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)

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.

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)

Menander's lost comedyThaiswith its famous protagonist, thehetairalover of Ptolemy I Soter and perhaps Alexander himself, was plainly well known at Rome, and is alluded to several times in Latin poetry of the Augustan and later periods, as Ariana Traill has shown. My purpose here is to argue that the literary characterisation of Thais in Menander's play underlies certain aspects of Lesbia as presented in the poetry of Catullus; that Catullus' poetry uses the plays of Menander has been demonstrated by (...) Richard Thomas, arguing that Catullus 8 shows clear traces of Demea's monologue in theSamia(325–56). (shrink)

The paper brings into light and discusses a concentric solar model briefly described in Chapter 5 of Section III of ‘Abd al-Raḥmān al-Khāzinī’s On experimental astronomy, a treatise embedded in the prolegomenon of his comprehensive Mu‘tabar zīj, completed about 1121 c.e. In it, the Sun is assumed to rotate on the circumference of a circle concentric with the Earth and coplanar with the ecliptic, but the motion of the vector joining the Earth and Sun is monitored by a small eccentric (...) hypocycle. The ratio between the distance of the hypocycle’s center from the Earth and the hypocycle’s radius is equal to the solar eccentricity in the eccentric model. The model is to account for the constancy of the apparent diameter of the solar disk as held by Ptolemy. The source of the model is unknown. Since the mechanism employed in it clearly resembles the pin-and-slot device, whose use in mechanical astronomical instruments has a long history from the Antikythera Mechanism to the medieval solar, lunar, and planetary equatoria and dials, we argue that the solar model can be positioned within this long-standing tradition and considered the result of the correct understanding of some Byzantine prototype and thus a typical example of the transmission of astronomical ideas via media of the material culture. (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)

LSJ s.v. A defines ἀληθινός as meaning ‘truthful, trusty’ of persons and ‘true, genuine’ of objects, and offers Amphis, fr. 26 as an example of the second sense:ὅστις ἀγοράζων ὄψον ἐξὸν ἀπολαύειν ἰχθύων ἀληθινῶνῥαφανῖδας ἐπιθυμεῖ πρίασθαι, μαίνεταιAnyone who, when shopping for dainties …wants to purchase radishes, when he has a chanceto enjoy alêthinoi fish, is crazy.The context of the fragment is unknown. But the speaker is patently drawing a contrast not between ‘real fish’ and something that resembles fish, as LSJ (...) would have it, but between a type of fish that any sensible person would buy for dinner, should the opportunity arise, and radishes, which are edible but unexciting fare. So too at Macho 28–32, when King Ptolemy's guests were served a variegated rockfish, three κωβιοί cut into steaks, and καράβων … ἀληθινῶν —literally ‘real crayfish’—they were astonished and delighted. The reaction suggests that the banqueters were happy because the crayfish Ptolemy served matched the quality of the other seafood he set before them, not because the king had declined to deceive them. (shrink)

From Antiquity through the early modern period, the apparent motion of the Sun in longitude was simulated by the eccentric model set forth in Ptolemy’s Almagest III, with the fundamental parameters including the two orbital elements, the eccentricity e and the longitude of the apogee λ A, the mean motion ω, and the radix of the mean longitude $$ \bar{\lambda }_{0} $$ λ¯0. In this article we investigate the accuracy of 11 solar theories established across the Middle East from (...) 800 to 1600 as well as Ptolemy’s and Tycho Brahe’s, with respect to the precision of the parameter values and of the solar longitudes λ that they produce. The theoretical deviation due to the mismatch between the eccentric model with uniform motion and the elliptical model with Keplerian motion is taken into account in order to determine the precision of e and λ A in the theories whose observational basis is available. The smallest errors in the eccentricity are found in these theories: the Mumtaḥan : − 0.1 × 10−4, Bīrūnī : + 0.4 × 10−4, Ulugh Beg : − 0.9 × 10−4, and Taqī al-Dīn : − 1.1 × 10−4. Except for al-Khāzinī, the errors in the medieval determinations of the solar eccentricity do not exceed 7.7 × 10−4 in absolute value, with a mean error μ = + 2.57 × 10−4 and standard deviation σ = 3.02 × 10−4. Their precision is remarkable not only in comparison with the errors of Copernicus and Tycho, but also with the seventeenth-century measurements by Cassini–Flamsteed and Riccioli. The absolute error in λ A varies from 0.1° to 1.9° with the mean absolute error MAE = 0.87°, μ = −0.71° and σ = 0.65°. The errors in λ for the 13,000-day ephemerides show MAE < 6′ and the periodic variations mostly remaining within ± 10′, closely correlated with the accuracy of e and λ A. (shrink)

Ptolemy reports three dated lunar eclipses observed by Hipparchus, and also refers to two more, without identifying them, which Hipparchus compared with two earlier counterparts (apparently, observed in Mesopotamia) to assess the validity of the Babylonian period relations of the lunar motion. Also, in Pliny the Elder’s Historia naturalis, we are told that a horizontal lunar eclipse (selenelion) at sunrise and moonset was reported (observed?) by Hipparchus. Reviewing a paper by G.J. Toomer in 1980, it is shown that the (...) pairs of the eclipses were, almost certainly, the ones occurring on “31 January 486 b.c. and 27 January 141 b.c.” and “19 November 502 b.c. and 14 November 157 b.c.”; and if Hipparchus observed from St. Stephen’s Hill in Rhodes, the most probable candidate for the selenelion at moonset was the lunar eclipse of 7 February 142 b.c., although he also had the chance to observe any of the four others, occurring on 3 July 150 b.c., 10 April 145 b.c., 26 November 139 b.c., and 15 November 138 b.c., on a sufficiently elevated mountain on the island. (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 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)

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)

Some variants in the materials related to the planetary latitudes, including computational procedures, underlying parameters, numerical tables, and so on, may be addressed in the corpus of the astronomical tables preserved from the medieval Islamic period, which have already been classified comprehensively by Van Dalen. Of these, the new values obtained for the planetary inclinations and the longitude of their ascending nodes might have something to do with actual observations in the period in question, which are the main concern of (...) this paper. The paper is in the following sections. In the first section, Ptolemy’s latitude models and their reception in Islamic astronomy are briefly reviewed. In the next section, the medieval non-Ptolemaic values for the inclinations and the longitudes of the nodal lines are introduced. The paper ends with the discussion and some concluding remarks. The derivation of the underlying inclination values from the medieval planetary latitude tables and determining the accuracy of the tables are postponed to “Appendix” in the end of the paper. (shrink)

Ibn al-Zarqālluh (al-Andalus, d. 1100) introduced a new inequality in the longitudinal motion of the Moon into Ptolemy’s lunar model with the amplitude of 24′, which periodically changes in terms of a sine function with the distance in longitude between the mean Moon and the solar apogee as the variable. It can be shown that the discovery had its roots in his examination of the discrepancies between the times of the lunar eclipses he obtained from the data of his (...) eclipse observations over a 37-year period in the latter part of the eleventh century and the predictions made on the basis of the lunar theories in the Mumta $$\textit{\d{h}}$$ an zīj (Baghdad, ca. 830) and al-Battānī’s zīj (Raqqa, d. 929), which were available to him at the time. What Ibn al-Zarqālluh found is, in fact, a special case of the annual equation of the Moon, which is applicable in the oppositions and, thus, in the lunar eclipses. The inequality was discovered independently by Tycho Brahe (d. 1601) and Johannes Kepler (d. 1630). As Ibn Yūnus (d. 1009) reports in his $$\textit{\d{H}}$$ ākimī zīj, Ibn al-Zarqālluh’s medieval Middle Eastern predecessors, the Persian astronomers Māhānī (d. ca. 880) and Nayrīzī (d. 922) as well as ‘Alī b. Amājūr (fl. ca. 920), were already acquainted with the problem of the eclipse timing errors, but it had remained unresolved until Ibn Yūnus provided a provisional, and incorrect, solution by reducing the size of the lunar epicycle. As we argue, the diverse ways to tackle the same problem stem from two different methodologies in astronomical reasoning in the traditions developed separately in the Eastern and Western regions of the medieval Islamic domain. (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)

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)

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.

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)

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)

Rudolf Pfeiffer believed that, as a young man, Callimachus wrote four books of Aetia. To these the poet added in his old age a Reply to his Critics , and a slightly revised version of his recent occasional elegy, the Lock of Berenice ; this revised Coma became the last poem in Aetia book 4, to be followed by an Epilogue which may mark a transition to the Iambi. Pfeiffer's theory generally held the field until the brilliant article of P. (...) J. Parsons, in ZPE 25 , 1–50. With the help of newly recovered papyrus fragments Parsons showed that a previously unplaced elegy celebrating a Nemean victory was connected to the story of Molorchus , who entertained Heracles before that hero killed the Nemean lion and instituted the Nemean Games; thus the poem belonged to Aetia book 3. Furthermore, various pieces of evidence converge to make it probable, if not wholly certain, that this substantial poem stood first in its book. So it appears that, at least in the final form of the Aetia, books 3–4 were framed by two poems honouring the wife of Ptolemy III Euergetes, namely Victoria Berenices and Coma Berenices. Soon afterwards a further important advance was made by E. Livrea , who perceived, on grounds of subject-matter as well as papyrology, that the poor man who sets a mousetrap in fr. 177 Pf. must be none other than Molorchus; note particularly the probable mention of Cleonae in fr. 177.37 Pf. = Supplementum Hellenisticum 259.37. Thus a new fragment of 38 lines accrued to the poem. These discoveries have some implications for the composition of the Aetia. Addition of a Coma Berenices to a pre-existent Aetia book 4 could be countenanced easily enough, but, as Parsons says , it would have required a much more radical, and therefore less plausible, revision for Callimachus to have added Victoria Berenices to a pre-existent Aetia book 3. Accordingly Parsons suggested that the original Aetia contained only books 1–2, united by the conversation with the Muses; then in his old age Callimachus compiled two more books, partly at least from poems already composed, and gave them a frame of two poems honouring Queen Berenice. Parsons' view has, I think, been widely accepted; Professor Lloyd-Jones wrote in SIFC 77 , 56 ‘No-one has yet argued against the simple modification of Pfeiffer's theory of the two editions of the Aetia which Mr. Parsons based on this discovery. The first edition comprised two books only.’. (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 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)

T. Kuhn’s theory of scientific revolutions has repeatedly been the subject of criticism. It is important to note that Kuhn pays very limited attention to the phenomenon of the scientific revolution itself, comparing the revolution either with a religious conversion or with a gestalt switch. Such comparisons, however, are very superficial. This paper outlines a new understanding of the scientific revolution as a result of the resonance of the intellectual trends of the early modern period. It was the quasi-simultaneous action (...) of various factors that led to revolutionary changes in natural philosophy, which, in turn, gave rise to the actual scientific revolution. In addition, the article shows that the Copernican Revolution cannot be described within the model of scientific revolution developed by T. Kuhn. Ptolemy’s theory was mathematically constructed so that it could not make inaccurate predictions of planetary motion, because – as we are now clear – the function characterizing the trajectory of planetary motion was actually represented as a Fourier series. The Copernican revolution was not a Kuhn-type scientific revolution, nor was it caused by the empirical failures of Ptolemaic astronomy. Events unfolded according to a different scheme. Copernicus set out to carry out the principle of the uniform circular motion of the planets more consistently than had been done in Ptolemy’s theory, at the same time presenting to this theory those requirements of an aesthetic and methodological order, which the cognitively fragmented system of Ptolemy, for all its flexibility, could not satisfy and, by the conditions of its creation, could not satisfy. In addition, the article shows that Copernicus, in constructing his heliocentric theory, was essentially seeking answers to the challenges that Alberti’s artificial perspective and Nicholas of Cusa’s theological speculation posed to the visual experience in the sixteenth century. (shrink)

Aristotle's Definition of a Science of Being qua Being Selected Bibliography on the Meanings of Being in Aristotle The Place of Metaphysics in the Ancient Divisions of Philosophy The Peripatos after Aristotle's and the Origin of the Corpus Aristotelicum Bibliography on the Ancient Catalogues of Aristotle and the Corpus Aristotelicum Ancient Catalogues of Aristotle's Works: English studies Diogenes Laërtius, Lives, V 22-27 Hesychius of Miletus and Ptolemy al-Garib Listes Anciennes des Ouvrages d'Aristote: études en français Diogène Laërce, Vies V, (...) 22-27 Hésychius de Milet et Ptolémée el-Garib The Oblivion of Being After Aristotle: Theophrastus' Metaphysics.. (shrink)

Ptolemy presents only one argument for the eccentricity in his models of the superior planets, while each one of them has two eccentricities: one for center of the uniform motion, the other for the center of the constant distance. To take into account the first eccentricity, he introduces the equant point, but he provides no argument for the eccentricity of the center of the deferent. Why is the second eccentricity different from the first one? The 13 th century astronomer (...) Quṭb al-Dīn al-Shīrāzī, a member of the famous school of Marāgha, who was interested in this problem, suggests the “retrograde arcs” as the empirical origin of the second eccentricity and develops an argument to justify this conjecture. Although his argument is not without difficulty, his suggestion is in line with the suggestions made by some historians of astronomy in recent decades. Résumé Ptolémée ne donne qu'un seul argument pour expliquer dans son système l'excentricité des planètes supérieures, alors que chacune d'elles a deux excentricités: l'une par rapport au centre du mouvement uniforme, l'autre par rapport au centre de la distance constante. Pour rendre compte de la première excentricité, il introduit le point équant, mais il ne donne en revanche aucun argument pour l'excentricité par rapport au centre du cercle déférent. Or, pourquoi la seconde excentricité est-elle différente de la première? Quṭb al-Dīn al-Shīrāzī, astronome du xiii e siècle membre de l'école de Marāgha, qui s'est intéressé à cette question, a fait l'hypothèse que les “arcs de rétrogradation” constituent l'origine empirique de cette seconde excentricité. Bien que l'argument sur lequel il appuie cette hypothèse ne soit pas exempt de difficultés, sa suggestion rejoint celles faites par des historiens de l'astronomie durant les dernières décennies. (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)

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)

This paper analyses a kinematic model for the solar motion by Quṭb al-Dīn al-Shīrāzī, a thirteenth-century Iranian astronomer at the Marāgha observatory in northwestern Iran. The purpose of this model is to account for the continuous decrease of the obliquity of the ecliptic and the solar eccentricity since the time of Ptolemy. Shīrāzī puts forward different versions of the model in his three major cosmographical works. In the final version, in his Tuḥfa, the mean ecliptic is defined by an (...) eccentric of fixed mean eccentricity and a mean obliquity fixed with respect to the celestial equator, and the center of the epicycle, which is inclined to the eccentric, moves on the eccentric with an annual period. By an additional slow motion of the sun on the epicycle, the true eccentricity of the solar deferent, defined by the annual motion of the sun, and the sun’s extreme declination from the equator change, accounting for the reduction of the eccentricity and the obliquity of the ecliptic since the time of Ptolemy. (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)

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)