Bryn Mawr Classical Review

Bryn Mawr Classical Review 2004.08.06

Alan C. Bowen, Robert B. Todd, Cleomedes' Lectures on Astronomy. A Translation of The Heavens with an Introduction and Commentary.   Berkeley:  University of California Press, 2004.  Pp. xiii, 238.  ISBN 0-520-23325-5.  $55.00.  

Reviewed by Nathan Sidoli, University of Toronto (
Word count: 1554 words

Almost all the substantial Hellenistic works of both Stoicism and technical astronomy have been lost. This unfortunate circumstance has caused Cleomedes' treatise on Stoic cosmology and astronomy to assume a value greater than its contents merit. For our current understanding of Stoic physical thought, however, and the dissemination of scientific ideas into the greater intellectual community, Cleomedes' work is an important source. Bowen and Todd's new translation, Cleomedes' Lectures on Astronomy, gives this key work its due. The level of scholarship in this book is of the highest caliber.

The translation itself, based on Todd's edition, is quite good.1 The English gives the reader a close sense of the original text without being awkward or unnecessarily literal. There are, of course, a few places where I would have chosen a different idiom; nevertheless, I found no places where I thought the text could not support the reading which is given. This book, however, is more than a reader's text of Cleomedes for an English speaking audience. The introduction and commentary by Bowen and Todd situate Cleomedes' work in the context of what we know about Stoic physics and ancient technical astronomy. A series of modern diagrams also helps the reader follow the many arguments which are based on the geometric configurations of the Stoic cosmos.

The book includes an interesting appendix on one of the most significant texts for our understanding of ancient philosophy of science. Simplicius, in his commentary on Aristotle's Physics, gives a passage which, although many times removed, has its origin in a work by Posidonius.2 This passage discusses the respective roles of the physicist and the astronomer and delineates the proper domains of the sciences they produce. Bowen and Todd translate this text and offer a new view of Posidonius' philosophy of science.

Bowen and Todd argue, I think rightly, against the tendency of historians of science to read Cleomedes as writing in the tradition of popularizing the technical sciences, as represented by Geminus' Introduction.3 Instead, they situate his two lectures on astronomy in a broader context of the physics section of a lecture series covering all three branches of Stoic thought: logic, physics and ethics. Whether or not we accept the hypothesis of a complete lecture series, it is clear that these two lectures are primarily exercises in Stoic cosmology. For example, Cleomedes discusses at length topics which mathematical astronomers tend to ignore: the existence of an extracosmic void, the physical causes for the reflective property of the moon and the fact that the sun is larger than a foot wide. Moreover, Cleomedes' overall concern is a description of the structure and properties of the Stoic cosmos.

The two lectures divide fairly cleanly into two books. Book I deals primarily with the earth while Book II covers the sun and the moon. The cosmological nature of the treatise is established in the first section, which sets out the basic structure and principles of the Stoic cosmos: the cosmos is a structured plenum, administered by nature, and surrounded by an infinite void. Both the earth and the sphere of the fixed stars are organized by five parallel circles: the equator, the tropics of Cancer and Capricorn, and the arctic and antarctic circles.4 In the heavens, these circles are determined by the rising and setting phenomena of the stars and the annual phenomena of the sun with respect to the local coordinates. On earth, these circles determine the geographic zones related to temperature. The rest of the book treats the shape and size of the earth and a few aspects of spherical astronomy, such as the annual variation in times of daylight and the differential in local times for simultaneous observations. Chapter 7 gives two procedures for calculating the size of the earth based on the principles of spherical astronomy. The first is the famous determination made by the librarian Eratosthenes. The second is a revision of this by Posidonius.

The second book deals with the sun and the moon. There is, however, nothing here concerning the proper motion of the luminaries. In fact, the only discussion of the Sun's annual orbit occurs in Cael. I 4, almost as an aside to a discussion of the varying lengths of daylight throughout the year. Lunar theory is never discussed. The focus of the second book is on the physical properties of the luminaries: their sizes, the properties and effects of their illumination and the physical causes of eclipses. The brief remarks on planetary periods in the last section are, as Bowen and Todd point out, probably an interpolation. The first section of Book II is the longest in the text. It invests considerable effort in attempting to refute two simultaneously inconsistent Epicurean positions: that the sun is the size it appears to be (whatever that might mean) and that the sun is one foot wide.5 Cleomedes begins by discussing the problems involved with allowing sense perception, in and of itself, to become a criterion of knowledge and then turns to the absurdity of claiming the sun is one foot wide. After amassing a series of more or less coherent arguments, he finally vents his spleen against Epicurus by degenerating into a diatribe of insults and antisemitism. The rest of the book concerns the sizes and physical properties of the luminaries. Cael. II 4, for example, deals with the physical causes of the reflectivity of the moon and contains important material for our understanding of ancient optics.6

Ultimately, I believe Cleomedes is more valuable to us as a witness to Stoic physics, optics and cosmology than mathematical astronomy. The actual mathematics handled in his lectures is quite modest.7 Moreover, all of the technical astronomy he reports goes back at least as far as Hipparchus. If Bowen and Todd are correct in their dating of Cleomedes, this would mean that it is between one and three centuries old.8 This is important for our understanding of the way in which the exact sciences made their way into philosophic practice. The Stoics are considered to be one of the more scientific of the ancient schools, and Posidonius one of the more scientific Stoics. There can be no doubt that Cleomedes took the bulk of his technical material from Posidonius. Nevertheless, the mathematical science preserved by Cleomedes is both humble and out of date.

The appendix on Posidonius' philosophy of science is quite interesting, but I found it to be somewhat disorganized. There is not a clear enough distinction between the new reading that is being advanced and a number of refutations of previous readings. According to the authors, Posidonius held that the proper function of the astronomer is to subordinate his research to the results of the Stoic physicist and start with hypotheses which are the results of successful physical investigation (pp. 195-6). If the astronomer fails to follow this path, she runs the risk of having to elaborate every hypothesis that will explain the phenomena; including absurd ones such as a stationary sun and a moving earth (pp. 202-1, F18EK 32-41). On the other hand, if she follows the lead of the physicist, she will produce a description of the heavenly motions which is an accurate representation of reality.

This interpretation is both useful and plausible. Unfortunately, the presentation is obscured by the authors' insistence that Posidonius maintained that a single astronomer would only ever put forward a single hypothesis (pp. 194, 196-7). If, however, Posidonius knew at least as much of the work of Aristarchus and Hipparchus as we believe we know, then he could not have held this view. Aristarchus is known to have used a concentric sphere to model the motion of the sun, and he is also reliably reported to have advanced a heliocentric hypothesis.9 Hipparchus is reported by Theon of Smyrna to have proposed both eccentric and epicyclic hypotheses for the sun; and by Ptolemy to have proposed both again for the moon.10 The authors concede that these were put forward as two models of the same phenomena (p. 202, n. 30),11 and whether or not we believe that Hipparchus knew and discussed the mathematical equivalence of these models there is no reason to believe that he (or anyone else) thought that they were physically equivalent.12 Moreover, I am not convinced that this subsidiary reasoning is necessary to the main argument. It seems perfectly possible that Posidonius could be seeking to establish normative practice in astronomy while still understanding that astronomers had not and did not always act as he thought they should.

A few scattered notes on the book itself are perhaps in order, which will pertain more to the choices of the publisher than those of the authors. The formatting, typeface and general organization of the text is accessible and attractive. The use of ascenders and descenders in the typeface of the numbers is handsome but can be distracting in the case of long numerals, fractions or calculations. Luckily, Cleomedes' arithmetic is meager enough that this does not cause much annoyance. The footnotes are at the foot of the page, where they belong. The quality of the diagrams is very fine and their presence helps to clarify a number of obscure arguments.

On the whole, this book is a welcome contribution to our understanding of Cleomedes. It will be essential reading for anyone working on Greco-Roman science and philosophy.


1.   Todd, R., Cleomedis Caelestia. Leipzig: 1990.
2.   Simplicius, In Phys. 291.21-292.21.
3.   Aujac, G., Géminos: Introduction aux phénomènes. Paris: 1975.
4.   In fact, Cleomedes defines the "arctic" and "antarctic" circles as the always visible and always invisible circles. [pp. 33-34] This is a poor choice since, in the next paragraph, he wants to associate these circles on the earth with geographic zones related to temperature. [p. 34] By this definition, however, the "arctic" and "antarctic" circles can be anywhere between the pole and the equator.
5.   Cleomedes' presentation suggests that these statements were somehow meant to be equivalent and that he accepted them as such. In fact, according to both modern and ancient optics, an object which is actually one foot wide and appears under the angular span of the sun would be close enough that one could hit it with a stone.
6.   For instance, a discussion of the moon's phases involves the fascinating claim that objects, which are luminous because of reflection (κατ' ἀνάκλασιν), send out light at right angles. [p. 139] Menn has suggested that this may be a misunderstanding of the well-known principle of standard reflection at equal angles. [p. 140, n. 14] The argument that Cleomedes gives, however, makes it clear that he, at least, intends perpendicular emanation. [p. 140] Figure 23 [p. 189] makes this argument transparent.
7.   The only mathematical tools employed are a simple statement of ratio theory (Elem. V 15, A:B = mA:mB) and the modicum of geometry necessary to establish a proportion. This theorem is used eight times, in just about every mathematical argument in the text; see pp. 16, 69, 74, 80, 83, 114, 116 & 132. In one instance, Cleomedes uses the statement A=B => A/n = B/n; see p. 79.
8.   The authors give good reason for discarding Neugebauer's date of the fourth or fifth century. [p. 89, n. 16] They argue, on cultural grounds, for a broad but conservative range of 50 BCE to 250 CE. [pp. 2-4].
9.   In On the Sizes 7, Aristarchus is explicitly working in the context of a concentric sphere model for the motion of the sun. On the other hand, according to Archimedes, in Sand Reckoner, Aristarchus put forward some form of a heliocentric hypothesis.
10.   Theon, Expos. p. 166 (Hiller) and Ptolemy, Alm. VI 11.
11.   I believe, although I cannot prove, that Hipparchus' statement that it is worthy of the attention of the mathematician to understand the reason why both hypotheses explain the same phenomena must have come as a sort of prefatory remark to his own disscussion of the equivalence. It serves this function for Theon [Expos. p. 166] by whom it is preserved; and it is safe to assume that it served a similar function in Adrastus. Here, as elsewhere, it is reasonable to assume that Adrastus is not advancing technical knowledge beyond what he found in his sources.
12.   The footnote on the equivalence of the eccentric and epicyclic models [p. 202, n. 31] is misleading on two counts. (1) The phrasing implies that Ptolemy is the first author we possess who treats the equivalence of the models. In fact, Theon, Ptolemy's older contemporary, also discusses the issue and bases his work on a discussion in Adrastus. Since it is highly unlikely that either of these authors discovered the equivalence, their work must be based on a predecessor who was a practicing mathematical astronomer. As I argue in the previous note, this was probably Hipparchus. (2) The statement that the equivalence of the hypotheses is "suggested" in Alm. III 3 but not "discussed" until Alm. XII 1 makes a distinction that is hard to find in Ptolemy's text. Different aspects of the equivalence, useful for different types of models, are demonstrated in three places: in Alm. III 3, IV 5 & XII 1. Alm. III 3 demonstrates the equivalence for the solar models, Alm. IV 5 for the simple lunar models, XII 1 for the complete lunar or planetary models.

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