The Argonautica is the dramatic story of Jason's quest for the Golden Fleece and his relations with the dangerous Colchian princess, Medea. The only extant Greek epic poem to bridge the gap between Homer and late antiquity, it is a major product of the brilliant world of the Ptolemaic court at Alexandria, written by Apollonius of Rhodes in the 3rd century BC. Apollonius explores many of the fundamental aspects of life in a highly original way: love, deceit, heroism, (...) human ignorance of the diven, the limits of science. This volume offers the first scholarly translation into English prose for many years, combining readability with accuracy and an attention to detail that will appeal to readers both with and without Greek. `Based on a deep understanding of the text, this translation, with informative notes and an excellent introduction, will bring Apollonius to the audience he deserves....' ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more. (shrink)

The Greek astronomer and geometrician Apollonius of Perga produced pioneering written work on conic sections in which he demonstrated mathematically the generation of curves and their fundamental properties. His innovative terminology gave us the terms 'ellipse', 'hyperbola' and 'parabola'. The Danish scholar Johan Ludvig Heiberg, a professor of classical philology at the University of Copenhagen, prepared important editions of works by Euclid, Archimedes and Ptolemy, among others. Published between 1891 and 1893, this two-volume work contains the definitive Greek text (...) of the first four books of Apollonius' treatise together with a facing-page Latin translation. Volume 1 contains the first three books, with the editor's introductory matter in Latin. (shrink)

The Greek astronomer and geometrician Apollonius of Perga produced pioneering written work on conic sections in which he demonstrated mathematically the generation of curves and their fundamental properties. His innovative terminology gave us the terms 'ellipse', 'hyperbola' and 'parabola'. The Danish scholar Johan Ludvig Heiberg, a professor of classical philology at the University of Copenhagen, prepared important editions of works by Euclid, Archimedes and Ptolemy, among others. Published between 1891 and 1893, this two-volume work contains the definitive Greek text (...) of the first four books of Apollonius' treatise together with a facing-page Latin translation. Volume 2 contains the fourth book in addition to other Greek fragments and ancient commentaries, notably that of Eutocius, as well as the editor's Latin prolegomena comparing the various manuscript sources. (shrink)

The Greek astronomer and geometrician Apollonius of Perga produced pioneering written work on conic sections in which he demonstrated mathematically the generation of curves and their fundamental properties. His innovative terminology gave us the terms 'ellipse', 'hyperbola' and 'parabola'. The Danish scholar Johan Ludvig Heiberg, a professor of classical philology at the University of Copenhagen, prepared important editions of works by Euclid, Archimedes and Ptolemy, among others. Published between 1891 and 1893, this two-volume work contains the definitive Greek text (...) of the first four books of Apollonius' treatise together with a facing-page Latin translation. Volume 1 contains the first three books, with the editor's Latin introductory matter. Volume 2 contains the fourth book in addition to other Greek fragments and ancient commentaries, notably that of Eutocius. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Two Sonnets DANIEL GALEF Thales to Thratta (spoken by “The Astrologer Who Fell into a Well”) All things are full of spirits. So said I, who plumbed the well of science, saw the sun made black and tracked its course across the sky, who, armed with muscle, wrote the river’s run. Where is my spirit? Thratta! I feel cold and wet. This well is deep. The world is wet (...) and cold. The world I knew was filled with gold and fire.... How quick the Olympic sun has set, how quick my words rewritten, and my land made palimpsest. The sea has left Miletus, the shore on which I walked and lectured—and the wise men who walked with me, whom I taught. The boundless sea, whose tides once rose to meet us has changed its shape, moved on. But I cannot. arion 27.2 fall 2019 Eudemus to Apollonius (spoken by the dedicatee of Apollonius of Perga’s first books of the Conic Sections) I write this note in the sand because I know the waves will wash it clean, and you won’t see it. Like the circles we traced here so long ago, our footprints fade from Pergamum. So be it. Your book was well-received. As was your son; his seems the echo of your dimming face. How did my thoughts, which like an hour-glass run, once hold the eternal laws of boundless space? The beach bends on forever. How might a man reckon every mote, each grit and grain? The universe of truths seems greater than could ever fit within the human brain— Yet love, which binds over such a greater span, all mortals its completeness can contain. 104 two sonnets... (shrink)

Epitome V (1621), and consisted of matching an element of area to an element of time, where each was mathematically determined. His treatment of the area depended solely on the geometry of Euclid's Elements, involving only straight-line and circle propositions – so we have to account for his deliberate avoidance of the sophisticated conic-geometry associated with Apollonius. We show also how his proof could have been made watertight according to modern standards, using methods that lay entirely within his (...) power. The greatest innovation, however, occurred in Kepler's fresh formulation of the measure of time. We trace this concept in relation to early astronomy and conclude that Kepler's treatment unexpectedly entailed the assumption that time varied nonuniformly; meanwhile, a geometrical measure provided the independent variable. Even more surprisingly, this approach turns out to be entirely sound when assessed in present-day terms. Kepler himself attributed the cause of the motion of a single planet around the Sun to a set of `physical' suppositions which represented his religious as well as his Copernican convictions; and we have pared to a minimum – down to four – the number he actually required to achieve this. In the Appendix we use modern mathematics to emphasize the simplicity, both geometrical and kinematical, that objectively characterizes the Sun-focused ellipse as an orbit. Meanwhile we highlight the subjective simplicity of Kepler's own techniques (most of them extremely traditional, some newly created). These two approaches complement each other to account for his success. (shrink)

The king therefore went down to the village, since the Wise Men's rule did not permit him to spend more than a day with them, but Iarchas said to the messenger, ‘Damis too we consider worthy of the secrets here, so tell him to come, while you look after the others in the village.’ When Damis had come, the Wise Men formed their usual circle and gave Apollonius permission to put questions. So he asked what they thought the (...) universe consisted of, to which they replied, ‘Elements.’ ‘Four, do you think?’ he said. ‘Not four’, said Iarchas, ‘but five.’ ‘What could a fifth one be’, said Apollonius, ‘besides water, air, earth, and fire?’ ‘Ether’, said Iarchas, ‘which we must consider to be the origin (γένεσιν) of the gods. All that breathes air is mortal, but what breathes ether is immortal and divine.’ Next Apollonius asked which of the elements came into existence first. ‘All came together’, said the other, ‘since a living being is not born one piece at a time.’ ‘Am I to consider the universe living?’, asked Apollonius. ‘Yes, if you reason correctly’, said Iarchas, ‘since itself it gives life to everything.’ ‘Should we then call it female’, asked Apollonius, ‘or of the contrary, male sex?’ ‘Of both’, was the answer, ‘since it has intercourse with itself, and performs both the mother's and the father's role with respect to generation. It feels a desire for itself more intense than that of any two other beings, and this joins and unites it, and there is nothing unreasonable about its coalescence. And just as the action of the hands and feet in a living creature comes from mobility and the intelligence (διὰ τὸν ἐκείνου νοῦν) that causes it, so also we must suppose that, because of the intelligence of the universe (κατὰ τὸν ἐκείνου ϕοιτᾷ νοῦν), its parts accommodate themselves to everything that undergoes birth and conception. For instance, the sufferings resulting from drought arise from the mind of the universe, when justice is banished from mankind and treated with dishonor. And this being guides itself not by one hand alone but by many unseen ones that it uses; though too large to be restrained, it moves obediently and tractably.’The doctrine contained in this extract – the only passage ofThe Life of Apollonius of Tyanatreating matters of ‘cosmogony’ – could be summarized in the six following propositions. First, the universe consists of five, not four elements, the fifth being the ether, the γένεσις θεῶν. Just as mortals breathe air, gods breathe ether. Secondly, there is no ‘primordial element’; all five came into being simultaneously. Thirdly, the universe is a living being. In the fourth place, the universe is both male and female at the same time. In the fifth place, as the universe is androgynous it feels desire (ἔρως) towards itself and it is this desire that makes it whole and united. And finally, the passion of the universe for itself is governed by Intelligence (ἐκείνου νοῦς). (shrink)

The latest book of Reviel Netz presents a highly erudite analysis of the style of Hellenistic mathematics. Besides the Introduction and Conclusion the book is composed of four chapters. Before turning to more general remarks I would like first to outline the contents of the book.The Introduction starts with the presentation of Archimedes’ Spiral lines. In a condensed form, the author outlines his approach and calls attention to the stylistic peculiarities of that work. Most of the themes discussed in more (...) detail in the following chapters, such as the analysis of the narrative structure of the treatise, its working with surprise, the exposition of the rhetorical devices, the discussion of technical tools, and the breaking of genre-boundaries emerge here side by side in a single treatise.The first chapter, called The carnival of calculation, starts with another work of Archimedes, the Stomachion, for which Netz offers a new interpretation as a treatise in geometrical combinatorics. Then he turns to Archimedes’ On the measurement of the circle, where, in a detailed analysis of the calculations made by Archimedes, Netz presents a pattern that he identifies in several other works of Hellenistic mathematics, a pattern he calls ‘asymptotic calculation’. It consists in a combination of strict geometric arguments with calculations of proportions, some precise, some only approximate, which together with rather arbitrary simplifications lead to a result that is achieved after an abrupt and unexpected halt. Netz shows that, according to the surviving testimonies, a similar pattern can be found in many Hellenistic authors, such as Aristarchus, Hipparchus, and Apollonius of Perga. "[I]n many Hellenistic mathematical works we see calculations that give rise to values that are big and unwieldy, or else are only asymptotically found. Such calculations end up not with the satisfaction of having simplified … ". (shrink)

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Apollonius Dyscolus’ use of ambiguity in grammatical problem-solving has in recent years had the benefit of two scholarly studies. David Blank, in the course of his analysis of the Syntax as a whole, has described the broad functions which Apollonius assigns to ambiguity. Jean Lallot's 1988 paper, ‘Apollonius Dyscole et l'ambigüité linguistique: problemes et solutions’, is devoted exclusively to the treatment of linguistic ambiguity in Apollonius’ work. Yet it is to be feared that the flood of (...) light thrown by these scholars on what had been an unregarded corner of ancient grammar has shown up rather more than Apollonius would have cared to admit, both about the nature, and about the prospects for success, of the enterprise on which he was engaged. At the same time, certain structural features of ancient grammar, at least of the ancient grammar which Apollonius himself constructed, have come into sharper focus: features clear enough with the benefit of hindsight, but glimpsed, it appears, all too dimly by Apollonius himslf. It is now worryingly clear not only that ambiguity was ambiguous for Apollonius, but also that the ambiguity of ambiguity represented a genuine threat to the coherence and value of his work. In this paper I set out to justify both these claims. (shrink)

Apollonius Dyscolus’ use of ambiguity in grammatical problem-solving has in recent years had the benefit of two scholarly studies. David Blank, in the course of his analysis of the Syntax as a whole , has described the broad functions which Apollonius assigns to ambiguity. Jean Lallot's 1988 paper, ‘Apollonius Dyscole et l'ambigüité linguistique: problemes et solutions’, is devoted exclusively to the treatment of linguistic ambiguity in Apollonius’ work. Yet it is to be feared that the flood (...) of light thrown by these scholars on what had been an unregarded corner of ancient grammar has shown up rather more than Apollonius would have cared to admit, both about the nature, and about the prospects for success, of the enterprise on which he was engaged. At the same time, certain structural features of ancient grammar, at least of the ancient grammar which Apollonius himself constructed, have come into sharper focus: features clear enough with the benefit of hindsight, but glimpsed, it appears, all too dimly by Apollonius himslf. It is now worryingly clear not only that ambiguity was ambiguous for Apollonius, but also that the ambiguity of ambiguity represented a genuine threat to the coherence and value of his work. In this paper I set out to justify both these claims. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Hierocles, a Stoic of the second century CE, famously deployed an image of the ‘concentric circles’ that surround each of us. The image should not be read as advocating absolute impartiality (in the style of classical utilitarianism) or as illustrating the Stoic theory of oikeiōsis. Instead, it is designed to illustrate how it is ‘appropriate to act’ in certain cases. Like other Stoics, Hierocles bases his investigation of appropriate acts on what is ‘in accordance with nature’. According to his view, (...) each of us has a duty of mutual aid towards every other human being—but a weightier duty towards those who are socially closer than those who are more distant. The fundamental principle is that each of us has the duty of being an ‘ally’ of every other human being in serving the natural purposes of all the circles to which we and that other human being both belong. (shrink)

The paper is devoted to the presentation and analysis of the philosophical views concerning logic and mathematics of the leading members of Cracow Circle, i.e., of Jan Salamucha, Jan Franciszek Drewnowski and Józef Maria Bocheński. Their views on the problem of possible applicability of logical tools in metaphysical and theological researches is also discussed.

As an Apollo-like Jason leaves home to start the long journey in quest of the Golden Fleece a strange incident occurs: The first thing to be said about this scene is that it is almost certainly an invention of Apollonius Rhodius.

As an Apollo-like Jason leaves home to start the long journey in quest of the Golden Fleece a strange incident occurs: The first thing to be said about this scene is that it is almost certainly an invention of Apollonius Rhodius.

"'There is only one thing that is certain, namely that we can have nothing certain; and therefore it is not certain that we can have nothing certain,' Samuel Butler once said, expressing in that mindbloggler all the elements required to form a classical paradox. Throughout the ages wise men and jesters alike have been intrigued by such mental twists and riddles which defy common sense and yet appear to be true." -- Dust jacket.

Regarding the influence of François Rabelais on the Giordano Bruno‟s works, up to now the criticism have only taken into consideration the lexical and thematic analogies. This article individualizes, in a passage of the Oratio Valedictoria, a literal quotation from the Gargantua et Pantagruel, showing that Rabelais was a direct source of inspiration for Bruno. The protagonist of the passage is the pythagorean Apollonius of Tyana, a character well known by the Nolan, who mentioned him in many occasions. He (...) represents the ideal medium with the oriental wisdom, that had so much influence on the thought of Bruno. Besides, he embodies the model of the "natural magician" in which the philosopher repeatedly identified himself, both in his works and life. (shrink)

The study of Homeric echoes and allusions in the Argonautica has overshadowed the influence of other literature, even when, as with tragedy, such influence is clear. The easiest framework for studying allusions to tragedy in Apollonius is comparison with the different types of allusion to Homer. Situations in the epic may recall situations and relationships in tragedy, and verbal similarities to passages in tragedy are also identifiable, despite differences of dialect and metre. The latter are often enhanced by rare (...) words, as Homeric hapax legomena and other Homeric rarities establish allusions to the Iliad and Odyssey. (shrink)

This article makes two claims. The first is that Archimedes’ On Floating Bodies included a punning reference, in its key diagrammatic figure AΠΟΛ: the precise purpose of the pun may not be recovered by us, but even so it remains a powerful example of the playful in Archimedes’ writing. The second is that Apollonius could have been Archimedes’ younger contemporary. The outcome could be that we find Archimedes addressing a playful, hidden message to Apollonius, providing us with a (...) unique insight into the communication of Greek mathematics. (shrink)

The beginning of the second entry of Apollonius Sophista's Lexicon Homericum reads as follows in the codex Coislinianus gr. 345, the only direct witness to this section : ἀάατος· ὁ ἀβλαβὴς καὶ εὐχερὴς καὶ δι’ οὗ ἄνευ ἄτης. ἐνίοτε δὲ τὸν ἐπιβλαβῆ καὶ δυσχερῆ …ἀάατος: ‘harmless’ and ‘easy’, and δι’ οὗ ‘without ἄτη’. But sometimes ‘hurtful’ and ‘difficult’ ….

At Argonautica 4.12–13, Medea, frightened and on the point of fleeing her home, 2 is compared to a young deer.

Hermeneutic studies of science locate a circle at the heart of scientific practice: scientists only gain knowledge of what they, in some sense, already know. This may seem to threaten the rational validity of science, but one can argue that this circle is a virtuous rather than a vicious one. A virtuous circle is one in which research conclusions are already present in the premises, but only in an indeterminate and underdeveloped way. In order to defend the (...) validity of science, the hermeneuticist must describe a method by which a vague and confused initial knowledge of nature gets transformed into a clear and determinate knowledge of nature. I consider three such methods. The first is regressus demonstrativa, favoured by the physicians of Padua during the fifteenth and sixteenth centuries. The second is mathēsis, introduced by Martin Heidegger in his discussion of seventeenth-century science. The third is Denkstil, a key concept in Ludwik Fleck’s history of syphilology. I conclude by listing three desiderata for a hermeneutic science studies: that it be anti-metaphysical, historical, and sociological. --- Reprinted in: Erich Otto Graf, Martin Schmid & Johannes Fehr (eds.), Fleck and the Hermeneutics of Science (Collegium Helveticum Heft 14) (Zürich, 2016), pp. 85-93. (shrink)