It is possible to say that Ptolemy saw the astronomical universe in four different ways: It was either a universe completely composed of Aristotelian spheres that could be described with the same language that was used in the Planetary Hypotheses, or a complementary world that was formed of those same spheres and represented by more precise predictive mathematical models as was done in the Almagest, or that it was a world that was already determined and its behavior tabulated as was done in the Handy Tables, or a world that was constantly at the mercy of the revolving celestial spheres that governed the world of change in the sublunar region in which we live, as was done in the Tetrabiblos.
For astronomers working in the Islamic civilization, the universe of the Handy Tables did not present much challenge, as it was a matter of fixing the mistakes of those Handy Tables by fresh observations whenever it was a matter of determining the positions of planets for any time and place. New parameters could do that, as was in fact done by generations of zīj writers who simply continued to update the Handy Tables. At times they added to them newer concepts that were not known in the Greek tradition that required tables of their own, such as tables for the visibility of the moon, or tables for prayer times, or qibla directions, etc., that were necessitated by the new religion of Islam and would not even occur to someone like Ptolemy. In such cases the newly established Islamic requirement of finding the best time and location for lunar visibility owed its inspiration to a religious practice rather than a scientific curiosity or astronomical need. And it is in such instances that religious thought would give rise to scientific thought and science could become a handmaiden of religion, as we shall see below.
The second Ptolemaic description of the world, that which was reflected in the Tetrabiblos, was quickly found to be way too general for use by the practicing astrologers. For although the Tetrabiblos gave a fairly sophisticated analysis of the manner in which the Aristotelian spheres and planets exerted their influence on the sublunar region, it did not offer detailed instructions on how to translate that theoretical analysis into practical horoscopes that could answer particular questions at specific times. For that reason more specific books had to be developed in order to make up for those shortcomings. Bīrūnī's book on the Elements of Astrology is a masterpiece in that regard,[240] as are the books of the various astrologers who attempted a more direct approach to the subject like the Introduction to Astrology of Abū Mā'shar.[241]
But the Ptolemaic books that caused the greatest amount of problems for the astronomers of the Islamic civilization were the Planetary Hypotheses and the Almagest. For although those two books were complementary to one another, yet they were mutually exclusive when it came to accounting for the Aristotelian cosmology in a more systematic fashion. From that perspective the Planetary Hypotheses spoke directly to a system of physical spheres, more or less in closer agreement with the Aristotelian spheres, while the Almagest spoke of circles representing spheres, and thus only implicitly acknowledged the Aristotelian spheres. Yet, both books spoke of physical impossibilities such as equants and the like. It was those impossibilities and absurdities that contradicted the Aristotelian cosmology that were found most objectionable.
It is not that Astronomers working in the Islamic civilization were enamored by Aristotelian cosmology and wanted to save it at any cost.[242] Rather it was that they saw in those two books clear indications of the Aristotelian assumptions about the composition of the universe and its constituent parts, and yet could not see the descriptive representations of that universe, as was done in the Almagest, really doing justice to the science of astronomy itself. When people read those two books, and they obviously read them together, as we have already mentioned at various occasions before, or when they read carefully the underlying assumptions as expressed in the Almagest too seriously, what they saw was a field that had accepted a set of Aristotelian cosmological premises, but went ahead and spoke about those premises in a language that contradicted their very essence. For instance, they saw Ptolemy speak about Aristotelian spheres as the constituent elements of the universe, and then turned around and represented those spheres with mathematical spheres whose properties would deprive them of their very sphericity. It was these kinds of fundamental contradictions that were thought of as detracting from the scientific basis of astronomy, and under no condition could serious astronomers accept those contradictions.
In what follows I only highlight the main features of these absurdities, and follow that with a description of innovative approaches that were taken by the astronomers of the Islamic civilization in order to emend, whenever possible, or create alternatives to the imported Ptolemaic astronomy.[243]
In the case of the sun, Ptolemy noted that if the observer were really located at the center of the Aristotelian universe, as the Aristotelian cosmology would require, then we would have routinely equal days the whole year round, we would have no seasons, and the sun would repeat its path around us day after day. But the observed reality was not like that. To account for that reality, Ptolemy first determined the basic parameters, like the length of a solar year, and then went ahead and proposed one of two solutions for the actual motion of the sun. He stipulated that the sun was either carried by an eccentric sphere, whose center did not coincide with the center of the Earth, as Aristotle would have wanted to insist, or that it was carried by another much smaller sphere — called epicycle — which itself was in turn carried by another sphere that was concentric with the Earth (figure 4.1).
In Book III of the Almagest, Ptolemy made sure first that both alternatives could still account for the observations well enough, and quickly resorted to the previous work of Apollonius (c. 200 B.C.) which in fact proved that both of these descriptions of motion could be represented by configurations that were mathematically equivalent in every respect. One did not have to chose, therefore, between them, if the purpose was only that of accounting for the observations.[244] In his own words "the mathematician's task and goal ought to be to show all the heavenly phenomena being reproduced by uniform circular motions,[245] and that the tabular form most appropriate and suited to this task is one which separates the individual uniform motions from the non- uniform [anomalistic] motion which [only] seems to take place, and is [in fact] due to the circular models; the apparent places of the bodies are then displayed by the combination of these two motions into one."[246]
Despite the fact that the actual motion of the sun could be represented in tabular form, both in terms of mean motion as well as in anomalisitic one, the problem still resided in the type of motions of the spheres that accounted for the observed motions. Obviously, Ptolemy's insistence on uniform motion here is undeniable. For he could not at the same time adhere to Aristotelian cosmology and yet allow any of the spheres to move at a varying speed as it pleased. And in case one forgets, in Book III, 3 of the Almagest, he made this uniform motion the general guiding principle of his astronomy in the following terms: "But first we must make the general point that the rearward displacements of the planets with respect to the heavens are, in every case, just like the motion of the universe in advance, by nature uniform and circular."[247]
239
For brief statements of such problems, see Saliba, "Greek Astronomy" and "Arabic Planetary Theories."
240
Abū al-Raiḥān, Muḥammad b. Aḥmad al-Bīrūnī (1048),
241
Abū Ma'shar al-Balkhī (d. 886),
242
In fact there is much evidence that Aristotelian cosmology was not all that secure in the Islamic domain, as F. Jamil Ragep recently demonstrated in "Ṭūsī and Copernicus: The Earth's Motion in Context" (
243
For a more detailed description of the alternatives that were developed during medieval Islamic times, see G. Saliba, "Arabic Planetary Theories after the Eleventh Century", in