Today the study of astronomy requires a deep understanding of mathematics and physics. It is important to realise that Greek astronomy (we are interested in the topic during the 1000 years between 700 BC and 300 AD) did not involve physics. Indeed, as Pannekoek points out in [7], a Greek astronomer aimed only to describe the heavens while a Greek physicist sought out physical truth. Mathematics provided the means of description, so astronomy during the 1000 years that interest us in this article was one of the branches of mathematics.

The Greeks began to think of philosophy from the time of Thales in about 600 BC. Thales himself, although famed for his prediction of an eclipse, probably had little knowledge of astronomy, yet he brought back from Egypt knowledge of mathematics into the Greek world and possibly also some knowledge of Babylonian astronomy. It is reasonable to begin by looking at what 'astronomy' was in Greece around this time. However we begin by looking further back than this to around 700 BC.

Basically at this time astronomy was all to do with time keeping. It is natural that astronomical events such as the day would make a natural period of time and likewise the periodic phases of the moon make the next natural time span. Indeed these provided the basic methods of time keeping around the period of 700 BC yet, of course, another important period of time, the year, was not easy to determine in terms of months. Yet a knowledge of the approximate length of the year was vital for food production and so schemes had to be devised. Farmers at this time would base their planting strategies on the rising and setting of the constellations, that is the times when certain constellations would first become visible before sunrise or were last visible after sunset.

Hesiad, one of the earliest Greek poets, often called the "father of Greek didactic poetry" wrote around 700 BC. Two of his complete epics have survived, the one relevant to us here is Works and Days describing peasant life. In this work Hesiad writes that (see [5], also [1] and [7]):-

... when the Pleiades rise it is time to use the sickle, but the plough when they are setting; 40 days they stay away from heaven; when Arcturus ascends from the sea and, rising in the evening, remain visible for the entire night, the grapes must be pruned; but when Orion and Sirius come in the middle of heaven and the rosy fingered Eos sees Arcturus, the grapes must be picked; when the Pleiades, the Hyades, and Orion are setting, then mind the plough; when the Pleiades, fleeing Orion, plunge into the dark sea, storms may be expected; 50 days after the sun's turning is the right time for man to navigate; when Orion appears, Demeter's gift has to be brought to the well-smoothed threshing floor.

For many hundreds of years astronomers would write works on such rising and setting of constellations indicating that the type of advice given by Hesiad continued to be used.

An early time scale based on 12 months of 30 days did not work well since the moon rapidly gets out of phase with a 30 day month. So by 600 BC this had been replaced by a year of 6 'full' months of 30 days and 6 'empty' months of 29 days. This improvement in keeping the moon in phase with the month had the unfortunate effect of taking the year even further out of phase with the period of the recurring seasons. About the same time as Thales was making the first steps in philosophy, Solon, a statesman in Athens who became known as one of the Seven Wise Men of Greece, introduced an improved calendar.

Solon's calendar was based on a two yearly cycle. There were 13 months of 30 days and 12 months of 29 days in each period of two years so this gave a year of about 369 days and a month of 29¹/₂ days. However, the Greeks relied mainly on the moon as their time-keeper and frequent adjustments to the calendar were necessary to keep it in phase with the moon and the seasons. Astronomy was clearly a subject of major practical importance in sorting out the mess of these calendars and so observations began to be made to enable better schemes to be devised.

Pythagoras, around 500 BC, made a number of important advances in astronomy. He recognised that the earth was a sphere, probably more because he believed that a sphere was the most perfect shape than for genuine scientific reasons. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star. There is a pleasing appeal to observational evidence in these discoveries, but Pythagoras had a philosophy based on mathematical 'perfection' which tended to work against a proper scientific approach. On the other side there is an important idea in the Pythagorean philosophy which had a lasting impact, namely the idea that all complex phenomena must reduce to simple ones. One should not underestimate the importance of this idea which has proved so powerful throughout the development of science, being a fundamental driving force to the great scientists such as Newton and particularly Einstein.

Around 450 BC Oenopides is said to have discovered the ecliptic made an angle of 24° with the equator, which was accepted in Greece until refined by Eratosthenes in around 250 BC. Some scholars accept that he discovered that the ecliptic was at an angle but doubt that he measured the angle. Whether he learnt of the 12 signs of the zodiac from scholars in Mesopotamia or whether his discoveries were independent Greek discoveries is unknown. Oenopides is also credited with suggesting a calendar involving a 59 year cycle with 730 months. Other schemes proposed were 8 year cycles, with extra months in three of the eight years and there is evidence that this scheme was adopted.

About the same time as Oenopides proposed his 59 year cycle, Philolaus who was a Pythagorean, also proposed a 59 year cycle based on 729 months. This seemed to owe more to the numerology of the Pythagoreans than to astronomy since 729 is 27², 27 being the Pythagorean number for the moon, while it is also 9³, 9 being the Pythagorean number associated with the earth. Philolaus is also famed as the first person who we know to propose that the earth moves. He did not have it orbiting the sun, however, but rather all the heavenly bodies went in circles round a central fire which one could never see since there was a counter earth between the earth and the fire. This model, certainly not suggested by any observational evidence, is more likely to have been proposed so that there were 10 heavenly bodies, for 10 was the most perfect of all numbers to the Pythagoreans.

Meton, in 432 BC, introduced a calendar based on a 19 year cycle but again this is similar to one devised in Mesopotamia some years earlier. Meton worked in Athens with another astronomer Euctemon, and they made a series of observations of the solstices (the points at which the sun is at greatest distance from the equator) in order to determine the length of the tropical year. Again we do not know if the 19 year cycle was an independent discovery or whether Greek advances were still based on earlier advances in Mesopotamia. Meton's calendar never seems to have been adopted in practice but his observations proved extremely useful to later Greek astronomers such as Hipparchus and Ptolemy.

That Meton was famous and widely known is seen from the play Birds written by Aristopenes in about 414 BC. Two characters are speaking, one is Meton [see D Barrett (trs.), Aristophanes, Birds (London, 1978)]:-

Meton: I propose to survey the air for you: it will have to be marked out in acres.

Peisthetaerus: Good lord, who do you think you are?

Meton: Who am I? Why Meton. THE Meton. Famous throughout the Hellenic world - you must have heard of my hydraulic clock at Colonus?

Meton and Euctemon are associated with another important astronomical invention of the time, namely a parapegma. A parapegma was a stone tablet with movable pegs and an inscription to indicate the approximate correspondence between, for example, the rising of a particular star and the civil date. Because the calendar had to be changed regularly to keep the civil calendar in phase with the astronomical one, the parapegma had movable pegs which could be adjusted as necessary. A parapegma soon also contained meteorological forecasts associated with the risings and settings of the stars and not only were stone parapegma constructed but also ones on papyri. Meton and Euctemon are usually acknowledged as the inventors of parapegmata and certainly many later astronomers compiled the data nessary for their construction.

There is evidence for other observational work being undertaken around this time, for Vitruvius claims that Democritus of Abdera, famed for his atomic theory, devised a star catalogue. We have no knowledge of the form this catalogue took but Democritus may well have described the major constellations in some way.

The beginning of the 4^th century BC was the time that Plato began his teachings and his writing was to have a major influence of Greek thought. As far as astronomy is concerned Plato had a negative effect, for although he mentions the topic many times, no dialogue is devoted to astronomy. Worse still, Plato did not believe in astronomy as a practical subject, and condemned as lowering the spirit the actual observation of the heavenly bodies. Plato only believed in astronomy to the extent that it encouraged the study of mathematics and suggested beautiful geometrical theories.

Perhaps we should digress for a moment to think about how the ideas of philosophy which were being developed by Plato and others affected the development of astronomy. Neugebauer [6] feels that philosophy had a detrimental affect:-

I see no need for considering Greek philosophy as an early stage in the development of science ... One need only read the gibberish of Proclus's introduction to his huge commentary on Book I of Euclid's Elements to get a vivid picture of what would have become of science in the hands of philosophers. The real "Greek miracle" is the fact that a scientific methodology was developed, and survived, in spite of a widely admired dogmatic philosophy.

Although there is some truth in what Neugebauer writes here, I [EFR] feel that he has overstated his case. It is true that philosophers came up with ideas about the universe which were not based on what we would call today the scientific method. However, the very fact that theories were proposed which could be shown to be false by making observations, must have provided a climate where the scientific approach could show its strength. Also the fact the philosophy taught that one should question all things, even "obvious" truths, was highly beneficial. Another important philosophical idea which had important consequences from the time of Pythagoras, and was emphasised by Plato, was that complex phenomena must be consequences of basic simple phenomena. As Theon of Smyrna expressed it, writing in the first century AD:-

The changing aspects of the revolution of the planets is because, being fixed in their own circles or in their own shperes whose movements they follow, they are carried across the zodiac, just as Pythagoras had first understood it, by a regulated simple and equal revolution but which results by combination in a movement that appears variable and unequal.

This led Theon to write:-

It is natural and necessary that all the heavenly bodies have a uniform and regular movement.

Perhaps the most telling argument against the above claim by Neugebauer is that our present idea of space-time, as developed from Einstein's theory of relativity, was suggested more by the basic philosophy of simplicity than by experimental evidence.

The advances made not long after the time of Plato by Eudoxus, incorporating the idea of basic simplicity as expressed in Pythagorean and Platonic philosophy, were made by an outstanding mathematician and astronomer. In fact Eudoxus marks the beginning of a new phase in Greek astronomy and must figure as one of a small number of remarkable innovators in astronomical thought. Eudoxus was the first to propose a model whereby the apparently complex motions of the heavenly bodies did indeed result from simple circular motion. He built an observatory on Cnidus and from there he observed the star Canopus. The star Canopus played an important role in early astronomy, for it is seen to set and rise in Cnidus yet one does no have to go much further north from there before it can never be seen. The observations made at Eudoxus's observatory in Cnidus, as well as those made at an observatory near Heliopolis, formed the basis of a book concerning the rising and setting of the constellations. Eudoxus, another who followed Pythagorean doctrines, proposed a beautiful mathematical theory of concentric spheres to describe the motion of the heavenly bodies. It is clear that Eudoxus thought of this as a mathematical theory, and did not believe in the spheres as physical objects.

Although a beautiful mathematical theory, Eudoxus's model would not have stood the test of the simplest of observational data. Callippus, who was a pupil of Polemarchus himself a pupil of Eudoxus, refined this system as presented by Eudoxus. The reason that we have so much information about the spheres ofEudoxus and Callippus is that Aristotle accepted the theory, not not as a mathematical model as originally proposed, but rather as spheres which have physical reality. He discussed the interactions of one sphere on another, but there is no way that he could have had enough understanding of physics to get anywhere near describing the effects of such an interaction. Although in many areas Aristotle advocated a modern scientific approach and he collected data in a scientific way, this was unfortunately not the case in astronomy. As Berry writes [2]:-

There are also in Aristotle's writings a number of astronomical speculations, founded on no solid evidence and of little value ... his original contributions are not comparable with his contributions to the mental and moral sciences, but are inferior in value to his work in other natural sciences ...

As Berry goes on to say, this was very unfortunate for astronomy since the influence of the writings of Aristotle had an authority for many centuries which meant that astronomers had a harder battle than they might otherwise have had in getting the truth accepted.

The next development which was absolutely necessary for progress in astronomy took place in geometry. Spherical geometry was developed by a number of mathematicians with an important text being written by Autolycus in Athens around 330 BC. Some claim that Autolycus based his work on spherical geometry On the Moving Sphere on an earlier work by Eudoxus. Whether or not this is the case there is no doubt that Autolycus was strongly influenced by the views of Eudoxus on astronomy. Like so many astronomers, Autolycus wrote a work On Risings and Settings which is a book on observational astronomy.

After Autolycus the main place for major developments in astronomy seemed to move to Alexandria. There Euclid worked and wrote on geometry in general but also making an important contribution to spherical geometry. Euclid also wrote Phaenomena which is an elementary introduction to mathematical astronomy and gives results on the times stars in certain positions will rise and set.

Aristarchus, Timocharis and Aristyllus were three astronomers who all worked at Alexandria and their lives certainly overlapped. Aristyllus was a pupil of Timocharis and in Maeyama [23] analyses 18 of their observations and shows that Timocharis observed around 290 BC while Aristyllus observed a generation later around 260 BC. He also reports an astounding accuracy of 5' for Aristyllus' observations. Maeyama writes [23]:-

The order of accuracy is an essential measure for the development of natural sciences. accuracy is in fact more than the mere operation of measuring. Accuracy increases only by virtue of active measuring. There cannot exist a high order of observational accuracy which is not connected with a high order of observations. Hence my assumption is that there must have been abundant accurate observations of the fixed stars made at least at the epochs 300 BC - 250 BC in Alexandria. They must have disappeared in the fires which frequently raged there.

Maeyama also points out that this is the period when the coordinate systems for giving stellar positions originated. Both the equatorial and the ecliptic systems appear at this time. But why were these observations being made? This is a difficult question to answer for on the face of it there seems little point in the astronomers of Alexandria striving for observational accuracy at this time. In [34] van der Waerden makes an interesting suggestion related to the other important astronomer who worked in Alexandria around this time, namely Aristarchus.

We know that Aristarchus measured the ratio of the distances to the moon and to the sun and, although his methods could never yield accurate results, they did show that the sun was much further from the earth than was the moon. His results also showed that the sun was much larger than the earth, although again his measurements were very inaccurate. Some historians believe that this knowledge that the sun was the largest of the three bodies, earth, moon and sun, led him to propose his heliocentric theory. Certainly it is for this theory, as reported by Archimedes, that Aristarchus has achieved fame. His sun-centred universe found little favour with the Greeks, however, who continued to develop more and more sophisticated models based on an earth centred universe.

Now Goldstein and Bowen in [16] attempt to answer the question of why Timocharis and Aristyllus made their accurate observations. These authors do not find a clear purpose for the observations, such as the marking of a globe. However van der Waerden in [34] suggests that the observations were made to determine the constants in the heliocentric theory of Aristarchus. Although this theory has strong attractions, and makes one want to believe in it, all the evidence suggests that Timocharis certainly began his observations some time before Aristarchus proposed his heliocentric universe.

Goldstein and Bowen in [16] make other interesting suggestions. They believe that the observations of Timocharis and Aristyllus recorded the distance from the pole, and the distances between stars. They argued that the observations were made by means of an instrument similar to Heron's dioptra. These are interesting observations since the work of Timocharis and Aristyllus strongly influenced the most important of all of the Greek astronomers, namely Hipparchus, who made his major contribution about 100 years later. During these 100 years, however, there were a number of advances. Archimedes measured the apparent diameter of the sun and also is said to have designed a planetarium. Eratosthenes made important measurements of the size of the earth, accurately measured the angle of the ecliptic and improved the calendar. Apollonius used his geometric skills to mathematically develop the epicycle theory which would reach its full importance in the work of Ptolemy.

The contributions of Hipparchus are the most important of all the ancient astronomers and it is fair to say that he made the most important contribution before that of Copernicus in the early sixteenth century. As Berry writes in [2]:-

An immense advance in astronomy was made by Hipparchus, whom all competent critics have agreed to rank far above any other astronomers of the ancient world, and who must stand side by side with the greatest astronomers of all time.

It is Hipparchus's approach to science that ranks him far above other ancient astronomers. His approach, based on data from accurate observations, is essentially modern in that he collected his data and then formed his theories to fit the observed facts. Most telling regarding his understanding of the scientific method is the fact that he proposed a theory of the motion of the sun and the moon yet he was not prepared to propose such a theory for the planets. He realised that his data was not sufficiently good or sufficiently plentiful to allow him to base a theory on it. However, he made observations to help his successors to develop such a theory. Delambre, in his famous work on the history of astronomy, writes:-

When we consider all that Hipparchus invented or perfected, and reflect upon the number of his works and the mass of calculations which they imply, we must regard him as one of the most astonishing men of antiquity, and as the greatest of all in the sciences which are not purely speculative, and which require a combination of geometrical knowledge with a knowledge of phenomena, to be observed only by diligent attention and refined instruments.

Although a great innovator, Hipparchus gained important understanding from the Babylonians. As Jones writes in [21]:-

For Hipparchus, the availability of the Babylonian predictive methods was a boon.

We will not describe the contributions of Hipparchus and Ptolemy in detail in this article since these are given fully in their biographies in our archive. Suffice to end this article with a quotation from [6]:-

Alexandria in the second century AD saw the publication of Ptolemy's remarkable works, the 'Almagest' and the 'Handy Tables', the 'Geography', the 'Tetrabiblos', the 'Optics', the 'Harmonics', treatises on logic, on sundials, on stereographic projection, all masterfully written, products of one of the greatest scientific minds of all times. The eminence of these works, in particular the 'Almagest', had been evident already to Ptolemy's contemporaries. this caused an almost total obliteration of the prehistory of the Ptolemaic astronomy.

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2. A Berry, A short history of astronomy (New York, 1961).
3. D R Dicks, Early Greek Astronomy to Aristotle (London, 1970).
4. J L E Dreyer, A history of astronomy from Thales to Kepler (New York, 1953).
5. B Hetherington, A chronicle of pre-telescope astronomy (Chichester, 1996).
6. O Neugebauer, A history of ancient mathematical astronomy (New York, 1975).
7. A Pannekoek, A history of astronomy (New York, 1989).
8. H Thurston, Early astronomy (New York, 1994).

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