Euclid's Elements and Ptolemy's Almagest

The modern world inherited two major scientific treaties from the civilization of Ancient Greece.

The first of these, the Elements of Euclid, is a large compendium of mathematical theorems concerning geometry, proportion, and number theory. These theorems were not necessarily discovered by Euclid himself--being largely the work of earlier mathematicians, such as Eudoxos of Cnidus, and Theaetetus of Athens--but were arranged by him in a logical manner, so as to demonstrate that they can all ultimately be derived from five simple axioms. The Elements is rightly regarded as the first, largely succesful, attempt to construct an axiomatic system in mathematics, and is still held in high esteem within the scientific community.

The second treatise, the Almagest of Claudius Ptolemy, is an attempt to find a simple geometric explanation for the apparent motions of the sun, the moon, and the five visible planets in the earth's sky. On the basis of his own naked-eye observations, combined with those of earlier astronomers such as Hipparchus of Nicaea, Ptolemy proposed a model of the solar system in which the earth is stationary. According to this model, the sun moves in a circular orbit, (nearly) centered on the earth, which maintains a fixed inclination of about $23^\circ$ to the terrestrial equator. Furthermore, the planets move on the rims of small circles called epicycles, whose centers revolve around the earth on large eccentric circles called deferents--see Fig. 30. The planetary deferents and epicycles also maintain fixed inclinations, which are all fairly close to $23^\circ$, to the terrestrial equator.

The scientific reputation of the Almagest has not fared as well as that of Euclid's Elements. Nowadays, it is a commonly held belief, even amongst scientists, that Ptolemy's mistaken adherence to the tenets of Aristotelian philosophy--in particular, the immovability of the earth, and the necessity for heavenly bodies to move uniformly in circles--led him to construct an overcomplicated, unwieldy, and faintly ridiculous model of planetary motion. As is well-known, this model was superseded in 1543 CE by the heliocentric model of Nicolaus Copernicus, in which the planets revolve about the sun in circular orbits. The Copernican model was, in turn, superseded in the early 1600's CE by the, ultimately correct, model of Johannes Kepler, in which the planets revolve about the sun in eccentric elliptical orbits.

The aim of this treatise is to re-examine the scientific merits of Ptolemy's Almagest.