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.
166
Saliba, "The Determination of the Solar Eccentricity and Apogee According to Mu'ayyad al-Dīn al-'Urḍī (d. 1266 A.D.)",
170
lbn al-Shāṭir,