At some time around 200 A.D., the Stoic philosopher and teacher Cleomedes delivered a set of lectures on elementary astronomy as part of a complete introduction to Stoicism for his students. The result was _The Heavens, _the only work by a professional Stoic teacher to survive intact from the first two centuries A.D., and a rare example of the interaction between science and philosophy in late antiquity. This volume contains a clear and idiomatic English translation—the first ever—of _The Heavens, _along (...) with an informative introduction, detailed notes, and technical diagrams. This important work will now be accessible to specialists in both ancient philosophy and science and to readers interested in the history of astronomy and cosmology but with no knowledge of ancient Greek. (shrink)

Scholars have long recognised the interest of the Stoics' thought on geometrical limits, both as a specific topic in their physics and within the context of the school's ontological taxonomy. Unfortunately, insufficient textual evidence remains for us to reconstruct their discussion fully. The sources we do have on Stoic geometrical themes are highly polemical, tending to reveal a disagreement as to whether limit is to be understood as a mere concept, as a body or as an incorporeal. In my view, (...) this disagreement held among the historical Stoics, rather than simply reflecting a doxographical divergence in transmission. This apparently Stoic disagreement has generated extensive debate, in which there is still no consensus as to a standard Stoic doctrine of limit. The evidence is thin, and little of it refers in detail to specific texts, especially from the school's founders. But in its overall features the evidence suggests that Posidonius and Cleomedes differed from their Stoic precursors on this topic. There are also grounds for believing that some degree of disagreement obtained between the early Stoics over the metaphysical status of shape. Assuming the Stoics did so disagree, the principal question in the scholarship on Stoic ontology is whether there were actually positions that might be called "standard" within Stoicism on the topic of limit. In attempting to answer this question, my discussion initially sets out to illuminate certain features of early Stoic thinking about limit, and then takes stock of the views offered by late Stoics, notably Posidonius and Cleomedes. Attention to Stoic arguments suggests that the school's founders developed two accounts of shape: on the one hand, as a thought-construct, and, on the other, as a body. In an attempt to resolve the crux bequeathed to them, the school's successors suggested that limits are incorporeal. While the authorship of this last notion cannot be securely identified on account of the absence of direct evidence, it may be traced back to Posidonius, and it went on to have subsequent influence on Stoic thinking, namely in Cleomedes' astronomy. (shrink)

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 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)

ACERBI Fabio“A Reference to Perfect Numbers in Plato's Theaetetus”, Archive for History of Exact Science, 59/2005, p. 319-348. Comptes-rendus - Cleomedes Lectures on Astronomy : a Translation of The Heavens with an Introduction and Commentary by Alan C. Bowen and Robert B. Todd, Berkeley and Los Angeles, University of California Press, 2004, dans Nunciu, 20/2005, p. 232-233. - D. Fowler, The Mathematics of Plato’s Academy: A New Reconstruction, Second Edition, Oxford, Clarendon Press (Oxford..

The paper is devoted to the reconstruction of some stage of the proces leading to the emergence in modern science the concept of Infinite „Euclidean” space to geometry of the Elements in late antiquity and the Middle Ages. Some historical medieval sources and views concerning Archytas, Cleomedes, Proclus, Simplicius, Aganis, al-Nayrizi and the Arabs, Boetius, Gerard of Cremona, Albertus Magnus et al., are described analyzed and compared. The small changes in the understanding of geometry in the Elements during the ages (...) are reconstructed up to the first explicit use of the concept of infinity in geometry by Nicole Oresme. (shrink)

ArgumentA Catoptrica attributed to Euclid appears in manuscripts amongst treatises dealing with elementary astronomy. Despite this textual background, the treatise has always been read literally as a theory of mirrors, and its astronomical significance has gone unnoticed. However, optics, catoptrics, and astronomy appear strongly intermingled in sources such as, amongst others, Geminus, Theon of Smyrna, Plutarch and Cleomedes. If one compares the optical reasoning put forward in these sources to account for the formation of moonlight with arguments of Catoptrica, one (...) is able to shed new light on several principles and propositions of Catoptrica, some of which had been deemed corrupt, meaningless, and obscure. Moreover, the present analysis offers a glimpse at the context of a specific stage in the evolution of ancient catoptrics: Whether literally or by analogy, several of its results appear to have been set against a wider astronomical background, which explains the inclusion of Catoptrica in the group of texts loosely defined as “little astronomy.”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Cambridge Companion to the StoicsJohn SellarsBrad Inwood, editor. The Cambridge Companion to the Stoics. New York: Cambridge University Press, 2003. Pp. ix + 438. Cloth, $70.00. Paper, $26.00.No doubt everyone will be familiar with the format and rationale of the Cambridge Companion series, each volume being designed to function as a "reference work for students and nonspecialists." Brad Inwood's Cambridge Companion to The Stoics follows the usual (...) plan, offering fifteen essays by an impressive line up of well-known Stoic scholars. The essays fall into four distinct groups. The first group (Sedley, Gill) offers a sketch of the history of the Stoa, and both essays are excellent. Of particular interest is Sedley's challenge to the traditional distinction between the orthodox "early" and eclectic "middle" Stoa (esp. 23-24). The second group (Hankinson, Bobzien, White, Algra, Frede, Brunschwig, Schofield, Brennan) forms the heart of the volume, each essay examining a central topic in Stoic philosophy. While all of these contributions are very good, those by Bobzien, Brunschwig, and Schofield stand out in particular. Hankinson offers a helpful discussion of Stoic epistemology but lapses into anachronistic descriptions at times; the Stoic position is "Lockean," the Stoics are good empiricists in the Humean fashion, they have "Leibnizian metaphysics" (63, 69). Brennan gives a very interesting discussion of Stoic moral psychology, but perhaps pitches it a little too high for a nonspecialist audience. The third group (Hankinson again, Blank and Atherton, Jones) explores the ancient Stoic tradition's relationship with medicine, grammar, and the astronomical sciences. Jones' discussion of the neglected Cleomedes is especially welcome (333-37). The final group (Irwin, Long) considers the reception of Stoic ideas in the Western intellectual tradition. Of these I found Long the more accessible and useful of the two (compare, for instance, their respective discussions of Butler, 357-62 and 382-89), although Irwin will no doubt prove stimulating to those already familiar with the issues he addresses.What is lacking from the collection as a whole, however, is any sense of the systematic unity of Stoic philosophy. While it has inevitably been divided up under various headings for the sake of exposition, there has not been much attempt to put it back together again (like Humpty Dumpty, Stoic philosophy is like an egg; Diogenes Laertius 7.40). Although many individual contributors signal the systematicity of Stoicism, there is no extended discussion of the way in which the various parts of Stoic philosophy fit together, nor how that system relates to the way in which the Stoics conceived philosophy, or their ideal of the Sage. [End Page 337]My principal concerns with the volume as a whole relate to the lack of any supporting material that might prove useful to the student or nonspecialist approaching the subject for the first time. There is no list or chronology of the principal Stoics, nor a guide to the ancient sources for Stoicism. There is a list of primary sources, but this contains all of the primary material cited by the contributors, including works by Aquinas, Butler, Duns Scotus, Hume, Leibniz, and Spinoza. There is no readily accessible table of abbreviations, and what nonspecialist will know that in order to find a text cited as 'S. E. M' they may end up opening a book entitled Against the Logicians (as 'M' 7 and 8 are called in the Loeb Classical Library series)? Some abbreviations are explained within the list of primary sources, but this is not immediately obvious. The bibliography is indeed substantial but it also simply lists the various items cited by the contributors. What might have been more useful in this companion is a structured guide to further reading, such as the one in A. S. McGrade's excellent Cambridge Companion to Medieval Philosophy, for instance. Even better would have been a bibliography along the lines of the one in Jonathan Barnes' Cambridge Companion to Aristotle. One other omission that is striking is the absence of a discussion of methodological problems that arise from relying on often hostile doxographical sources. Although a number of the contributors do touch on such issues en route, a more sustained treatment might have... (shrink)

Epikurs Lehre erfreut sich wachsender Aufmerksamkeit. Doch verdient auch die Geschichte des Epikureismus, insbesondere der Kaiserzeit, Interesse. Keineswegs verschwindet die diesseits orientierte Lehre Epikurs trotz wachsendem Streben der Philosophie nach Transzendenz in der Spatantike. Eine Analyse paganer wie auch christlicher Autoren zeigt, dass insbesondere Epikurs Ethik und ihr Angebot praktischer Lebenshilfe als Teil einer "praeparatio philosophica" uberlebt, ins Mittelalter vermittelt wurde und in der Renaissance Auferstehung feierte. Die Vortrage dieses Bandes begeben sich deshalb auf Spurensuche. Unter verschiedenen Gesichtspunkten gehen sie (...) der Tradition des Epikureismus in der spaten Republik und der Kaiserzeit nach und folgen ihnen bis zur Renaissance. Inhalt: Einleitung Graziano Arrighetti: Filodemo fra poesia, mito e storia Marcello Gigante: Seneca, ein Nachfolger Philodems? Dieter Timpe: Der Epikureismus in der romischen Gesellschaft der Kaiserzeit Martin F. Smith: Digging up Diogenes: New Epicurean texts from Oinoanda in Lycia Diskin Clay: Diogenes and his gods Matthias Baltes: Epikureische Theologie Mauro Tulli: L'epitome die Epicuro e la trasmissione del sapere nel Medioplatonismo Carlos Levy: Philon d'Alexandrie et l'epicurisme Tiziano Dorandi: Plotina, Adriano e gli Epicurei di Atene Franco Ferrari: La falsita delle asserzioni relative al futuro: un argomento epicureo contro la mantica in Plut. Pyth. orac. 10 Keimpe A. Algra: The Treatise of Cleomedes and its Critique of Epicurean Cosmology Christoph Markschies: Epikureismus bei Origenes und in der origenistischen Tradition Jose Kany-Turpin: Lactance, un critique mesestime de l'epicurisme Therese Fuhrer: Zwischen Skeptizismus und Platonismus: Augustins Auseinandersetzung mit der epikureischen Lehre in conf. 6 Dominic O'Meara: Epikur bei Simplikios Clemens Zintzen: Epikur in der Renaissance Michael Erler: Epikur in Raffaels "Schule von Athen"? Register. (shrink)