Ptolemy's Almagest, usually known as 'The Almagest', is an astronomy book written in the 2nd Century AD. It is a guide to the apparent motion of the Sun, Moon, stars and planets. It allows astronomers to predict accurately the positions of these objects in the sky at any time. The work was a scientific one, being based on careful observation of the skies, and includes sections explaining how to build the instruments used for making the observations. It was such a thorough work that it became the standard work on astronomy for more than a thousand years.

The calculation methods used in the Almagest were based on the assumption that the Earth was a sphere at the centre of the universe and that the other objects revolved around it. This is known as the 'geocentric' view of the universe, from 'geo' meaning Earth. This assumption went unchallenged until Nicolaus Copernicus published his theory that the Earth was a planet and that it and all the other planets revolved around the Sun (the 'heliocentric' view). While this fits better with the way we now think of the Solar System, Copernicus' work was not based on detailed observations and was more guided by esoteric concepts of perfection. His model of the Solar System, with the planets travelling in circular orbits at a constant speed, is less accurate than the Almagest when it comes to predicting the position of the planets in our sky. It was only with Johannes Kepler's discovery that the planets move in elliptical orbits at varying speeds that the central Sun model became a better way of describing the universe than the Almagest's central Earth model.

The author of the Almagest was a Greek-speaking mathematician from the city of Alexandria in Egypt. His name was Klaudios Ptolemaios, often written in its Latin form as Claudius Ptolemaeus, but in English usually just as Ptolemy¹. We don't know the exact dates of his birth and death but he probably lived from about 100 to 175 AD. Alexandria was a Greek city despite being in Egypt, and Ptolemy was well acquainted with the works of the most eminent Greek astronomer, Hipparchos (c190–c120 BC).

The Almagest was written some time between 141 and 161 AD, probably not earlier than 150 AD. Its published name was Mathêmatikê Syntaxis, meaning 'mathematical systematic treatise'. We haven't got Ptolemy's original manuscript but the work was considered important enough that it was copied many times. There are copies in Greek and also many translations into Arabic². In fact the first version of this work to become known in Western Europe during the Renaissance was a translation into Latin from Arabic. The name 'Almagest' comes from Arabic, being the Arabic word 'Al' ('the') with a corruption of the Greek word 'megistê' meaning 'greatest'. So Almagest means 'The Greatest'.

Worth Reading?

Much of the Almagest is of little interest to the modern reader because its elaborate calculations have become outdated. There is an interesting star catalogue giving descriptions and locations of just over a thousand of the brightest stars in the sky. It also can be fascinating to dip into the earlier sections of the book and see the methods Ptolemy used.

For example, he published trigonometrical tables. You may have been told that trigonometry was unknown to the ancient Greeks. In this respect, Ptolemy was not an ancient Greek, but a more recent one. It was during his era that trigonometry was invented. He only uses one trigonometric function, the chord, which is a variant on the sine function, being twice the sine of half the angle.

Ptolemy's assumptions that led him to pursue the geocentric (Earth-centred) view of the universe are particularly interesting because they are all perfectly reasonable:

• Objects when released fall towards the Earth. Heavy things fall hardest; light things like feathers fall slowly and really light things like clouds don't fall at all or so slowly that we can't detect it. Heavenly bodies such as the Sun, the Moon and planets don't fall at all so they must be very light.
• It's easy to move a light thing, while more difficult to move a heavy thing.
• The apparent motion of the heavens and the things in them can be explained by assuming that the heavens are stationary and the Earth is moving or that the Earth is stationary and the heavens are moving.
• It is reasonable to conclude, although not proved, that the Earth which is heavy and resistant to movement is fixed while the heavens which are light and easy to move are moving.

This was no crazy guy building a theory on ideas of the way things should be. It all makes perfect sense, and clearly Ptolemy would be the first to accept a different theory if it fitted the facts better.

We wouldn't recommend anybody to read Almagest from cover to cover - it's very heavy going and unless you are a student of Greek mathematics and science there's not a lot to be gained from it. On the other hand, dipping into it can be a fascinating foray into a different, much more logical way of looking at the universe.

The Star Catalogue

Ptolemy lived in Alexandria, while the astronomer Hipparchos had lived about 300 years earlier and further north, in what is now Greece. We know that Hipparchos published a star catalogue but there are no copies of his work in existence. Ptolemy's star catalogue appears to be just Hipparchos' catalogue with a few amendments. It goes into great detail on the stars that are visible from Greece, but is rather skimpy on stars that are visible from Alexandria but not from Greece, suggesting that Ptolemy threw in a few observations of his own but basically just re-used Hipparchos' star catalogue.

Constellations

The catalogue divides the stars into those in constellations, striking patterns of stars, and those which are not in a constellation but are close to it. For each star there is a brief description, usually saying where it is in the constellation, for example, 'on the horn of the bull'. Unfortunately there are no pictures of the constellations. The constellations are listed in order of closeness to the ecliptic north pole, starting with the Little Bear and working through the northern constellations, then the constellations along the ecliptic, finishing with the southern constellations, the last being the Southern Fish. The sky further south than this is not covered because it was not visible from Ptolemy's location in Egypt.

Ptolemy listed 48 constellations, 47 of which are still used to this day, although some with slightly different names. The 48th constellation, Argo, was considered by modern astronomers to be too big so it was split up into three: Carina, Vela and Puppis.

The modern constellations which are based on Ptolemy's constellations are as follows, presented in the order that Ptolemy listed them:

Ursa Minor, Ursa Major, Draco, Cepheus, Boötes, Corona Borealis, Hercules, Lyra, Cygnus, Cassiopeia, Perseus, Auriga, Ophiuchus, Serpens, Sagitta, Aquila, Delphinus, Equuleus, Pegasus, Andromeda, Triangulum, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpius, Sagittarius, Capricornus, Aquarius, Pisces, Cetus, Orion, Eridanus, Lepus, Canis Major, Canis Minor, Hydra, Crater, Corvus, Centaurus, Lupus, Ara, Corona Australis and Piscis Austrinus. Ptolemy's 48th constellation, Argo, was positioned between Canis Minor and Hydra.

Our names for these are in Latin, but Ptolemy used Greek versions. Most of them are the same but there are a few slight differences:

Stars

The star catalogue also gives the coordinates of each star, using an ecliptic-based coordinate system which is different from the one normally used today, but which can be converted simply to our system. Finally the brightness of the star is classified into one of six magnitudes, with 1 being brightest and 6 being only barely visible.

Only 11 of the stars in the catalogue are given specific names. These don't even include some of the brightest stars in the sky visible from Greece or Alexandria, such as Betelgeuse or Rigel. Ptolemy wasn't particularly interested in the stars, which he called the fixed stars, because they were fixed and didn't do anything. He was really only interested in the Sun, Moon and planets.

Of course, the names he gives to these stars are in Greek. Most of the star names we use today are Arabic, but some are Latin. We can divide the stars that Ptolemy names into three groups.

Those whose modern names are a re-spelling of Ptolemy's name:

• Arktouros, the bear guard, modern name Arcturus
• Antarês, the rival of Mars, modern name Antares
• Prokyôn, the pre-dog, modern name Procyon
• Kanôbos, of unknown meaning, modern name Canopus

Those whose modern names are translations into Latin of his name:

• Stachys, the ear of corn, modern name Spica
• Basiliskos, the little king, modern name Regulus
• Protrygêtêr, the bringer of harvest, modern name Vindemiatrix
• Aix, the she-goat, modern name Capella

Those whose names are different:

• Kyôn, the dog, modern name Sirius, the scorching (one)
• Lyra, the lyre, modern name Vega, the diving (eagle)
• Aetos, the eagle, modern name Altair, the soaring (eagle)

Some stars are listed in the catalogue twice because they were considered to belong simultaneously to two different constellations. For example, the 'top left' corner of the Great Square of Pegasus is listed as belonging to both Pegasus and Andromeda. This star is now officially alpha Andromedae, but was until 1930 also known as delta Pegasi.

Ecliptic Coordinates

The ecliptic is the apparent path of the Sun in the sky against the background of all the other stars (the 'fixed stars' in Ptolemy's terminology). It is a great circle, that is, a circle with its centre at the centre of the Earth. The part of the sky along and on either side of the ecliptic is called the Zodiac, from the Greek phrase 'Zôdiakos Kyklos', circle of animals. This is because virtually all of the constellations in the Zodiac represent animals. The ecliptic north and south poles are the points in the sky which are furthest from the ecliptic, and the line joining them is perpendicular to the plane of the ecliptic.

The positions of the stars are given in the catalogue in ecliptic coordinates. Just as longitude and latitude on the Earth's surface give the angular distance along the equator and from the equator, ecliptic coordinates give the angular distance along the ecliptic and away from it. Ptolemy explains that he uses this system because it allows old star positions to be easily corrected for the passage of time. The effect called precession causes the positions of all the stars to change over centuries, but if ecliptic coordinates are used, all the positions can be corrected by adding the same number to one of the two coordinates of every star. This means that he could use Hipparchos' data and correct it for the three centuries since it had been written down.

Epicycles

As seen from the Earth, the planets appear to move against the background of 'fixed stars'. Normally they move forward by a small amount, but sometimes they move backward along the path they have already traversed. This is called 'retrograde motion' and was a major headache for the astronomers of old to explain. We now know that this is because the Earth is moving around the Sun and so are the other planets. The motion of the Earth at times makes it look as if the outer planets, which are travelling more slowly, are going backwards. The same effect can be seen from a fast car passing a slow car on a motorway - it can look as if the slow car is going backwards relative to the fixed trees and houses at the side of the road.

Ptolemy thought that the Earth was fixed so he had to come up with some other explanation for the retrograde motion of the planets. He also thought that circular motion was the simplest type of motion. Ideally, the planets should travel around the Earth in perfectly circular orbits, but this could not explain the observed behaviour, so he came up with a more elaborate system. In this, an imaginary point travels around the Earth in a circle and the planet orbits this imaginary point in a smaller circle known as an epicycle. While this might sound ludicrous, we must remember that Ptolemy wasn't trying to explain why the planets did this. He was using a mathematical construct that would allow the calculation of the planet's position and his system did this very well.

In fact, the ellipse, the shape that we now know the planets travel in around the sun, is a particular case of the epicycle - if the planet orbits the imaginary point at the same angular speed as the point orbits the Earth but in the opposite direction, then it is in fact travelling around the Earth in an ellipse. So Ptolemy was working along the right lines. His mistake was trying to centre it all on the Earth. The planets don't travel around the Earth in ellipses, they travel around the Sun in ellipses, and the Earth also moves around the Sun in an ellipse, so the position of the planets relative to the Earth is a combination of two ellipses.

Ptolemy's Theories Finally Superseded

Ptolemy's view of the universe went unchallenged for nearly 14 centuries until 1543, when a Polish astronomer, Nicolaus Copernicus, published his alternative explanation. In this 'heliocentric' view, the Sun is at the centre of the Universe and the Earth is a planet. All the planets orbit the Sun in perfectly circular orbits at a uniform speed. Copernicus' theory was based on how he thought the universe should operate, rather than on actual observations. It was less accurate than Ptolemy's view in predicting the positions of the planets in the Earth's sky. As a result, Copernicus' view was little known in the scientific community and not highly regarded by those who did know about it.

In 1616, Italian astronomer Galileo Galilei came into conflict with the Roman Catholic Church over his support of Copernicus' heliocentric theory. In modern accounts of this conflict, Ptolemy and the Church are often presented together as closed-minded fools refusing to accept the real world, while Galileo was the wronged scientist who used facts rather than dogma. This view is unfair to Ptolemy who was very much the scientist and used all the facts at his disposal.

Galileo designed and built himself a telescope and discovered a few facts which were unknown to Ptolemy, such as that there are moons orbiting Jupiter, and that Venus and Mercury show phases in the same way as the Moon. While these supported the heliocentric theory, they didn't prove it. Galileo was reprimanded by the Church and eventually put under house arrest because they felt that the heliocentric theory contradicted the Bible. They were not willing to countenance such a thing without actual proof.

Ptolemy's world view was superseded when Kepler showed that the planets, including the Earth, travel around the Sun in elliptical rather than circular orbits and that they do not travel at constant speeds, but go faster when closer to the Sun. Kepler had published his laws between 1609 and 1619 but their implications were not realised until later that century. With Newton's publication of his laws of motion and gravitation in 1687, an explanation was provided as to why the planets should move in the way described by Kepler. Thus by about 1690, the world had an explanation of the Sun and planets, now known as the Solar System, which made sense and fitted all the known data.

Ptolemy the philosopher would have approved.

Image courtesy of archive.org