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)

Ptolemy I set aside his eldest son Ptolemy Ceraunus and instead made his younger son Ptolemy (by Berenice) his successor. Various explanations have been advanced, but none is compelling. In this article, I put forward two hitherto unexplored avenues: first, Ptolemy’s relations with Eurydice and Berenice, and second, Ceraunus’ own ambitions as they pertained to mastery of Greece and Macedonia. The latter especially led Ptolemy, motivated by his own failures in trying to secure Greece and (...) how they compromised the security of his rule, to view Ceraunus as overly ambitious, and so prefer the less military-minded younger Ptolemy. (shrink)

Ptolemy of Lucca's sympathetic description of republican self-rule together with his unfavourable view of monarchy in the De regimine principum has led many scholars to categorize him as a pioneer of civic republicanism. The present study refutes this common opinion. It illuminates Ptolemy's theory of government through its relationship to the papalism he repeatedly expressed in several works. This study argues that Ptolemy's theory of government in the De regimine principum was inspired by his papalist convictions, and (...) demonstrates how that theory clearly reflected Ptolemy's papalist point of view, especially in the context of the feud between Pope Boniface VIII and the kings of Western Europe, in particular, Philip the Fair of France. (shrink)

The model of scientific revolution genesis and structure, extracted from Einstein’s revolution and described in author’s previous publications, is applied to the Copernican one . In the case of Einstein’s revolution I had argued that its cause consisted in the clash between the main classical physics scientific programmes: newtonian mechanics, maxwellian electrodynamics, classical thermodynamics and statistical mechanics. Analogously in the present paper it is argued that the Copernican revolution took place due to realization of the dualism between mathematical astronomy and (...) Aristotelian qualitative physics in Ptolemy’s cosmology and the corresponding efforts to eliminate it. The works of Copernicus, Galileo, Kepler and Newton were all the stages of the mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on divine phenomena. (shrink)

The incursions of Ptolemy Soter into Coelê-Syria and Phoenicia after the death of Perdiccas have received scant attention from scholars in recent years, and the little they have received has failed to draw some vital conclusions. The sources are compressed, but unanimous, that very soon after the settlement of Triparadeisus, Ptolemy subverted and overran the region, fortified and garrisoned the cities, and returned to Egypt. He seems to have held this satrapy until it became a major arena in (...) the third Diadoch war, c. 315–311 B.C. (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)

In his Harmonics, Ptolemy constructs a complex set of theoretically ‘correct’ forms of musical scale, represented as sequences of ratios, on the basis of mathematical principles and reasoning. But he insists that their credentials will not have been established until they have been submitted to the judgement of the ear. They cannot be audibly instantiated with the necessary accuracy without the help of specially designed instruments, which Ptolemy describes in detail, discussing the uses to which each can be (...) put and cataloguing its limitations. The best known of these instruments is the monochord, but there are several more complex devices. This paper discusses one such instrument which is known from no other source, ancient or modern, whose design was prompted by the geometrical construction known as the helikôn. It has several remarkable peculiarities. I examine its design, its purposes, and the merits and shortcomings which Ptolemy attributes to it. An appendix describes an instrument I have built to Ptolemy’s specifications, in an attempt to find out how satisfactorily such a bizarre contraption will work; and it explains how various practical problems can be resolved. Keywords: Ptolemy; Greek harmonics; Scientific instruments; Helikôn; Experiment; Mathematics. (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 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)

This is an addendum to an earlier essay on the Purāṇic cosmograph interpreting it in terms of the principles of stereographic projection: Kloetzli (Hist Relig 25(2): 116–147, 1985). That essay provided an approach to understanding the broad structures of the Purāṇic cosmograph but not the central island of Jambudvīpa or its most important region (varṣa) of Bhārata. This addendum focuses on the works of Ptolemy as a resource for understanding the Purāṇic materials. It reaffirms the broad outlines of earlier (...) conclusions, but by understanding the major concerns of Ptolemy’s Geography, is able to provide a far ranging interpretation of the Purāṇic central island of Jambudvīpa. Viewed in the light of the main features of Ptolemy’s Geography, Jambudvīpa, the central island of the Purāṇic cosmograph, can be seen as a geograph modeled on the principles of Ptolemy’s Geography embedded within a larger cosmograph modeled on the principles of Ptolemy’s Planisphaerium—the earth at the center of the universe. Parallels between the seven Ptolemaic climates and the Purāṇic varṣas, the Nile and the Ganges, and the inhabited world (oikumene) and Bhārata deepen our sense of shared tradition as do representations of Bhārata alternately as Alexandria and Babylon. (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)

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)

Scholarly opinion about Ptolemy Soter's history of Alexander has been far from unanimous. Not long ago Ptolemy was held to stand in the first rank of ancient historians. His history was described as brilliant, rational, straightforward, and exhaustive, while he himself was proclaimed a ‘second Thucydides’. In recent years, however, Ptolemy's reputation has seriously declined. His shortcomings, acknowledged also by his admirers, have been stressed and extensively analysed. Fritz Schachermeyr clearly reflected current opinion when he equated a (...) ‘version from the Hauptquartier's circles’ with a lie, a fraud, and an intentional omission. The purpose of this paper is to examine the recent reassessment of the nature and the aims of Ptolemy's work. (shrink)

SummaryThis paper reassesses the importance of the Benedictine monasteries of St Benoît of Fleury and St Mesmin of Micy (both on the outskirts of Orléans), and the Cathedral of Chartres for the early diffusion of Arabic learning concerning the astrolabe, and it relates this diffusion to that of the judicial astrology of ‘Alchandreus philosophus’ and the astronomical tables of the Preceptum canonis Ptolomei. Evidence is given for the fact that already, by the turn of the millennium, the elements were in (...) place for a corpus of a new, mathematically based, practical science of the stars, consisting of works partly of Arabic and partly of Greek inspiration. This corpus was progressively revised and inspired, in turn, further translations from Arabic, until it reached its most mature form in the mid-twelfth century. Until recently, scholarship has tended to concentrate on the cathedral schools of North-east France and Lotharingia, and the monastic schools of South Germany, and to see Gerbert d'Aurillac, the Archbishop of Reims, as the pivotal figure. While these schools were undoubtedly important in the diffusion of the new science of the stars in the eleventh century, it is argued that a key role in the initial stages of the diffusion was played by the interrelated centres of Fleury, Micy and Chartres at the beginning of the century, and Gerbert may not have contributed as much as has been believed. Additional sections are devoted to the authorities in this corpus, ‘King Ptolemy’ and ‘Alchandreus’. A reworking of the Arabic material on the construction of the astrolabe by Ascelin of Augsburg was copied into this corpus. The text has previously been known from only one manuscript; a new edition, from five manuscripts, is provided here, together with a translation and commentary. (shrink)

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)

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

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)

: To honor Bernard Goldstein, this article highlights in the "Defense of Theon against George of Trebizond" by Regiomontanus (1436-1476) themes that resonate with leading strands of Goldstein's scholarship. I argue that, in this poorly-known work, Regiomontanus's mastery of Ptolemy's mathematical astronomy, his interest in making astronomy physical, and his homocentric ideals stand in unresolved tension. Each of these themes resonates with Gold- stein's fundamental work on the Almagest, the Planetary Hypotheses, and al-Bitruji's Principles of Astronomy. I flesh out (...) these tensions with an intriguing interpretation of the history of astronomy, in which Regiomontanus contrasts the two-dimensional "eccentric astronomy" attributed to the Almagest and the Arabs with the three-dimensional spheres of the "later" astronomers. A similar contrast reappears when Regiomontanus portrays as a "fictitious art" an astronomy that does not go beyond the accommodation of computations to the appearances. To conclude, I use Regiomontanus's expression to reinstate (pace Goldstein and Barker in this journal, 1998) fictionalism as an actor's category in Osiander and sixteenth-century astronomy. (shrink)

Ptolemy's Almagest, a brilliant treatise on theoretical astronomy combined with a practical handbook for computation, includes many compromises to reconcile discordant observations. This defense of Ptolemy examines in some detail a critical case concerning the model for Venus, which has sometimes been used as evidence for Ptolemy's perfidy. There the Alexandrian astronomer demonstrated his ingenuity when orbital constraints made it impossible to obtain directly the observed configurations he might have preferred.

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)

“Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena, “henceforth the [visible] representations of objects should be considered as paintings [ picturae ] that are actual[ly projected] on paper or some other screen.” While not intended as a historical generalization, this claim nonetheless reflects historical reality. Virtually all visual theorists before Kepler did, in fact, conceive of optical images as subjective, not objective constructs (...) – or, to put it in modern terms, as virtual rather than real entities. By current lights, of course, the distinction between virtual and real images is both obvious and common-place: whereas the latter can be physically projected upon a screen, the former cannot. (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)

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)

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)

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)

RésuméLe savant Ibn al-Ṣalāḥ est connu pour ses petits traités portant sur des questions particulières d'ouvrages mathématiques et philosophiques grecs. Il consacre plusieurs de ses travaux aux erreurs, plus ou moins importantes, qu'il trouve dans les travaux d'Euclide, de Ptolémée et d'Aristote. Le but de cet article, qui se concentre sur trois traités de Ptolémée et d'Aristote, est de décrire la méthode d'Ibn al-Ṣalāḥ et les objectifs qu'il poursuit dans les traités en question. Je suggère que ses traités sur l’Almageste, (...) le Traité du ciel et les Seconds analytiques suivent une structure semblable et qu'ils sont d'une grande valeur pour la recherche moderne en raison des éléments bibliographiques fournis par Ibn al-Ṣalāḥ. Pour ne citer qu'un exemple, Ibn al-Ṣalāḥ atteste de l'existence d'une traduction arabe des Seconds analytiques d'Aristote inconnue jusqu'ici. Cet article établit ainsi pour la première fois le profil de savant d'Ibn al-Ṣalāḥ : ses travaux nous disent quelles sources étaient disponibles aux savants actifs à Bagdad et Damas au XIIe siècle et comment il a tenté de résoudre les contradictions entre les différentes versions des textes faisant autorité. Cet article offre donc une contribution à notre connaissance de la transmission gréco-arabe des textes scientifiques et philosophiques. (shrink)