The Arabic Version of Ptolemy's Planisphere Or Flattening The

SCIAMVS 8 (2007), 37–139 The Arabic version of Ptolemy’s Planisphere or Flattening the Surface of the Sphere: Text, Translation, Commentary Nathan Sidoli J. L. Berggren Department of Mathematics Department of Mathematics Simon Fraser University Simon Fraser University There are currently no known manuscripts containing the Greek text of Ptolemy’s Planisphere.1 Nevertheless, there are two medieval translations from which an as- sessment of the original work can be made. The oldest of these is in Arabic, un- dertaken by an unknown scholar, presumably as part of the Baghdad translation movement [Kunitzsch 1993, 97; Kunitzsch 1995, 150–153]. There has never been any doubt that this was based on a Greek text written by Ptolemy, and those who are familiar with Ptolemy’s Almagest will notice many similarities of style and struc- ture between the two texts, despite the different rhetorical tendencies of Greek and Arabic prose. Moreover, Ptolemy assumes that the reader of the Planisphere has already read his Almagest, which he refers to in a number of places. In the 12th century, a loose Latin translation was made by Hermann of Carinthia on the basis of a different Arabic version than that found in the two known Arabic manuscripts.2 Hermann’s version was edited by Heiberg [1907, 227–259], translated into German by Drecker [1927], and has been the source of much of the modern schol- arship on the text.3 Hermann’s text served as the basis for the early-modern Latin editions, the most influential of which was by Commandino [1558], who appended a commentary that includes a study in linear perspective.4 Although Anagnostakis [1984] produced an English translation and study of one of the Arabic manuscripts as part of his dissertation, the text has never been formally 1The 10th-century Suidas gives the Greek title as the VAplwsic âpifaneÐac sfaÐrac, Simplification of the Sphere [Adler 1928–1938, 254]. Kaufmann corrected the fist word to âxĹplwsic, which he took as “unfolding” [Pauly-Wissowa 1894–1980, vol. 2, 1801], and Neugebauer [1975, 870–871] accepted this correction. It is possible to read either of these words as “unfolding” or “spreading out.” 2An earlier Latin translation survives only in fragments [Kunitzsch 1993]. There is too little of this text to be able to say much about the Arabic source. 3There is also a medieval Hebrew translation, but this appears to have been based on the Latin [Lorch 1995, 276, n. 11]. 4Commandino’s text, as well as two earlier modern editions, was reprinted by Sinisgalli and Vastola [1992], who also provided an Italian translation. Commandino’s commentary is reprinted, with an Italian translation, by Sinisgalli [1993]. 38 Sidoli and Berggren SCIAMVS 8 edited. The present study supplies a critical edition of the extant Arabic text, along with our translation and commentary. The commentary provides a new reading of the text that encompasses the entire treatise and integrates it into its context as a work in the Greek mathematical tradition. There have been relatively few historical studies of the Planisphere as a whole. Probably, the most useful summary of the mathematics underlying Ptolemy’s approach is by Neugebauer [1975, 857–868], who read the text as principally concerned with the construction of astrolabes [Neugebauer 1949, 247–248]. The commentary of Sinisgalli and Vastola [1992] is likewise useful for understanding the text in terms of modern mathematical methods and projective geometry. In neither case, however, is there much attempt to understand Ptolemy’s project in terms of ancient mathematical methods. Moreover, both of these studies are based on the Latin text. Anagnostakis [1984], in his study of the Arabic text, gave a commentary to the whole treatise, but did not attempt to situate the overall approach and goals of the treatise in the context of ancient mathematical methods. These last issues have been addressed in papers by Berggren [1991], who sought to understand Ptolemy’s aim in the Planisphere by comparison with his Geography, and Lorch [1995], who compared Ptolemy’s methods with those of a medieval commentator. Our reading makes use of these studies; however, we make some key differences of interpretation, which are discussed in the commentary. Moreover, ours is the first reading based on a critical edition of the oldest extant version of the text. The Planisphere is the first known treatise that develops a plane diagram of the celestial sphere using methods mathematically related to stereographic projection. Although Ptolemy wrote the text, the methods contained in it probably go back at least as far as Hipparchus [Neugebauer 1975, 868–869]. Moreover, the text appears to have been written for the advanced student, or expert, in mathematical astronomy. For these reasons, the Planisphere should be of great interest to historians of the ancient and medieval exact sciences. By studying this text, we may learn what sort of knowledge could be assumed on the part of a mathematically competent reader in the 2nd century, and probably for a number of centuries before this time. In this way, historians of astronomy can produce a more detailed picture of the mathematical methods of ancient astronomers, and historians of mathematics can develop a broader understanding of the range and methods of Greek mathematics. The kinds of mathematical thought preserved in the Planisphere are especially important if we are interested in those cultures that inherited the Greek mathematical tradition. The Greek conception of the celestial sphere, in both its geometric and arithmetic articulations, was of great interest during the medieval period to scholars working in Sanskrit, Pahlavi, Arabic, Hebrew and Latin. Although many modern historians have a tendency to draw disciplinary divisions between astronomy and mathematics, such distinctions would hardly have been evident to ancient and medieval scholars. In particular, there would have been little of the institutional and SCIAMVS 8 Ptolemy’s Planisphere 39 professional segregation that we now take so much for granted. The different ways of categorizing and arranging the mathematical sciences were nearly as numerous as the practitioners, but mathematical studies of the celestial sphere were always seen as an important branch of the exact sciences. In the medieval and early modern periods, the projection of the sphere onto the plane became a fruitful area of new research and Ptolemy’s text was understood as fundamental to the field. It is our hope that this study will bring new understanding to the endeavors of the ancient and medieval scholars who investigated the fundamental mathematical structures of their cosmos. I Editorial Procedures We have prepared the text on the basis of images of the only two manuscripts presently known and available. I: Istanbul, Aya Sofya 2671 T: Tehran, Kh¯anMalik S¯as¯an¯ı Anagnostakis [1984, 226–267] printed the first of these in facsimile, while the second is described in detail by Kunitzsch [1994a], who collated the two and listed what he considered to be the superior readings of T. A third ms is listed by Beaure- cueil [1956, 19] as having belonged to the Maktabat Ri-¯asatal-Mat.b¯u,¯atin Kabul; however, this library has not survived the recent wars. Our apparatus refers to three other sources which are not mss but which have been useful in establishing the text. Mas: Maslama’s notes Her: Hermann’s Latin translation Ana: Anagnostakis’s English translation The 10th-century Andalusian astronomer Ab¯ual-Q¯asimMaslama ibn Ah. mad al-Farad.¯ıal-Majr¯ıt.¯ıstudied the treatise and produced a series of notes and supple- mentary material of use for the construction of astrolabes [Vernet and Catalá1965, 1998; Kunitzsch and Lorch 1994]. As well as being useful for understanding the mathematics of the treatise, Maslama’s notes contain sixteen citations, all but one of which can be usefully compared to the text contained in TI. There are, however, differences between the text Maslama quotes and that preserved in TI. These are usually minor, but in places they are enough to show that the two versions could not be edited so as to produce a single text (for examples, see lines 423, 481, 498, Mas107). 40 Sidoli and Berggren SCIAMVS 8 Hermann’s Latin translation was made on the basis of some version of Maslama’s edition and included Maslama’s notes and additional material [Kunitzsch and Lorch 1994, 34–71]. We have used this text to justify a number of corrections to the Arabic, especially in the numbers. The superior readings found in Hermann’s text are probably corrections introduced by Maslama, or less likely Hermann, as opposed to evidence for a more pristine text. Nevertheless, they represent medieval readings without which the text would, in a number of cases, make no mathematical or astronomical sense. It would also be possible to correct many of the letter names of geometric objects on the basis of Hermann’s text, but since he often uses different lettering, and sometimes a slightly different figure, this would be more trouble than it could be worth. There are numerous errors in the letter names of geometric objects. In the early part of the treatise, a more recent hand has corrected many of these in T. Moreover, in his translation, Anagnostakis [1984, 99–101] introduces many corrections, most of which concern the letter names. Where we follow these corrections, they are attributed to one or both of these sources. I.1 Orthography In the edited text, we have attempted to follow the orthography of the manuscripts, so that where TI agree on a particular form, we follow that even when it differs from modern conventions.5 For example, since they both write IÊ K for HC K, we have printed the former.

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