On Ptolemy's Theory of the Motion of Heavenly Spheres

In Ptolemy's explanation of the movement of heavenly spheres, he introduces two separate theories on the sun's movement about the earth. The first of these is that the sun, and the other planets, moves in a perfect circle equal to that about the earth but around a point slightly removed from it, and the second is that they each move in individual circles whose centers are on the ecliptic. He comes to these ideas in trying to explain the anomaly of the sun, that is, its irregular motion.

It seems that Ptolemy's general purpose is to find a regular pattern in the motions of these bodies, and in doing so adheres very strongly to the idea of regular circles and constant- both continuous and regular- motion about these circles. To the reader such as myself, this limit he imposes on his theories seems to be fairly narrow and idealistic. However, taking into account both the views of astronomy in his time and the work of his predecessors that he uses to build upon (Euclid, Plato, Apollonius, Hipparchus, and others) this seemingly idealistic approach actually seems the most logical for Ptolemy to take. The problems that this causes him seem like red flags, but he does not seem bothered by these in the least and is constantly finding ways to account for them. Actually he seems to be quite the optimist. While this gives the impression, at least to me, that his proofs are very contrived, it is at the same time very admirable to see someone have such faith in an idea and take such pains to prove it.

Ptolemy's treatment of his original hypothesis says a great deal in turn about himself as a scientist, mathematician, and even philosopher. By this I mean that characteristics of each of these seem to be shown by his choice of theory, his exploration of it, and the way in which he deals with the problems that arise. The idea of constant and regular motion seems very philosophical in regard to the logic and awe with which he explores this 'phenomena'. It does remind me in many ways of the Timaeus, but is also philosophical in they way that I found Euclid to be, mainly in trying to explain the world we know and see in terms of an ideal situation. The difference I believe is that Euclid realized that the things he dealt with were in a sense forms, that they did not physically exist in our world. Ptolemy, on the other hand, is thoroughly convinced that his method explains the actual motions of the universe. Perhaps also the fact that anything separate from the earth must have seemed and still does seem very awesome and intriguing gave him a little more liberty in explaining these bodies. His work as a mathematician is evident, and my view of him as a scientist arises from the fact that he tries to explain natural phenomena that he sees not simply through speech or logic, as a philosopher would, but also through mathematics. He needs all of these abilities to work through problems of the complexity and magnitude that he does.

In these problems, I believe the greatest is the aforementioned anomaly of the sun. He first proves that the sun revolves about the earth in a perfect circle, but it is its apparent irregularity in motion that forces him to create the idea of the eccentric. He realizes that the sun moves at different rates throughout one revolution about the earth, in such a way that the length of days changes throughout the year, and most importantly that the sun actually appears to be moving backwards along the concentric circle. He shows that the sun moves in a regular circular motion about a fixed point that is not the earth, the eccentric hypothesis, which he uses to explain the different speeds of the sun's revolutions. Included in this are the concepts of apogee and perigee, the explanations of the solstices.

To account for all of this another way, he introduces the second idea of epicycles. In this he reasons that the sun moves in a circular motion, the diameter of this epicycle being equal to distance by which they apogee and perigee vary from the ecliptic, explaining its apparent 'backwards' motion.

I have a problem distinguishing the two theories, for it seems necessary that they coexist in order for his system to function in accordance with both his previous ideas and his actual observations. For, to hold with his theory on regular movement, the sun must move about the earth in a regular, predictable way. The sun must move about the earth regularly while its distance from the earth changes. I am not sure, however, if it is so easy to combine the two theories because while they seem to explain the same thing, neither more stable an argument than the other. Ptolemy even admits that, as long as the ratio of the distance between the center of vision and center of eccentric to the radius of the eccentric in the eccentric hypothesis stays in proper ratio with that of the radius of the epicycle and the radius in the deferent in the epicycle hypothesis, the results of both hypotheses will be the same. He goes on, however, to prove these same results in several situations. Gradually he moves away from the epicycle theory and progresses with the eccentric, as it seems simpler and in turn, more in accordance with his initial ideas of natural simplicity and order.