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Geminos's Introduction to the Phenomena

Princeton University Press

Introduction

For the modern reader, Geminos provides a vivid impression of an educated Greek's view of the cosmos and of astronomy around the beginning of our era. Moreover, he is frequently a graceful and charming writer, constantly aware of his audience, and his book remains quite readable today. Indeed, it is one of a very small number of works of ancient astronomy that can be read right through with appreciation and understanding by a nonspecialist. Because Geminos covers most of the central topics of ancient Greek astronomy, histext provides an excellent general survey of those parts of that astronomy not dependent on sophisticated mathematical models. An English translation of the Introduction to the Phenomena should thus be useful not only to historians of astronomy but also to historians of science more generally, to those interested in classical civilization, and to astronomers who would like to know more about the history of their discipline.

We have furnished our translation with a commentary, printed at the foot of the page and signaled in the text by superscript numerals. The purpose of the commentary is not to summarize all that is known on the topics at hand, but to open up Geminos's text, to make it more comprehensible, and to reveal its connections with other ancient sources- philosophical and literary, as well as scientific. It should serve, as well, to direct readers to the specialized scholarly literature. Textual notes, signaled in Geminos's text by superscript roman letters, are grouped together in appendix 1.

1. SIGNIFICANCE OF GEMINOS'S INTRODUCTION TO THE PHENOMENA

Geminos's Introduction to the Phenomena, a competent and engaging introduction to astronomy, was probably written in conjunction with teaching. Geminos discusses all of the important branches of Greek astronomy, except planetary theory. This he promises to take up "elsewhere." Perhaps he did discuss planetary theory in another work, but if so, it has not survived. Topics covered in Geminos's Introduction include the zodiac, solar theory, the constellations, the theory of the celestial sphere, the variation in the length of the day, lunisolar cycles, phases of the Moon, eclipses, heliacal risings and settings of the fixed stars, terrestrial zones, and an introduction to Babylonian lunar theory. Because the work was written for beginners, it does not often get into technical detail-except in the discussion of lunisolar cycles, where Geminos does indulge in a bit of arithmetic.

Geminos's book is important to the task of filling gaps in the history of Greek astronomy in several ways. In general terms, Geminos provides an overview of most of astronomy in the period between Hipparchos (second century b.c.) and Ptolemy (second century a.d.), and thereby provides a good deal of insight into what was current and common knowledge in Geminos's own day. One of the more charming aspects of his work, frequently in evidence, is his desire to set straight common misconceptions about astronomical matters. In this way, he offers us valuable information about the beliefs of his own audience.

More specifically, Geminos provides detailed discussions of several topics not very well treated by other ancient sources. (1) His discussion of Babylonian lunar theory is an important piece of the story of the adaptation of Babylonian methods by Greek astronomers. (2) His discussion of the 8- and 19-year lunisolar cycles is the most detailed by any extant Greek source. (3) His discussion of Hipparchos's rendering of the constellations provides information not found in other sources. (4) 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.

In the extant manuscripts, Geminos's book concludes with a parapegma (star calendar) that permits one to know the time of year by observation of the stars. Many scholars believe that this compilation is older than Geminos by a century or more. Whether by Geminos or not, this parapegma is one of our most important sources for the early history of the genre. The Geminos parapegma was based substantially upon three earlier parapegmata-those by Euktemon (fifth century b.c.), Eudoxos (early fourth century b.c.), and Kallippos (late fourth century b.c.). Because the Geminos parapegma scrupulously cites its sources, it permits us to trace the stages in the evolution of the parapegma between the time of Euktemon and the time of Kallippos. Our book includes a translation of the Geminos parapegma, as well as a synoptic table of its contents (appendix 2), which should be useful in the study of this important historical document.

Although ancient and medieval Greek readers would have recognized Geminos's book as belonging to a class of "phenomena" literature (see sections 3 and 4 below), we cannot be sure that Introduction to the Phenomena is the title that Geminos himself gave it. This is a common difficulty with ancient scientific texts, the conventional titles of which are not always authorial. The Greek manuscripts of Geminos's text do provide good evidence for the commonly accepted title, although there are several variants. Indeed, the three best and oldest Greek manuscripts present a bit of a puzzle: one gives as its title Geminos's Introduction to the Phenomena; another gives Geminos's Introduction to the Things on High (meteora); and still another gives neither title nor author's name, since the copyist never filled in this information. Some later Greek manuscripts simply have "The Phenomena" of Geminos. As we shall see below (sec. 14), the Latin and Hebrew translations made in the twelfth and thirteenth centuries (from an Arabic intermediary) also show that there was considerable confusion about the title and author of the text. For the sake of simplicity, we shall always refer to Geminos's book by the title commonly used today, and best supported by the Greek manuscripts, Introduction to the Phenomena.

2. GEMINOS'S OTHER WORKS

Geminos was the author of two other works that have not come down to us. One was a mathematical work of considerable length that discussed, among other things, the philosophical foundations of geometry. Fortunately, a large number of passages from this work (whether in quotation or in paraphrase) are preserved by Proklos in his Commentary on the First Book of Euclid's Elements. The exact title of Geminos's book is uncertain, but in one passage Proklos remarks, "so much have I selected from the Philokalia of Geminos." (Philokalia means "Love of the Beautiful.") In one passage of considerable interest, Geminos discussed the branches of mathematical science and their relationships to one another. This is the most detailed such discussion that has come down to us from the Greeks. Moreover, it is clear that Geminos was discussing, not merely abstract divisions of mathematics, but actual genres of mathematical writing. Because several of Geminos's branches of mathematics pertain to astronomy (e.g., sphairopoiïa, dioptrics, and gnomonics), his discussion sheds light on the relationship of astronomy to other mathematical endeavors. Because of its interest for the history of astronomy, we have included a translation of this passage from Geminos's Philokalia as fragment 1.

Geminos was also the author of a meteorological work, which was perhaps a commentary on, or an abridgement of, a now lost Meteorology of Poseidonios. A fragment of some length is preserved by Simplikios in his Commentary on Aristotle's Physics. Apparently, by Simplikios's time, Geminos's meteorological book had been lost, for Simplikios makes it clear that he is quoting Geminos, not from Geminos's own work, but from some work by Alexander of Aphrodisias. In the course of his citation, Simplikios says that Alexander drew these remarks from Geminos's "Concise Exposition of the Meteorology of Poseidonios." The fragment from Geminos preserved by Simplikios is of considerable interest, for it is devoted to the limits of astronomical knowledge. In this passage, Geminos discusses the relationship of astronomy to physics (or natural philosophy), arguing that astronomy is, of itself, unable to decide between competing hypotheses and must rely on physics for guidance about first principles. We include a translation of this passage from Geminos's lost meteorological work as fragment 2.

3. ON "THE PHENOMENA" IN GREEK ASTRONOMY

Geminos's Introduction to the Phenomena had its roots in a well-established genre. In order to explain what the writers and readers of this genre considered to be relevant, we must say a little about what Greek astronomical writers mean by the phenomena. The word "phenomena" is a participle of the passive verb phainomai, which carries the meanings of "to come to light, come to sight, be seen, appear." The last two are definitive for the astronomical sense of the word, which is "things that are seen/appear in the heavens."

A late source, Simplikios, quotes Sosigenes as having attributed to Plato the statement that the task of astronomy was to show how, by a combination of uniform circular motions, one could "save (i.e., account for) the phenomena." The ascription to Plato is controversial (see sec. 10 below), but in any case the word Phenomena appears as the title of a work by an associate of Plato, Eudoxos of Knidos (early fourth century b.c.). Eudoxos's work has not survived, but its essence is preserved in a poem of the same name by Aratos (early third century b.c.). The poetic Phenomena of Aratos was the subject of a commentary by the great astronomer Hipparchos of Rhodes (second century b.c.), who was able to compare it with the text of Eudoxos and demonstrate that Aratos had indeed relied upon Eudoxos. It appears from these sources that Eudoxos's work was devoted to a detailed description of the placement of the fixed stars and the constellations, relative to some standard reference circles on the celestial sphere. The following passages give a sense of the character of Eudoxos's book, and also an idea of what sort of "phenomena" it was occupied with. We quote directly from Hipparchos's Commentary, and in each case Hipparchos has made it clear that he is himself directly reporting on Eudoxos's text:

There is a certain star that remains always in the same spot; this star is the pole of the universe.

Between the Bears is the tail of the Dragon, the end-star of which is above the head of the Great Bear.

Aratos, following Eudoxos, says that it [the Dragon's head] moves on the always-visible circle, using these words: "Its head moves where the limits of rising and setting are confounded."

Because Aratos includes in his poem a discussion of the principal circles of the celestial sphere (ecliptic, equator, tropics, arctic circle, as well as the Milky Way), we may surmise that the same material was treated, in more detail, by Eudoxos. So, by the early fourth century, the basic theory of the celestial sphere had been established, and a detailed description of the constellations given. Such were the phenomena of Eudoxos.

The oldest extant work named The Phenomena is that of Euclid (c. 300 b.c.). Unlike the work of Eudoxos, Euclid's book has no place for uranography. Rather, a short (and possibly spurious) preface introduces the north celestial pole and the principal circles on the celestial sphere (including the parallel circles, the ecliptic, the horizon, and the Milky Way). The author also introduces the arctic and antarctic circles relative to a given locality and the consequent division of stars into those that never rise, those that rise and set, and those that never set. Thus Eudoxos's descriptions of the constellations have been eliminated in favor of a geometrical exploration of the sphere.

After this beginning, Euclid's treatise proceeds by a series of propositions with proofs and accompanying diagrams, in the style of his more famous Elements. These begin with proposition 1 on the central position of the Earth in the cosmos, and then progress through three propositions on the risings and settings of stars. Propositions 8-13 deal with the risings and settings of arcs of the ecliptic, particularly the zodiacal signs, and the work concludes with five propositions on how long it takes equal arcs of the ecliptic to cross the visible and invisible hemispheres. The very format of the work illustrates what had become a commonplace among Greek thinkers, namely that celestial phenomena can be explained rationally.

Other extant early Greek texts for which the celestial phenomena form the subject matter include two works of Euclid's contemporary, Autolykos of Pitane, both of them written in the theorem-proof style one finds in Euclid's book. In On the Moving Sphere, Autolykos treats some of the phenomena arising from the uniform rotation of a sphere around its axis relative to a horizon that separates the visible from the invisible portions of the sphere. It is striking that in On the Moving Sphere, the descriptions of all circles other than the horizon are as abstract and geometrical as possible, and there is no explicit mention of the astronomical applications of the theorems. As an example we quote proposition 8: Great circles tangent to the same [parallel circles] to which the horizon is tangent will, as the sphere rotates, fit exactly onto the horizon. The abstract character of many of these propositions illustrates how far the Greek geometrization of astronomy had been carried by the time of Euclid and Autolykos. Many of the propositions are hard to prove, but are easy to illustrate on a celestial globe.

Autolykos's other book, On Risings and Settings, is devoted to heliacal risings and settings-the annual cycle of appearances and disappearances of the fixed stars. This had been a part of Greek popular astronomy from the earliest days, as illustrated by Hesiod's use of the heliacal risings and settings of the Pleiades, Arcturus, and Sirius to tell the time of year in his poem, Works and Days (c. 650 b.c.). Clearly, the sidereal events in the annual cycle were a part of what the Greeks considered "phenomena." Autolykos's goal in On Risings and Settings is to provide a mathematical foundation, in the form of theorems, for a field that had previously been in the domain of popular lore. Geminos devotes chapter xiii of his Introduction to the Phenomena to the same subject. Indeed, Geminos's heading for chapter xviii is the same as the title of Autolykos's book. As we point out in our commentary on that chapter, Geminos follows Autolykos in all significant details, but eliminates the proofs.

(Continues...)

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Excerpted from Geminos's Introduction to the Phenomena by James Evans J. Lennart Berggren Copyright © 2006 by Princeton University Press. Excerpted by permission.
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