Almagest

Overview

The Almagest is seven hundred pages in thirteen books, written in Greek at Alexandria around 150 CE. Its real title is the Mathematical Syntaxis; Almagest is what came back from Arabic, where it had been called al-majisti, the greatest, which tells you how the Islamic astronomers rated it.

It is a technical manual and it does not pretend otherwise. Ptolemy assumes you know Euclid, builds the trigonometry he needs from scratch in Book I, and then proceeds through models and tables. There is very little philosophy and almost no rhetoric. What there is, in quantity, is geometry and arithmetic.

Nobody reads it cover to cover except specialists, and the honest recommendation is to read Book I, the opening of Book III, and the first chapters of Book IX, and then read a modern account of how the models work. Toomer’s translation is the one to use; it is complete, accurate and full of the explanatory notes a non-specialist needs.

What the book is doing is worth stating plainly, because it is easy to be condescending about it. Ptolemy is not trying to say what the heavens are made of. He is trying to build geometry that will tell you where Mars will be next March, and his system does that to within a degree or two, which is close to the limit of what naked-eye observation could check.

The argument

Book I: the frame. Ptolemy sets out the cosmology before building anything. The heavens are spherical and rotate. The earth is spherical, is at the centre, is negligible in size compared with the distance of the stars, and does not move.

The arguments for a stationary earth repay reading, because they are good. If the earth rotated, a stone thrown straight up would land west of where it started, and clouds and birds would be left behind. The atmosphere would tear past. And if the earth moved around a centre, the stars would shift their relative positions over the year, which they visibly do not. Ptolemy knows that some have proposed a moving earth, mentions it, and rejects it on this evidence. He is wrong, and he is wrong for reasons that were sound until the physics of motion was rebuilt by Galileo and the distances of stars were understood to be enormous.

He then constructs the mathematical apparatus, including a table of chords, the ancestor of the sine table, computed at half-degree intervals, which is a formidable piece of arithmetic in a system without decimal fractions.

Books III to VI: sun and moon. The sun’s motion is handled with an eccentric circle, the earth displaced from its centre, which accounts for the unequal lengths of the seasons.

The moon is much harder, and Ptolemy’s model is a genuine advance over his predecessor Hipparchus. It accounts for the second irregularity, evection, that had defeated everyone. Its famous defect is that it requires the moon’s distance to vary enormously, so that its apparent diameter should nearly double in a month, which it plainly does not. Ptolemy does not mention this, and it is the first thing Copernicus complains about.

Book VI treats eclipses, and this is the part that made the book indispensable in practice.

Books VII and VIII: the stars. A catalogue of 1,022 stars in forty-eight constellations, with longitudes, latitudes and magnitudes. Much of it derives from Hipparchus with a constant added for precession, and there has been a long and inconclusive argument about how much Ptolemy observed himself. It remained the standard star catalogue until Tycho Brahe.

Books IX to XIII: the planets. The most sophisticated part, and the reason the system lasted.

Three devices do the work. The deferent, a large circle around a centre near the earth. The epicycle, a small circle whose centre rides the deferent and on which the planet actually moves, which accounts for retrograde motion, the apparent backward loop a planet makes. And the equant, which is Ptolemy’s own contribution and the source of all the later trouble: a point on the other side of the deferent’s centre from the earth, from which the motion of the epicycle’s centre appears uniform.

The equant is what makes the models accurate. It is also a violation of the principle Ptolemy states himself, that celestial motion must be uniform circular motion, because the motion is uniform about a point that is not the centre of the circle. Copernicus found this intolerable, said so, and built his own system largely to remove it. He therefore did not object to epicycles, which he kept, and used about as many as Ptolemy.

How to read it

Read Book I entire, and take the arguments for a stationary earth seriously as arguments. They are the best case anyone could make in 150 CE and they are a useful antidote to the idea that the old astronomy was credulous.

Then read a modern explanation of deferent, epicycle, eccentric and equant, with diagrams, before attempting the planetary books. Toomer’s notes will do this, as will any good history of astronomy.

Use Toomer’s translation. Older ones are unreliable and the notes here are what make the text usable.

Keep the purpose in view. Ptolemy is building a predictive instrument, and by that standard the Almagest is a triumph. Asking whether he believed the epicycles were real machinery is a question he mostly refuses, and his separate work, the Planetary Hypotheses, suggests he did give them a physical interpretation, so the refusal is tactical rather than principled.

Read it before Copernicus rather than after. The heliocentric argument is much more interesting when you know it was aimed at something that worked.

Questions it raises

• The arguments for a stationary earth are sound given the physics available. What does it take to recognise that a good argument rests on a premise nobody has thought to question?
• Ptolemy demands uniform circular motion and then introduces the equant, which breaks it. Is that pragmatism, inconsistency, or a tacit admission that the principle was never doing real work?
• His lunar model implies the moon’s size should visibly change and it does not. How should a theory’s known failures be weighed against its successes?
• Is a model that predicts correctly but posits machinery nobody can see a description of the world or a calculating device?
• Fourteen centuries is a long run. What made this system so hard to displace, and what does that suggest about theories that are currently secure?
• Copernicus kept the epicycles and removed the equant. What does that tell you about what he thought was actually wrong?