Islamic Science and the Making of the European Renaissance

3. Encounter with the Greek Scientific Tradition

Like all messages that suffer from the reputation of the messenger, the incoming translations of Greek and Sanskrit texts, that began to be produced toward the end of the Umayyad and beginning of the Abbāsid period, as a result of 'Abd al-Malik's reforms, began to be naturally associated with those classes of people who were now considered outside the bureaucracy of the dīwān, thus foreign to the body politic of the government hierarchy itself. On the opposing side were those who acquired their new jobs by virtue of their mastery of the Arabic language, which was now the new language of the dīwān. The natural allies of the second group were those who had also staked a position for themselves that depended on the mastery of the Arabic language as well. But their dependency was for slightly different purposes. These allies who were mainly religious figures and jurists required the mastery of the Arabic language in order to use it as an authoritative tool that allowed them to master the Qur'ānic text, in the first place, as well as master the other ancillary sciences like the prophetic traditions (ḥadīth), grammar, lexicography, literature, poetry, as well as all disciplines that served the purpose of deriving juridical opinions from such texts. Those two groups: the religious scholars and jurists on one side and the new bureaucrats of the government on the other, whose claims to authority were based on their mastery of the Arabic language, began to be perceived together as one larger group only when they were contrasted with those whose main claim to power was based on their mastery of those "foreign sciences" that were being recently translated, and were naturally from outside the culture. In this context it is easy to see why the early epistemological division between "foreign sciences" and "Islamic sciences" could very quickly gain ground, in this early period and could persist throughout Islamic intellectual history.

Although the translations came from the two main cultural depositories of India and Persia, in the east, and from Hellenistic lands, in the west, the Greek classical tradition soon began to outshine the other competing traditions. We have already seen that some major Sanskrit texts began to be translated during the reign of the second Abbāsid caliph al-Manṣūr (754-775) if not before,[144] some texts on logic even before that,[145] and it has been generally accepted that the Persian and Sanskrit texts, few as they were, were indeed the first to be translated.[146] The fact that the Sanskrit and Persian translations seem to have come first, must mean that members of the Persian-speaking community were the first to arrive at the conscious realization of the need to import "foreign sciences", in order to compete in the new government market. It may also explain the proliferation of rebellions during the first half of the eighth century, all led by Persians who contested the authority of the then decaying Umayyad empire and whose rebellious efforts were finally crowned by the success of the Abbāsid "revolution" in the middle of that century. That revolution was mainly perceived, at first, as an alliance of various factions including several Persian ones, who were by then all dissatisfied with the Umayyads.[147]

It was after the initial successes of this Persian community that the Syriac-speaking community began to follow suite and to commence the translation of the Greek texts into Arabic. For the philosophical and scientific sources, the forerunners of the Syriac translations included, for example, the early attempts of Ibn al-Muqaffa' to translate the Persian texts on logic.[148] One has to assume that at least some other Sanskrit/Persian texts, dealing with medicine and pharmacology, quickly followed suit. And they would have obviously included the attempts of al-Fazārī and Ibn Ṭāriq, who were already mentioned before, to translate the Sanskrit astronomical texts into Arabic and to produce Arabic texts that were modeled after the Sanskrit ones. Those compositions may have also included especially modified Sanskrit texts that allowed their contents to fit the new Arab environment by adjusting, for example, the years of the mean motions into Arab years, meaning Hijra years that are smaller than the solar years by about 11 days each. This conversion task was not a trivial task as we have said before. But we are quite certain that it was in fact accomplished according to the report of al-Nadīm about al-Fazārī when he says that the latter had produced a "zīj 'alā sinīy al-'Arab" (an astronomical table according to Arab years).[149]

From a cultural perspective, and in contrast, the Arabic translations of Greek sources, which were mainly executed by the Syriac-speaking community, were much more comprehensive, and included, besides the pure sciences and medicine, very sophisticated texts on philosophy and logic. Taken as a whole, the Greek philosophical corpus, which was also understood to include such disciplines as medicine, astronomy and mathematics, appeared as a self contained and integrated body of knowledge that could explain many varied phenomena by resorting to an all encompassing philosophical system such as the Aristotelian system. And in all likelihood, this system was found particularly appealing, especially because of its general applicability to various phenomena and because of the interconnectedness of the various parts of the scientific principles embedded into the formulations of that system. Within a few years, that is, in just half a century or so, between 820 and 870, almost all translations shifted, for all practical purposes, from the Persian and Sanskrit, as source languages, to Greek as the preferred language to be tapped on all levels.

The success of the latter translation attempt was unparalleled. It included almost all serious philosophical and scientific Greek texts. And technically speaking, the translations themselves began to be more organized, more systematic, involving teamwork, and at times operated very much like workshops in their own right. When one thinks of someone like Ḥunain b. Isḥāq and his son Isḥāq as well as his nephew Ḥubaish,[150] all involved in similar activities or joint projects during that same period, one can begin to detect the family structure of that activity. One may also anticipate the possible abuse of these activities by monopolizing entrepreneurs, or by patrons who at times wished to control the information those translations were bringing into Islamic civilization. These conditions could also explain why Ḥunain b. Isḥāq almost devoted his full time translating for Banū Mūsā, while he also occupied the formal position of the Caliph's physician, especially during the reign of al-Mutawakkil (847-861).

The monopolizing entrepreneurs did at times include professionals who required translations of specific Greek texts into Syriac rather than Arabic, so that they would at least monopolize the information for a while before the text would eventually be translated into Arabic. We know from Ḥunain's account of the translations of the Galenic books that he had translated some into Syriac for physicians like Jibrā'īl b. Bakhtīshū' ,[151] The same may be true of all the Aristotelian books that were reported by al-Nadīm[152] to have been translated into Syriac as well during this period, or just before. As we already said, the so-called "old translations" (naql qadīm), may have also been part of this competitive attempt at monopolizing information by the Syriac-speaking community.

To those who were not involved in the translation activity themselves, the world looked like it was already governed by two main groups. On the one hand, there were those who possessed the information contained in the "foreign sciences" now understood to be mainly Greek. Those same people were either employed at the highest echelons of the government offices like advisers to the caliphs or were competing for those same jobs from outside the government. On the other hand, there were those who possessed the mastery of the Arabic language and who worked at the lower echelons of the government at the old dīwān jobs but now allied to religious figures mentioned before who also jointly claimed the same sources of power: Arabic linguistic sciences. This intellectual split continued to express itself, as we just saw, in various forms like "foreign" versus "indigenous", "ancient" versus "modern", "rational" versus "traditional", etc., all signifying those two main centers of the new power structures.

In such an environment, and with the affiliations of the people involved in the pursuit of those sciences, it is easy to explain the appearance of such movements as the shu'ūbīya movement, which was widespread during the first half of the ninth century, and which pitted Arab versus non-Arab in almost every field of life. By the ethnic term Arab at this period one should probably understand it to mean an Arabophile as well, or designate people who laid their claim to power through the use of the Arabic language. Anecdote after anecdote relates this sentiment, even when the purpose of the anecdote was purely entertainment. Al-Jāḥiẓ's story, for example, as reported in his book al-Bukhalā',[153] about the Arab physician Asad b. Jānī (before 850) speaks directly to this widespread sentiment. Asad was once told that his medical business was expected to flourish during a plague year, to which he answered that it was no longer possible for someone like him to make a living. When asked for the reason he said: that he was a Muslim— and people always thought, even before he became a physician or he was even born, that Muslims would never succeed in medicine; his name was Asad when it should have been Saliba, Morayel (sic), Yūḥannā or Pīrī; his agnomen (kunya) was Abū al-Ḥārith when it should have been Abū 'Īsā, Abū Zakarīyā, or Abū Ibrāhīm. Moreover, he said, he wore a white cotton cloth, when it should have been a black silk robe. And his diction was Arabic, when it should have been the tongue of the people of Jundīshāpūr.

The competition between Arabs and non-Arabs, and among Muslims, Christians, and Jews, could not have been expressed any better. Furthermore, the anecdote illustrates the clear separation between those who depended on the foreign languages to make a living, like the people of Jundīshāpūr, and those Arabs or Arabophiles who sought to establish their authority through the Arabic Language. The anecdote also illustrates why people like Asad would naturally ally themselves with their co-religionists who also sought their power through the Arabic language.

In that environment we can also understand why even non-Arabs, mainly those of Persian descent, like Sībawaih (765-796), would also attempt to master the Arabic language once they apparently realized that they could not compete in the realm of the "foreign sciences"; the latter were being quickly monopolized by those who knew Greek rather than Persian. Those linguists, although of non-Arab origin but were probably Arabophiles, would eventually ally themselves with the religious sciences as well, and with those who steered away from the proximity of political power, in opposition to those who kept on translating "foreign" sciences into Arabic and getting closer and closer to the person of the caliph himself through the patronage of high ranking bureaucrats. The areas that depended on the acquisition of the foreign sciences, at the highest echelons of government, were the areas that became indispensable to the government as was already mentioned before.

This does not mean that the competition was restricted to people of differing linguistic groups and ethnicities, if one could speak of ethnicities at that time. For we know that the deadly race definitely spread throughout the bureaucracy to include at times people of the same religion and profession as we have seen with the case of Ḥunain b. Isḥāq at the caliphal court of al-Mutawakkil.

In such an environment, it would be natural to expect that any intrusion from the outside would be welcomed by some and immediately rejected by others. And since any imbalance in the available fields of knowledge, now understood as tools to political power, would necessarily mean the loss of livelihood for some and boon to others, as had already happened with the dīwān translations, a fact that was still fresh in people's minds during the eighth and early ninth century. Under those conditions then, everyone concerned would quickly scrutinize the introduction of any new idea. And this scrutiny would be first conducted by the opponents of those who were importing the new idea, or science in this case, and then by its proponents in order to make sure that it could withstand the attacks from the opposing camps. It would not even be unusual to have some of those new incoming ideas also attacked by those who were in the same camp, but who were themselves also competing and jostling for a greater share of power. It was in such an environment that the newly imported Greek sciences were cast.

The importers of Greek astronomy had to make sure that their field was dissociated from astrology, which was religiously frowned upon. In order to accomplish that, it was those very astronomers who succeeded in re-casting their discipline and in creating the new astronomy, which came to be known as 'ilm al-Hay'a and for which there was no Greek equivalent term as such. Once they could shun the discipline of astrology, then the importers of Greek astronomy, as well as the composers of the hay'a texts could simply pose as allies of the religious establishment as well, and could then flourish within that establishment as they brought their work to bear on the religious sciences themselves. This trend explains the creation of the new field of mīqāt[154] toward the beginning of the eleventh century, in addition to the creation of 'ilm al-hay'a itself, as much as it also explains the creation of the mathematical discipline of 'ilm Farā'iḍ around the same period.

In that polarized environment, which survived throughout Islamic history, we can explain the appearance of certain new disciplines and the disappearance of others. We can also detect the flexibility of scientific production when it acclimatized itself to new social conditions. These developments proved to be crucial to the lasting character of Islamic science in general, and were to cast a particular shadow on the developments that took place within the particular field of astronomy, where the brunt of this conflict was focused. And it is for that reason that the reception of the Greek astronomical tradition offers us the best illustrative glimpse of the general conditions the other disciplines must have encountered as well. The emergence of Islamic astronomy as a discipline on its own is very much conditioned by these early labor-pangs the discipline went through and continued to color its developments in the later centuries.

It is easy to see why the seekers of the Greek scientific texts were less vulnerable than those who sought the philosophical ones; or say that their battle was easier to win. In the case of the sciences, especially the exact ones, like mathematics and astronomy, it was easier to detect errors and to prove the superiority of one opinion against another. Only when such disciplines as astrology were included with those sciences, as was done in the Greek tradition, the situation became slightly more complex.

In the purely scientific texts, as we shall soon see, there were those astronomical values in the Greek tradition that could easily be proved wrong. And that in itself could constitute a danger to those who were bringing those sciences into Arabic. For if they were not extra careful to weed out the mistakes, their whole enterprise could easily be denounced. In the case of philosophical ideas the boundaries between true and false were not as sharp, and the domains they covered overlapped dangerously with some of the domains reserved for religious speculation.

While it would be of great scientific significance to find out that Ptolemy's measurement of this or that parameter was wrong and thus needed to be corrected, this very finding would not have any dangerous immediate social implications. But trying to uphold the philosophical idea that the world was eternal as some of the Greek philosophical texts would say would immediately run into problems with the religious circles that were definitely set in their belief in the doctrine of the creation of the world, by a unique God.

By paying attention to such social conditions we can then appreciate the circumstances under which certain ideas were accepted while others were rejected. Those conditions will also shed light on the very process of the importation of the "foreign" sciences and the battles those sciences had to endure. The fact that the proponents of the foreign sciences themselves were extra alert to the kind of science they were importing, and wanted to make sure that this science was free of any blemish, so that it can withstand the attacks we just described, this care could now explain the reason why someone like al-Ḥajjāj b. Maṭar would end up correcting the Ptolemaic text of the Almagest as he was translating it.

In the text of the Almagest [IV, 2], al-Ḥajjāj found Ptolemy's report about the length of the lunar month. In it Ptolemy says that he was simply following Hipparchus who had in turn taken two lunar eclipses that were separated by 126,007 days and 1 hour, during which the moon made 4,267 revolutions. Ptolemy went on to say that if one divided the number of days by the number of revolutions, that is, divided 126,007^d and 1^h by 4,267, one would get the length of the lunar month to be 29 days, 31 minutes, 50 seconds, 8 thirds, 20 fourths (or alternatively written as 29;31,50,8,20^d). In fact if one were to carry out the division, as prescribed by Ptolemy, the answer would not be the one given in the Ptolemaic text, rather it would be 29;31,50,8,9,20^d, which is exactly the number found in the earliest surviving Arabic translation of the Almagest by al-Ḥajjāj.[155]

Remembering that al-Ḥajjāj was apparently conscious of the environment of competition that we just spoke about, he could not afford to have what looked like a mistake in the translation, and took it upon himself to correct the Greek text. Now whether this number was in fact a 'mistake' in the Ptolemaic text or not, a problem that was already confronted by Asger Aaboe almost half a century ago, is immaterial here.[156] The important point to make is that al-Ḥajjāj must have thought that it was a mistake, and thus felt that he had to correct it, so that another more competent translator or astronomer would not point to it and thus belittle his scientific abilities.

The classic narrative could not possibly explain such nuances in the translation process, for it did not pay any attention to the competition generated by 'Abd al-Malik's reforms, nor did it acknowledge the experience gained by the translators of the elementary sciences of the dīwān for a generation or two that could give someone like al-Ḥajjāj the necessary skill to carry out the correction. But with the alternative narrative all such activities become quite natural, and historically understandable.

On the observational side, the competition was not any less severe. We know from early reports that astronomers were eager to correct the astronomical values of the classical Greek tradition, not only because they were probably driven by the same motives as al-Ḥajjāj, i. e. to make sure that the texts they were translating were free of mistakes, but that they could also benefit from the passage of time in order to double-check the Greek astronomical parameters that lend themselves to refinements over time.[157] For example, the Greek value for the motion of precession was taken to be 1°/100 years (or about 0;0,36°/year), as recorded in Ptolemy's Almagest [VII, 2, et passim]. If that were true, it would have meant that during the first half of the ninth century—that is, some 700 years later—the fixed stars, and particularly the star Regulus (α Liones) whose longitude was easy to observe due to its proximity to the ecliptic, would have been displaced in longitude from the position at which they were observed during Ptolemy's time by about 7°. Instead the longitudes varied by as much as 11° during that period, thus necessitating a new value of precession: about 1°/66 years (0;0,54,54°/year), or about 1°/70 years ( 0;0,51°/year), whereas the modern value for this parameter is around 0;0,50°/year.

Once the new value was found, astronomers working during the first half of the ninth century began to use it in their works as was actually done by the Ma'mūn astronomers.[158] Ibn Kathīr al-Farghānī (c. 861), who wrote his summary of astronomy around the same time, however, continued to use the old Ptolemaic value of 1 °/100 years,[159] most likely in an attempt to be true to the Greek tradition. At other times, as in the case of the adoption of the new value for the inclination of the ecliptic, he did not hesitate to abandon the Ptolemaic value and to side with the new observations of his time.

As we have also seen before, the inclination of the ecliptic which was determined by Ptolemy to be 23;51,20° was found to be too large, and the new measurements that took place in Baghdad, sometime during the early part of the ninth century, concluded that it was closer to 23;33°, a value[160] that is still in use today.

These new values must have come as a result of refinements that were obviously applied to both the methods of observations, as we shall soon see, and the types of instruments used for the purpose, as well as the size of those instruments.

Then there was the solar apogee, which was taken to be fixed at 5:30° of Gemini by Ptolemy, and which was also seen to have moved considerably by the ninth century. In fact the motion of this apogee was found to correspond very closely to the precession motion of the fixed stars, and thus by the time it was observed in Baghdad it was found to have moved by some 11°.[161]

All these findings must have been definitely determined by very competent astronomers, at least as competent as Ptolemy if not more so. As a result they force us to raise the very same question that was raised before: Who trained those astronomers to conduct such refined observations and to determine such precise values that have obviously withstood the test of time as we still find them in current use today? The classical narrative would, at this point, fail dramatically to explain this phenomenon. But if we take the implications of 'Abd al-Malik's reforms into consideration, and assume the competition we have been assuming, then it becomes plausible to suggest that this very competition may have generated enough care and seriousness so that each astronomer would try to outsmart the others and continuously keep trying to find better and better values for those basic astronomical parameters.

But the sheer accumulation of so many parameters that were at variance with those reported in the Greek texts must have led to more serious research in early Abbāsid times. For we find that sometime during the first half of the ninth century new methods of observations were suggested in order to avoid the pitfalls of the Greek ones, and in order to improve over the Greek results. People began to discuss the impact of the instruments themselves, as well as the strategies for the observations, all in an attempt to explain the reasons why they were finding results that were certainly different from those that were found by Ptolemy some 700 years earlier.

One of the early challenges to the Ptolemaic observational methods came in that same century, when someone suggested that the position of the solar apogee could be determined by a more refined technique. The new technique involved observing the daily declination of the sun at the midpoints of the seasons, rather than their beginnings as was done by Ptolemy. That is, those ninth-century astronomers understood that Ptolemy's observational strategy, which required that the observations be carried out at the time when the sun would cross the equinoxial and solsticial points, was woefully flawed. And they also understood that this strategy would necessarily lead to the difficulty of determining the daily declination of the sun, say, on a mural quadrant, no matter how big, particularly when the sun was around the solstices. In fact, at those points the sun would not exhibit any appreciable declination and the daily variation in declination would actually be very small. Thus it could not be observed accurately. Those astronomers must have reasoned, therefore, that one would be much better off if he were to observe that declination when the sun was crossing the midpoints of the seasons, that is, the fifteenth degrees of Taurus, Leo, Scorpio, and Aquarius, and where the declinations would be much more apparent. The new method that was used for these observations was dubbed the Fuṣūl method (method of the seasons) on account of its reliance on the midpoints of the seasons as points of observation, in clear contradistinction to the beginnings of the seasons as was done by Ptolemy.

With this shift in observational techniques, and in one full swoop, the new values for the solar apogee, the solar eccentricity, as well as the concomitant value of the maximum solar equation could all be determined at the same time, and to a much higher degree of precision. And so they were, as was reported in the so-called mumtaḥan zīj (Verified astronomical table) that was presumably composed during the reign of al-Ma'mūn (813-833).[162]

All that was happening during the early part of the ninth century, a feat that could not have been accomplished by novices who were just beginning to acquaint themselves with such sophisticated Greek texts that they were translating at the same time. Several generations of earlier translators of elementary sciences must have paved the way for such activities, as the alternative narrative now wishes to propose.

Such activities continued to be performed on regular basis, and methods of observations continued to be checked and double-checked. New research on the types and sizes of instruments must have also been undertaken, and must have continued in the later centuries to constitute a tradition by itself. We have echoes of all this in reports preserved from the tenth century. One copy of such reports has been quoted in the thirteenth-century biobibliographical dictionary, the Ta'rīkh al-ḥukamā' Qifṭī.[163] In it we are told that during the early Buyid times, i.e. during the latter half of the tenth century, the famous astronomer Abū Sahl al-Kūhī (c. 988) was called upon to conduct fresh observations in order to double-check these same values for the solar apogee, the solar eccentricity as well as the maximum equation of the sun. The report went on to say that Abū Sahl preferred to determine the sun's entry into the summer solstice and the autumnal equinox, just as was done by Ptolemy before him. But, more importantly, we are also told that Abū Sahl had a whole group of people present at the time of the observations, including religious scholars, judges, mathematicians, astronomers, the famous bureaucrat Abū Hilāl al-Ṣābi' (d. 1010) as well as other officials. Abū Sahl had all those officials affix their signatures to the report of the observation. The sheer variety in the professions and ranks of the individuals involved can only emphasize the social significance of such activities at that time. But the question remains: Why would Abū Sahl choose the method of Ptolemy, when he should have known that it was already super- ceded by the fuṣūl method more than a century before? Was he trying to "outsmart" Ptolemy by carrying out the very same observation?

Other echoes of the research on better and larger instruments also come to us from the works of al-Khujandī (d. ca. 1000), in which we are told that he attempted to build very large instruments in a continuous bid to get more precise results.[164] Khujandī was supposed to have attempted to build a sextant whose radius was some 20 cubits, and graduated in such a way that it would allow the observer to measure down to minutes of arc rather than degrees.[165]

In later centuries, similar activities continued to be pursued, and instruments continued to be further refined. By the thirteenth century, the same fuṣūl method itself, first invented in the first half of the ninth century, was itself refined as well, and another new method was developed that required solar observations to be taken at only three points on the ecliptic instead of four, and only two of the observations had to be diametrically apart.[166]

Other mistakes that were found in the Almagest were slightly more sophisticated in nature, and were not apparently immediately noticed as the text of the Almagest was first translated into Arabic. Two examples of such mistakes should suffice at this point.

The first of these has to do with a statement made by Ptolemy in connection with the relative apparent sizes of the two luminaries as they affect eclipses.[167] At that point Ptolemy does not only say that the apparent size of the solar disk appears to the observer on the Earth to be just as large as the lunar disk when the moon was at its greatest distance from the Earth, but that it was always so and that it did not exhibit any change in size for the same observer. Of course when the moon was closer to the observer, there was no question of its relative size with respect to the solar disk for then the duration of solar eclipses would settle the point. But the occurrence of annular eclipses, a phenomenon not even mentioned by Ptolemy, would certainly provide a counter example to the Ptolemaic statement. Such annular eclipses could then demonstrate that when the moon was at its farthest distance, its apparent size was still smaller than that of the sun, otherwise the sun would not appear like a ring around the disk of the moon during such annular eclipses. In his Taḥrīr, Ṭūsī (d. 1274) singled that phenomenon out and supplied records of more recent observations that actually documented such annular eclipses.[168] He went on to say further that the apparent solar disk itself was not in fact fixed, as Ptolemy had maintained, but that it changed in size. And that change could be detected by calculations of the various durations of eclipses at various relative positions of the luminaries. The same conclusion was reached a century or so later by Ibn al-Shāṭir (d. 1375) of Damascus, who even went as far as calculating the variations in the apparent size of the same solar disk, and was forced to construct a mathematical model describing the motion of the sun in order to accommodate those fresh calculations that he probably based on his own detailed analysis of eclipses.[169] We shall have occasion to return to the analysis of this construction by Ibn al-Shāṭir when we discuss the alternative solutions that were given to such Ptolemaic problems during Islamic times.

The second example of sophisticated but subtle mistakes that were found in the text of the Almagest involved the mathematical configuration that was described by Ptolemy in connection with the movements of the moon. In that specific configuration, which gave Ptolemy a considerable amount of trouble before he settled on a final version of it [Almagest V, 5-10], Ptolemy had to concoct a crank-type mechanism that could account for the variation in the second equation of the moon from a value of about 5;1°, when the moon was in conjunction or opposition with the sun, to about 7;40°, when the moon was at quadrature from the sun (i.e. some 90° away from the solar mean position). The Ptolemaic mathematical model worked reasonably well when it came to predicting the position of the moon in longitude. But as it was correctly observed by the same Ibn al-Shāṭir the model also "required that the diameter of the Moon should be almost twice as large at quadrature than at the beginning, which is impossible, because it was not seen as such lam yura kadhālika."[170]

Ibn al-Shāṭir was absolutely right in affirming that such a variation in the apparent size of the moon would result from the Ptolemaic model for the lunar motion. And because of his apparent reliance on his own newly conducted observations of eclipses, Ibn al-Shāṭir had to construct an alternative model for the motion of the moon that will also be discussed in the context of the solutions that were developed during Islamic times in opposition to those of Ptolemy.

All of these corrections, new techniques, new solutions, and developed refinements would not have been generated had the astronomers who produced them not read the Ptolemaic astronomical text with a critical spirit. Nearly all of the astronomical parameters that they had encountered in the Almagest, proved fundamentally defective, and a basic program of observation was needed to correct them. What seems to have happened in this early period is exactly that, for we hear of one astronomer after another all attempting to negotiate a way out of the difficulties that the Almagest had confronted them with. The resulting body of literature that they produced in response, whether in treatises devoted to the subject of methods of observation, or in the production of new astronomical tables called mumtaḥan (verified), or the like, could all be regarded as the logical results of that critical approach with which those early astronomers received the Greek scientific masterpieces. At the same time, this new literature could also be seen as a by-product of the clear desire to establish more reliable parameters for the new field of astronomy that was then emerging; parameters that would eventually be far superior to the ones that gave rise to the problems embedded in the Almagest.

Critiques and correction of fundamental parameters and critiques of the methods that produced them were not the only things that led the receiving culture to negotiate the difficulties encountered in the Ptolemaic text. One section of the Almagest, Books VII and VIII, dealt specifically with constellations and descriptions of constituent stars that the receiving culture had some experience with; although it did not seem to have had the comparatively systematic tabulation of such stars. But in this domain we still lack substantial information about the events that took place during this early period. What can be asserted, however, is that some modifications of the Greek text did already take place on the occasion of the various translations themselves, where alternative names were given to constellations either in addition to the ones that were being translated from Greek or to replace them altogether.

By the tenth century, the literature on the fixed stars began to generate two competing traditions of its own: One was directly derivative from the Greek, and was thus recorded in astronomical handbooks and the like, and of course perpetuated in the various translations of the Almagest and the books that derived from them. While the other tradition was represented by a whole host of texts devoted to anwā' literature[171] that can best be characterized as being concerned with the utility of the risings and settings of constellations for agricultural purposes and for the general purposes of daily life. This latter tradition approached the subject from a native Arabic background by drawing on the native sciences and the native knowledge of the constellations known from the widely read Arabic literary sources themselves.

Here again one could detect the opposing camps splitting along lines similar to the ones discussed above: There were those who favored reliance on the non-Arab "ancient" sciences, and were themselves identified as higher government bureaucrats, and those who preferred to rely on the ways of the Arabs in the non-governmental or lower bureaucratic circles. As a result an enormous literature began to be written on the subject of the stars. And because of the various traditions it involved, the same body of literature begged for systematization.

It was 'Abd al-Raḥmān al-Ṣūfī (d. 986) who undertook that job by producing a masterpiece on the constellations that was not surpassed until modern times. His book Ṣuwar al-Kawākib al-thābita (Figures of the Fixed Stars) did not only include a general background description of each constellation and its constituent stars in both the Greek and the Arabic traditions, identifying, whenever possible, the multiple names given to the same star or groups of stars, but included as well systematic tables of longitude, latitude and magnitude of the individual stars themselves. This text, which is available only in a preliminary edition from Hyderabad,[172] has never been studied in any detail.[173] But even a casual reading of it reveals that it contains lengthy dialogues with the Greek tradition, particularly expressed in terms of objections to the Ptolemaic received text. One cannot help but notice the many occasions when Sufi would say that this or that star or constellation is such and such according to Ptolemy, but I say it ought to be this or that, and the Arabs, in contrast, say this about it.[174] On account of its deliberate comprehensiveness, and probably on account of its authoritative standing as the standard reference book on the constellations that it must have become, this text lent itself to royal patronage production, and copies of it were so beautifully illustrated that many of them are still considered among the chefs d'œuvres of Islamic art.[175]

Two other types of criticism that were directed at Ptolemy's Almagest, also need to be mentioned in this context, although they touch on slightly different issues from the ones that have been discussed so far. This group of critical ideas did not touch the issues of mistakes in the Almagest per se, as was done before. Rather it touched upon two other areas of the text where it could stand some updating: First, there was the criticism that could be classified under the heading of attempts to update the text of the Almagest, i.e. bring the mathematical approaches deployed in the text into par with the current mathematical knowledge of the time. For example, the very famous mathematical theorems that were used at the beginning of the Almagest to set up a trigonometric system that was used throughout the text, employed the classical Greek spherical trigonometric theorem which used chord functions as was done, for example, by the Menelaos theorem.[176] To his exposition of the theorem, and his proof of it, Ptolemy attached a chord table in order to facilitate the following computations in the rest of the book. It was this material that became an obvious target of the various revisions in early Islamic times. And that should have been expected, since by then the astronomers who were reconstructing the discipline of astronomy had at their disposal an almost fully developed trigonometric system of sines, cosines, tangents, and the like. In addition, this system was already fully embedded in the receiving culture into which the Almagest was being translated, and at times could very comfortably co-exist with the inherited Greek chord system with its comparative clumsiness for everyone to see.

From the translators themselves we would not know of the existence of this other field of trigonometry, which was itself unknown to the Greek tradition. But the various writers who were producing their own astronomical works, as the Almagest was being translated, did not shy away from using the new trigonometric functions to describe the same phenomena that were described in the Almagest. Of the several examples that can be cited regarding the use of the new mathematics to update the text of the Almagest, by far the best one comes from a slightly later period, around the middle of the thirteenth century. In Ṭūsī's Taḥrīr al-majisṭī (Redaction of the Almagest), already mentioned before, that was written in 1247, Ṭūsī approached this section of the Almagest in the following fashion. After concluding his exposition of the Almagest's table of chords, he went on to make the following remark: "I say, since the method of the moderns, which uses the sines at this point instead of the chords, is easier to use, as I will explain below, I wish to refer to it as well."[177] He then went on to give a spherical sine theorem equivalent to that of Menelaos and affixed to it another configuration using the tangent function instead of the sine. He concludes that section by producing tables for sines and tangents to complete the mathematical and trigonometric tools for the rest of the book.

This updating of the Almagest, although not stressed often enough in the literature, is of crucial importance to understanding the life of the Almagest in the Islamic domain. And when we juxtapose this treatment of the Almagest text in the later centuries with the independent works of someone like Ḥabash al-Ḥāsib from the ninth century, in which we see these trigonometric functions used so freely as we shall soon see, we can then clearly appreciate the immediacy of the Almagest text to the practicing astronomers, and clearly see their willingness to merge its contents with the kind of astronomy they were already practicing.

In a parallel development, and this was also to be expected, one finds those same astronomers, using the results of the Almagest, at times, whenever they thought that those results were still valid, while at other times they would reject them completely in favor of new ideas of their own. This multiplicity of approaches to the Almagest text can only signal the very vital reactions it must have created within the receiving culture of early Islamic times. But one should also remember that at all instances this very vitality produced an Almagest text that was considerably enriched by the process.

Returning to the earlier astronomers, such as Ḥabash al-Ḥāsib (fl. ca. 850) in particular, who produced their own independent zījes (Astronomical Handbooks), that were only constructed in the tradition of Ptolemy's Handy Tables, we find that they too have also used the most recent and fully developed trigonometric functions in those works.[178]

Looking at the complete picture of that period, and after examining the scientific sources themselves, one can begin to see a process in which one finds that as soon as the Greek scientific texts were being translated, they were also being immediately updated by the currently known material and put to use in new compositions, all in order to improve the kind of science that was then produced.[179]

The second type of intervention in the text of the Almagest, had less to do with updating it mathematically or correcting its errors as we have already seen. Instead it was more like reconstructing it or re-editing it so that it would become more useful for students of astronomy. In this regard great liberties were taken with the text, feeling completely free to add to it and delete material from it, all in order to make it a more up-to-date functional text.

The best illustration of this type of intervention is also exemplified by Ṭūsī's Taḥrīr, which was mentioned before and in which one finds a new treatment of some chapters of the Almagest, such as Almagest X,7, where Ptolemy used an iterative method to compute the eccentricity of one planet and then repeated it in great detail for each of the other planets.[180] Instead of the Ptolemaic approach, Ṭūsī adopted a new technique of explaining the method in great detail in the case of one planet and then generalizing it to the others without repeating it in every case.

I mentioned the corrections Ṭūsī had introduced in the same text regarding the apparent size of the solar disk, and the counterexample of the annular eclipses that were apparently unknown to Ptolemy. I also mentioned the correction of other factual errors, including errors in the rate of precession, the inclination of the ecliptic, and the motion of the solar apogee, as well as the development of the methods of observations like the introduction of the fuṣūl method. In all those instances, we find the text of the Almagest critically reviewed and updated before it could become useful to the receiving culture. Far from being a model to be followed, although one could argue that it was in some sense, it was more like a foundation to build upon, but only after making sure that it was a safe foundation and that its errors and contradictions had been already weeded out. There were other instances in which the text of the Almagest was also found wanting, but this time for much more fundamental considerations than the ones that have been discussed so far.

By considering only the factual corrections that have been discussed so far, one could easily arrive at the conclusion that the text of the Almagest would have become functionally serviceable once those corrections were adopted. The text would have been sufficient, for example, for practicing astronomers and astrologers and no further elaborations of it would have been necessary. But with astrology and its practice facing a veritable resistance from the main intellectual centers of the society, especially the religious ones, and thus its relationship to astronomy being consciously severed by the theoretical astronomers who invented the discipline of hay'a as we have already seen, the purpose of the discipline of astronomy was apparently defined in a slightly more nuanced fashion. This purpose can best be seen if one reads the two most famous works of Ptolemy together. Those works are: the Almagest, where one finds a detailed account regarding the relationship between the observed phenomena and the construction of geometric predictive models that explained the behavior of the planets at all times, and the Planetary Hypotheses, where one would find a detailed account of the celestial spheres that were made, in a true Aristotelian fashion, responsible for the motion of those planets. By reading those two texts together, as most people did, once they became available in Arabic, some serious cosmological problems began to appear. Most of those problems focused on Ptolemy's violation of the most basic cosmological tenet of Greek astronomy: the uniform circular motion of the planets around a fixed Earth located at the center of the universe.

That the Earth was fixed at the center of the universe was undoubtedly at the core of that Aristotelian cosmology, so much so that if one did not have such an Earth one would have had to suppose the existence of such an Earth at the very center of heaviness around which everything else revolved.[181] The real challenge was to explain the apparent phenomena from within that cosmological vision, and still retain some predictability in the geometric models that described the planetary motions.

From that cosmological perspective, the Almagest failed at almost every count. While there is the Ptolemaic pretense that the universe, which was being described, was an Aristotelian universe, within which all the Aristotelian elements were to be found as the building blocks of that universe, yet at every juncture the Almagest described situations that were physically impossible when looked upon from the perspective of the Planetary Hypothesis that emphasized that Aristotelian cosmology. It is this inconsistency between the mathematical models constructed in the Almagest to account for the motion of the planets, and the physical objects those models were supposed to represent that I have so often referred to as the major problem of the Greek astronomical tradition.[182]

Because these inconsistencies are of a completely different nature than the ones that were touched upon before, and because they were a direct byproduct of the application of Aristotelian cosmology, some people have referred to them as philosophical problems. As a result they tried to read the Almagest as divorced from that same cosmology that was wholeheartedly adopted in the Planetary Hypotheses, the text that was supposed to complement the Almagest, which it followed. And yet these inconsistencies were perceived as touching the very foundation of science; in the sense that science should not harbor contradictions, as Ptolemy seems to have allowed it to do, between the physical side of the science and the mathematical representation of the same physical universe that was being described.

One can only assert that such problems were philosophical problems, if one were to think of them only in the medieval sense of natural philosophy, where such cosmological issues were properly discussed. But they also did matter to the scientists who were also trying to make sense of the physical phenomena around them, and who would have demanded that their scientific disciplines did not contradict each other. In that sense, those problems became real scientific problems, and did not remain only in the domain of philosophical speculation.

Take, for example, the physical spheres that were supposed to constitute the Aristotelian universe, and which were simply represented by circles by Ptolemy in the text of the Almagest. If one were to limit himself to philosophical speculations only, then those spheres would pose no serious problem if they were understood as mere mathematical representations that had no connection to reality. But if at the end of the day one used those spheres to account for the motion of planets and used them to predict the positions of those planets for a specific time, then one had to face their reality in a much deeper sense than is already admitted. And when that reality was reiterated in the Planetary Hypotheses, the contradictions became much more serious. Again, there would be no problem if one were only using those models of spheres to compute positions of planets only. But when one says that those spheres were actually physical in nature, in the Aristotelian sense of physical, it would become then impossible to think of them, for example, as being able to move uniformly, in place, around an axis that did not pass through their centers.

This was the most important impossibility in the whole of Greek astronomy, or at least it was so perceived. Such glaring absurdities that were embedded in almost every model of the Almagest could not pass unnoticed by astronomers, who were not only being watched over by their opponents in the society, who in turn did not want them to bring those "ancient" sciences into the Islamic domain in the first place, but they were also being watched by their own fellow astronomers who definitely believed, as al-Ḥajjāj must have done, that they could outsmart their fellow astronomers if they could cleanse the imported system from those blemishes.

That people were really thinking along those lines is best illustrated by one of the earliest texts to address the sheer physicality of the spheres: the text of Muḥammad b. Mūsā b. Shākir (d. 873), who was not only one of the major patrons of the translation of Greek scientific and philosophical texts, but was also himself a scientist in his own right. In his capacity as a practicing scientist, he devoted a treatise to the absurdity of assuming the existence of a ninth sphere, as Ptolemy had done. According to Ptolemy that last ninth sphere was responsible for the motion of the eighth sphere, which, in turn, carried the fixed stars. And yet Ptolemy had both spheres share the same center of the universe. The problem was then reduced to the impossibility of having two concentric spheres move one another without assuming a phenomenon like friction, which could not be allowed in the celestial realm of the Aristotelian universe where celestial spheres, by their very ethereal nature, did not allow friction to take place.[183]

That Ptolemy himself was thinking along the same lines is evident from the preface of the Almagest, where he says that the celestial motions should not be compared to the motions that we observe around us, for they belonged instead to some form of a deity. To which one could respond: if that were the case, and if the deities were responsible for the motion of the planets, then there would be no need for the science of astronomy, nor would there be any need for scientific observations, for who are the humans who could predict the behavior of deities? The readers of the Ptolemaic texts in their Arabic translation saw a different world, and could not simply resort to such whimsical deities in the midst of a competitive society that was watching every step they took.

This incompatibility between the mathematics of the Almagest and the physics of the Planetary Hypotheses would not have been noticed had those two books not been read together. And in the tense environment in which they were thrust their coming into conflict with one another was simply unavoidable. In addition, if one were to remember that those problems were being raised by Muḥammad b. Mūsā b. Shākir toward the middle of the ninth century, when the first translation of the Almagest by al-Ḥajjāj was barely two decades old, and the translation of Isḥāq b. Ḥunain (d. 911) had not yet taken place, one can then begin to appreciate the sophistication with which the Greek astronomical tradition was being received as it was being translated, a sophistication that could not be explained by the classical narrative. Furthermore, it is a kind of sophistication that could only come from this comprehensive understanding of the Greek philosophical tradition, where cosmology was read together with observational science, a reading that was nowhere to be found in any other civilization up till that time.

In later centuries, as other contradictions began to appear, further sophistication began to be necessary. But all the basic problems still focused around this major issue of the lack of consistency in the imported Greek astronomical tradition. In a word they still dealt with these foundational issues of science.

Once those issues were widely recognized by the various sectors of the society, they began to develop a tradition of their own. The various treatises that began to appear in the later centuries, and in which those issues were recounted, began to constitute a scientific genre of their own normally referred to with such titles as Shukūk (doubts). And because of the social dynamics within which those doubts were expressed, they were by no means restricted to the field of astronomy alone.

The similar text by Abū Bakr al-Rāzī (Latin Rhazes, d. 925) called al-Shukūk 'alā Jālīnūs (Doubts Against Galen), falls in this category as well, and with it we can easily detect a general cultural trend that has yet to be elaborated. Only skeletal sketches of these developments and of the major issues that were raised in those texts could be attempted at this time. Of course the astronomical tradition still received the lion's share of those discussions, and can only be used here as a representative model of the other discussions that were obviously taking place in the other disciplines.

If one were to disregard the earlier objections to the Ptolemaic observational parameters, or even the cosmological questions by Muḥammad b. Mūsā b. Shākir, just mentioned, as early expressions of doubts that had not yet developed into a genre of their own, then one will have to say that the genre was born with Rāzī's book, which was expressly called Shukūk, despite the fact that in the case of Rāzī his book was restricted to medical and philosophical doubts. Astronomical Shukūk were soon to follow, even though they seem to have taken a slightly different route.

During the eleventh century, possibly in the latter half of that century, an Andalusian astronomer, whose name is yet to be identified, has left us a treatise called Kitāb al-Hay'a (A Book on Astronomy), which is still preserved in an apparently unique copy at the Osmania library at Hyderabad (Deccan, India). In this treatise the author had several comments to make about the problems in the received Greek astronomy. But almost every time he made such comments he would quickly say that he had gathered those problems in a book that he called al-Istidrāk ['alā Baṭlamyūs] (which could be freely translated as: Recapitulation Regarding Ptolemy). This book has yet to be located. But from the context in which it is mentioned, and the problems it seems to refer to, it sounds like it was of the same nature as the other shukūk texts under discussion.[184]

In the east, and around the same time, Abū 'Ubayd al-Jūzjānī (d. ca. 1070), the student of Ibn Sīnā (Latin Avicenna d. 1037), also left us a small treatise On the Construction of the Spheres. In this treatise he mentioned that he had discussed with his teacher, Ibn Sīnā, the famous Ptolemaic absurdity, which was by then known as the problem of mu'addil al-masīr (Equator of Motion, or equant for short).[185] The fact that both such texts existed, one from Al-Andalus, the farthest western reaches of the Islamic world at the time, and one from Bukhara, the farthest east, and the fact that the second text comes from the philosophical circle of Ibn Sīnā and not from the circle of astronomers and mathematicians, could only mean that the cosmological issues that were perceived to have plagued Ptolemaic astronomy were by then circulating in widespread intellectual and geographical circles; they were no longer restricted to the elite of astronomical theoreticians. The equant problem itself, which had the longest staying record, is none other than the physical absurdity of proposing that a physical sphere could move uniformly, in place, around an axis which did not pass through its center. This absurdity permeated almost all of the models, which were proposed in Ptolemy's Almagest. What the texts of al-Andalus and Bukhara suggest is that by the eleventh century that proposition was apparently widely recognized as a physical impossibility.

In his own rather humorous story Abū 'Ubayd informs us that when he discussed the proposed solution for this Ptolemaic absurdity of the equant, with his teacher Ibn Sīnā, he was told by Ibn Sīnā himself that he had also resolved it, but refrained from giving out the solution in order to urge the student to find it for himself. In the very next sentence the student went on to say that he did not believe that his teacher had ever resolved that problem.

The anecdote, legendary as it may be, is still indicative of the kind of problems those custodians of the "foreign sciences", the philosophers in particular, were competing to solve, and the challenges they were facing, as well as the fame they hoped to acquire if they could rid the Greek astronomical tradition of its absurdities. The anecdote also indicates that if the philosophers were already aware of this joint reading of the Ptolemaic texts (the

Almagest and the Planetary Hypotheses) in which such problems would arise, this must mean that the astronomers were obviously much more deeply entrenched in that perspective. And the debates of the latter must have informed the former.

For the good fortune of the astronomers, it also appears that their debates over such kinds of issues were socially condoned. They did not only transcend their circles to reach the circles of the philosophers, but they probably also gave rise to the likelihood of rebutting the incoming Greek tradition altogether, since they were being critical of it.

Such discussions had no direct bearing on the other more socially controversial perception of the Greek tradition: its willingness to harbor those astrological sciences that were not as widely accepted as the theoretical critiques seem to have been. For our immediate purposes, however, it is important to document the tradition of the critiques themselves in order to demonstrate the sophistication of that tradition, and its wider implication on the very formation of Islamic science.

Again in the same century, and still in the east, we find the prolific polymath and famous astronomer Abū al-Raiḥān al-Bīrūnī (d. ca. 1048) who also had something to say about the physical absurdities of the Ptolemaic system. This, despite the fact that Bīrūnī's main astronomical production was really geared toward the mathematical observational part of astronomy and paid much less attention to the cosmological aspects of the discipline. In his Ibṭāl al-buhtān bi-īrād al-burhān (Disqualifying Falsehood by Expounding Proof), which seems to have been lost but which was quoted by the astronomer Quṭb al-Dīn al-Shīrāzī (d. 1311), Bīrūnī had this to say about the Ptolemaic description of the latitudinal motion of the planets: "As for the motions of the five epicyclic apogees in inclination, as it is commonly known, and is mentioned in the Almagest, those would require motions that were appropriate for the mechanical devices of Banū Mūsā, and they do not belong to the principles of Astronomy."[186] That was Bīrūnī's polite way of saying that Ptolemy's discussion of the planetary latitudes was not astronomy proper, and that it amounted to nothing. Such was the extent of criticism of Ptolemy, even by people who had a vested interest in defending him against his detractors. And yet they could not remain silent about the Ptolemaic absurdities, probably because they apparently felt that they had a greater interest in competing amongst themselves by demonstrating that they could outsmart Ptolemy.

The best-preserved and most elaborate text in the genre of shukūk was a criticism of Ptolemy that was leveled by another polymath, by the name of Ibn al-Haitham (d. ca. 1040 Latin Alhazen), who was also a contemporary of the astronomers mentioned above, and whose work on Optics was the only work that was known in the Latin West and which earned him his well deserved fame. His critique of Ptolemaic astronomy is contained in an Arabic text which has survived, but which was apparently never translated into Latin. The text in question is his extensive al-Shukūk 'alā Baṭlamyūs (Dubitationes in Ptolemaeum) \Shukūk\,[187] in which he took issue with several of Ptolemy's works in which he found fault.

The three Ptolemaic works in question included the Almagest, the Planetary Hypotheses, and the Optics. Their mere grouping is a clear indication that those works were read together, in a comprehensive manner, and not in isolation as is sometimes claimed.[188] For Ibn al-Haitham, the common thread that connected the three books together is that they all contained problems or doubts (shukūk) that revealed contradictions that could not be explained away (lā ta'awwul fīhā).[189] This phraseology also indicates that every effort was already made to give Ptolemy the benefit of the doubt. Problems were obviously explained away wherever that was possible,[190] and only those absurdities that could not be justified were attacked. Ptolemy's books were taken up in the following order: the Almagest, which had the lion's share, to be followed by the Planetary Hypotheses, and then the Optics. In the sequel I will take a few select examples from this treatise in order to illustrate the kind of issues that attracted the attention of Ibn al-Haitham.

In his critique of the Almagest, Ibn al-Haitham passes very quickly over the early chapters of that book, and commences the real critique with the Ptolemaic description of the model for the lunar motion. In it Ptolemy assumes that the motion of the moon, on its own epicycle, is measured from a line that passes through the center of the epicycle, but is directed, not to the center of the world, around which the motion of the epicycle itself is measured, nor to the center of the sphere that carries the epicycle, called the deferent, but to a point, called the prosneusis point (nuqṭat al-muḥādhāt) by Ptolemy. In the Ptolemaic model, this point falls diametrically opposite to the center of the deferent from the center of the world. In his overall assessment of this model Ibn al-Haitham clearly said that it was basically fictitious and that it had no connection to the real world it was supposed to describe. He singled out the soft spot in the model with the following remark: "The epicyclic diameter is an imaginary line, and an imaginary line does not move by itself in any perceptible fashion that produces an existing entity in this world."[191] Furthermore: "Nothing moves in any perceptible motion that produces an existing entity in this world except the body which [really] exists in this world."[192] Later on, he went on to affirm once more: "no motion exists in this world in any perceptible fashion except the motion of [real] bodies." And then he concluded this section by stating that a single epicycle could not possibly move the moon by its own anomalistic motion and at the same time move in such a way that its diameter will always be directed toward the prosneusis point. That would entail that a single sphere was supposed to move in two separate motions by itself, which was impossible.

Books VI-VIII of the Almagest did not bother Ibn al-Haitham very much. Instead he moved very quickly to Book IX where the issue of the equant is discussed. In Almagest IX, 2, Ptolemy made the explicit statement that the upper planets moved in a uniform circular motion, just like the other planets he had discussed before. But by Almagest IX, 5, Ptolemy had laid the foundation for the equant problem when he insisted that "we find, too, that the epicycle centre is carried on an eccentre which, though equal in size to the eccentre which produces the anomaly, is not described about the same centre as the latter."[193]

The point that Ptolemy was trying to make at that occasion was that the two spheres, whose combined motion was responsible for the motion of the planet, were distinct spheres: one, the deferent, simply carried the epicycle of the planet, and the second, taken to be equal to the deferent in size, was responsible for the uniform motion of the planet's epicycle, but explicitly stating that the motion of the last sphere did not take place around the same center as the deferent. It was the center of the latter fictitious sphere, the sphere of uniform motion, that was later called the equant. In chapter IX, 6 of the Almagest, Ptolemy went on to describe much more clearly the equant center. There he defined it as a point along the line of apsides such that its distance above the center of the deferent was equal to the distance of the deferent's center from the center of the world.

Moreover, the line connecting this equant point to the center of the epicycle, when extended, constituted the line from which the mean motion of the epicycle was measured. In effect, this said that the deferent sphere, which carried the epicycle, was forced to move uniformly around a center, now called the equant, other than its own center, which was physically impossible.

By then, Ibn al-Haitham seems to have obviously realized the seriousness of the problem, as his following statement indicates: "What we have reported is the truth of what Ptolemy had established for the motion of the upper planets; and that is a notion that necessitates a contradiction."[194] This was in fact the contradiction between the physical reality of the celestial spheres and the mathematical model that was supposed to represent them. For as Ptolemy had accepted the uniform motion of the upper planets, the epicyclic centers of those planets were carried by deferents, which were supposed to move in this uniform motion. But with the equant proposition, one was told that the epicyclic center described equal arcs in equal times, i.e. moved uniformly, around a center that was not the center of the deferent that carried it.

But by Ptolemy's own proof in Almagest III, if a body moved uniformly around one point it could not move uniformly around any other point. Therefore the epicyclic center, as stipulated by Ptolemy, must move non- uniformly around the center of its own carrier, the deferent. And since the equant sphere was a fictitious sphere, and thus could not produce any perceptible motion of its own, as was often repeated by Ibn al-Haitham, the only sphere that could produce a real motion was that of the deferent, and that was now proved to be moving non-uniformly around its own center. This contradicts the assumption of uniform motion that was accepted by Ptolemy in the first place, hence the contradiction that was realized by Ibn al-Haitham. The other alternative was to assume that the same physical sphere, the deferent, could move uniformly around an axis that did not pass through its own center which was physically impossible, for it was exactly the physical absurdity mentioned before.

All the other models of the Almagest, except the model of the sun, which had problems of its own, shared this absurd feature of the equant. In the case of the moon, its epicycle too was also supposed to be carried on a deferent that moved in such a way that the epicyclic center of the moon did not describe equal arcs around its own deferent center, in equal times, but rather around the center of the world. That was in essence requiring a sphere to move uniformly around an axis that did not pass through its own center as well, which was exactly the point of the equant problem.

Mercury's model, which was considerably more complicated than the other planetary models, shared this feature as well. There too, the deferent that carried the epicycle of Mercury moved in such a way that its motion was not uniform around the deferent's center but around a point that was along the line of apsides half way between the center of the world and the center of another director sphere that carried the deferent sphere of Mercury.

Furthermore, both in the case of Mercury as well as the case of the upper planets, Ptolemy did not even attempt to demonstrate how he arrived at the location of the equant. It was simply stated to occupy such and such a position without any further discussion as to why, or any proof, as would have been expected in a mathematical science such as astronomy. It was this issue in particular that gave rise to the question, which was raised by another Andalusian astronomer by the name of Jābir b. Aflaḥ (middle of the twelfth century) and was singled out in his own research.[195]

From all those Ptolemaic configurations, Ibn al-Haitham could draw only one conclusion: that they were all extraneous to the field of astronomy. This much was even admitted by Ptolemy himself in Almagest IX, 2, where he had stated, in no ambiguous terms, that he was using a configuration that was contrary to accepted principle (khārija 'an al-qiyās as in the Arabic translation of the text, or "not from some readily accepted principle" as in Toomer's translation of the Almagest). From that admission, Ibn al-Haitham could then only conclude with a rebellious voice against the whole of Ptolemaic astronomy, articulated in the following terms:

This was not a criticism of Ptolemy. Rather, it was an extremely well- articulated condemnation of the very foundation of Ptolemaic astronomy and an open call for its toppling in favor of an alternative astronomy that did not suffer from such contradictions. It did not only expose the fatal mistakes and contradictions in Ptolemaic astronomy, but rose to the occasion of articulating a new set of principles upon which an alternative new astronomy had to be based.

Such attacks, articulated by various astronomers working in the Islamic tradition, did in fact constitute an essential shift in the very conceptualization of the new Islamic science that was being articulated. The new conceptualization did not only condemn the Greek legacy, but laid the foundation for the new consistent science. In the new science, which was then born out of those attacks during Islamic times, physical objects would be, from then on, mathematically represented by models that did not deprive them of their physicality as was done by Ptolemy.

Ptolemy's latitude theory, as expounded in the Almagest, did not fair any better. In it Ptolemy himself had expressed doubts about its exact workings, an admission that only encouraged Ibn al-Haitham to conclude:

What Ibn al-Haitham was referring to was the seesawing motion of the inclined planes, which carried the epicycles of the lower planets of Mercury and Venus. That motion was also another impossibility that could not be tolerated by Ibn al-Haitham, and was simply dismissed as another grave error on the part of Ptolemy. Ibn al-Haitham's argument can be summarized as such: with such motions Ptolemy was forcing physical bodies to move in opposite motions, which was in itself physically impossible.

Over and over again, Ibn al-Haitham returned to the vision of the new astronomy he would like to see—an astronomy based on the new principles of consistency between the physical reality of the universe we live in and the mathematics one uses to represent that reality. In the new astronomy, those two fields of science had to be constantly consistent, otherwise we would end up talking about imaginary motions as was done by Ptolemy:

Furthermore, Ptolemy knew very well that he was embracing such contradictions as he was quoted by Ibn al-Haitham to have said: "We know that the use of such things is not detrimental to our purpose, as long as no significant excesses are introduced on account of them."[199] To which Ibn al-Haitham could only say:

In this long passage, Ibn al-Haitham leaves no doubt as to his real intentions. He obviously means that real physical bodies do exit in the universe and once that was assumed those bodies must be represented by mathematical models that did not violate their true physical nature, as was done by Ptolemy when he assumed the existence of an equant that would force a physical sphere to move uniformly, in place, on an axis that did not pass through its center. That was physically absurd in Ibn al-Haitham's new astronomy.

In the larger cultural context, this passage also demonstrates the extent to which these cosmological debates began to influence the very foundation of science; they allowed for the new requirement of consistency to be clearly demonstrated with such vivid examples from the field of astronomy.

The timing of those remarks is also important, for they allow us to conclude that the eleventh century, which has produced so many critiques of Ptolemaic astronomy as we have already seen, seems to have been the time when new research projects were launched, and new re-organization of the sciences on new conceptual grounds must have begun to take place. The appearance of the new disciplines of mīqāt, and farā'iḍ, soon after that or very close to that time, are only few of the features that must have characterized this period. Similar results can be derived from an analysis of the developments in the mathematical and medical disciplines, and those who work in those fields may also reach similar conclusions. For astronomy, this vigorous discussion of the foundations of science seems to have given rise to long-term developments whose repercussions eventually led to truly revolutionary results. Those results, in turn, led to the final overthrow of the Greek astronomical edifice.

Returning to Ibn al-Haitham's critique of Ptolemy's Almagest, I will quote his conclusion at some length, not only because it draws the real demarcation lines of the new astronomy Ibn al-Haitham was calling for, but also because it demonstrates the utter dissatisfaction that was obviously felt with Greek astronomy. No one could possibly chart the contours of the new astronomy, or express the sentiments of dissatisfaction with the old, better than Ibn al-Haitham himself. In his own words:

With this summary condemnation of Ptolemaic astronomy, Ibn al-Haitham was obviously setting the field of Arabic astronomy on completely new footing. He could not stress any more forcefully the need for the consistency between the assumptions about the nature of the bodies that constitute the universe, and the construction of mathematical models for planetary motions that could represent those bodies without violating the very physical reality of the spheres of which the world was supposed to be made. That is the most succinct statement of the principle of consistency that was to characterize the new astronomy from that time on.

Put briefly, it should be clear that one does not accept a set of principles regarding the physical formation of the universe, and then develop mathematical models to illustrate the behavior of that universe in such terms that would contradict the very physicality of the objects that were originally accepted, or transform them so that they would no longer be recognizable. It is like assuming the world is made of a sphere and then for purposes of demonstrating how it moves one ends up representing the world with the mathematical figure of a triangle.

Similar criticisms were also directed at the Ptolemaic texts in the earlier centuries, as was documented before, and some of them had hinted to this new approach of consistency between the physical world and its presumed behavior. But at no time before Ibn al-Haitham was this new understanding of the fundamentals of new astronomy so well articulated.

The text of the Planetary Hypotheses did not fare much better in Ibn al-Haitham's estimation, and most certainly did not advance the new ways of thinking about astronomy. In contrast to the Almagest, where one could find excuses for Ptolemy and claim that he was talking about imaginary circles and lines, i.e. abstract mathematical models, and not about real physical bodies whose motions would entail the absurdities enumerated, in the case of the Planetary Hypotheses Ptolemy spoke of physical bodies explicitly. Thus the type of criticism advanced by Ibn al-Haitham became much more pertinent with respect to that book. In addition, since the Planetary Hypotheses was written after the Almagest, Ibn al-Haitham then took advantage of that chronology, and seized the opportunity to compare Ptolemy's thinking about the subject at two different stages of his scientific career and in two different works. He combed the second work, the Planetary Hypotheses, in order to determine if the absurdities of the Almagest had by then been resolved.

Surprisingly, he found out that the problems became much worse. Instead of resolving some of the outstanding problems of the Almagest, Ptolemy added some new ones in the Planetary Hypotheses.

Ibn al-Haitham went through both texts and produced a comparative list of spheres and motions that were described in the Almagest, and were now changed in the Planetary Hypotheses. While the configuration that was drawn for the sun remained the same in the two texts, and while the motions of the moon were nominally also the same, the motion that was described in the Almagest as producing the correction for the prosneusis phenomenon was not mentioned in the Planetary Hypotheses. In the case of Mercury only five of its motions that were mentioned in the Almagest were retained, and three were dropped. Similarly in the case of Venus, four motions were retained and three were dropped. The upper planets retained all the motions that were described in the Almagest and only the latitude motion around the small circles was dropped. But there were some more drastic changes made in the rest of the arrangement that Ptolemy had stipulated for the motion of the planets in latitude.

After going through this comparative survey in some detail, Ibn al-Haitham reached the preliminary conclusion that the configurations that were described in the Planetary Hypotheses were different from those described in the Almagest, if for no other reason except that some ten motions were no longer mentioned in the new text and the motion in latitude was overhauled. To which Ibn al-Haitham says:

After a thorough study of the various motions that were described in the Planetary Hypotheses, and their causes, Ibn al-Haitham found himself quoting Ptolemy, in several passages, where Ptolemy would be caught saying that all those motions should be accounted for by real spherical bodies that were responsible for them. That left Ibn al-Haitham with one conclusion: that Ptolemy had explicitly committed himself to "finding for every motion that was mentioned in the Almagest a corresponding body that moved by that motion."[203]

As for obvious contradictions, even in the same book, those were definitely used as further fodder to support Ibn al-Haitham's thesis. To give just one example of the kind of issues Ibn al-Haitham emphasized, he noted that in the second treatise of the Planetary Hypotheses Ptolemy had said that motion by compulsion was not permissible in the celestial spheres, when he had already said in the first treatise that each one of those spheres would have a motion of its own and another one that was forced upon it.[204]

As for the new physical bodies that were introduced by Ptolemy in the Planetary Hypotheses, namely the slices of spheres (manshūrāt) instead of the full spheres that were assumed in the Almagest, Ibn al-Haitham thought that the manshūrāt were a step in the wrong direction. For those slices in turn entailed "absurd impossibilities (muḥālāt fāḥisha), which are of two kinds: One takes place when the body empties one space to fill another, and the second when the body had to move in different and contrary motions."[205]

In the case of the full spheres that were assumed in the Almagest, they at least entailed "only one kind of impossibilities, and that is the different and contrary motions, and did not entail the other, namely, the emptying of one space and filling the other."[206] The example of the spheres, which had to move in different and contrary motions, is mentioned once more in connection with the equant problem that was already faced in the Almagest.[207]

Ibn al-Haitham's attitude toward those spherical slices of the Planetary Hypotheses were echoed two centuries later, in the work of Mu'ayyad al-Dīn al-'Urḍī (d. 1266), who also said that, as far as those spherical slices were concerned,

Ibn al-Haitham had this to say about the motion in latitude, which Ptolemy had described in the Almagest by using a device of two small circles that would move the epicyclic radii, a feature that was dropped in the Planetary Hypotheses:

Similarly, in the case of the inferior planets, Mercury and Venus, the small circles that were described in the Almagest to account for the motion of their epicycles in latitude, and which were now dropped in the Planetary Hypotheses had to lead to the conclusion that Ptolemy was either wrong in dropping them now, or in mentioning them in the Almagest in the first place. In whichever case, the treatment in the two books was contradictory, and that was one more obvious sign that the two books were read together.

Toward the end of the second treatise of the Planetary Hypotheses, Ptolemy seemed to lean toward the belief that it was possible to think of planets that would move by themselves, i.e. not to require a sphere that would move them. Ibn al-Haitham documented such statements very carefully only to conclude that not even the motion of rolling (tadaḥruj) should be permitted. For then

In essence, Ibn al-Haitham was saying if planets could exhibit all those motions on their own, without any bodies moving them, then all of those assumptions of spheres and slices of spheres and the like would be completely superfluous. And here again 'Urḍī adopted a similar attitude in his own critique of Ptolemy in a slightly different context:

Ibn al-Haitham concluded his critique of Ptolemy's Planetary Hypotheses with the following statement:

By moving from the critique of the Planetary Hypotheses directly to the Optics of Ptolemy, Ibn al-Haitham did not only demonstrate that the Greek astronomical tradition was essentially flawed but that the other sciences, like optics, suffered from the same inconsistencies as well. This is a clear indication of the pervasiveness of this critical spirit in Islamic times, and confirms what was stated before about the social motivations for such critiques that were by no means restricted to astronomy alone. Furthermore, it also demonstrates the extent to which the Greek scientific tradition itself was taken as a whole; and as a whole was criticized from various perspectives. But the concentrated critiques of the astronomical tradition, as was amply illustrated so far, must convince us of the need to consider this stage of Islamic astronomy as a new beginning for astronomy, in the sense that the need for a new astronomy had by then been clearly demonstrated.

In order to illustrate the fecundity of our new historiographic approach, and appreciate the repercussions of such critiques of the Greek scientific tradition as the ones that were leveled by someone like Ibn al-Haitham, and against the expectations of the classical narrative that marks this period after the eleventh century as a period of steady decline, I now turn to some later critiques in order to demonstrate the longevity of that tradition, and to indicate the direction it continued to follow. Rather than preserve the Greek scientific tradition, these later critiques, to which we now turn, illustrate the pervasiveness of the attacks against it.

The astronomical developments that took place after the time of Ibn al-Haitham have special significance for another reason. Not only do they illustrate the continuity of the earlier critical tradition, but also demonstrate the kind of new questions that began to emerge, and the similarity between those questions and the ones that were raised later on during the European Renaissance.

Naṣīr al-Dīn al-Ṭūsī (d. 1274), who was mentioned before in connection with the various critiques of the Ptolemaic text of the Almagest, had his own doubts about the cosmological issues that have been raised so far. In his Taḥrīr al-majisṭī (completed in 1247), he only criticized Ptolemy sporadically. But in his later work, the Tadhkira (completed in 1260), he devoted much longer sections to the cosmological questions and proceeded to formulate his own mathematical models to replace those of Ptolemy. We shall have occasion to return to Ṭūsī's reformed models later. For now, and in the context of the encounter with the Greek tradition, the remarks he made in his Taḥrīr should give us an idea of his thoughts on the subject around the middle of the thirteenth century.

By comparing Ṭūsī's various works it becomes apparent that he began to ponder the importance of the cosmological issues for the first time when he was composing the Taḥrīr, a book that was devoted to the production of a useful, updated version of the Almagest, thus naturally offering an ideal occasion to voice his own reservations about the book he was re-editing.

In the Taḥrīr, and while discussing the lunar model of Ptolemy, Almagest [V, 2], Ṭūsī concluded that section with the following remark: "As for the possibility of a simple motion on a circumference of a circle, which is uniform around a point other than the center, it is a subtle point that should be verified."[213] Doubtless, this is the same irregularity that was mentioned before in the context of the equant problem, i.e. the absurdity arising from the situation when a sphere is forced to move uniformly, in place, around an axis that did not pass through its center.

Furthermore, in the case of the prosneusis point of the lunar model, Ṭūsī simply said: "This motion is similar to the motion of the five [planets] in the inclination and the slanting, as will be shown later on, except that that is a motion in latitude while this one is in longitude. One must look into the possibility of the existence of complete circular motions that would produce such observable motions [i.e. similar to the oscillating prosneusis motion of the epicyclic diameter.] Let that be verified."[214] One could easily see how this perplexity could have been at the origin of Ṭūsī's thinking, and which later led him to invent his famous mathematical theorem, now called the Ṭūsī Couple in the literature. The theorem itself achieved just that: an oscillatory motion produced by a combination of two circular motions.

In fact the latitudinal motion of the planets shares many features with the motions of the lunar spheres, and in particular with the slanting of the prosneusis point. That is, the oscillation of the axis, which marks the beginning of the epicyclic motion of the moon, is similar to the oscillation of the inclined planes of the lower planets. And it was this particular Ptolemaic theory of planetary latitudes that exhausted Ṭūsī's patience. He saved his sharpest criticism just for that notion. In a nutshell, Ptolemy accounted for the motion of the planetary inclined planes in latitude by suggesting that one could affix the tips of the diameters of those planes to a pair of small circles along which the tips of the diameters of the said planes would move. And as soon as he suggested those small circles he knew that he was not abiding by the accepted principles, as we hinted before, and thus felt that he had to justify his solution in the following manner: "Let no one, considering the complicated nature of our devices, judge such hypotheses to be over-elaborated. For it is not appropriate to compare human [constructions] with divine, nor to form one's beliefs about such great things on the basis of very dissimilar analogies.''[215] To this, Ṭūsī could only say:

In the context of this very criticism of Ptolemy, Ṭūsī did not only redefine the function of the astronomer with respect to the observations and the mathematical methods with which these observations should be explained, but he went on to propose a new theorem that could resolve this specific predicament of Ptolemy. The new theorem, which was expressed in the

Taḥrīr in a preliminary fashion only to be developed further into the just-mentioned Ṭūsī Couple later on in the Tadhkira, will be revisited in the sequel when we return to the context of the non-Ptolemaic models that were constructed for the specific purpose of formulating alternatives to Ptolemaic astronomy.

Returning to the shukūk tradition, we note that about three centuries later, by the end of the fifteenth century, when the classical narrative had already preached the death of Islamic science, the problems (shukūk/ishkālāt) of Ptolemaic astronomy continued to attract the attention of the working astronomer. In fact those very problems became so famous, and so widespread by then, that they were taken up on their own and made into subjects of individual works, in a manner reminiscent of the specialized shukūk of Rāzī and Ibn al-Haitham almost half a millennium before.

One such fifteenth-century work (of about forty folios in one manuscript) was composed by Muḥyī al-Dīn Muḥammad b. Qāsim, known as al-Akhawayn (d. ca. 1500). The title of the work is simply al-ishkālāt fī 'ilm al-hay'a (Problems in the Science of Astronomy), and seems to have been taken from the first sentence of the book which followed the usual introduction. The sentence began immediately with the enumeration of the famous problems of astronomy. By al-Akhawayn's count, those problems were reducible to seven, and they were all to be found in the received Ptolemaic astronomy.

Al-Akhawayn's treatise began thus:

Al-Akhawayn's advantage over Ibn al-Haitham, with whose shukūk al-Akhawayn's treatise could be easily compared, lied in the fact that Al-Akhawayn could not only enumerate the famous problems of Ptolemaic astronomy, but by his time he could also offer solutions to them. Some were simple straightforward solutions already suggested in the Ptolemaic texts themselves. Others required much more ingenuity and were developed by later astronomers working in the Islamic civilization. Al-Akhawayn quoted both solutions when he could, but remained very brief, as if intending his treatise to be an introductory text for an advanced course on astronomy where the student's appetite would be only whetted by such problems and solutions and students would be urged to delve further in the more advanced texts.

As a result, the treatise managed to summarize not only the status of the problems in Ptolemaic astronomy at this relatively late date, but gave account of the many solutions that had become famous on their own. Al-Akhawayn did not offer all the known solutions to every problem, but restricted himself only to a few, well chosen ones. He only selected from the enormous corpus of solutions that had already accumulated during the few centuries before his time. Modern research has already documented those solutions in some detail. But the ones that were preferred by al-Akhawayn clearly carried the earmarks of a personal touch that is usually encountered whenever an anthology is attempted. Without going into great details, as anthologies are prone to do, al-Akhawayn simply stated, but explicitly so, that some of those problems were particular to specific planets, and that one should not expect each of those problems to be found in all the planets for which Ptolemy had suggested a mathematical model.

After a short introduction, al-Akhawayn devoted the rest of the treatise to a systematic exposition of the configurations of each planet, as given in the famous Ptolemaic astronomy, enumerated the number of problems that the specific configuration suffered from, and proceeded to give the solutions that he knew of. As such his treatise can be thought of as an interesting, simplified anthology of the kind of research that was done for almost half a millennium, and which was also focused on the shortcomings of Ptolemaic astronomy. As a result, one can simply say that by the sixteenth century there had accumulated a large corpus of critiques of, as well as alternative solutions to, almost all the major problems that plagued Ptolemaic astronomy. By the beginning of the sixteenth century, no self- respecting astronomer would have continued to uphold the long-discarded and obsolete astronomy of Ptolemy.

Nevertheless, for astronomers working at later dates, this astronomy was not completely forgotten. They continued to mention its major problems. But that should be read as a sign not of their intention to criticize Ptolemy in specific, but as an indication that the knowledge of such problems had become so widespread in the later centuries, as was stated before. By these later times, the discipline of astronomy itself, as it was reconstituted by the successive generations of critics, could no longer be pursued by seriously- minded astronomers without at least mentioning that such problems existed.

In hindsight, it appears that the so-called age of decline, after the twelfth century, could be characterized as an age during which theoretical astronomy, i.e. the pursuit of planetary theories, began to fork into two separate traditions. There were those who pursued the subject of the critiques themselves, which formed by then a well established genre of astronomical writing. And there were those who attempted to remedy the problems of Ptolemaic astronomy and who constituted a tradition of their own: the tradition of reconstructing Ptolemaic astronomy rather than just satisfying themselves with its criticism. A good representative of the former group was Ibn al-Haitham himself who offered his elaborate and scathing critique of Ptolemaic astronomy and offered no alternatives of his own. And for that failure he was severely criticized, in turn, by the later astronomer 'Urḍī.

It was not unusual to find astronomers attempting to resolve these problems one at a time, rather than undertaking a whole reconstruction of Ptolemaic astronomy as was done by other astronomers such as 'Urḍī and Ibn al-Shāṭir. In the fifteenth century, we find, for example, a good representative of the former group in the famous astronomer 'Alā al-Dīn al-Qushjī (d. 1474). He singled out one of the most notorious problems in Ptolemaic astronomy: the problem of the equant of Mercury, which could not be solved even by Ṭūsī, as he himself had already expressly confessed in his own Tadhkira. In contrast, and as a step in the right direction, Qushjī confidently expounded the problem in great detail, and immediately followed that by offering one of its most elegant solutions, all in a short treatise of few pages.[218] We will also have occasion to return to this solution in connection with the long tradition of alternatives that were proposed for the reformation of Ptolemaic astronomy.

But as far as criticism was concerned, such specific attempts at isolating individual problems for treatment eloquently express the continued dissatisfaction with at least some aspects of the Ptolemaic tradition. And as isolated problems, they should be best understood as advanced research topics quite similar to our modern practice of devoting individual articles to the treatment of particular issues in advanced journals.

Qushjī's grandson, Mīram Çelebī (d. 1524), who was an astronomer in his own right, and who was also the grandson of another distinguished fifteenth-century astronomer by the name of Qāḍīzādeh al-Rūmī (fl. 1440), left several astronomical works; some of them were direct commentaries on the more general works of his grandfather Qushjī. In one of those commentaries, he stated explicitly that he was going to devote an elaborate separate treatise to the problems of Ptolemaic astronomy, which he would call Dhayl al-Fatḥīya (Appendix to the Fatḥīya), where the Fatḥīya itself, his grandfather's work, did not mention any such problems. Instead, it was a rather straightforward exposition of Ptolemaic astronomy. The occasions at which Mīram mentioned the Dhayl were in connection with the problems of the Ptolemaic configurations for the Moon and Mercury. But until the text of the Dhayl is located and studied its full contents still remain unknown.[219]

The sixteenth century witnessed similar efforts by astronomers who mostly came from Persia. One of them was Ghiyāth al-Dīn Manṣūr b. Muḥammad al-Ḥusainī al-Dashtaghī al-Shīrāzī (d. 1542/3), who produced at least two works on planetary astronomy: al-Hay'a al-manṣūrīya (The Manṣūrī Astronomy), and al-Lawāmi' wa-l-Ma'ārij (The Sparkles and the Ascensions), the second of which has not yet been identified. But in a third extant work, al-Safīr, he stated explicitly that he did not only criticize Ptolemy in those two earlier works, but that he even proposed new solutions for the Ptolemaic problems detailed therein, and spoke very flatteringly of the ones he produced in the Lawāmi'. Discussing the configuration for the Moon in al-Safīr, he said:

And while explaining the prosneusis problem in the safīr, he went on to say: "This prosneusis is also among the problems (ishkālāt)... The truth (concerning) it is what I have established in al-Hay'a al-manṣūrīya, which shines with the sparkles (Lawāmi') of light."[221]

And in the course of discussing the equant problem in the configuration for the upper planets, he went on to say: "This too is among the problems (ishkālāt), which al-Hay'a al-manṣūrīya is capable of solving."[222]

With such explicit references, there is no doubt that this sixteenth- century astronomer was interested in pursuing the critical tradition that had already grown around the problems of Ptolemaic astronomy. But here too, unless his other two works are identified and studied in some depth, their actual contents and their real import still remain enigmatic and only speculative at this point.

Similarly, the Syrian astronomer Ghars al-Dīn Aḥmad b. Khalīl al-Ḥalabī (d. 1563) voiced similar concerns in his telling treatise that he called Tanbīh al-nuqqād 'alā mā fī al-hay'a al-mashhūra min al-fasād (Warning the Critics About the Faults of the Generally Accepted Astronomy). In it he even raised an issue that has not been raised so far in this discussion, but which will be taken up in the section dealing with the relationship between astronomy and philosophy. For our current purposes, it is enough to signal that the issue itself expressed doubts regarding the permissibility of the eccentrics that were used in the Ptolemaic configurations. In that context, Ghars al-Dīn proclaimed:

The fourth chapter of that treatise was devoted to the problems of the lunar configuration, and the treatise itself was dated to 1551 A.D.

The same century also witnessed the most extensive, ingenious and unparalleled works of Shams al-Dīn al-Khafrī (d. 1550), which combined both the critical tradition as well as the tradition of alternative constructions to Ptolemaic astronomy. Some of those works have already been subjected to some analysis by the present author, and we shall have occasion to return to them in the section dealing with alternatives to Ptolemaic astronomy.[224]

The next century witnessed the production of the prolific scientist Bahā' al-Dīn al-'Āmilī (d. 1622), who did not seem to have confronted the Ptolemaic problems directly, as they do not seem to be especially mentioned in his treatise Tashrīḥ al-aflāk. But his commentators did not observe such reserve. Instead they composed full texts of their own, or added marginalia to 'Āmilī's text which was by then heavily read and widely distributed in schools, and thus continued to expose and indirectly popularize the faults of Ptolemaic astronomy. One of those commentators on al-'Āmilī's text added a marginal note in which he gave a quasi history of those faults and the people who had addressed them before. In one manuscript, the note reads:

This quasi-historical synopsis, despite its historical shortcomings, at least reveals two important trends: First, it signaled that there were people who were themselves interested in the history of astronomy, and second that the problems of Ptolemaic astronomy continued to be discussed after the middle of the seventeenth century when this note was probably written. In addition, it also reveals that the works of Dashtaghī had by then become the standard references, at least as far as the author of this marginal note was concerned.

Historians of Arabic astronomy have not yet made any forays in the centuries that followed in order to determine the extent of criticism, if there was any, or to find out if the later astronomers continued to construct alternatives to Ptolemaic astronomy. This particular research would be of the utmost importance, especially in light of the fact that in these later centuries one would want to know how those astronomers dealt with the reception of modern post-Copernican astronomy in Islamic countries. Or whether the old Ptolemaic astronomy could still survive the onslaught of post Copernican astronomy. What little research has been done in this domain, i.e. in the domain of criticism of the natural philosophical underpinnings, reveals that during the latter part of the nineteenth century there were still those who defended Ptolemaic astronomy against its detractors, when the detractors had by then adopted the alternative Copernican and more modern astronomy.[226]

Finally, there were objections of another kind: more theoretical in nature, in the sense that they addressed such theoretical issues that touched upon the very foundations of all scientific activities and were not only restricted to astronomy. And there were those who proposed new mathematical models to account for the same observations of Ptolemy, without explaining their motivations. But their alternative works can only mean that they were dissatisfied with the existing Ptolemaic models, and thus their activity must be perceived as an objection in itself. So when we come to survey the various alternative models that were proposed to replace the Ptolemaic ones, one could read that survey as an elaborate statement of theoretical objections to Ptolemaic astronomy as well.

Others raised further theoretical questions that could be read together with the philosophical questions that will be touched upon later on as we discuss the relationship of science to philosophy in the case of astronomy. In the present context of the encounter with the Greek tradition those questions gain a special significance as they touched upon the philosophy of science in a more focused sense. That is they tried to determine the domain in which one astronomer was justified in raising objections to the work of another. What was it exactly that one was allowed to object to, and what kind of evidence one was required to bring to the argument in order to make the case? What was the role of the observations in astronomy and what was an acceptable account of them? For this type of questioning the best representative was the Damascene astronomer Mu'ayyad al-Dīn al-'Urḍī, whose name was mentioned several times already. In his extensive treatise, Kitāb al-Hay'a,[227] which could be read in its entirety as a comprehensive statement of objections to Ptolemaic astronomy, he isolated such issues in particular when he attempted to reform, for example, the proposed Ptolemaic configurations for the planet Mercury. After enumerating the various spheres, their motions, and their relative positions with respect to one another, he went on to say:

By questioning the relationship between the observations and the kind of results one was allowed to deduce from them, 'Urḍī wished to direct the attention of his reader to the activity of model building itself. What part of it was dictated by the observations and what part was left to the astronomer himself to construct? And in the case of the model for the planet Mercury, 'Urḍī had this to say:

In very clear terms, this demonstrates the type of engagement that 'Urḍī had sought to achieve with the Ptolemaic tradition. To some of its parts, especially the observational aspects, he had no objections to make because he had no observations of his own to bring to bear. The periods of the planets, he also had to accept as he also did not have better ancient sources to deduce his own. Ptolemy's mathematics was also superb, especially after it had been already updated by the generations of astronomers who worked on it since the ninth century. But when it came to conjecture (ḥads), 'Urḍī's term for theorizing, there was no reason to prefer Ptolemy's theories over others, especially when those theories could not account for the observations and yet remain faithful to the Aristotelian cosmology that was already accepted by Ptolemy. It is not that astronomers like 'Urḍī were blaming Ptolemy for abandoning Aristotle, and that they were so enamored by the latter to wish to re-install him through the adoption of his cosmology, but what they found objectionable was the theoretical contradiction between Ptolemy's acceptance of a set of principles on the one hand, no matter whose principles, and his contradicting those very principles when he came to describe the mathematical constructs that represented the same principles. On that level of theorization they felt that Ptolemy should have no priority over them. In fact they felt better qualified to theorize simply because they avoided the contradictions that plagued Ptolemy's astronomy. And yet their alternative models accounted for the observations just as well as Ptolemy's models could. Virtuous as he was, Ptolemy's authority could not overcome his inability to theorize properly.

At this stage, the Islamic astronomical tradition had obviously reached such maturity that it could profitably raise issues that were not raised before. It could contemplate problems, relationships, theoretical strategies, that were not dreamt by Ptolemy. The confidence in the new foundations of science gave these astronomers the ability to go beyond the criticism of Ptolemy, and to dare to oppose his models with their own, by either redeploying the same mathematics that he used, or by devising some of their own to replace it. This confidence also allowed them to look at the universe from a different perspective and to lay down new rules for the science that would eventually describe it. Such matters that were being explored in that manner touched the foundation of every science and were no longer restricted to astronomy alone. Again they should be borne in mind when we discuss the relationship of science to philosophy later on.

In the present context, and even at the expense of some overlapping with the later chapter, these theoretical issues should be highlighted here as well. The theoretical lines that were developed in response to the Greek astronomical tradition also gave rise to the debate over the admissibility of eccentrics and epicycles among the celestial spheres, a debate that was not in essence a debate over the violation of the physicality of the spheres as was discussed so far, but a discussion over whether in principle the celestial realm admitted such configurations at all. The origin of the problem was already locatable in several of the Aristotelian works, but most notably in the De Caelo, where Aristotle proved, with impeccable philosophical rigor, not only that the whole universe was spherical, but also that the Earth was at its center. And if one did not have an Earth there, one had to assume an Earth as the fixed point of any moving sphere, besides being the ultimate point of heaviness of the universe.[230] The argument was therefore of a necessary nature and not a merely convenient option to place the Earth at the center of the universe or not. Astronomers could debate as much as they wanted whether the observable phenomena could be explained by the assumption of a fixed Earth at the center of the universe, or by a revolving Earth around its own axis or around the sun. Some of them did raise these very possibilities in pre-Aristotelian and post Aristotelian times as well as during Islamic times, as was done by Aristarchus of Samos (c. 230 B.C.), for example, and by Bīrūnī (1048) centuries after him. They did acknowledge that the same phenomena could either be explained by a fixed Earth at the center or by a moving one. But that did not change the Aristotelian cosmological conditions one bit. According to Aristotle that "theoretical" Earth had to be motionless at the very center of the universe in the same way every moving sphere must have a motionless point at its very center.

The discussion that revolved around the admissibility of eccentrics and epicycles lied at the core of this theoretical discussion, and those who would not allow such concepts took the position that such eccentrics and epicycles would then introduce a center of heaviness, other than the Earth, around which celestial simple bodies would then move. Ptolemy tried to resolve the debate by introducing the Apollonian theorem, which allowed for the replacement of an eccentric with a simple concentric sphere carrying an epicycle. But the problem could not be resolved so easily as the epicycle itself was also found objectionable for it also introduced a center of heaviness around which the epicycle itself revolved, and worse yet the epicycle had to be placed out there in the world of the Aristotelian ether which was defined as the ultimate simple element par excellence.

Andalusian astronomers such as Ibn Bāja (Avempace d. 1138/9), Ibn Ṭufayl (d. 1185/6), Ibn Rushd (Averroes d. 1198), and al-Biṭrūjī (c. 1200), each in his own style, expressed their dissatisfaction with Ptolemaic astronomy specifically because it harbored such appalling non-Aristotelian bodies as eccentrics and epicycles. Al-Biṭrūjī went farther than all of them by undertaking to construct a complete alternative configuration that avoided these eccentrics.[231]

Al-Biṭrūjī's success was spoiled by the inability of his configuration to account for the observations in a quantitative manner that would allow for the predictability of the planetary positions for any time and any place. That fundamental test of any astronomical proposition was the main hurdle against which al-Biṭrūjī's configuration collapsed. It was only an attempt to resuscitate the old Eudoxian spheres that had at one point enchanted Aristotle himself, but could not even then predict the position of any planet at any time, despite the fact that they could give a rather naive description of a planet's general behavior. And so was the case with Al-Biṭrūjī's construction, which also failed to account for the observable motions of the planets. For that reason alone Biṭrūjī's account remained to be a curious proposition that was not pursued any further by later astronomers. I suppose no practicing astronomer or astrologer, who needed to compute positions of planets, could take it seriously.

On more serious grounds, and for all those who wished to uphold the Aristotelian universe, at some point they had to admit that the Arsitotelian universe was not all that consistent anyway. Again we shall return to this philosophical issue later on. But in the context of this chapter, where we are focusing on the reception of the Greek scientific tradition into the Islamic civilization, let us complete the picture by indicating the range of objections the astronomers who worked in Islamic times were prepared to raise. According to Aristotle, all celestial bodies, spheres, stars and planets, were all supposed to have been made of the same Aristotelian simple element, ether. That element was supposed to be divine, thus the simplest of all elements, capable only of one motion: the circular motion that had no beginning, nor end. As a result the simple element ether did not partake of any composition or any generation or corruption, as was the case with the other sublunar elements that experienced linear contrary motions. If that Aristotelian proposition were to be taken literally, and there were some who did take it so, then one would wonder how could a sphere, say, that carried the sun, in the same fashion a ring carried a crown, emit such a bright light as the light of the sun, from only one part of it, where the sun is located, while the rest of its body acted like a crystalline transparent spherical substance that did not emit any light? This, when the sun and its carrying sphere were both assumedly made of the same element ether.

Ibn al-Shāṭir of Damascus confronted the Aristotelian universe along these very lines and with this exact understanding. In his own way though, he posed the question in the following manner: He said that since the stars, and the planets, were themselves different from the spheres that carry them, as in the case with the sun that emits light while the sphere that carries it does not, then Aristotle would have to admit that the celestial world was not all that simple and must admit of some type of composition. Now, since astronomers, Aristotelian ones included would know that some of the fixed stars were in fact considerably bigger than the largest epicycles of the planets, then if a composition is allowed for the fixed stars, the same composition must also be admitted for the much smaller epicycles as well. Ibn al-Shāṭir would then conclude that he was entitled to as much composition in the celestial spheres that would allow for the epicycles as Aristotle would allow for the fixed stars. He then went on to say, that while Aristotle and those who followed him could be right about the inadmissibility of the eccentrics, they were all wrong on the inadmissibility of the epicycles. The immediate consequence of this position led Ibn al-Shāṭir to construct very complicated mathematical models that would replace the Ptolemaic models, but at the same time they were all constructed without a single eccentric sphere. In his defense he simply changed the Aristotelian assumption to stipulate that the universe was not as simple and consistent as Aristotle had thought, but according to Ibn al-Shāṭir, that it admitted of some form of composition. In a real sense, Ibn al-Shāṭir's novel assumption was the only one I know of where an astronomer actually confronted the Aristotelian assumptions with a set of his own. This should have serious philosophical repercussions when taken in the context of the gradual collapse of the Aristotelian universe that culminated with the Newtonian final coup de grace.

In the context of the encounter with the Greek scientific tradition, and in the context of the relationship of the science of astronomy to the other sciences, a particular case should be made for mathematics. Not only because the astronomers used this discipline so profusely, nor because it was the demonstrative science par excellence, but because those same astronomers who went on to criticize Ptolemaic astronomy, and with their extensive proposals for alternative constructions, began to unravel the nature of the discipline of mathematics as well, by noticing that there were so many mathematical constructions that could explain the same observational results. The standard case in this regard was that of the Apollonius theorem which was used by Ptolemy himself to account for the same observations either by an eccentric construction or by an epicyclic one. Ptolemy was conscious of the fact that those two mathematical constructions depicted the same observational results, and opted to use the eccentric construction on account of its simplicity since it involved only one motion as he put it.

What Ptolemy did not say was that both constructions, the eccentric as well as the epicyclic, violated the Aristotelian cosmology. For in the first case, the eccentric assumed a fixed center of heaviness other than the Earth, which was inadmissible, and in the second case of the epicycle it assumed a center of heaviness out in the celestial realm as we just described.

Later astronomers who had no vested interest to defend the Aristotelian universe one way or another were at times ambivalent about those constructions and went along with the Ptolemaic choice of the eccentric constructions. As we have just said, only Ibn al-Shāṭir objected to the eccentrics and avoided using them in his reformulation of astronomy.

But what was also left unsaid was the validity of the discipline of mathematics itself in relationship to astronomical theory. How was one to assess which mathematical construction was to be preferred and which one was not, especially when both constructions could explain the observational data just as the Apollonius theorem could? We have already seen how 'Urḍī, for example, already succumbed to the Ptolemaic use of mathematics, and did not raise any doubts in that regard. Only when he had to reformulate Ptolemy's mathematical model for the upper planets, he felt obliged to introduce a mathematical theorem that was not found in the Greek texts, and used that theorem only to account for the observations in a much better model than that of Ptolemy. But he went no further than that.

Not until later did astronomers stop to think about the connection between mathematics and astronomy, and as we have just said, did so only when they began to notice that there were many mathematical constructions that could lead to the same results, that is, account for the observations equally well. By the sixteenth century, the astronomer Shams al-Dīn al-Khafrī (d. 1550), who was already mentioned, employed this very same new understanding of mathematics to its fullest, where in his own description of the new models that he and others had developed he would supply several models for the same planetary motions. That is, he would give several mathematical alternatives to interpret the same observations in exactly the same fashion. In the case of the motions of the planet Mercury, for example, he gave in one of his works four different mathematical models all yielding exactly the same mathematical results, and thus all accounting for the observations in the same fashion. And in his own words he offered these models one after the other simply as different ways (which he called wujūh) of looking at the same physical reality. This new understanding, that mathematics was only a language that allowed the astronomer to describe the same physical reality in so many different ways, is nowhere better exhibited than in the works of Khafrī.[232]

This brief overview should have made it very clear that the Greek astronomical tradition, especially that which was represented by the most important texts of that tradition, the Ptolemaic texts, was not simply preserved in the Islamic culture, as is so often asserted, but that it had received a very critical assessment from the very beginning. From correcting the perceived mistakes in the Greek texts by the translators themselves, to the critical re- evaluation of the observational results that led to changing the most fundamental astronomical parameters of that tradition, to raising objections against that tradition for its detected disregard of its own natural philosophical premises that were firmly grounded in the Aristotelian tradition, to the theoretical objections against that tradition for its lack of systematic consistency, and finally to the theoretical objections that were raised in regard to the actual foundations of astronomy itself, how the science itself was structured and which components of it were subservient to which other components, and which of the other sciences were deployed in it and in what capacity, all of those aspects of the Greek astronomical tradition were subjects of great dispute.

First, the most important aspect of the ensuing debate was that it was carried out with the most classical Greek authors, an observation that confirms our earlier assumptions about the lack of scientific sophistication of the contemporary Byzantine and Sasanian cultures. None of the critiques that we have signaled so far were of current Byzantine or Sasanian doctrines, rather they were directed against Ptolemy, Galen, Aristotle and the like. The most important feature of this encounter with the Greek tradition is that it was a confrontation with the classical authors, and thus in a round about way the confrontation itself brought those classical ideas back into currency, at the same time as they were being refuted and modified. It was not a polemic against contemporary Byzantine authors, which affirms once more that there was no such advanced civilization in Byzantium to come in contact with, as we have already repeated again and again.

Second, this confrontation took place in the context of very complex social forces that were at odds with each other, for political and social reasons, and were only secondarily directed against the very science itself. As we have already seen, the science and the philosophy that were being brought into the Islamic civilization were directly connected to the social position of the persons who were bringing them, usually political and economic positions, and in a sense their final chances of acceptance or rejection in the target Islamic civilization were conditioned by the success or failure of the groups that sponsored those activities.

Third, the Greek scientific and philosophical sources were being sought for reasons connected to the on-going debate that was taking place within Islamic civilization, a debate that was generated by the reforms of 'Abd al-Malik, as I have maintained all along, and were not sources that were encountered by chance through innocent contacts between two civilizations. This conscious and willful selection of texts to be translated, which Sabra and before him Lemerle would want to call appropriation, because they served a specific purpose in the debate, also colored the manner in which those texts were accepted or rejected in the acquiring civilization. They were not ill-directed chance encounters that could bring their own momentum from the outside. Thus the Greek texts that were translated into Arabic simply enforced certain pre-selected directions and did not create their own directions, except in very tangential ways when they began to generate philosophical schools of their own in later centuries.

Fourth, because the texts that were being sought during the eighth and ninth centuries were already written some 700 years earlier, and in some cases even more, their scientific contents were already obsolete in the sense that their mistakes were already exaggerated with the passage of time. For example, Ptolemy's small mistakes, which resulted from his comparison of his own observations with those of Hipparchus who observed some two centuries earlier, were now quite exaggerated after the passage of some seven centuries before they were re-examined again in ninth-century Baghdad. Only from that perspective we can understand why it was easy to note the differences between the ninth-century results, such as precession, position of solar apogee and the like, and the results that were determined by Ptolemy some seven centuries earlier.

Fifth, these results, whether they were directly acquired from the Greek sources, or were modified by the fresh observations, were always used within the ongoing struggle between the proponents of the "ancient sciences", whose claim to power depended directly on those new results, and the proponents of the more Islamic classical orientation whose claim to power depended on their knowledge of the Arabic language. And because this main competition between those two groups also generated another competition with fellow scientists who were also trying to prove their relevance to political authority which employed them in the final analysis, then every scientist who was engaged in acquiring Greek texts had to worry about the two sets of opponents who were looking over his shoulder: the fellow scientists who wanted to claim greater authority to the texts that they had acquired, and thus compete for the same government jobs, and the opponents whose authority rested on their knowledge of the Arabic language that was already affiliated with the religious sciences where it was desperately needed. As we have already stated this phenomenon itself can explain why someone like al-Ḥajjāj b. Maṭar had to make sure that his translation was written in the best Arabic, in order to compete against those who possessed the Arabic language, and its contents had to be corrected from the scientific point of view so that his work would be better than the work of the other translators who at times simply translated the text mistakes and all. This may also explain why Ḥajjāj's translation was not the first, and that it was already an improvement over an older translation, as we are told by al-Nadīm. Furthermore, it had less transliterated words from Greek than the translation that was completed some fifty years later by Isḥāq b. Ḥunain a clear indication that this linguistic competition had already faded by Isḥāq's time and was then transformed into another competition based on ethnic and religious affiliation, which was highlighted by the Shu 'ūbīya movement.

Ghazālī's later attack on the essentialism of the Greek causal philosophy could also be read as a continuation of the debate against the Aristotelian essentialism that required a fixed Earth at the center of the universe, and a strict adherence to the Aristotelian cosmological universe that was not always followed by Ptolemy. In other words, those within Islamic civilization who saw in the works of Aristotle a strict essentialist philosophy could not tolerate the divergences of Ptolemy and thus initiated a whole series of attacks against his deviations. But it was those same persons with that same strict Aristotelian essentialist interpretation who were perceived by the religious camp represented by Ghazālī as going too far in their essentialism on issues of causality for example. Thus in an ironic turn of events one can say that the objections that were raised by astronomers working in the Islamic domain against Ptolemy's astronomy were motivated by Aristotelian purist astronomers who were at the same time fighting their own battle with religious people who wanted to understand Aristotle in a much more relaxed sense, almost in the same relaxed manner in which Ptolemy understood Aristotle.

Moreover, the debate that expressed itself in the Shukūk literature, of which we have seen several examples, can be perceived as one feature of a much larger phenomenon that included religious attacks against Greek astrology, observational mistakes, factual errors in medicine, etc., where such disciplines also developed under the double watchful eyes of enemies from without, who competed over the sources of authority and who had the right to claim the possession of that source, and enemies from within who competed over who was the better scientist who could qualify for the government job.

It is within this complex environment that new disciplines such as Hay a, Mīqāt and Farā'iḍ, came into being in order to satisfy the outside competition with the religiously inclined opponents, but at the same time to carve purely independent disciplines that could compete against the traditional ones, which were being promoted by fellow scientists from within so to speak. In that environment a science like hay'a became at once a religiously acceptable science, and at the same time a more rigorous science that carried the brunt of the attacks against Greek astronomy in order to prove its rigor and its good religious standing.

Within the same environment we can better understand this insistence on scientific rigor as the motivation behind the constant emphasis by hay'a authors on the inner consistency of science mentioned above, an emphasis that characterized the long history of the hay'a tradition. Hay'a authors were obviously trying to keep this double edge advantage over their fellow astronomers, such as authors of zījes for example, by remaining more stringent in their scientific consistency requirements and by remaining religiously acceptable to the society at large. In that regard they scored a tremendous success as their discipline continued to be taught till recent times, and sometimes well within the religious educational institutions themselves.

Once we can see the double motivation to attack the Greek tradition, we expect this phenomenon to have had similar effects in other fields as well. And when we consider the field of medicine for example, we arrive at very similar results. We already had a chance to refer to the text of Abū Bakr al-Rāzī in which he objected to Galen's theories but also went ahead and composed his own rigorous scientific book on the difference between smallpox and measles, a difference that was apparently unknown to Galen, despite Rāzī's protestations.

This same critical spirit was also exhibited in the work of 'Abd al-Laṭīf al-Baghdādī (d. 1231)[233] who visited Egypt toward the beginning of the thirteenth century and who also found himself on a collision course with Galen at certain medical points. In his account of his trip to Egypt, he mentioned that he had found certain anatomical points very difficult to explain to his students, and for them to understand those points, because in theory the written word was always less evident than the observation, or that "observation is always much stronger than words" as he put it.[234] This should not be surprising since dissection was not commonly practiced in premodern times. But Baghdādī went on to say that he profited from a recent plague that had befallen Egypt, and visited with his students the piles of skeletons, which were still lying on the outskirts of Cairo. During their investigation, Baghdādī related that he noted the jawbone of those skeletons, and that he found it to have been a single bone rather than two, as Galen had asserted. He went on to relate that he repeated the observation several times, in many skeletons, and that he always found it to be one bone. He then asked several other people who had also observed it in his presence and on their own and they all agreed that it was one bone. He then promised to write a treatise in which he would describe the differences between what he saw and what he read in the books of Galen. But he continued to say that he kept on investigating this issue in graveyards of various ages in order to see if a seam or a split would be observed in that bone with age. And as much as he wished to save the Galenic text, he found none.

In another instance, the same Baghdādī also reported that his original investigation was contrary to the teachings of Galen, but that later repeated observations confirmed the Galenic texts.

The works of Ibn al-Nafīs of Damascus (d. 1288), already mentioned before, fall in the same category, in that they exhibit this tendency to try to save the Greek texts from their own folly, so to speak, but having to object to them when there was better evidence of their error. Ibn al-Nafīs's discovery of the smaller pulmonary circulation of the blood comes from the same tradition as that of Rāzī and Baghdādī, and represents the empowerment that the scientists of the Islamic domain must have felt once they started noticing the exposure of a whole sequence of mistakes in the classical Greek scientific texts, and once they started believing in what they saw with their own eyes.

Other disciplines witnessed similar transformations in that they managed to cleanse the mistakes of the Greek tradition, whenever possible, but also went beyond to forge their own new terrain that the Greek authors did not know about. In particular the discipline of mathematics seems to have received a very interesting boost toward the sixteenth century when its relationship to astronomy was finally correctly understood at the hand of someone like Khafrī (d. 1550) who could finally see that mathematics was just a tool that could be used to describe physical phenomena, and that it did not retain the Truth itself.

The only astronomical criticism that was not touched upon in any detail in this overview was the criticism that was implicit in the various attempts of generations of astronomers who sought to reform Ptolemaic astronomy by constructing new mathematical models that could render the reality of observations, and the theoretical natural philosophical foundations in a much more coherent and consistent fashion. These will be explored in the chapter, which will survey the non-Ptolemaic models as was already promised.

The Islamic civilization did not seem to have produced a rigorous astronomical criticism of the type that would have questioned the natural philosophical foundations of Greek astronomy themselves. Although some religiously inspired cosmologies did in fact speak to that point, yet there were no astronomers that I know of who adopted these views or sought to interpret the astronomical implications of such cosmologies. The final rejection of Aristotelian cosmology had to come late in the history of astronomy, and only after a long and arduous struggle that was initiated by modern science under conditions that were completely different from those that prevailed in the Islamic civilization.