seems to be by the existence of the fixed stars, then the existence of epicycles could be of the same nature and thus one is allowed to use them.
As for the eccentrics, we have already stated that Ibn al-Shāṭir had accepted that they indeed violated the Aristotelian principles and thus should be avoided at any cost. It is for that reason that all the models that were developed by Ibn al-Shāṭir for planetary motions were all conceived as strictly geocentric models, as we have stated repeatedly before. And thus Ibn al-Shāṭir gave himself the full freedom to use as many epicycles as was necessary to account for all the observable motions. And so did Copernicus after him, who apparently faced the same problem from a slightly different angle when he shifted the center of the universe to the sun.
Whether it was a problem of eccentrics, epicycles, or the nature of celestial motion itself, almost all of the astronomers who were engaged in addressing the conflicting demands of Aristotelian cosmology as against the Ptolemaic formulation of that cosmology were not only blaming Ptolemy for his failures but were also trying to explain the difficulty of understanding the Aristotelian universe. Each in his own way was beginning to make the case against the Aristotelian conception of the universe, and was exposing the inadequacies of that conception. To Ibn al-Shāṭir, for example, the very essence of the definition of the element ether was no longer adequate and had to be changed if one were to make sense of the natural phenomena around us.
Whether Ibn al-Shāṭir, or any of the other astronomers who were engaged in this enterprise had the "right" solution for those problems or not is immaterial at this point. The important fact is that they brought the discussion to the point of collision with the Aristotelian world-view and thus pressed for the need to change it. If modern science is to be understood as an expression of the final collapse of the Aristotelian world-view, then the roots of that collapse have to be sought in those elementary, yet daring steps that were exposing the inadequacies of the view.[285]
As for the intersection between religion and astronomy, and through it the intersection between science and religion, we have already seen that the new astronomy of hay'a was developed in tandem with the religious requirements of early Islam. In a sense this new astronomy could be defined as religiously guided away from astrology. With the pressure from the anti- astrological quarters, usually religious in nature or allied with religious forces, astronomy had to re-orient itself to become more of a discipline that aimed at a phenomenological description of the behavior of the physical world, and steer away from investigating the influences its spheres exert on the sublunar region as astrology would require. Most hay'a texts if not all, would systematically avoid any discussion of the obvious astrological doctrines. For that reason those texts continued to be accepted in the religious circles. One can even go as far as saying that the very discipline of hay'a was itself born within the critiques of the religious circles that frowned upon anyone who sought the guidance of the stars in the same way the astrologers did. Within that context it is not therefore difficult to see that most hay'a writers were also at the same time renowned religious scholars themselves, as we shall soon see.
284
See Galileo's text as cited in Edward Grant, ed.,
285
On the continuity of this "nibbling" at the edges of the Aristotelian universe in the writings of the Islamic astronomers and philosophers, see Ragep, "Ṭūsī and Copernicus" and "Freeing Astronomy."