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History's Hinge - 'Ain Jalut

[Bart]

The watchmaking aspect of this would appear to be fairly simple for an experienced watchmaker. The mathematical/ theoretical aspect seems to be likewise fairly simple for an experienced/ trained mathemetician. It would be extraordinary for one person to posess both skills, as I see it. While the math capabilities of that era are well known, the mechanical creation of the device in that era is the surprising factor. It appears to me that the idea of the device could have come from recording astronomical observations, specifically orbits.

- Bart

[Diving Doc]

Jose,
It's all about mathematics, but foretelling the movement of the planets is a bit more difficult than a watch, wouldn't you say? Accuracy to the fourth decimal place?
Doc

[Tayopa]

Gentlemen:  Apparantly I am being taken slightly out of context.  I am simply referring to the ability to re-construct this fantastic Device with "hand tools only".  This includes the spacing of the teeth and size of the wheels to achive whatever ratio one would wish.

As to the knowlege behind it, one only has to turn to some of our latest scientific devices,  Nuclear fision bombs or generators for example.    The mechanical part of it is easily handled by technicians but the knowledge behind it is restricted to only  few.

Tropical Tramp

[Diving Doc]

Jose,
Then you understand that the study of astronomy and geometry was very far advanced in Ancient times. This is now only becoming knowledge. That is what makes this device so extraordinary.
Cheers,
Doc

[Solomon]

In search of lost time
Jo Marchant- News Editor, Nature
Abstract

The ancient Antikythera Mechanism doesn't just challenge our assumptions about technology transfer over the ages ? it gives us fresh insights into history itself.

It looks like something from another world ? nothing like the classical statues and vases that fill the rest of the echoing hall. Three flat pieces of what looks like green, flaky pastry are supported in perspex cradles. Within each fragment, layers of something that was once metal have been squashed together, and are now covered in calcareous accretions and various corrosions, from the whitish tin oxide to the dark bluish green of copper chloride. This thing spent 2,000 years at the bottom of the sea before making it to the National Archaeological Museum in Athens, and it shows.


There are 82 remaining fragments of the mechanism that contain a total of 30 gears. The largest piece contains 27 of the gears. (Image copyright of the Antikythera Mechanism Research Project)

But it is the details that take my breath away. Beneath the powdery deposits, tiny cramped writing is visible along with a spiral scale; there are traces of gear-wheels edged with jagged teeth. Next to the fragments an X-ray shows some of the object's internal workings. It looks just like the inside of a wristwatch.

This is the Antikythera Mechanism. These fragments contain at least 30 interlocking gear-wheels, along with copious astronomical inscriptions. Before its sojourn on the sea bed, it computed and displayed the movement of the Sun, the Moon and possibly the planets around Earth, and predicted the dates of future eclipses. It's one of the most stunning artefacts we have from classical antiquity.

No earlier geared mechanism of any sort has ever been found. Nothing close to its technological sophistication appears again for well over a millennium, when astronomical clocks appear in medieval Europe. It stands as a strange exception, stripped of context, of ancestry, of descendants.

Considering how remarkable it is, the Antikythera Mechanism has received comparatively scant attention from archaeologists or historians of science and technology, and is largely unappreciated in the wider world. A virtual reconstruction of the device, published by Mike Edmunds and his colleagues in this week's Nature (page 587), may help to change that. With the help of pioneering three-dimensional images of the fragments' innards, the authors present something close to a complete picture of how the device worked, which in turn hints at who might have been responsible for building it.

But I'm also interested in finding the answer to a more perplexing question ? once the technology arose, where did it go to? The fact that such a sophisticated technology appears seemingly out of the blue is perhaps not that surprising ? records and artefacts from 2,000 years ago are, after all, scarce. More surprising, to an observer from the progress-obsessed twenty-first century, is the apparent lack of a subsequent tradition based on the same technology ? of ever better clockworks spreading out round the world. How can the capacity to build a machine so magnificent have passed through history with no obvious effects?

Astronomic leaps
In search of lost time

A. WRIGHT

Model success: Michael Wright devoted his life to decoding and replicating the Antikythera Mechanism.

To get an idea of what the mechanism looked like before it had the misfortune to find itself on a sinking ship, I went to see Michael Wright, a curator at the Science Museum in London for more than 20 years and now retired. Stepping into Wright's workshop in Hammersmith is a little like stepping into the workshop where H. G. Wells' time machine was made. Every inch of floor, wall, shelf and bench space is covered with models of old metal gadgets and devices, from ancient Arabic astrolabes to twentieth-century trombones. Over a cup of tea he shows me his model of the Antikythera Mechanism as it might have been in his pomp. The model and the scholarship it embodies have consumed much of his life (see 'Raised from the depths').

The mechanism is contained in a squarish wooden case a little smaller than a shoebox. On the front are two metal dials (brass, although the original was bronze), one inside the other, showing the zodiac and the days of the year. Metal pointers show the positions of the Sun, the Moon and five planets visible to the naked eye. I turn the wooden knob on the side of the box and time passes before my eyes: the Moon makes a full revolution as the Sun inches just a twelfth of the way around the dial. Through a window near the centre of the dial peeks a ball painted half black and half white, spinning to show the Moon's changing phase.

On the back of the box are two spiral dials, one above the other. A pointer at the centre of each traces its way slowly around the spiral groove like a record stylus. The top dial, Wright explains, shows the Metonic cycle ? 235 months fitting quite precisely into 19 years. The lower spiral, according to the research by Edmunds and his colleagues, was divided into 223, reflecting the 223-month period of the Saros cycle, which is used to predict eclipses.

To show me what happens inside, Wright opens the case and starts pulling out the wheels. There are 30 known gear-wheels in the Antikythera Mechanism, the biggest taking up nearly the entire width of the box, the smallest less than a centimetre across. They all have triangular teeth, anything from 15 to 223 of them, and each would have been hand cut from a single sheet of bronze. Turning the side knob engages the big gear-wheel, which goes around once for every year, carrying the date hand. The other gears drive the Moon, Sun and planets and the pointers on the Metonic and Saros spirals.

To see the model in action is to want to find out who had the ingenuity to design the original. Unfortunately, none of the copious inscriptions is a signature. But there are other clues. Coins found at the site by Jacques Cousteau in the 1970s have allowed the shipwreck to be dated sometime shortly after 85 BC. The inscriptions on the device itself suggest it might have been in use for at least 15 or 20 years before that, according to the Edmunds paper.

The ship was carrying a rich cargo of luxury goods, including statues and silver coins from Pergamon on the coast of Asia Minor and vases in the style of Rhodes, a rich trading port at the time. It went down in the middle of a busy shipping route from the eastern to western Aegean, and it seems a fair bet that it was heading west for Rome, which had by that time become the dominant power in the Mediterranean and had a ruling class that loved Greek art, philosophy and technology.

The Rhodian vases are telling clues, because Rhodes was the place to be for astronomy in the first and second centuries BC. Hipparchus, arguably the greatest Greek astronomer, is thought to have worked on the island from around 140 BC until his death in around 120 BC. Later the philosopher Posidonius set up an astronomy school there that continued Hipparchus' tradition; it is within this tradition that Edmunds and his colleagues think the mechanism originated. Circumstantial evidence is provided by Cicero, the first-century BC Roman lawyer and consul. Cicero studied on Rhodes and wrote later that Posidonius had made an instrument "which at each revolution reproduces the same motions of the Sun, the Moon and the five planets that take place in the heavens every day and night". The discovery of the Antikythera Mechanism makes it tempting to believe the story is true.

And Edmunds now has another reason to think the device was made by Hipparchus or his followers on Rhodes. His team's three-dimensional reconstructions of the fragments have turned up a new aspect of the mechanism that is both stunningly clever and directly linked to work by Hipparchus.

One of the wheels connected to the main drive wheel moves around once every nine years. Fixed on to it is a pair of small wheels, one of which sits almost ? but not exactly ? on top of the other. The bottom wheel has a pin sticking up from it, which engages with a slot in the wheel above. As the bottom wheel turns, this pin pushes the top wheel round. But because the two wheels aren't centred in the same place, the pin moves back and forth within the upper slot. As a result, the movement of the upper wheel speeds up and slows down, depending on whether the pin is a little farther in towards the centre or a little farther out towards the tips of the teeth (see illustration on page 551).

The researchers realized that the ratios of the gear-wheels involved produce a motion that closely mimics the varying motion of the Moon around Earth, as described by Hipparchus. When the Moon is close to us it seems to move faster. And the closest part of the Moon's orbit itself makes a full rotation around the Earth about every nine years. Hipparchus was the first to describe this motion mathematically, working on the idea that the Moon's orbit, although circular, was centred on a point offset from the centre of Earth that described a nine-year circle. In the Antikythera Mechanism, this theory is beautifully translated into mechanical form. "It's an unbelievably sophisticated idea," says Tony Freeth, a mathematician who worked out most of the mechanics for Edmunds' team. "I don't know how they thought of it."

"I'm very surprised to find a mechanical representation of this," adds Alexander Jones, a historian of astronomy at the University of Toronto, Canada. He says the Antikythera Mechanism has had little impact on the history of science so far. "But I think that's about to change. This was absolutely state of the art in astronomy at the time."

Wright believes that similar mechanisms modelled the motions of the five known planets, as well as of the Sun, although this part of the device has been lost. As he cranks the gears of his model to demonstrate, and the days, months and years pass, each pointer alternately lags behind and picks up speed to mimic the astronomical wanderings of the appropriate sphere.
Greek tragedy

Almost everyone who has studied the mechanism agrees it couldn't have been a one-off ? it would have taken practice, perhaps over several generations, to achieve such expertise. Indeed, Cicero wrote of a similar mechanism that was said to have been built by Archimedes. That one was purportedly stolen in 212 BC by the Roman general Marcellus when Archimedes was killed in the sacking of the Sicilian city of Syracuse. The device was kept as an heirloom in Marcellus' family: as a friend of the family, Cicero may indeed have seen it.

So where are the other examples? A model of the workings of the heavens might have had value to a cultivated mind. Bronze had value for everyone. Most bronze artefacts were eventually melted down: the Athens museum has just ten major bronze statues from ancient Greece, of which nine are from shipwrecks. So in terms of the mechanism, "we're lucky we have one", points out Wright. "We only have this because it was out of reach of the scrap-metal man."

But ideas cannot be melted down, and although there are few examples, there is some evidence that techniques for modelling the cycles in the sky with geared mechanisms persisted in the eastern Mediterranean. A sixth-century AD Byzantine sundial brought to Wright at the Science Museum has four surviving gears and would probably have used at least eight to model the positions of the Sun and Moon in the sky. The rise of Islam saw much Greek work being translated into Arabic in the eighth and ninth centuries AD, and it seems quite possible that a tradition of geared mechanisms continued in the caliphate. Around AD 1000, the Persian scholar al-Biruni described a "box of the Moon" very similar to the sixth-century device. There's an Arabic-inscribed astrolabe dating from 1221?22 currently in the Museum of the History of Science in Oxford, UK, which used seven gears to model the motion of the Sun and Moon.

But to get anything close to the Antikythera Mechanism's sophistication you have to wait until the fourteenth century, when mechanical clockwork appeared all over western Europe. "You start to get a rash of clocks," says Wright. "And as soon as you get clocks, they are being used to drive astronomical displays." Early examples included the St Albans clock made by Richard Wallingford in around 1330 and a clock built by Giovanni de'Dondi a little later in Padua, Italy, both of which were huge astronomical display pieces with elaborate gearing behind the main dial to show the position of the Sun, Moon, planets and (in the case of the Padua clock) the timing of eclipses. The time-telling function seems almost incidental.

It could be argued that the similarities between the medieval technology and that of classical Greece represent separate discoveries of the same thing ? a sort of convergent clockwork evolution. Wright, though, favours the idea that they are linked by an unbroken tradition: "I find it as easy to believe that this technology survived unrecorded, as to believe that it was reinvented in so similar a form." The timing of the shift to the West might well have been driven by the fall of Baghdad to the Mongols in the thirteenth century, after which much of the caliphate's knowledge spread to Europe. Shortly after that, mechanical clocks appeared in the West, although nobody knows exactly where or how. It's tempting to think that some mechanisms, or at least the ability to build them, came west at the same time. As Fran?ois Charette, a historian of science at Ludwig Maximilians University in Munich, Germany, points out, "for the translation of technology, you can't rely solely on texts". Most texts leave out vital technical details, so you need skills to be transmitted directly.

But if the tradition of geared mechanisms to show astronomical phenomena really survived for well over a millennium, the level of achievement within that tradition was at best static. The clockwork of medieval Europe became more sophisticated and more widely applied fairly quickly; in the classical Mediterranean, with the same technology available, nothing remotely similar happened. Why didn't anyone do anything more useful with it in all that time? More specifically, why didn't anyone work out earlier what the gift of hindsight seems to make obvious ? that clockwork would be a good thing to make clocks with?

Serafina Cuomo, a historian of science at Imperial College, London, thinks that it all depends on what you see as 'useful'. The Greeks weren't that interested in accurate timekeeping, she says. It was enough to tell the hour of the day, which the water-driven clocks of the time could already do fairly well. But they did value knowledge, power and prestige. She points out that there are various descriptions of mechanisms driven by hot air or water ? and gears. But instead of developing a steam engine, say, the devices were used to demonstrate philosophical principles. The machines offered a deeper understanding of cosmic order, says David Sedley, a classicist at the University of Cambridge, UK. "There's nothing surprising about the fact that their best technology was used for demonstrating the laws of astronomy. It was deep-rooted in their culture."

Another, not mutually exclusive, theory is that devices such as the Antikythera Mechanism were signifiers of social status. Cuomo points out that demonstrating wondrous devices brought social advancement. "They were trying to impress their peers," she says. "For them, that was worth doing." And the Greek ?lite was not the only potential market. Rich Romans were eager for all sorts of Greek sophistication ? they imported philosophers for centuries.

Seen in this light, the idea that the Antikythera Mechanism might be expected to lead to other sorts of mechanism seems less obvious. If it already embodied the best astronomy of the time, what more was there to do with it? And status symbols do not follow any clearly defined arc of progress. What's more, the idea that machines might do work may have been quite alien to slave-owning societies such as those of Ancient Greece and Rome. "Perhaps the realization that you could use technology for labour-saving devices took a while to dawn," says Sedley.

There is also the problem of power. Water clocks are thought to have been used on occasion to drive geared mechanisms that displayed astronomical phenomena. But dripping water only provides enough pressure to drive a small number of gears, limiting any such display to a much narrower scope than that of the Antikythera Mechanism, which is assumed to have been handcranked. To make the leap to mechanical clocks, a geared mechanism needs to be powered by something other than a person; it was not until medieval Europe that clockwork driven by falling weights makes an appearance.
Invention's evolution

Bert Hall, a science historian at the University of Toronto in Canada, believes a final breakthrough towards a mechanical weight drive might have come about almost by accident, by adapting a bell-ringing device. A water clock could have driven a hammer or weight mechanism swinging between two bells as an alarm system, until someone realized that the weight mechanism would be a more regular way of driving the clock in the first place. When the new way to drive clocks was discovered, says Hall, "the [clockwork] technology came rushing out of the wings into the new tradition".

Researchers would now love further mechanisms to be unearthed in the historical record. "We hope that if we can bring this to people's attention, maybe someone poking around in their museum might find something, or at least a reference to something," says Edmunds. Early Arabic manuscripts, only a fraction of which have so far been studied, are promising to be fertile ground for such discoveries.

Charette also hopes the new Antikythera reconstruction will encourage scholars to take the device more seriously, and serve as a reminder of the messy nature of history. "It's still a popular notion among the public, and among scientists thinking about the history of their disciplines, that technological development is a simple progression," he says. "But history is full of surprises."

In the meantime, Edmunds' Antikythera team plans to keep working on the mechanism ? there are further inscriptions to be deciphered and the possibility that more fragments could be found. This week the researchers are hosting a conference in Athens that they hope will yield fresh leads. A few minutes' walk from the National Archaeological Museum, Edmunds' colleagues from the University of Athens, Yanis Bitsakis and Xenophon Moussas, treat me to a dinner of aubergine and fried octopus, and explain why they would one day like to devote an entire museum to the story of the fragments.

"It's the same way that we would do things today, it's like modern technology," says Bitsakis. "That's why it fascinates people." What fascinates me is that where we see the potential of that technology to measure time accurately and make machines do work, the Greeks saw a way to demonstrate the beauty of the heavens and get closer to the gods.

The Antikythera Mechanism will be explored in an episode of Unearthing Mysteries on BBC Radio 4 on 12 December.

Interactive Relighting of the Antikythera Mechanism

[Bart]

                        Mystery of ancient astronomical calculator unveiled

Public release date: 29-Nov-2006

Contact: Stephen Rouse


Cardiff University

     An international team has unravelled the secrets of a 2,000-year-old computer which could transform the way we think about the ancient world.

     Professor Mike Edmunds and Dr Tony Freeth, of Cardiff University led the team who believe they have finally cracked the workings of the Antikythera Mechanism, a clock-like astronomical calculator dating from the second century BC.

     Remnants of a broken wooden and bronze case containing more than 30 gears was found by divers exploring a shipwreck off the island of Antikythera at the turn of the 20th century. Scientists have been trying to reconstruct it ever since. The new research suggests it is more sophisticated than anyone previously thought.

     Detailed work on the gears in the mechanism show that it was able to track astronomical movements with remarkable precision. The calculator was able to follow the movements of the moon and the sun through the Zodiac, predict eclipses and even recreate the irregular orbit of the moon. The team believe it may also have predicted the positions of some or all of the planets.

     The findings suggest that Greek technology was far more advanced than previously thought. No other civilisation is known to have created anything as complicated for another thousand years.

     Professor Edmunds said: "This device is just extraordinary, the only thing of its kind. The design is beautiful, the astronomy is exactly right. The way the mechanics are designed just makes your jaw drop. Whoever has done this has done it extremely well."

     The team was made up of researchers from Cardiff, the National Archaeological Museum of Athens and the Universities of Athens and Thessaloniki, supported by a substantial grant from the Leverhulme Trust. They were greatly aided by Hertfordshire X-Tek, who developed powerful X-Ray computer technology to help them study the corroded fragments of the machine. Computer giant Hewlett-Packard provided imaging technology to enhance the surface details of the machine.

     The mechanism is in over 80 pieces and stored in precisely controlled conditions in Athens where it cannot be touched. Recreating its workings was a difficult, painstaking process, involving astronomers, mathematicians, computer experts, script analysts and conservation experts.

     The team is unveiling its full findings at a two-day international conference in Athens from November 30 to December 1 and publishing the research in the journal Nature . The researchers are now hoping to create a computer model of how the machine worked, and, in time, a full working replica. It is still uncertain what the ancient Greeks used the mechanism for, or how widespread this technology was.

     Professor Edmunds said: "It does raise the question what else were they making at the time. In terms of historic and scarcity value, I have to regard this mechanism as being more valuable than the Mona Lisa."

http://www.eurekalert.org/pub_releases/2006-11/cu-moa112806.php

[Solomon]

Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism
Letter

Nature 444, 587-591 (30 November 2006) | doi:10.1038/nature05357; Received 10 August 2006; Accepted 17 October 2006
Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism

T. Freeth1,2, Y. Bitsakis3,5, X. Moussas3, J. H. Seiradakis4, A. Tselikas5, H. Mangou6, M. Zafeiropoulou6, R. Hadland7, D. Bate7, A. Ramsey7, M. Allen7, A. Crawley7, P. Hockley7, T. Malzbender8, D. Gelb8, W. Ambrisco9 and M. G. Edmunds1

   1. Cardiff University, School of Physics and Astronomy, Queens Buildings, The Parade, Cardiff CF24 3AA, UK
   2. Images First Ltd, 10 Hereford Road, South Ealing, London W5 4SE, UK
   3. National and Kapodistrian University of Athens, Department of Astrophysics, Astronomy and Mechanics, Panepistimiopolis, GR-15783, Zographos, Greece
   4. Aristotle University of Thessaloniki, Department of Physics, Section of Astrophysics, Astronomy and Mechanics, GR-54124 Thessaloniki, Greece
   5. Centre for History and Palaeography, National Bank of Greece Cultural Foundation, P. Skouze 3, GR-10560 Athens, Greece
   6. National Archaeological Museum of Athens, 1 Tositsa Str., GR-10682 Athens, Greece
   7. X-Tek Systems Ltd, Tring Business Centre, Icknield Way, Tring, Hertfordshire HP23 4JX, UK
   8. Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, California 94304, USA
   9. Foxhollow Technologies Inc., 740 Bay Road, Redwood City, California 94063, USA

Correspondence to: M. G. Edmunds1 Correspondence and requests for materials should be addressed to M.G.E. (Email: ).
Top of page

The Antikythera Mechanism is a unique Greek geared device, constructed around the end of the second century bc. It is known1, 2, 3, 4, 5, 6, 7, 8, 9 that it calculated and displayed celestial information, particularly cycles such as the phases of the moon and a luni-solar calendar. Calendars were important to ancient societies10 for timing agricultural activity and fixing religious festivals. Eclipses and planetary motions were often interpreted as omens, while the calm regularity of the astronomical cycles must have been philosophically attractive in an uncertain and violent world. Named after its place of discovery in 1901 in a Roman shipwreck, the Antikythera Mechanism is technically more complex than any known device for at least a millennium afterwards. Its specific functions have remained controversial11, 12, 13, 14 because its gears and the inscriptions upon its faces are only fragmentary. Here we report surface imaging and high-resolution X-ray tomography of the surviving fragments, enabling us to reconstruct the gear function and double the number of deciphered inscriptions. The mechanism predicted lunar and solar eclipses on the basis of Babylonian arithmetic-progression cycles. The inscriptions support suggestions of mechanical display of planetary positions9, 14, 15, now lost. In the second century bc, Hipparchos developed a theory to explain the irregularities of the Moon's motion across the sky caused by its elliptic orbit. We find a mechanical realization of this theory in the gearing of the mechanism, revealing an unexpected degree of technical sophistication for the period.

In search of lost time
Nature 444, 534-538 (30 November 2006)

Hear the sound of the Antikythera Mechanism recreated on the 30 November
Nature Podcast.

[Bart]

Googling the phrase " Babylonian arithmetic-progression cycles " found within your article, resulted in the following treatise. - Bart

               Geminos's Introduction to the Phenomena:
     A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren

Part 1 of 6

Introduction

     Geminos, a Greek scientific writer of wide-ranging interests, has been assigned dates ranging from the first century b.c. to the first century a.d., with, we believe, the first century b.c. the more likely. We know nothing of the circumstances of his life. Of three works he is believed to have written, only one, the Introduction to the Phenomena, has come down to us. (This work is also frequently referred to as the Isagoge, from the first word of its Greek title, Eisagoge eis ta phainomena.) The translation of his Introduction to the Phenomena here presented is the first complete English version ever published.

     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, his text 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, helical 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 Hipparchus (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 helical 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.1 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.

http://press.princeton.edu/chapters/i8330.html

[Bart]

Geminos's Introduction to the Phenomena:
A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 2 of 6

                                                       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 Proklos2 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.?3 (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., sphairopoi?a, 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.4 A fragment of some length is preserved by Simplikios5 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.6 In the course of his citation, Simplikios says that Alexander drew these remarks from Geminos?s ?Concise Exposition of the Meteorology of Poseidonios.?7 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.

http://press.princeton.edu/chapters/i8330.html

[Bart]

                               Geminos's Introduction to the Phenomena:
            A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 3 of 6

       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.8

     Between the Bears is the tail of the Dragon, the end-star of which is above the head of the Great Bear.9

     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.?10

     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.11

     The oldest extant work named The Phenomena is that of Euclid (c. 300 b.c.).12 Unlike the work of Eudoxos, Euclid?s book has no place for uranography. Rather, a short (and possibly spurious) preface introduces the north celestial pole13 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.

     The other major writer on the phenomena was Theodosios of Bithynia (c. 100 b.c.), whose On Habitations and On Days and Nights are the earliest extant works devoted to a discussion of how the phenomena change from one locality to another: as an observer moves north or south, the stars that are visible will become different and the lengths of the day and night may change. An example of a proposition from the first of these is:

     For those living under the north pole14 the same hemisphere of the cosmos is always visible and the same hemisphere of the cosmos is always invisible, and none of the stars either sets or rises for them, but those in the visible hemisphere are always visible and those in the invisible [hemisphere] are always invisible.15
Geminos?s use of Theodosios is quite clear, for the Greek heading of Geminos?s chapter xvi is the same as that of Theodosios?s On Habitations,16 and the heading of chapter vi is only trivially different (singular nouns instead of plurals) from that of Theodosios?s On Days and Nights.

      Many of the founding works on the phenomena, such as those by Euclid, Autolykos, and Theodosios, survived because they were short enough and elementary enough for use in teaching. They became staples of the curriculum for mathematics and astronomy, and so survived through late Antiquity and into the Middle Ages, in both the Arabic and Latin worlds.

     The motions of the Sun, Moon, and planets around the zodiac are also part of what the Greeks considered ?phenomena.? Several features of planetary motion posed challenges for explanation: the Sun appears to move more slowly at some times of year, and more rapidly at others. The planets are even more puzzling, since they occasionally stop and reverse direction in what is known as retrograde motion. Most scholars believe that the earliest Greek effort to explain the complex motions of the planets was the book On Speeds by Eudoxos. It is lost, but we have two rather lengthy discussions of it, one by Aristotle, who was a contemporary of Eudoxos, and one by Simplikios, who lived 900 years later, and whose account must therefore be used with caution. Probably by the time of Apollonios of Perge (late third century b.c.) and certainly by the time of Hipparchos, Eudoxos?s approach of modeling the planetary phenomena by the gyrations of nested, homocentric spheres had given way to eccentric circles and epicycles lying in a plane. But this was daunting material to address in an elementary work.17

http://press.princeton.edu/chapters/i8330.html

[Bart]

                                 Geminos's Introduction to the Phenomena:
            A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 4 of 6

4. THE GREEK GENRE OF ASTRONOMICAL SURVEYS

     In the Hellenistic period, there emerged a demand for popular surveys? works that would take students through the celestial phenomena without forcing them through theorems and proofs. The poetic Phenomena of Aratos can be considered one of the first such popularizations. The new popular surveys eschewed the austere geometrical demonstrations of Euclid, Autolykos, and Theodosios tended simply to summarize mathematical results in plain language. They also tended to include a greater variety of subjects of interest to the broad public?phases of the Moon, eclipses, and elements of astronomical geography, such as the theory of terrestrial zones. Of course, all of these topics had deep roots in the history of Greek science. What was new was the attempt to produce comprehensive astronomy textbooks written at an elementary level.

     The popular surveys of astronomy could be read for their own sake, but some were clearly intended to form part of the curriculum of studies expected of a well-born student. The geographical writer Strabo (c. 64 b.c. to c. a.d. 25) mentions that students can learn in the elementary mathematics courses all the astronomy they will need for the study of geography. He mentions as an example of the standard astronomical curriculum the theory of the celestial sphere?tropics, equator, zodiac, arctic circle, and horizon.18 The sort of elementary astronomy course that Strabo had in mind is well represented by Geminos?s Introduction to the Phenomena. Diogenes Laertios tells us that instruction in basic astronomy was part of the curriculum of Stoic teachers.19 And, of course, astronomy had long been part of the quadrivium of mathematical studies in the Platonist school.20 Whether for the sake of popular reading, or for liberal education, or as part of the preparation for more advanced studies, introductions to the astronomical phenomena permeated Greek culture from about 200 b.c. to the end of Antiquity.

     It is quite appropriate, then, that Geminos?s work is named Introduction to the Phenomena, for eisagoge (?introduction?) carries two meanings. On one hand, this is a regular word for an elementary treatise on a subject; on the other, it can denote a conduit, or channel, into a harbor. Thus an eisagoge could serve either as a liberal arts survey of astronomy, complete in itself, or as the preparatory course for higher studies in the subject.

     Geminos occasionally employs demonstrative mathematical arguments (e.g., in his treatment of lunisolar cycles in chapter viii), and he did not write his book for those who were afraid of numbers or geometry. However, his motto seems to have been ?mathematics if necessary, but not necessarily mathematics??and in any case he makes no use of formal mathematical proofs. Nor does Geminos?s work smell of the mathematics classroom. There is none of the graded progression from the easy to the complicated that one finds in, for example, Euclid?s Phenomena. Had Geminos intended to write a textbook of mathematics he would surely have put chapters iv (the axis and the poles) and v (circles on the sphere) at the beginning, and in any case before chapter i (on the zodiac). A third feature of his work is its blending of the topics of the two earlier genres of phenomena literature (the descriptive uranography of Eudoxos and the mathematical topics of Euclid and his successors) with topics outside of these traditions, namely those he treats in chapters viii?xii, xvii, and xviii. Geminos even stretches the definition of the phenomena to include the astrological aspects of the zodiac signs, in chapter i. In summary, Geminos, in his account of the celestial phenomena, extended the tradition of topics treated to include virtually anything having to do with the fixed stars, the Sun, and the Moon. And he did so in a way that was not simply systematic or mathematical, but discursive and, in a broad sense of the word, scientific.

     Geminos?s Introduction to the Phenomena is but one of several Greek elementary textbooks of astronomy that survive from Antiquity. The two most nearly comparable examples are Theon of Smyrna?s Mathematical Knowledge Useful for Reading Plato21 (second century a.d.) and Kleomedes? Meteora22 (probably early third to mid-fourth century a.d.). These three surveys have a fair amount of overlap?for example, they all discuss the eccentric-circle theory of the motion of the Sun. But each of the three also treats subjects not covered by the other two. For example, Theon of Smyrna gives an introduction to the deferent-and-epicycle theory of planetary motion, a subject avoided by Kleomedes and Geminos. Kleomedes, for his part, is our most detailed source for the famous measurement of the Earth by Eratosthenes. And Geminos gives a detailed discussion of lunisolar cycles, a subject avoided by Theon and Kleomedes.

     These three textbooks of astronomy also differ markedly in tone. While Theon?s book is pervaded by Platonism, Kleomedes? book is steeped in Stoic physics and concludes with a savage attack on the Epicureans. Theon and Kleomedes, then, give us nice examples of how an introduction to astronomy could be incorporated into a general course in philosophy?and we have examples in two flavors, Platonist and Stoic. By contrast, Geminos?s Introduction to the Phenomena is remarkable for its comparative freedom from philosophy, for he is very much a straightforward astronomer. Geminos does, however, display a certain literary bent, and is fond of quoting poets, such as Aratos or Homer, in illustration of astronomical points. His Introduction to the Phenomena is also considerably earlier than the textbooks of Theon and Kleomedes, and sheds light on the Greeks? reactions to Babylonian astronomy and astrology, which, in Geminos?s day, were in the process of being absorbed and adapted.

     An earlier, though shorter and much less polished, survey of astronomy is the Celestial Teaching (Ouranios Didascalea) of Leptines.23 See fig. I.1. This famous papyrus, conserved in the Louvre, is the oldest existing Greek astronomical document with illustrations. It was composed in the decades before 165 b.c. by a certain Leptines as an introduction to astronomy for members of the Ptolemaic court. (So it seems that, despite what Euclid is supposed to have said about geometry, there was a royal road to astronomy.) Modern writers sometimes refer to this tract as the ?Art of Eudoxos,? a name that comes from an acrostic poem on the verso of the papyrus, in which the initial letters of the twelve lines of verse spell out Eudoxou Techne. But the colophon on the recto clearly gives the title as the Ouranios Didascalea of Leptines. In any case, the contents of the treatise are certainly not by Eudoxos. Rather, the tract is a brief and rather choppy account of standard astronomical matters. The text includes a short parapegma, an account of the progress of the Sun and Moon around the zodiac, descriptions of the circles on the celestial sphere, a discussion of eclipses, and values for the lengths of the four seasons according to various authorities. This fare overlaps considerably with the material treated more gracefully by Geminos in the next century.

     Finally, numerous commentaries on Aratos?s poem Phenomena often served as introductions to astronomy. One of the most complete is that of Achilleus (often called Achilles Tatius, probably third century a.d.), whose Introduction to the ?Phenomena? of Aratos formed a part of his On the All (Peri tou Pantos).24 In our commentary on Geminos, we shall occasionally make comparisons to these other works, which can be thought of as constituting a genre of elementary astronomy textbooks.

http://press.princeton.edu/chapters/i8330.html

[Bart]

                          Geminos's Introduction to the Phenomena:
        A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 5 of 6

     5. GEMINOS?S SOURCES FOR HIS INTRODUCTION

     Appendix 4 lists the writers that Geminos cites in his Introduction to the Phenomena.    He enjoys quoting the poets Homer, Hesiod, and Aratos in illustration of scientific points. This reflects not only his own tastes but also his concession to the literary training of his students and readers. He is not, however, one to ascribe too much scientific knowledge to Homer, and feels that critics such as Krates have sometimes gone overboard in this regard. (The occasional use of poetry occurs in other elementary surveys as well, e.g., those of Kleomedes, Theon of Smyrna, and Leptines.)

    Of the astronomical writers, Geminos names Euktemon, Kallippos, Philippos, Eratosthenes, and Hipparchos, though he may not have known the works of all these people firsthand. Geminos was quite well-informed about lunisolar cycles, but we cannot tell from his remarks on those matters whose works he really had access to. He seems to have used some work of Hipparchos on the constellations that was different from Hipparchos?s Commentary on The Phenomena of Eudoxos and Aratos. For, in chapter iii, he mentions three decisions of Hipparchos regarding the constellations that have no counterpart in the Commentary. The clearest and most significant of these is the attribution of the constellation Equuleus (Protome hippou) to Hipparchos. Geminos?s is the first mention of this constellation in the Greek tradition. Perhaps it comes from Hipparchos?s star catalogue. In any case, Ptolemy adopted this constellation name in the Almagest. Among writers on such geographical questions as mountain heights, the extent of Ocean, and the arrangement and habitability of the zones, Geminos cites Dikaiarchos, Pytheas, Kleanthes, and Polybios.

     Geminos was clearly influenced by the Stoic Poseidonios in his philosophical musings and in his work on meteorology. (See fragment 2.) In sec. 7 we address the controversial question of whether Geminos, in writing the Introduction to the Phenomena, might have used a lost textbook of Stoic astronomy and physics written by Poseidonios. Here, it suffices to point out that he does not mention Poseidonios a single time in the Introduction to the Phenomena. The material of Geminos?s Introduction consists largely of notions that were the common property of all astronomers. His contribution was in the selection and shaping of material, in his graceful prose, and in the tasteful incorporation of literary examples.25 He would have needed no help from Poseidonios for this.

     But Geminos does leave some of his most important sources unnamed. For as we have seen, and though he does not cite them by name, Geminos clearly knows the material in Euclid?s Phenomena, Autolykos?s On the Moving Sphere and On Risings and Settings, and Theodosios?s On Habitations and On Days and Nights. We shall see below that he probably knew also Hypsikles of Alexandria?s Anaphorikos. Geminos?s merit as a teacher is to absorb all this rather dry mathematical material and transform it into graceful prose?though often at the expense of the original mathematical rigor.

     Highly significant are Geminos?s citations of the ?Chaldeans,? by which he means Babylonian astronomers. We should say a few words about this term. The Chaldeans were a group of tribes who moved into southern Mesopotamia by about 1000 b.c. They assumed a growing importance, and in the eighth century succeeded in putting a king on the throne of Babylonia. Within a few decades, the Chaldean kings lost control to the Assyrian kings, who intervened repeatedly in Babylonian affairs. But under Nabopolassar a new Chaldean dynasty was established, which ruled Babylonia from 625 b.c. until the Persian conquest in 539.26 Ancient Greek writers often used the term ?Chaldeans? (Chaldaioi) simply to mean Babylonians. But because Babylon had a reputation for arcane knowledge, ?Chaldean? also came to mean an astronomer or astrologer of Babylon. Here are a few examples that span the range of meanings from ?Babylonian? to ?astronomer of Babylon? to ?astrologer or magus?: In the Almagest, Ptolemy refers to the ?Chaldean? (i.e., Babylonian) calendar. Vitruvius says that Berossus came from the ?Chaldean city or nation? to spread the learning of this people. Theon of Smyrna says that the Chaldeans save the phenomena by using arithmetic procedures. For Herodotos, the Chaldeans are priests of Bel (i.e., Marduk). This is quite reasonable, since astronomy and astrology were concentrated in the temples, and many of the practitioners were priestly scribes. In Daniel 2.2?4, the Chaldeans are interpreters of dreams and are associated with magicians and sorcerers. For Sextus Empiricus, Chaldeans are astrologers.27

     By about 300 b.c. the Babylonians had developed very successful theories for the motions of the planets, Sun, and Moon. These theories were based upon arithmetic rules, rather than on the geometrical models that characterized the Greek approach. When the Greeks began to deal quantitatively with planetary theory, they were able to base their geometrical models on numerical parameters borrowed from the Babylonians. This process was well under way in the second century b.c. In the Almagest (second century a.d.), Ptolemy begins with planetary periods that he ascribes to Hipparchos (second century b.c).28 But in fact these parameters were of Babylonian origin and turn up on cuneiform tablets. In his discussion of the Moon?s mean motions, Ptolemy again starts with Hipparchos?s values, but in this case says explicitly that Hipparchos had made use of Chaldean observations.29 Hipparchos?s works on lunar and planetary theory have not come down to us, so we do not know exactly how he came into contact with the Babylonian parameters.

     In the period between Hipparchos and Ptolemy, the Greek geometrical planetary theories had not yet reached maturity, and were not capable of yielding accurate numerical values for planet positions. But the rise of astrology (which entered the Greek world from Babylonia in the second or first century b.c.) imposed a need for quick, reliable methods of calculating planetary phenomena. Greek astronomers and astrologers adopted the Babylonian planetary theories with enthusiasm. Astronomical papyri from Egypt show Greeks of the first century a.d. using Babylonian planetary theories with complete facility. Ptolemy?s publication of his planetary theories and tables in the Almagest and the Handy Tables produced a major change in the way practical astronomy was done. But calculating methods based on Babylonian procedures still existed side by side with methods based on Ptolemy?s tables in the fourth century a.d.

     In chapter ii of the Introduction to the Phenomena, Geminos shows that he is familiar with some features of Chaldean astrology, though he mentions only a few doctrines in passing, and does not seem intensely interested in the subject. In any case, nothing about the level of his familiarity with Chaldean astrology is surprising for a writer of his time. Far more detailed and more historically significant is Geminos?s discussion of the Babylonian lunar theory in chapter xviii. His discussion there 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. In particular, Geminos explains a scheme for the motion of the Moon, according to which the daily displacement increases by equal intervals from day to day, until it reaches a maximum, then falls by equal increments from one day to the next. The numerical parameters of Geminos?s theory are in exact agreement with cuneiform sources. Geminos?s treatment of the Babylonian lunar theory is discussed below in sec. 13, below, where we also address the question of the form that his source for the Babylonian lunar theory might have taken. In chapter xi, Geminos mentions that eclipses of the Moon take place in an eclipse zone (ekleiptikon) that is 2 degrees wide. Though he does not mention the Chaldeans in this passage, the 2-degree eclipse zone also comes from Babylonian astronomy. In total, Geminos?s remarks provide important information about the adoption and adaptation of Babylonian knowledge by the Greeks of his time. By contrast, Geminos cites the ?Egyptians? simply for the general structure of the Egyptian calendar and the circumstances of a festival of Isis.

http://press.princeton.edu/chapters/i8330.html

[Bart]

Geminos's Introduction to the Phenomena:
A Translation and Study of a Hellenistic Survey of Astronomy

James Evans & J. Lennart Berggren


Part 6 of 6

                                          6. GEMINOS?S COUNTRY AND DATE

     Modern scholars sometimes refer to our astronomer as ?Geminos of Rhodes,?30 but there is no ancient mention of his native land or city. The few ancient writers who cite him refer to him simply as Geminos, or as ?Geminos the mathematician.? The evidence for placing him in Rhodes is suggestive, but not conclusive. In several passages in the Introduction to the Phenomena, Geminos uses Rhodes as an example in making some astronomical point?involving the length of the longest day, or the portion of the summer tropic cut off above the horizon, or the meridian altitude of the star Canopus, or the date of the morning rising of the Dog Star.31 But although he does use Rhodes most frequently for such examples, he also gives examples for Alexandria, Greece, Rome, and the Propontis.32 Does his proclivity for using Rhodes suggest a fondness for his native city, or merely reflect Rhodes?s usefulness in astronomical examples, owing to its roughly central location in the Greek world? Geminos remarks (xiv 12) that celestial globes and armillary spheres were commonly constructed for this klima, or band of latitude. And it is noteworthy that in the second century a.d., Ptolemy, who lived at Alexandria, still found it natural to construct examples for the parallel through Rhodes, ?where the elevation of the pole is 36 degrees and the longest day 141⁄2 hours.?33 Or perhaps, as Dicks suggests,34 Geminos?s use of the klima of Rhodes reflects examples he found in his sources, which may have included the geographical or astronomical works of Hipparchos. Blass makes an interesting point about Geminos?s use of two geographical examples. Geminos (xvii 3) refers to Mt. Kyllene, and immediately specifies that it is ?the highest mountain in the Peloponnesos?; but in the very next sentence he refers to Mt. Atabyrion without making any similar specification that it is on the island of Rhodes.35 Does this suggest that he expected his readers to be familiar with Rhodian geography?

     Finally, we know that Geminos wrote some sort of abridgment of, or commentary on, the Meteorology of Poseidonios, whose native land was Rhodes. And a likely dating of Geminos?s Introduction to the Phenomena would make Geminos a younger contemporary of Poseidonios, and thus potentially his student. (Geminos?s possible debts to Poseidonios will be discussed below.) Near the end of her own discussion of this issue, Aujac concludes, ?Let us allow, then, since no other better hypothesis presents itself, that Geminos was born at Rhodes and that he there received his first instruction.?36 This is not an unreasonable position to take, since no convincing evidence exists for placing him elsewhere.37 But we simply do not know. In any case, as Tannery has pointed out,38 all the writers who cited Geminos were associated with Alexandria or with Athens, which suggests that his works circulated mainly in the Greek world of the eastern Mediterranean.

     Whether Geminos is a Greek name or a Hellenization of a Latin name (Geminus) has been the subject of dispute. As Aujac remarks, ?Petau made it a Latin name, Manitius a Greek name, Tittel again a Latin name (!)?39 A crucial point in the argument is the length of the central vowel? a long vowel favoring the Greek. Whatever the origin of his name, Geminos was thoroughly Greek in education, intellectual interests, and manner of expression.

     But when did Geminos write? There are two ways to narrow the possibilities. Appendix 4 lists the writers that Geminos mentions. The latest datable writers cited in the Introduction to the Phenomena are Hipparchos, Polybios, and Krates of Mallos, who all flourished in the middle of the second century b.c. Conversely, Geminos was quoted by Alexander of Aphrodisias, the Aristotelian commentator, who flourished at the end of the second century a.d. Thus we may place Geminos between 150 b.c. and a.d. 200.

     It appears possible to date Geminos more closely by his remark (viii 20?22) concerning the wandering year of the Egyptians:

. . . most of the Greeks suppose the winter solstice according to Eudoxos to be at the same time as the feasts of Isis [reckoned] according to the Egyptians, which is completely false. For the feasts of Isis miss the winter solstice by an entire month. . . . 120 years ago the feasts of Isis happened to be celebrated at the winter solstice itself. But in 4 years a shift of one day arose; this of course did not involve a perceptible difference with respect to the seasons of the year. . . . But now, when the difference is a month in 120 years, those who take the winter solstice according to Eudoxos to be during the feasts of Isis [reckoned] according to the Egyptians are not lacking an excess of ignorance.
The feasts of Isis (ta Isia) were celebrated at a fixed date in the Egyptian year. But as the Egyptian year consists of 365 days (with no leap day), the feast days shift with respect to the solstice by 1 day every 4 years. Because the Egyptian year is too short, the feast days gradually fall earlier and earlier in the natural, or solar, year. If we knew the Egyptian calendar date on which this Isis festival was observed, it would be easy to calculate the year in which the festival coincided with the winter solstice. We would then place Geminos 120 years after that year.

     Most writers on the subject have tried to date Geminos by the use of a remark by Plutarch (late first to early second century a.d.):

. . . they say that the disappearance of Osiris occurred in the month of Athyr. . . . Then, among the gloomy rites which the priests perform, they shroud the gilded image of a cow with a black linen vestment, and display her as a sign of mourning for the goddess, inasmuch as they regard both the cow and the Earth as the image of Isis; and this is kept up for four days consecutively, beginning with the seventeenth of the month.40
Denis Petau, in his Uranologion of 1630,41 used Plutarch?s remark to date Geminos?s composition, with the following result:

year 4537 of the Julian period,
fourth year of Olympiad 175,
year 677 after the founding of Rome,

or, as we would say, 77 b.c. Petau was followed by most later writers on the subject, with only minor adjustments. Thus, most writers who have accepted this evidence put Geminos?s composition of the Introduction to the Phenomena in the 60s or 70s b.c.42 But as we shall see, the margin of error should be taken quite a bit wider.

     The reasoning is straightforward. Let us work with 19 Athyr, the 3rd day of the 4-day festival. Athyr is the 3rd month of the Egyptian calendar, so 19 Athyr is the 79th day of the Egyptian year.43 In Table I.1, the first column lists years of the Julian calendar. In the second column, we have written the date of 1 Thoth, the 1st day of the Egyptian year that began in the course of the given Julian calendar year.44 Thus, in −200, a new Egyptian year began on 12 October.45 To obtain column 3, we add 78 days to the dates in column 2. In this way, we move from the 1st day of the Egyptian year (1 Thoth) to the 79th day (19 Athyr). Thus, in the Julian year −200, the 19th of Athyr fell on 29 December. The 4th column gives the date of the winter solstice46 for each of the given Julian calendar years. Comparing the 3rd and 4th columns, we see that the winter solstice fell on 19 Athyr sometime between −200 and −150. Interpolation gives −179. Geminos wrote 120 years later, or around the year −59.

     An error of 3 days in the date of the solstice could shift the date by ?12 years.47 Again, Geminos speaks in rough fashion of a whole month, as the difference by which the Isis festival missed the solstice in his own day. He might have spoken in this same way if the actual difference were, say, as small as 28 days or as great as 32, which introduces another ?8 years of uncertainty. Finally, the festival itself stretched over a period of 4 days, which gives us 4 more years of uncertainty after 60 b.c. and 8 more years before. Putting all this together, we find the period 88?36 b.c. as the most likely for the composition of the Introduction to the Phenomena, or, to speak in round numbers, 90?35 b.c.

     In 1975, Otto Neugebauer proposed a date for Geminos about a century later, around a.d. 50.48 Although Neugebauer?s dating was influential for a while, we shall see that it can no longer be sustained. The argument that follows will be somewhat intricate. But at the end we shall not abandon the dating of 90?35 b.c. that we have just explained. Thus, readers with little enthusiasm for details of ancient chronology should feel no guilt in skipping ahead to the next section.

     The key question that Neugebauer posed is whether Petau?s argument, based on Plutarch?s remark, involved a confusion between the Egyptian and the Alexandrian calendars. After Egypt became a province of the Roman empire, Augustus reformed the Egyptian calendar by introducing a leap day once every four years, the first such day being inserted at the end of the Egyptian year 23/22 b.c. In the reformed calendar, now usually called ?Alexandrian? to distinguish it from the original Egyptian calendar, three years of 365 days were followed by a year of 366 days. The reformed calendar thus was very similar to the Julian calendar, which had been used at Rome since 45 b.c. Of course, the Alexandrian calendar continued to use the old Egyptian months of 30 days each, as well as the original Egyptian month names. For dates near 23 b.c., a given day has nearly the same date in both the Egyptian and the Alexandrian calendars. But gradually, at the rate of 1 day in 4 years, the calendars diverge. Moreover, the two calendars continued to be used side by side. For example, Ptolemy, in the Almagest, used the old calendar for astronomical calculation, because of its simpler structure, nearly two centuries after it had been abandoned for civil use. In his parapegma, however, Ptolemy adopted the Alexandrian calendar, because the heliacal risings and settings of a given star have more nearly fixed dates in this calendar. When an ancient writer, writing after Augustus?s reform, says ?the 17th of Athyr,? it is not immediately clear whether he is expressing the date in terms of the Egyptian calendar or the Alexandrian calendar. One must examine the context carefully.

     Neugebauer was troubled by a second reference in Plutarch to what was apparently the same Isis festival:

. . . then Osiris got into [the chest] and lay down, and those who were in the plot ran to it and slammed down the lid, which they fastened by nails from the outside and also by using molten lead. They say also that the date on which this deed was done was the seventeenth of Athyr, when the Sun passes through Scorpio. . . . 49
We have again the date Athyr 17, but now with the added information that the Sun passes through Scorpio during the month of Athyr. As Neugebauer pointed out, this was true in the Alexandrian, but not in the Egyptian calendar, for Plutarch?s time. The Alexandrian month of Athyr runs from 28 October to 26 November (Julian), which corresponds rather closely to the sign of Scorpio. In Plutarch?s time, say a.d. 118, the Egyptian and Alexandrian calendars were out of phase by 35 days: 1 Athyr (Egyptian) then fell on September 23 (Julian), corresponding to the Sun?s entry into Libra, not Scorpio. Neugebauer concluded that Plutarch was using the Alexandrian, and not the Egyptian, calendar. Moreover, he surmised that Plutarch (or his source) took the original date of the Isis festival, as expressed in the Egyptian calendar, and converted it to an Alexandrian equivalent. The Alexandrian calendar was, after all, the one in official use, and the one more likely to be understood by Plutarch?s readers in the wider Roman world.

     Neugebauer found the Egyptian date for what he took to be the same festival in a hieroglyphic text in the East Osiris Chapel on the roof of the Temple of Hathor in Dendera.50 The text describes the rituals of an Osiris festival that lasted from 12 to 30 Choiak. The text is not later than 30 b.c. and thus predates the reform of the calendar. Moreover, as Neugebauer also pointed out, the papyrus Hibeh 27 (c. 300 b.c.) mentions an Osiris festival on 26 Choiak.51 Now in Plutarch?s time (a.d. 118), the date 26 Choiak (Egyptian) = 21 Athyr (Alexandrian), which appeared to confirm Plutarch?s use of the Alexandrian calendar when he placed the rites on 17?20 Athyr. Neugebauer then computed the year when the winter solstice fell on 15 Choiak (Egyptian). (This date is within the span of rituals mentioned by the text in the East Osiris Chapel.) The answer is the year −70; Geminos wrote 120 years later, or around a.d. 50, according to Neugebauer. The new dating by Neugebauer, pushing Geminos forward into the first century a.d., was gradually adopted by historians of ancient astronomy.

     Alexander Jones reexamined the question in 1999.52 As Jones points out, Neugebauer deserved credit for being the first to use papyrological evidence for the date of the Isis festival. The advantage of such evidence is that it comes from a time when the Isis festival was a living custom, that it comes directly from Egypt without having passed through the hands of other writers, and that some of it comes from a date before the reform of the Egyptian calendar, thus removing any possibility of confusion between the calendars. But there was much more such evidence (in both the Greek and Egyptian languages) available than Neugebauer had realized.

     Jones adduces a good deal of evidence showing that Neugebauer had wrongly taken the Osiris festival of 12 to 30 Choiak (Egyptian) to be the same festival as the Isia that Plutarch mentions. Jones also points out that Geminos refers to the festival simply as ta Isia, without any further specification. This implies that the festival was so well known that Geminos had no fear that it would be confused by his readers with other festivals associated with Isis or Osiris. Now, as Jones points out, there are at least nineteen references in Greek papyri to a festival called the Isia (also spelled Iseia or Isieia). Only a few of these provide calendrical information. But enough do that it is possible to confirm Plutarch?s dates of

50 For a bibliography pertaining to this text, see Porter and Moss 1927, vol. 6, 97.
51 Grenfell and Hunt 1906, 144, 148.
52 Jones 1999a. 17?20 Athyr, and to be sure that these dates indeed apply to the old (Egyptian) calendar. For example, several papyri from before the calendar reform are private letters or records, with dates in Athyr, concerned with ordering or issuing supplies (logs and lamp oil) for the Isia. One papyrus gives the dates of the Isia in terms of the Macedonian calendar. These dates can be converted to the Egyptian calendar (with an uncertainty of 1 day) and indeed correspond to 17?20 Athyr. Slightly altering the chronological assumptions and broadening the error bars, Jones concludes that it is very probable that Geminos wrote his Introduction to the Phenomena ?between 90 and 25 b.c., and definitely not during the first century of our era.?53 There is an irony in the fact, confirmed by the papyri, that after the calendar reform, the Isia continued to be celebrated on days called 17?20 Athyr, but in the new calendar. Thus, Plutarch?s dates turn out to refer to the reformed calendar after all! (But they should not be converted back into the old calendar to obtain the dates that Geminos would have been familiar with.)

     One minor problem with dating Geminos to the first century b.c. involves his mention of Hero of Alexandria in fragment 1. The dating of Hero has been controversial, with suggested dates from the middle of the second century b.c. to the middle of the third century a.d.54 In Dioptra 35, however, Hero mentions a lunar eclipse observed simultaneously in Alexandria and Rome. Although Hero does not mention the year of the eclipse, he is detailed about its other circumstances: 10 days before the vernal equinox, 5th seasonal hour of the night at Alexandria. Neugebauer55 has shown that these circumstances were satisfied by only one lunar eclipse between about −200 and +300, namely that of March 13, a.d. 62. If Hero used an eclipse of recent memory, we must place him in the second half of the first century a.d. Thus, if the dating of Geminos to the first century b.c. is correct, we must suppose that Proklos or a later copyist interpolated the name of Hero in fragment 1.

     Finally, we note that Geminos writes about Babylonian astronomy and astrology as if they were still new to his Greek readers. This well suits a dating to the first century b.c., when this material was still being absorbed and adapted by the Greeks.56

http://press.princeton.edu/chapters/i8330.html

[Solomon]

Many thanks, Bart: a most useful addition to our knowledge of the instrument.

Posidonius
Posidonius (Greek: Ποσειδώνιος / Poseidonios) "of Rhodes" (ο Ρόδιος) or, alternatively, "of Apameia" (ο Απαμεύς) (ca. 135 BCE - 51 BCE), was a Greek Stoic philosopher, politician, astronomer, geographer, historian, and teacher. He was acclaimed as the greatest polymath of his age. None of his vast body of work can be read in its entirety today as it exists only in fragments.

Life
Posidonius (also spelled Poseidonius), nicknamed "the Athlete", was born to a Greek family in Apamea, a Roman city on the river Orontes in northern Syria, and probably died in Rome or Rhodes.

Posidonius completed his higher education in Athens, where he was a student of the aged Panaetius, the head of the Stoic school.

He settled around 95 BCE in Rhodes, a maritime state which had a reputation for scientific research, and became a citizen.

Political offices
In Rhodes, Posidonius actively took part in political life, and his high standing is apparent from the offices he held. He attained the highest public office as one of the prytaneis (presidents, having a six months tenure) of Rhodes. He served as an ambassador to Rome in 87 - 86 BCE, during the Marian and Sullan era.

Along with other Greek intellectuals, Posidonius favored Rome as the stabilizing power in a turbulent world. His connections to the Roman ruling class was for him not only politically important and sensible but was also important to his scientific researches. His entry into the highest government circles enabled Posidonius to undertake his travels into the west beyond the borders of Roman control, which, for a Greek traveler, would have been impossible without such Roman support.

Travels
After he had established himself in Rhodes, Posidonius made one or more journeys traveling throughout the Roman world and even beyond its boundaries to conduct scientific research. He traveled in Greece, Hispania, Africa, Italy, Sicily, Dalmatia, Gaul, Liguria, North Africa, and on the eastern shores of the Adriatic.

In Hispania, on the Atlantic coast at Gades (the modern Cadiz), Posidonius studied the tides. He observed that the daily tides were connected with the orbit and the monthly tides with the cycles of the Moon, and he hypothesized about the connections of the yearly cycles of the tides with the equinoxes and solstices.

In Gaul, he studied the Celts. He left vivid descriptions of things he saw with his own eyes while among them: men who were paid to allow their throats to be slit for public amusement and the nailing of skulls as trophies to the doorways. But he noted that the Celts honored the Druids, whom Posidonius saw as philosophers, and concluded that even among the barbaric 'pride and passion give way to wisdom, and Ares stands in awe of the Muses'. Posidonius wrote a geographic treatise on the lands of the Celts which has since been lost, but which has been assumed to be one of the sources for Tacitus Germania.

School
Posidonius's extensive writings and lectures gave him authority as a scholar and made him famous everywhere in the Graeco-Roman world, and a school grew around him in Rhodes. His grandson Jason, who was the son of his daughter and Menekrates of Nysa, followed in his footsteps and continued Posidonius's school in Rhodes. Although little is known of the organization of his school, it is clear that Posidonius had a steady stream of Greek and Roman students.

Partial scope of writings
Posidonius was celebrated as a polymath throughout the Greco-Roman world because he came near to mastering all the knowledge of his time, similar to Aristotle and Eratosthenes. He attempted to create a unified system for understanding the human intellect and the universe which would provide an explanation of and a guide for human behavior.

Posidonius wrote on physics (including, meteorology and physical geography), astronomy, astrology and divination, seismology, geology and mineralogy, hydrology, botany, ethics, logic, mathematics, history, natural history, anthropology, and tactics. His studies were major investigations into their subjects, although not without errors.

None of his works survive intact. All that we have found are fragments, although the titles and subjects of many of his books are known.[1]

Philosophy
For Posidonius, philosophy was the dominant master art and all the individual sciences were subordinate to philosophy, which alone could explain the cosmos. All his works, from scientific to historical, were inseparably philosophical.

He accepted the Stoic categorization of philosophy into physics (natural philosophy, including metaphysics and theology), logic (including dialectic), and ethics. These three categories for him were, in Stoic fashion, inseparable and interdependent parts of an organic, natural whole. He compared them to a living being, with physics the meat and blood, logic the bones and tendons which held the organism together, and ethics ? the most important part ? the soul. His philosophical grand vision was that the universe itself was similarly interconnected, as if an organism, through cosmic "sympathy", in all respects from the development of the physical world to the history of humanity.

Although a firm Stoic, Posidonius was, like Panaetius and other Stoics of the middle period, eclectic. He followed not only the older Stoics, but Plato and Aristotle. Although it is not certain, Posidonius may have written a commentary on Plato's Timaeus.

He was the first Stoic to depart from the orthodox doctrine that passions were faulty judgments and posit that Plato's view of the soul had been correct, namely that passions were inherent in human nature. In addition to the rational faculties, Posidonius taught that the human soul had faculties that were spirited (anger, desires for power, possessions, etc.) and desiderative (desires for sex and food). Ethics was the problem of how to deal with these passions and restore reason as the dominant faculty.

Posidonius upheld the Stoic doctrine of Logos, which ultimately passed into Judeo-Christian belief. Posidonius also affirmed the Stoic doctrine of the future conflagration.

Physics
In Stoic physics, Posidonius advocated a theory of cosmic "sympathy", the organic interrelation of all appearances in the world, from the sky to the earth, as part of a rational design uniting humanity and all things in the universe, even those that were temporally and spatially separate. Although his teacher Panaetius had doubted divination, Posidonius used the theory of cosmic sympathy to support his belief in divination - whether through astrology or prophetic dreams - as a kind of scientific prediction.

Astronomy
Some fragments of his writings on astronomy survive through the treatise by Cleomedes, On the Circular Motions of the Celestial Bodies, the first chapter of the second book appearing to have been mostly copied from Posidonius.

Posidonius advanced the theory that the Sun emanated a vital force which permeated the world.

He attempted to measure the distance and size of the Sun. In about 90 BCE Posidonius estimated the astronomical unit to be a0/rE = 9893, which was still too small by half. In measuring the size of the Sun, however, he reached a figure larger and more accurate than those proposed by other Greek astronomers and Aristarchus of Samos.

Posidonius also calculated the size and distance of the Moon.

Posidonius constructed an orrery, possibly similar to the Antikythera mechanism. Posidonius's orrery, according to Cicero, exhibited the diurnal motions of the sun, moon, and the five known planets.

Geography, ethnology and geology
Poseidonios?s fame beyond specialized philosophical circles had begun, at the latest, in the eighties with the publication of the work "about the ocean and the adjacent areas". This work was not only an overall representation of geographical questions according to current scientific knowledge, but it served to popularize his theories about the internal connections of the world, to show how all the forces had an effect on each other and how the interconnectedness applied also to human life, to the political just as to the personal spheres. In this work, Posidonius detailed his theory of the effect on a people?s character by the climate, which included his representation of the "geography of the races". This theory was not solely scientific, but also had political implications -- his Roman readers were informed that the climatic central position of Italy was an essential condition of the Roman destiny to dominate the world. As a Stoic he did not, however, make a fundamental distinction between the civilized Romans as masters of the world and the less civilized peoples.

Posidonius measured Earth's circumference from the position of the star Canopus. As explained by Cleomedes, Posidonius used the elevation of Canopus, to determine the difference in latitude between Rhodes and Alexandria. Due to observational errors, his result was about 24,000 miles. This was 1,000 miles less than the distance calculated by Eratosthenes but still very close to the correct distance of 24,901 miles. See history of geodesy and Greek distances.

Like Pytheas, he believed the tide is caused by the Moon. Posidonius was, however, wrong about the cause. Thinking that the Moon was a mixture of air and fire, he attributed the cause of the tides to the heat of the Moon, hot enough to cause the water to swell but not hot enough to evaporate it.

He recorded observations on both earthquakes and volcanoes, including accounts of the eruptions of the volcanoes in the Aeolian Islands, north of Sicily.

Meteorology
Posidonius in his writings on meteorology followed Aristotle. He theorized on the causes of clouds, mist, wind, and rain as well as frost, hail, lightning, and rainbows.

Mathematics
In addition to his writings on geometry, Posidonius was credited for creating some mathematical definitions, or for articulating views on technical terms, for example 'theorem' and 'problem'.

History and tactics
In his Histories, Posidonius continued the World History of Polybius. His history of the period 146 - 88 BCE is said to have filled 52 volumes. His Histories continue the account of the rise and expansion of Roman dominance, which he appears to have supported. Posidonius did not follow Polybius's more detached and factual style, for Posidonius saw events as caused by human psychology; while he understood human passions and follies, he did not pardon or excuse them in his historical writing, using his narrative skill in fact to enlist the readers' approval or condemnation.

For Posidonius "history" extended beyond the earth into the sky; humanity was not isolated each in its own political history, but was a part of the cosmos. His Histories were not, therefore, concerned with isolated political history of peoples and individuals, but they included discussions of all forces and factors (geographical factors, mineral resources, climate, nutrition), which let humans act and be a part of their environment. For example, Posidonius considered the climate of Arabia and the life-giving strength of the sun, tides (taken from his book on the oceans), and climatic theory to explain people?s ethnic or national characters.

Of Posidonius's work on tactics, The Art of War, the Roman historian Arrian complained that it was written 'for experts', which suggests that Posidonius may have had first hand experience of military leadership or, perhaps, utilized knowledge he gained from his acquaintance with Pompey.

Reputation and influence
In his own era, his writings on almost all the principal divisions of philosophy made Posidonius a renowned international figure throughout the Graeco-Roman world and he was widely cited by writers of his era, including Cicero, Livy, Plutarch, Strabo (who called Posidonius "the most learned of all philosophers of my time"), Cleomedes, Seneca the Younger, Diodorus Siculus (who used Posidonius as a source for his Bibliotheca historia ("Historical Library"), and others. Although his ornate and rhetorical style of writing passed out of fashion soon after his death, Posidonius was acclaimed during his life for his literary ability and as a stylist.

Posidonius appears to have moved with ease among the upper echelons of Roman society as an ambassador from Rhodes. He associated with some of the leading figures of late republican Rome, including Cicero and Pompey, both of whom visited him in Rhodes. In his twenties, Cicero attended his lectures (77 BCE) and they continued to correspond. Cicero in his De Finibus closely followed Posidonius's presentation of Panaetius's ethical teachings. Posidonius met Pompey when he was Rhodes's ambassador in Rome and Pompey visited him in Rhodes twice, once in 66 BCE during his campaign against the pirates and again in 62 BCE during his eastern campaigns, and asked Posidonius to write his biography. As a gesture of respect and great honor, Pompey lowered his fasces before Posidonius's door. Other Romans who visited Posidonius in Rhodes were Velleius, Cotta, and Lucilius.

Ptolemy was impressed by the sophistication of Posidonius's methods, which included correcting for the refraction of light passing through denser air near the horizon. Ptolemy's approval of Posidonius's result, rather than Eratosthenes's earlier and more correct figure, caused it to become the accepted value for the Earth's circumference for the next 1,500 years.

Posidonius fortified the Stoicism of the middle period with contemporary learning. Next to his teacher Panaetius, he did most, by writings and personal contacts, to spread Stoicism in the Roman world. A century later, Seneca referred to Posidonius as one of those who had made the largest contribution to philosophy.

His influence on philosophical thinking lasted until the Middle Ages, as is shown by citation in the Suda, the massive medieval lexicon.

At one time, scholars perceived Posidonius's influence in almost every subsequent writer, whether warranted or not. Today, Posidonius seems to be recognized as having had an inquiring and wide-ranging mind, not entirely original, but with a breadth of view that connected, in accordance with his underlying Stoic philosophy, all things and their causes and all knowledge into an overarching, unified world view.

The Posidonius crater on the Moon is named for him.

[Solomon]

Cleomedes
Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies.

Placing his work chronologically
His birth and death dates are not known--historians have suggested that he wrote his work sometime between the mid-1st Century B.C. and 400 C.E. The earlier estimates rely on the fact that Cleomedes refers extensively in his writing to the work of mathematician and astronomer Posidonius of Rhodes (135 BC-51 BC), and yet seemingly not at all to the work of Ptolemy (85-165 C.E.). These conclusions have been challenged on the grounds that Cleomedes' work was in relatively elementary astronomy, and that reference to Ptolemy would not necessarily be expected. The 20th Century mathematician Otto Neugebauer, however, looked closely at the astronomical observations made by Cleomedes, and concluded that a date of 371 C.E. (?50 years) better explains what is found there. Neugebauer's estimate has been challenged on the grounds that Cleomedes makes observational errors with enough frequency that there is difficulty in deciding which observations to trust for the purpose of dating his work.

On the Circular Motions of the Celestial Bodies
The book for which Cleomedes is known is a fairly basic astronomy textbook in two volumes. His purpose in writing seems to have been as philosophical as it was scientific--he spends an extensive amount of time criticizing the (admittedly fallacious) scientific ideas of the Epicureans (Cleomedes appears to have been a dedicated Stoic).

Cleomedes' book is criticized by most modern astronomers as being poorly written--it is valued primarily for preserving, apparently verbatim, much of Posidonius' writings on astronomy (none of Posidonius' books have survived to the modern day). Cleomedes is accurate in some of his remarks on lunar eclipses, especially his conjecture that the shadow on the Moon suggests a spherical Earth. He also remarks presciently that the absolute size of many stars may exceed that of the Sun (and that the Earth might appear as a very small star, if viewed from the surface of the Sun).

This book is the original source for the well-known story of how Eratosthenes measured the Earth's circumference. Although the story is now believed by some to be purely legendary, many modern mathematicians and astronomers believe the description to be reasonable (and believe Eratosthenes' achievement to be one of the more impressive accomplishments of ancient astronomy).