In effect, then, the plane of the epicycle seemed to perform a seesawing motion of its own, as the position of the epicycle changed by the motion of the deferent. Since this kind of motion never completed a full circle, it was obviously deemed to be in the same category as the oscillating prosneusis of the moon. And thus it was as far as it could be from the uniform circular motion, which Aristotle would have required, since only full circular motions were the natural motions of the simple element ether of which all the celestial bodies were composed.
No word from Ptolemy in this regard. And although he had claimed that he was adhering to the Aristotelian cosmology, he still behaved in the same fashion as he did before when such violations were committed. That is, he still made no effort to explain them away as one would have expected. Instead, he invited the reader to imagine that the tips of the epicyclic diameters could be attached to pairs of "small circles." Those circles could be placed perpendicular to the plane of the deferent. And as the tips of the diameters moved along those "small circles" the resulting oscillating motions would produce the seesawing effects that were needed. He then had a problem synchronizing those motions of the tips of the diameters along their "small circles" and the motions of the epicycles themselves along their deferents, since the deferents themselves were eccentric, as we have already seen. To solve the problem, he resorted once more to the assumption that the diameter tips too had their own form of equants just like those of the other larger models of the planets, since they did not seem to be partaking of a uniform circular motion around their own centers.
Now, even if one could accept the motion of the diameter tips for the purposes of producing the seesawing effect, which was in turn "justifiably" required by the observations, one could easily see that any such "unnatural" seesawing would also create a wobbling effect that would interfere with the longitudinal component for which much pain was suffered when it was computed in the first place.
It was this specific feature of the latitudinal motion in the Ptolemaic model that led the thirteenth-century astronomer Naṣīr al-Dīn al-Ṭūsī (d. 1274) to proclaim, in his Taḥrīr al-majisṭī in 1247, that Ptolemy's speech was indeed intolerable, or, in his own polite words, beyond what was permitted in the craft (khārij 'an al-ṣinā'a).[254]
The latitudinal motion of the second group, the lower planets Mercury and Venus, did not fare any better in this regard. For them the inclination of the carrying plane itself varied as the epicycle moved along its circumference. One should always remember that those planes were supposed to be the equators of physical spheres, the only bodies capable of generating such motions in an Aristotelian universe. In the case of Venus, when the epicycle was at the northernmost end of the inclined plane that plane itself tilted northwards and the epicycle on its northern edge tilted away from the carrying plane along the eastern edge. But as the epicycle moved to the nodes one of its diameters coincided with the ecliptic, while the other still tilted along the eastern edge. When the epicycle reached the southernmost end, the whole inclined plane tilted in the opposite direction so that its southern end now pointed to the north, and the epicycle still inclined away from it along the eastern edge again. In effect then both the inclined plane as well as the plane of the epicycle itself would undergo the same kind of seesawing motion that was noticed in the model of the upper planets. And here again, the only solution Ptolemy had to offer was to propose the same kind of "small circles" to be attached to the seesawing diameters so that they could be forced to perform the latitude motion. And here again that arrangement would still force the whole plane to wobble and destroy the longitudinal component as before. We just saw what Ṭūsī would say of such an arrangement.
In sum, Ptolemy's models for the movements of the moon and the five planets introduced notions that were not only in violation of the Aristotelian presuppositions, but as we have seen, with the case of the motions in latitude of the planets, included arrangements that also destroyed the longitudinal components that worked rather well on their own. It looked like Ptolemy could not compute any component of the motion without destroying the other. In total exasperation, he ended up confessing that only gods were capable of such perfection, not the mere humans.[255] With this realization, the whole Ptolemaic configuration seems to fall apart, despite the fact that, on the computational level, it seems to have been able to predict the positions of the planets, and can still do, with a rather remarkable accuracy.
The reforms of this astronomy that were to take place in Islamic civilization after the thirteenth century went to great pain to retain that predictive value of Ptolemaic astronomy. But they definitely aimed to reform the conceptual arrangements of the spheres that were supposed to carry out these various motions. Toward the end of the twelfth century, when Averroes had to give his assessment of the Ptolemaic astronomy, an astronomy that was still the norm in his time, he had the following to say: "The science of astronomy of our time contains nothing existent (lays minhu shay'un maujūd), rather the astronomy of our time conforms only to computation, and not to existence (lā li-l-wujūd)."[256]
We have already seen several levels of responses to what was perceived as factual mistakes in the Ptolemaic tradition. Whether it was in simple mistakes in texts, or basic parameters, or even methods of observations, those were attended to and began to be fixed as early as the ninth century. New genres of writings addressing specifically the totality of those Ptolemaic problems, called shukūk, istidrāk, and the like were developed and sophisticated with time, so much so that they became subjects of discussion on their own by people who were not even astronomers by profession.
Serious attention to the philosophical and physical underpinnings of the Ptolemaic edifice, otherwise signaled as model building, and serious attempts to replace the inadequate Ptolemaic models did not begin until the eleventh century. But once it began, almost every serious astronomer felt that he had to take part in the enterprise. In the sequel I will only signal those who made fundamental shifts in the way astronomy was practiced to the neglect of others who kept the discipline alive by supplying the commentaries and the individual modifications that they saw the major shifts required, or simply made use of those shifts to overhaul the then current astronomy in order to incorporate those changes.[257] For example, when the trigonometric functions were introduced into the Islamic scientific tradition, and were perfected after being originally derived from the few functions already known in India, the tendency was to use those functions in any theoretical discussion of astronomy instead of the chord functions that were used in the Almagest and its translations.
It is these kinds of shifts that produced the astronomy that could then be called Arabic/Islamic astronomy, and whose example we hope the other disciplines had followed. In what follows, however, I will pay a special attention to the most subtle shifts that played, in my judgment, a catalytic role in producing other astronomical innovations, and became part of the universal legacy of astronomy. As was already said, I will neglect those who periodically took in those conceptual shifts and integrated them in their works without producing any shifts of their own.
255
In Ptolemy's own words (
256
Averroes,
257
For a full survey of these attempts to create new planetary theories see Saliba, "Planetary Theories" and Saliba "Alternative", already referred to above.