ArgumentIn theAlmagest, Ptolemy finds that the apogee of Mercury moves progressively at a speed equal to his value for the rate of precession, namely one degree per century, in the tropical reference system of the ecliptic coordinates. He generalizes this to the other planets, so that the motions of the apogees of all five planets are assumed to be equal, while the solar apsidal line is taken to be fixed. In medieval Islamic astronomy, one change in this general proposition took (...) place because of the discovery of the motion of the solar apogee in the ninth century, which gave rise to lengthy discussions on the speed of its motion. Initially Bīrūnī and later Ibn al-Zarqālluh assigned a proper motion to it, although at different rates. Nevertheless, appealing to the Ptolemaic generalization and interpreting it as a methodological axiom, the dominant idea became to extend it in order to include the motion of the solar apogee as well. Another change occurred after correctly making a distinction between the motion of the apogees and the rate of precession. Some Western Islamic astronomers generalized Ibn al-Zarqālluh's proper motion of the solar apogee to the apogees of the planets. Analogously, Ibn al-Shāṭir maintained that the motion of the apogees is faster than precession. Nevertheless, the Ptolemaic generalization in the case of the equality of the motions of the apogees remained untouchable, despite the notable development of planetary astronomy, in both theoretical and observational aspects, in the late Islamic period. (shrink)

The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. -/- In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical (...) agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. -/- A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection. (shrink)

The science called 'harmonics' was one of the major intellectual enterprises of Greek antiquity. Ptolemy's treatise seeks to invest it with new scientific rigour; its consistently sophisticated procedural self-awareness marks it as a key text in the history of science. This book is a sustained methodological exploration of Ptolemy's project. After an analysis of his explicit pronouncements on the science's aims and the methods appropriate to it, it examines Ptolemy's conduct of his investigation in detail, concluding that despite occasional uncertainties, (...) the declared procedure is followed with remarkable fidelity. Ptolemy pursues tenaciously his novel objective of integrating closely the project's theoretical and empirical phases and shows astonishing mastery of the concept, the design and the conduct of controlled experimental tests. By opening up this neglected text to historians of science, the book aims to provide a point of departure for wider studies of Greek scientific method. (shrink)

So far am I from rejecting the use of what has been well stated by others, that I would wish that everyone said the same things about the same things and, as Socrates puts it, in the same words, and then there would be no undisputed quarrelling among men about the matters at hand.

The paper presents three strong arguments advocating for the exclusion of the table of Ptolemy’s own planetary terms from the original text of the Tetrabiblos. This table was vastly used by Renaissance astrologers, and much work on its rationale and its manuscript variant readings has been published recently. The author argues that the table was the product of the systematic analysis of Ptolemy’s instructions for the terms in the late antique commentary on the Tetrabiblos edited by Wolf in (...) 1559, and that it entered the direct transmission of Ptolemy’s text in the Byzantine period, probably in the 11th century through cod. Laur. 28,34. The absence of the table in the original Tetrabiblos would explain Ptolemy’s recourse to a probably invented manuscript find and his limited account of the system’s workings. (shrink)

In the Planetary Hypotheses, Ptolemy summarizes the planetary models that he discusses in great detail in the Almagest, but he changes the mean motions to account for more prolonged comparison of observations. He gives the mean motions in two different forms: first, in terms of ‘simple, unmixed’ periods and next, in terms of ‘particular, complex’ periods, which are approximations to linear combinations of the simple periods. As a consequence, all of the epoch values for the Moon and the planets are (...) different at era Philip. This is in part a consequence of the changes in the mean motions and in part due to changes in Ptolemy’s time in the anomaly, but not the longitude or latitude, of the Moon, the mean longitude of Saturn and Jupiter, but not Mars, and the anomaly of Venus and Mercury, the former a large change, the latter a small one. The pattern of parameter changes we see suggests that the analyses that yielded the Planetary Hypotheses parameters were not the elegant trio analyses of the Almagest but some sort of serial determinations of the parameters based on sequences of independent observations. (shrink)

Porphyry's Commentary, the only surviving ancient commentary on a technical text, is not merely a study of Ptolemy's Harmonics. It includes virtually free-standing philosophical essays on epistemology, metaphysics, scientific methodology, aspects of the Aristotelian categories and the relations between Aristotle's views and Plato's, and a host of briefer comments on other matters of wide philosophical interest. For musicologists it is widely recognised as a treasury of quotations from earlier treatises, many of them otherwise unknown; but Porphyry's own reflections on musical (...) concepts and his snapshots of contemporary music-making have been undeservedly neglected. This volume presents the first English translation and a revised Greek text of the Commentary, with an introduction and notes designed to assist readers in engaging with this important and intricate work. (shrink)

Summary The Almagest of Ptolemy (mid-second century ad) contains eleven dated reports of observations of the positions of planets made during the third century bc in Babylon and Hellenistic Egypt. The present paper investigates the character, purpose, and conventions of the observational programmes from which these reports derive, the channels of their transmission to Ptolemy's time, and the fidelity of Ptolemy's presentation of them. Like the Babylonian observational programme, about which we have considerable knowledge through cuneiform documents, the Greco-Egyptian ones (...) were not directed towards the deduction of mathematical models of celestial motion but appear to have investigated patterns, correlations, and periodicities of phenomena. Ptolemy's immediate sources most likely were not the original series of observational records, but treatises by various astronomers of the intervening four centuries, including Hipparchus. While Ptolemy does not appear to have tampered with the wording of the reports, he faced difficulties and uncertainties in interpreting them; critically, he lacked sufficiently detailed information about the ancient calendars to be able to convert the reported dates accurately into his own chronological framework based on the Egyptian calendar. (shrink)

The eighth-century Latin manuscript Milan, Veneranda Biblioteca Ambrosiana, L 99 Sup. contains fifteen palimpsest leaves previously used for three Greek scientific texts: a text of unknown authorship on mathematical mechanics and catoptrics, known as the Fragmentum Mathematicum Bobiense (three leaves), Ptolemy's Analemma (six leaves), and an astronomical text that has hitherto remained unidentified and almost entirely unread (six leaves). We report here on the current state of our research on this last text, based on multispectral images. The text, incompletely preserved, (...) is a treatise on the construction and uses of a nine-ringed armillary instrument, identifiable as the “meteoroscope” invented by Ptolemy and known to us from passages in Ptolemy's Geography and in writings of Pappus and Proclus. We further argue that the author of our text was Ptolemy himself. (shrink)

Review of Liba Taub, Ptolemy's universe; The natural philosophical and ethical foundations of Ptolemy's astronomy. Chicago: Open Court 1993. xiv, 188 p.

Voici, pour la premiere fois edite et traduit, un texte grec antique perdu dans la langue originale et conserve en arabe. Il s'agit d'une lettre redigee par un mysterieux Ptolemee, philologue aristotelicien actif a Alexandrie autour de l'an 200 apres J.-C., dans laquelle celui-ci rapporte la Biographie et le Testament d'Aristote, ainsi qu'un Catalogue d'une centaine de titres inconnu par ailleurs. Ce vestige est l'une de nos meilleures sources d'information - et la seule qui soit interne a l'ecole peripateticienne - (...) sur la vie d'Aristote. Elle permet de reconstituer les liens entre Aristote et le pouvoir macedonien - Philippe, Alexandre le Grand et le general Antipatros - ainsi que l'emancipation progressive d'Aristote a l'egard de Platon. C'est aussi notre seul temoignage sur la premiere edition, dans l'Antiquite, des ecrits savants du Philosophe. Instantane pris sur le vif de l'etat de la philologie aristotelicienne, a Alexandrie, a la fin du IIe siecle, ce texte est une lecture essentielle pour quiconque s'interesse a la question de savoir ce que nous lisons quand nous lisons Aristote. (shrink)

The purpose of this essay is to show that there was one person, perhaps only one, who developed a rigorously scientific cosmology nearly two thousand years ago. Cosmology is the largest of all subjects, with a long history, and the cosmology considered here is the one that endured for the longest part, nearly three-quarters, of that history. By cosmology I mean a description of the universe as a whole and of the arrangement of its principal parts. But by scientific cosmology, (...) I mean something more. For a cosmology to be considered scientific, three criteria must be met: it must be quantitative, physical, and empirical. Quantitative means that it must assign some scale of distances and sizes to its parts. Physical means that it must rest upon some kind of physical or mechanical principles, causes, for the ordering and motion of its parts. Finally, empirical means that it must either be derived from observation or, if derived theoretically, as from physical or mechanical principles, it must be confirmed by observation. I set out these criteria, which may not be exclusive or exhaustive but are surely within reason, in order to define our subject and exclude mythological or theological cosmologies, which generally meet none of the criteria, and philosophical cosmologies, as those of Plato, Aristotle, and Descartes, which may meet one or two in some way, although not rigorously, but surely do not meet all three. I am not concerned with whether the cosmology or the criteria upon which it is based are correct. Compared to our present understanding, the scale may be off by orders of magnitude, the physics may be entirely mistaken, and the observations may be inaccurate. But if all three are present I would call the cosmology scientific, and if not I would not call the cosmology scientific. (shrink)

The assumption that Ptolemy adopted star coordinates from a star catalog by Hipparchus is investigated based on Hipparchus’ equatorial star coordinates in his Commentary on the phenomena of Aratus and Eudoxus. Since Hipparchus’ catalog was presumably based on an equatorial coordinate system, his star positions must have been converted into the ecliptical system of Ptolemy’s catalog in his Almagest. By means of a statistical analysis method, data groups consistent with this conversion of coordinates are identified. The found groups show (...) a high degree of agreement between Hipparchus’ and Ptolemy’s data. The value of the obliquity of the ecliptic underlying the conversion is estimated by adjustment and statistically agrees with Ptolemy’s value of this parameter. The results allow the assumption that Ptolemy’s coordinates were determined from Hipparchus’ coordinates by an accurate star globe or even by calculation. For a calculative derivation of ecliptical coordinates from equatorial ones, possible calculation methods are discussed considering the mathematics of the Almagest. (shrink)

In this article, I analyze the coincidence of the prediction of the Earth–Sun distance carried out by Ptolemy in his Almagest and the one he carried out, with another method, in the Planetary Hypotheses. In both cases, the values obtained for the Earth–Sun distance are very similar, so that the great majority of historians have suspected that Ptolemy altered or at least selected the data in order to obtain this agreement. In this article, I will provide a reconstruction of some (...) way in which Ptolemy could have altered or selected the data and subsequently will try to argue in favor of its historical plausibility. (shrink)

Arrian's enthusiasm for Ptolemy's account of Alexander has often been echoed in modern times. With much justification it is generally agreed that Arrian's account of Alexander, through its reliance on the works of Ptolemy and Aristobulus, is our best and, on the whole, most reliable account of Alexander. Recent work, however, has illuminated Ptolemy's weaknesses, and we can no longer regard Ptolemy as utterly reliable in every important respect. His version of the Alexander story is centred on Alexander, therefore Alexander (...) is depicted out of the close context of the Macedonian court. It is only through the information preserved in other writers—traditionally, but undiscriminatingly, considered unreliable—that, for instance, the picture of Alexander's struggle with his Macedonian nobles has begun to emerge. And in matters of this kind Ptolemy's version is so much the court ‘official’ version that it cannot be regarded as trustworthy. (shrink)

Herodotus’s Scythians and Ptolemy’s Central Asia: Semasiological and Onomasiological Studies. By Helmut Humbach and Klaus Faiss. Wiesbaden: Dr. Ludwig Reichert Verlag, 2012. Pp. xii + 91.

A fascinating epistemology of science book, to be read alongside contemporary accounts.

The paper explores the historical reasons why Ptolemy’s Almagest was cultivated in Antiquity as a legitimate part of ancient culture. It tries to elucidate first the precise nature of Ptolemy’s project in the Almagest, its relation to ethics as well as to the particular conception that Ptolemy had of mathematics. It then proposes an explanation for the fact that this treatise, both in Ptolemy's period and afterwards, was studied within the milieu of ancient astrologers.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 123-124 [Access article in PDF] Andrew Barker. Scientific Method in Ptolemy's Harmonics. New York: Cambridge University Press, 2001. Pp. viii + 281. Cloth, $69.95. Ptolemy's Harmonics is an important source not only for the history of music, but also for the history and philosophy of science. Two recent monographs, by J. Solomon, and A. Barker, now provide a basis for a (...) more widespread discussion of this much neglected work. Barker focuses on the part that is concerned with musical science proper (I, 1-III, 3), and more specifically on the scientific method it displays.Barker uses an analysis of Ptolemy's programmatic statements in I, 1/2, as a key to a reading of Ptolemy's treatise. His exposition has the format of a commentary, with special emphasis on the methodologically relevant passages. For the most part, he follows the order of Ptolemy's text closely, providing historical background information in excursus form. One needs to read a complete text of Ptolemy's treatise along with Barker's exposition in order to understand some of his arguments. It is preferable to also use Düring's [End Page 123] edition of the Greek text. One is rewarded with a detailed and in-depth analysis of the passages that helps one understand Ptolemy's method in harmonics as it unfolds in his treatise. This is so even if one disagrees with Barker's claims concerning Ptolemy's methodology.These claims are outlined in chapter 2, on the basis of I, 1/2 of the Harmonics. The methodological program Barker filters out of the text remains vague in a number of important respects. One misses, for example, a clear exposition on what will count as a sufficient integration of "empirical and theoretical phases," and on what will count as "empirical." This is a serious drawback, since Barker claims that Ptolemy instantiates a complex scientific methodology with a decisive, fully integrated empiricist trait. The drawback is aggravated by the fact that the already vague terms of the postulated methodology have to be watered down considerably in the subsequent chapters to make them fit with Ptolemy's actual procedures. Ptolemy does not seem to deliver even on the vague terms. One may very well remain unconvinced both by Barker's initial arguments concerning Ptolemy's methodology, and by his attempts to show that Ptolemy's procedure in the Harmonics can count as a satisfactory instantiation. Perhaps Ptolemy's intentions are less ambitious. When he states (5.13 ff. Düring, ed.) that "the aim of the student of harmonics must be to preserve the hupotheseis..., as never in any way conflicting with the perceptions that correspond to most people's estimation," he may just mean that he intends to vindicate an essentially Pythagorean (locally modified) account by showing it does not conflict with the phenomena. In my view, he certainly delivers on this less ambitious program. In fact, it seems to me that the understanding of Ptolemy's argumentative path is impeded by Barker's interpretation of Ptolemy's goal of "saving the hupotheseis" as a commitment to the integration of a genuine empiricist trait.Chapters 7 and 8 give an exposition of Ptolemy's tetrachord divisions. For the reader interested in an evaluation of the theoretical aspect of Ptolemy's scientific method, these are the central chapters of Barker's book. Barker provides a detailed analysis, together with an exposition of the historical and technical information needed for a non-specialist to follow both his and Ptolemy's argument. Barker's analysis reveals inter alia that a considerable part of Ptolemy's theory has no counterpart in the realm of phenomena perceived as musical, and that another part, concerning the single most important division of musical practice, is not justified, and not justifiable, by derivation from the principles. It is difficult to see how Ptolemy's account can nevertheless be viewed as a genuine integration of empirical and theoretical aspects. It appears to be an attempt at showing that an essentially Pythagorean theory... (shrink)