In the third century b.c.e., Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. Cleomedes gives a short account of Eratosthenes’ method, his numerical assumptions, and the final result of 250,000 stades. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that (...) class='Hi'>Eratosthenes later made better measurements and revised his estimate or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved in the doxographical literature. This essay shows that Eratosthenes’ result of 252,000 stades for the Earth’s circumference follows from a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. The essay discusses the consequences for our understanding of his program. (shrink)

Phot. Lex. ε 100 Theodoridis: ἔγχουσαν οἱ Ἀττικοὶ λέγουσι τὴν ῥίζαν, οὐ δὴ ἄγχουσαν, ἣν ἀπείρως Ἐρατοσθένης φυκίον. Ἀμειψίας Ἀποκοτταβίζουσι· ‘δυοῖν ὀβολοῖν ἔγχουσα καὶ ψιμύθιον’.Phot. Lex. ε 100 Theodoridis: The Attic writers call the root enchusa, not anchusa, which Eratosthenes out of ignorance a seaweed. Ameipsias in the Cottabus-Players : ‘alkanet and white lead at the price of two obols’.

Summary This paper presents a new argument against the widely accepted view that Eratosthenes and some other Greek authors of the pre-Roman period measured distances in special stades that were much shorter than the ‚common‘ stade of 185 m attested by the majority of sources.

This article presents texts recovered by post-processing of multispectral images from the fifth- or sixth-century underwriting of the palimpsest Codex Climaci Rescriptus. Texts identified include the Anonymous II Proemium to Aratus’ Phaenomena, parts of Eratosthenes’ Catasterisms, Aratus’ Phaenomena lines 71–4 and 282–99 and previously unknown text, including some of the earliest astronomical measurements to survive in any Greek manuscript. Codex Climaci Rescriptus also contains at least three astronomical drawings. These appear to form part of an illustrated manuscript, with considerable (...) textual value not merely on the basis of its age but also of its readings. The manuscript undertexts show significant overlap with the Φ Edition, postulated as ancestor of the various Latin Aratea. (shrink)

This article discusses Lysias’ Against Eratosthenes as an ancient Athenian instance of the superior orders plea, a line of defence made notorious during the Nuremberg trials, which in turn became the cornerstone of modern war crime legislation. Whereas the pre-Nuremberg jurisdiction largely embraced the principle of superior responsibility, whereby a subordinate executing criminal orders was not to be held liable for them, the trials of the Nazi war criminals brought about a complete reversal of this doctrine. While remaining faithful (...) to the spirit of the Nuremberg jurisdiction, the subsequent legislative acts sought to further elaborate its underlying principle of absolute liability, in order to precisely determine the question of guilt and innocence. I argue that despite the close relationship between modern legal systems and Roman law, which fully embraced the doctrine of superior responsibility, it is in the juridical thought of ancient Athens that one finds the archetype of contemporary war crime legislation. (shrink)

The tenth prefatory letter of Pollux’ Onomasticon transmits two otherwise unattested pieces of information concerning the existence of an anonymous commentary on Xenophon and of a treatise by Eratosthenes of Cyrene entitled Σκευογραφικός. The corrupt state of the text in the manuscript tradition, which the standard edition by E. Bethe has not improved, has so far hindered the full understanding of this passage. This article argues that two corrections should be introduced in 10.2–3 Bethe; suggests that the anonymous commentary (...) on Xenophon quoted by Pollux concerned not only the Περὶ ἱππικῆς, as traditionally assumed, but also the Ἱππαρχικός; and re-examines the evidence supporting the hypothesis that Eratosthenes’ Σκευογραφικός was not part of the better-known Περὶ τῆς ἀρχαίας κωμῳδίας, but an independent work. (shrink)

This article explores the role and modes of operation of metaphorical framing in ancient Greek and modern European and American political discourse. It looks at how concepts such as citizenship, ownership, family, morality, finance, sport, war, domination, human life, and animals are used to reframe political issues in ways promoted by the speaker, and how they may continue to be reshaped in the ongoing political discourse. The analysis of examples of ancient Athenian public rhetoric and of modern European and American (...) political debates reveals the differences and some striking similarities in the ways political and civic values were expressed and reframed in antiquity and how they are used today. This essay also discusses the potential effects of such framing in antiquity and in more recent times. (shrink)

The figure of the cordial host of the Academy, who invited the most gifted mathematicians and cultivated pure research, whose keen intellect was able if not to solve the particular problem then at least to show the method for its solution: this figure is quite familiar to students of Greek science. But was the Academy as such a center of scientific research, and did Plato really set for mathematicians and astronomers the problems they should study and methods they should use? (...) Our sources tell about Plato's friendship or at least acquaintance with many brilliant mathematicians of his day (Theodorus, Archytas, Theaetetus), but they were never his pupils, rather vice versa -- he learned much from them and actively used this knowledge in developing his philosophy. There is no reliable evidence that Eudoxus, Menaechmus, Dinostratus, Theudius, and others, whom many scholars unite into the group of so-called "Academic mathematicians," ever were his pupils or close associates. Our analysis of the relevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' "Catalogue of geometers", and Philodemus' "History of the Academy", etc.) shows that the very tendency of portraying Plato as the architect of science goes back to the early Academy and is born out of interpretations of his dialogues. (shrink)

This book describes in detail the various theories on the shape of the Earth from classical antiquity to the present day and examines how measurements of its form and dimensions have evolved throughout this period. The origins of the notion of the sphericity of the Earth are explained, dating back to Eratosthenes and beyond, and detailed attention is paid to the struggle to establish key discoveries as part of the cultural heritage of humanity. In this context, the roles played (...) by the Catholic Church and the philosophers of the Middle Ages are scrutinized. Later contributions by such luminaries as Richer, Newton, Clairaut, Maupertuis, and Delambre are thoroughly reviewed, with exploration of the importance of mathematics in their geodetic enterprises. The culmination of progress in scientific research is the recognition that the reference figure is not a sphere but rather a geoid and that the earth’s shape is oblate. Today, satellite geodesy permits the solution of geodetic problems by means of precise measurements. Narrating this fascinating story from the very beginning not only casts light on our emerging understanding of the figure of the Earth but also offers profound insights into the broader evolution of human thought. (shrink)

(I) Aristotle of Stagira (384-322 BC) 0) A closed geocentric spherical cosmology. (Adopted from the great mathematician, Eudoxus, c. 400 to 347 BC; via Calippus; but Aristotle unifies their separate schemes for different heavenly bodies). (Aristotle cites mathematicians as estimating radius of earth: in fact 200% of correct figure. Eratosthenes ca. 250 BC estimates radius of earth as 120% of correct).

(I) Aristotle of Stagira (384-322 BC) 0) A closed geocentric spherical cosmology. (Adopted from the great mathematician, Eudoxus, c. 400 to 347 BC; via Calippus; but Aristotle unifies their separate schemes for different heavenly bodies). (Aristotle cites mathematicians as estimating radius of earth: in fact 200% of correct figure. Eratosthenes ca. 250 BC estimates radius of earth as 120% of correct).

Heracles had gone to Arcadia to fetch the Erymanthian boar; when he had just returned he heard of the voyage of Argo, and, hastily depositing the boar at Mycenae, departed to join Jason without the knowledge of Eurystheus. λυρκήιον Αργος άμείψας is supposed to mean ‘having come to Lyrceian Argos’. But, first, άμείβω Αργος ought not to mean ‘I come to Argos’; άμείβω and άμείβομαι alike mean either change or pass or leave; enter they do not mean. The lexica quote (...) passages as meaning enter which do not mean any such thing; Θύρας or βαλόν άμείβω is ‘I pass’ the door or threshold, πόλιν έκπόλεως άμείβω or άμείβομαι is ‘I change one city for another,’ άμείβομαι έρκοςόδότων ‘I pass the hedge of the teeth,’ and so on. Until I see an instance of it I shall not believe that πόλιν άμείβω can mean merely I enter or come to a city. Nor can we take it to mean pass in this place, because the road from Arcadia to Mycenae does not pass Argos. Secondly, what is Lyrceian Argos ? Whether a river or a mountain be implied by Lyrceian, it is not a Greek expression; we do not speak of Hymettian Athens or Cephisian Athens, of Cithaeronian or Asopian Thebes or Boeotia. There is indeed found the expression Πηλιωτιν 'Ιωλκόν in Euripides, Medea 484, and the scholiast on iv. 131 says that Τιτνίδος Αίης means Aea of the river Titen, referring to Eratosthenes as his authority for the river, but no one else knows anything about it, and it is more than probable that Mr. Mooney is right in regarding it with suspicion. (shrink)

An examination of Wealth 160-69 sheds further light on the portrayal of adulterers (moichoi) in ancient Greek comedy and oratory. The moichos is routinely presented as undermining the financial fortunes of a household as well as its domestic harmony. On the Greek comic stage, and in the Athenian courtroom, the moichos is less a Don Juan figure than a treacherous intruder, intent on exploiting his seductive charms to the detriment of another male citizen’s household. Such an understanding of the Greek (...) moichos helps to shed light on figures such as the Eratosthenes of Lysias 1, the youthful lover in the concluding scenes of Wealth, and Apollodorus’ presentation of the former slave Phormion. It also yields further insights into popular attitudes toward women and marriage. (shrink)

Interest in νομαστìκωμδєȋν began early. Even before the compilation of prosopo-graphical κωμδούμєνο in the second century B.C., Hellenistic study of Aristophanes had devoted attention to the interpretation of personal satire. The surviving scholia contain references to Alexandrian scholars such as Euphronius, Eratosthenes and Callistratus which show that in their commentaries and monographs these men had dealt with issues of νομαστì κωμδєȋν Much material from Hellenistic work on Old Comedy was transmitted by later scholars, particularly by Didymus and Symmachus in (...) their variorum editions, and was eventually embodied in the scholia, though of course in an abridged and sometimes distorted form. Many of our fragments of Old Comedy, preserved in the scholia or in medieval works of reference as parallels to passages in Aristophanes, are direct evidence of the long ancient tradition of interest in the genre's large element of personal satire. What we find in the scholia should not therefore be treated as representative only of the latest and most derivative stages of ancient scholarship. It is the purpose of this article to argue that the scholia on Aristophanes allow us to see that in matters of νομαστì κωμδєȋν certain assumptions about the nature of this type of comic material were persistently made by ancient scholars, and that certain interpretative habits were consequently developed from them. It is my further aim to suggest that this pattern of interpretation has been widely but unjustifiably perpetuated in later work on Aristophanes. (shrink)

One of the most ingenious arguments in all of Attic oratory is to be found in the speech Lysias wrote for Euphiletus to deliver at his trial for the murder of Eratosthenes . In his speech Euphiletus first describes to the court how his wife was seduced by Eratosthenes, then recounts how he discovered the affair, caught the adulterer in the act, and, despite an offer to pay compensation, slew him. Euphiletus defends his action by citing the law (...) of the Areopagus that whoever kills an adulterer caught in flagranti with his wife cannot be convicted of murder. Euphiletus further points out that the same exemption applies to the man who catches someone seducing his pallakē. If the lawgiver regarded the seduction of a pallakē as so serious that it merited the death penalty, Euphiletus argues, he must have regarded the seduction of a wife as even more reprehensible, deserving a penalty worse than death. (shrink)

From immemorial time, many Tyrrhenian places of ancient Sicily and Italy were identified with the main stages of the return of Ulysses. Some Hellenistic critics assumed that it was from the various ancient and pre-Homeric myths that Homer drew inspiration, in the same way that he did with the myth of the Trojan War, which certainly occurred before him. Thus, the voyage of Ulysses, after his losing the course because of the storm at Cape Malea, had to be located in (...) those sites. But how can one explain the fact that Homer places the voyage from Circe to the Hades over the Ocean? Is it only a pseudogeographic poetic touch, aimed to magnify the exploit? Crates of Mallus did not think so: in his opinion, only some of the numerous adventures had taken place in the Tyrrhenian Sea, whereas Homer had purposefully placed some other exactly on the Atlantic Ocean, beyond the Pillars of Hercules. Whichever of the two models one chooses, the route of Ulysses seems to be completely unlikely, both from the point of view of objective reality and from the point of view of poetic imagination. It appears to be a senseless coming and going that takes the shape of some sort of a labyrinth. Furthermore, the navigation times suggested by the text do not accord at all with the distances among the real sites. For this reason, Eratosthenes held that, from Cape Malea onwards, Ulysses switched from the real world to that of fantasy, or better still to the world of some narrative fable that does not heed geography at all. The modern critics are inclined to agree with him and this thesis is nowadays the most popular one. Yet, a very serious objection can be raised here: the myth and the epos, are strictly linked to the geography and the topography as well – they are radically refractory to a narrative fable that totally contradicts the then realities of time and space. Why should Ulysses plunge from Cape Malea onwards straight into the Neverland kingdom? If we combine Odyssey’s data with those we can reconstruct for the earliest form of the Argonautic saga, then we get the solution that neither the ancient nor the modern critics have guessed correctly: up to around the middle of the 8th century B.C., the Greeks thought the Ocean to flow just after the Sicily Channel, essentially coinciding with the so-called Tyrrhenian Sea, still completely unknown at that time. This new perspective can well justify the objective disorder of Ulysses’ route. Above all, it also bears a deeper poetic sense: the Hero had the chance to know and to experience not only some far and exotic countries in general terms, but he also met the very boundaries of the surfacing lands and the rushing waters which encircle the terrestrial disc, bordering the external cosmic abyss. Ulysses came back home alive. He was able to tell the stories about the lands where no human being could ever sail. This borderline that geographically is clearly located marks at the same time the insurmountable chasm between the physical and the meta-physical world. (shrink)

The tenth prefatory letter of Pollux’ Onomasticon transmits two otherwise unattested pieces of information concerning the existence of an anonymous commentary on Xenophon and of a treatise by Eratosthenes of Cyrene entitled Σκευογραφικός. The corrupt state of the text in the manuscript tradition, which the standard edition by E. Bethe has not improved, has so far hindered the full understanding of this passage. This article (a) argues that two corrections should be introduced in 10.2–3 Bethe; (b) suggests that the (...) anonymous commentary on Xenophon quoted by Pollux concerned not only the Περὶ ἱππικῆς, as traditionally assumed, but also the Ἱππαρχικός; and (c) re-examines the evidence supporting the hypothesis that Eratosthenes’ Σκευογραφικός was not part of the better-known Περὶ τῆς ἀρχαίας κωμῳδίας, but an independent work. (shrink)

A reiteration of the main details of the case may be helpful. Euphiletus killed Eratosthenes and was prosecuted for premeditated homicide by Eratosthenes' relatives. The present speech, our sole source of information concerning the case, was written for the defendant, partially or totally, by a professional speechwriter, presumably Lysias. In this speech Euphiletus admits killing Eratosthenes. He pleads, however, that, since he killed Eratosthenes after catching him in the act of adultery with his own wife, this (...) was a case of justified homicide. At the same time, he denies a charge of the prosecution that he had killed Eratosthenes for reasons unrelated to the adultery. The speech was delivered before a court of fifty-one judges especially set up to judge such cases, as is attested elsewhere:T1Arist. Ath. Pol. 57.3: ‘If…a person admits that he has killed someone but claims that he had a right to do so, as, for instance, when he has surprised an adulterer in the act,… then the trial takes place in the Delphinion’. (shrink)

Ancient Greek music was purely or predominantly melodic; and in such music subtleties of intonation count for much. If our sources of information about the intervals used in Greek music are not always easy to interpret, they are at any rate fairly voluminous. On the one hand we have Aristoxenus, by whom musical intervals were regarded spatially and combined and subdivided by the processes of addition and subtraction; for him the octave consisted of six tones, and the tone was exactly (...) divisible into fractions such as the half and quarter, so that the fourth was equal to two tones and a half, the fifth to three tones and a half, and so on. On the other hand we have preserved for us in Ptolemy's Harmonics the computations of a number of mathematicians, who realized correctly that intervals could only be expressed as ratios , that the octave was less than the sum of six whole tones and that this tone could not be divided into equal parts. These authorities are Archytas, the Pythagorean of the early fourth century, Eratosthenes , Didymus and Ptolemy himself . To these we must add the scale of Plato's Timaeus and, closely related to it, the computations of the pseudo-Philolaus and of Boethius himself . Aristoxenus is less easy to understand than the mathematicians because of the unscientific nature of his postulates. His importance, however, is very great, not only from his comparatively early date but because he claims to champion the direct musical consciousness against the scientific approach of some of his predecessors and contemporaries. (shrink)