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.
173
Laurel Brown of Columbia University is preparing a Ph.D. dissertation that will include a detailed analysis of this text and its implication for the Arabic critical tradition that was beginning to take shape during the tenth century.
175
It is not surprising therefore to find that most Western major libraries include several copies of Ṣūfī's text among their holdings. See for example the various copies at the British Library, Or 5323, Or 1407, IOISL 621, IOISL 2389, and Add 7488, among others.
177
George Saliba, "The Role of the