If significant for no other reason, Geminus’ Introduction to the Phenomena —most likely written during the first century B.C.E.1—provides a snapshot of astronomical knowledge existing in the period between the two pillars of ancient Greek astronomy: Hipparchus in the second century B.C.E. and Ptolemy in the second century C.E. In their edition of the text, James Evans and J. Lennart Berggren have produced the first complete English translation of the Introduction ever published. Even more, they include a translation of the parapegma attached to the manuscripts of the Introduction as well as translations of two fragments from Geminus’ other works. The first is an excerpt from Geminus’ mathematical treatise, the Philokalia; the second is a quotation from Geminus’ Concise Exposition of the Meteorology of Posidonius.
In addition to providing a careful and clear translation of Geminus’ extant writings, the authors have included an extensive introduction and commentary to the texts. They situate Geminus’ astronomy within a fixed, standardized tradition of ancient astronomical observation and modeling. Stressing the pedagogical purpose of Geminus’ Introduction, Evans and Berggren have strived to produce an edition accessible to the non-specialist. Because so little is known about Geminus and astronomical practice in the first century B.C.E., Evans and Berggren have framed their study as an introduction to the principles and context of Hellenistic astronomy in general. Accordingly, they have attached four appendices to serve as reference materials. The most striking is Appendix 3, “Glossary of Technical Terms in Geminos’s Introduction to the Phenomena“, which explains the most elementary principles of ancient astronomy. More than a translation of Geminus’ Introduction to the Phenomena, Evans and Berggren’s book is itself an introduction to the ancient Greek astronomical tradition.
In his Introduction to the Phenomena, Geminus provides a relatively low-level survey of astronomical knowledge existing in the Hellenistic period. The topics he discusses include the zodiac, the constellations, the celestial sphere, lunar and solar cycles, the phases of the Moon, lunar and solar eclipses, heliacal risings and settings, geographical zones, and weather signs. While Geminus was no doubt familiar with mathematical astronomy,2 he includes very little mathematics in his Introduction. He incorporates some demonstrative mathematical arguments, as in his arithmetical analysis of lunisolar cycles, but no formal mathematical proofs. Evans and Berggren account for this lack of mathematics by emphasizing the purpose of an eisagoge as “an elementary treatise on a subject” (9). In other words, incorporating mathematical astronomy would, according to Evans and Berggren, make the astronomical concepts inaccessible to a beginning student.
Indeed, Evans and Berggren, throughout their commentary, forgive Geminus for his rudimentary treatment of the material as well as his minor, technical oversights by appealing to the purpose of the Introduction as a pedagogical tool. They suggest that the text was most likely composed in conjunction with teaching and, as a result, could not include advanced mathematical astronomy (2). For example, Geminus does not introduce models of planetary motion. He discusses stations and retrogradations (198), and he claims that he will explain the cause of their anomalous motions “elsewhere” (
Furthermore, the abrupt conclusion of the Introduction suggests that the text is incomplete. It is not clear why Geminus would end his Introduction with a very technical and mathematical analysis of Babylonian lunar theory. If one compares Geminus’ Eisagoge to Cleomedes’ Meteora,4 one is led to believe that a pedagogical introduction to astronomy would most likely conclude with at least a brief examination of planetary motion. Unlike Geminus, after explaining the cause of lunar eclipses, Cleomedes closes his second lecture with an account of planetary periods. While Geminus does present approximations of planetary periods in Ch. I, the abrupt closure of Geminus’ Introduction with a technical account of lunisolar cycles suggests that (1) the extant text of the Introduction could be incomplete, and (2) the hypothetical, lost section(s) may have included planetary theory.
On the other hand, Geminus’ Introduction to the Phenomena contains some unique content. In his chapter on lunisolar cycles, Geminus uses numerical parameters that are in exact agreement with those utilized in cuneiform tablets. As Evans and Berggren emphasize, Geminus’ text “is important because his is the oldest extant classical text to display familiarity with the technical details of a Babylonian planetary theory based on an arithmetic progression” (15). More specifically, Geminus uses a modification of System A and, in applying the exeligmos to Babylonian lunar theory, he utilizes the linear zigzag function of System B (99). While the majority of Geminus’ Introduction is rather basic in content, his discussion of lunisolar cycles is the most technical and mathematical chapter of the text; nonetheless, Evans and Berggren excel in their explanation of mathematical astronomy and make the concepts comprehensible to even the most elementary student of the history of astronomy.
The other topic Geminus discusses which is not well treated by other Greek sources is his critique of parapegmata and the seemingly causal relationship between meteorological and astronomical phenomena. Evans and Berggren state, “His refutation of the then-common view that changes in the weather are caused by the heliacal risings and settings of the stars is the most patient and detailed such argument that has come down to us” (2). Geminus argues that the relation between star phases and meteorological phenomena is merely correlative, not causal. Moreover, Geminus maintains that the same parapegma is not applicable to different locations, as the dates of the risings and settings of stars vary depending on one’s latitude (221).5
Following their translation of the Introduction, Evans and Berggren include an original translation of the parapegma which follows the Introduction in the existing manuscripts of Geminus’ text. In Appendix 2, the authors describe the debate over the authorship of the parapegma as well as offer a comparative analysis of the sources for the parapegma, principally Euctemon, Eudoxus, and Callippus (276). Given that Geminus critiques the use and interpretation of parapegmata in the Introduction, it would have been useful if Evans and Berggren had presented an analysis of the (in)consistencies between the data presented in the parapegma and the corresponding material in the Introduction. Evans and Berggren have decided, however, to leave the authorship of the parapegma an open question and instead focus on comparing its content to that of other Greek parapegmata.
While Evans and Berggren’s strength lies in their ability to clearly and succinctly explain astronomical theories, their commentary on meteorological and philosophical aspects of Geminus’ texts seems wanting in precision and scope. Their discussion of the causes of meteorological phenomena, especially, is inexact at times. For example, their account of Aristotle’s explanation of the Milky Way ignores the intricacies of Aristotle’s cosmology. They maintain that Aristotle placed the hot and dry exhalation “at the outer boundary of the air” (160) rather than identifying the exhalation with the element fire. Similarly, they suggest that the hot and dry exhalation simply “bursts into flame in the vicinity of bright stars” (160) rather than recognizing that this ignition is the effect of efficient causation. According to Aristotle’s Meteorologica, aether lying below the stars rubs against the hot and dry exhalation, creating friction, and it is this friction which ignites the exhalation.6
Moreover, when introducing their translation of the fragment of Geminus’ Concise Exposition of the Meteorology of Posidonius, Evans and Berggren do not recognize the natural philosophic distinction between meteorology and astronomy. They claim, “It may seem odd that Geminos and Poseidonios should have discussed the relation between physics and astronomy in works called Meteorology. For the Greeks, however, meteorology is the ‘study of things raised on high.’ It has potentially as much to do with astronomy as with things in the upper air, such as rainbows” (251). Instead of conflating meteorology and astronomy, Evans and Berggren could have appealed to the context in which Geminus propounded his classification of the sciences, mainly in response to Posidonius’ natural philosophy.
Nevertheless, throughout their commentary, Evans and Berggren stress the influence of Stoicism, and Posidonius especially, on Geminus. They state, “Geminos is usually considered to have been a Stoic, and is often said to have been a disciple of Poseidonios (c. 130-50 B.C.)” (23). On the other hand, the authors admit that Geminus often strays from the traditional tenets of Stoic astronomy and natural philosophy. For example, he disagrees with the Stoic (and Posidonian) belief that mundane exhalations nourish the stars. He contends, “For exhalations from the Earth are varied and irregular, and therefore cannot extend to the sphere of the fixed stars; rather, the clouds do not [even] reach up to ten stades in height” (217). This explanation demonstrates the influence of Aristotelianism, not Stoicism, on Geminus’ meteorology. Similarly, as Evans and Berggren have also observed, Geminus’ distinction of mathematical genres is Platonic in character (43). That Geminus’ natural philosophy is not always in accord with Stoic tenets and on occasion demonstrates the influence of other philosophical schools suggests that a more complicated eclecticism underlies Geminus’ astronomy.
As Evans and Berggren emphasize, “It must be said that, if Geminos were truly a Stoic, he wore his Stoicism lightly. Geminos’s Introduction is remarkably free of philosophical interpolations, unlike those of Kleomedes and Theon of Smyrna, which show us what philosophically oriented surveys of astronomy look like” (25-6). Very little philosophy is apparent in Geminus’ Introduction. Still, this dearth of philosophy is itself interesting, as are certain subtle philosophical matters that arise in the text, such as Geminus’ passing comments on knowledge gained by reason as opposed to by observation alone (159, 167).
In addition to their translation of the Introduction to the Phenomena and the parapegma, Evans and Berggren have included translations of two fragments attributed to Geminus. The first is, according to Evans and Berggren, a passage from Geminus’ mathematical treatise, Philokalia, preserved in Proclus’ Commentary on the First Book of Euclid’s Elements. The second is Geminus’ discussion on the relationship between astronomy and physics, a passage from his Concise Exposition of the Meteorology of Posidonius preserved in Simplicius’ Commentary on Aristotle’s Physics. From Simplicius’ text, it is clear that the fragment is indeed a quotation from Geminus’ work. As concerns the first fragment, it is ambiguous whether the text is indeed a quotation. Yes, Evans and Berggren brand it as a quotation, but Proclus appears merely to be summarizing the ideas of various philosophers. In addition to referencing Geminus, Proclus also cites Ktesibios of Alexandria, Hero of Alexandria, and the Timaeus (248-9). Whether this fragment is a quotation, a paraphrase, or a second-hand report merits more discussion.
As for the translation of Geminus’ texts, Evans and Berggren have produced an extremely clear translation. True to their intent, it appears faithful to the rhythm and flow of Geminus’ writing (107). Rather simple in style and vocabulary, Geminus’ prose has lent itself to a mainly literal translation that is easily comprehendible by the reader. The translators have, at times, chosen to leave technical terms transliterated rather than translated. In such cases, they have promptly explained their reasoning for doing so. Germaine Aujac’s edition of the Introduction to the Phenomena has provided the basis for the translation.7 In addition, the translators have consulted the edition of Manitius8 as well as half a dozen manuscripts (102).
As for Evans and Berggren’s book itself, Princeton University Press has delivered an attractive and highly organized product. The numerous tables and diagrams are especially impressive. Included at the most technical junctures of the text, they efficiently and clearly explain the astronomical principles being introduced.
On the whole, Evans and Berggren’s book is an excellent translation and welcome commentary on Geminus’ texts. The translation of the Introduction to the Phenomena is a much-needed resource for the study of Hellenistic astronomy, and the introduction, commentary, and appendices the authors provide make the book a useful educational tool accessible to even the most elementary student of the history of astronomy.
Notes
1. Evans and Berggren adopt Alexander Jones’ dating of Geminus as presented in Jones, A. 1999. “Geminus and the Isia,” Harvard Studies in Classical Philology 99, 255-67.
2. Geminus wrote a (now lost) mathematical work discussing, among other topics, the various branches of mathematics, including sphairopoiia, dioptrics, and gnomonics (4).
3. Dupuis, U. 1892. Théon de Smyrne, Philosophe platonicien: Exposition des connaissances mathématiques utiles pour la lecture de Platon (Paris: Hachette. Reprinted, Bruxelles: Culture et Civilisation, 1966).
4. Todd, R. 1990. Cleomedis Caelestia. (Leipzig: Teubner).
5. A parapegma inscription from Miletus demonstrates how astronomers from vastly different locations—including Greek astronomers such as Euctemon, Eudoxus, and Philip as well as “the Egyptions” and “Kalaneus of the Indians”—were cited as authorities on local astrometeorological phenomena. See Lehoux, Daryn. 2005. “The Parapegma Fragments from Miletus,” Zeitschrift für Papyrologie und Epigraphik 152, 125-40.
6. Aristotle. Meteorologica, I. viii.
7. Aujac, G. 1975. ed. and trans. Géminos, Introduction aux phénomènes (Paris: Les Belles Lettres).
8. Manitius, Carolus. 1898. ed. and trans. Gemini Elementa astronomiae (Leipzig: Teubner; reprinted Stuttgart: Teubner, 1974).