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: