Hellenistic astronomy reached its apex with Claudius Ptolemy's Mathematical Syntaxis, or Almagest (taken from the Arabic ألمجسطي "al-mjsty" meaning "the greatest"), in the second century A.D., Ptolemy built on the theoretical models of previous astronomers, and took advantage of advances in quantitative analysis of astronomical observation made by Hipparchus (Lindberg 98-99). An avid believer in mathematics, Ptolemy advocated that mathematical astronomy and physical astronomy were two distinct fields, the latter being nothing more than guesswork.
Little is known about Ptolemy himself, no life history or portraits have survived. He was involved in every aspect of mathematical physics besides astronomy - including optics and cartography. His greatest work was the Almagest which drew together new and old astronomical methods in an exhaustive, technically sophisticated collection of thirteen books.
Book I : An introduction to astronomy, which contains Ptolomey's basic cosmology. It includes his theories about the movements of the Earth, celestial and terrestial physics, and mathematics as the form of true knowledge.
Book II : Measuring standards, definitions and reference points.
Book III : Solar Theory (derived from Hipparchus).
Books IV-VI : Lunar Theory.
Books VII-VIII : Star catalog and precession of the equinoxes.
Books IX-XIII : Planetary Theory.
Ptolemy’s astronomical models were so comprehensive and so skillfully done that he rendered earlier works essentially obsolete, and remained the definitive source of astronomic theory for several centuries. Ptolemy created a model explaining the movement of the Sun and all the planets up to Saturn on the celestial sphere. It was very successful at making quantitative predictions of the positions of the planets in relation to the fixed stars, although it had no relation to their physical movement.
The Ptolemaic system is based on three fundamental concepts: the eccentric model, the epicycle-on-deferent model and the equant point. The "eccentric circle" and epicycle concepts he took from previous astronomers.
Observations show that the seasons are not of equal length, and so the Sun must travel some parts of the ecliptic faster than others. This problem Ptolemy solved by moving the Earth away from the center of the Sun's path. As viewed from the center, when the Sun was behind the Earth its movement against the fixed stars would quicken, when in front, it would slow down. Another way to approach this same problem would be the introduction of epicycles, with a rotation contrary to the movement along the deferent. Ptolemy chose the "eccentric circle" model because it was simpler.
The epicycle-on-deferent model was necessary, however, in the case of planets to explain their retrograde motion. The deferent is the circular path the center of the epicycle follows in its motion across the Zodiak. The epicycle is a smaller circle the planet makes on the deferent. By requiring that the rotation of the epicycle be in the same direction as that of the deferent, and through the proper adjustments of the radius and angular speed of the epicycle, the retrograde motion of the planets against the fixed stars can be reconstructed.
Even the epicycles were not enough to make the model work however. Ptolemy had to introduce yet another concept he called the equant point. When the Earth is made to be offcenter in relation to the deferent, the point exactly opposite the Earth (with respect to the center) is the equant point. Ptolemy defined the uniformity of the motion along the circular deferent as uniform angular motion (equal angles swept in equal times) measured not at the center of the circle, but at the equant point. Predictive power necessitated a departure from the stronger form of uniformity.
The Ptolemaic system had many complications as can planely be seen. The above models had to be combined and sometimes additional techniques had to be used to force agreement with empirical data. In the case of the Moon for example, the center of the deferent itself revolves around the Earth. The fundamental role of circles along with the condition of uniform motion (even the weaker condition) were formidable hurdles, so the Ptolemaic system was an astonishing accomplishment, a true testimony to the geometrical prowess of the Greeks. One might of course criticize the blind adherence to uniform circular motion, but it should be remembered that even Copernicus, when he proposed his heliocentric theory, did not complain about the inticacies of the Ptolemaic system, he believed Ptolemy did not go far enough in preserving uniform circular motion. As a matter of fact, Copernicus' model also involved epicycles and Ptolemy's model was still superior to his!
Ptolemy did attempt to add physical substance to his model in the Planetary Hypothesis, but he acknowledges that this is a very theoretical and incomplete work.
It is this love of the contemplation of the eternal and unchanging which we constantly strive to increase, by studying those parts of these sciences which have already been mastered by those who approached them in a genuine spirit of enquiry, and by ourselves attempting to contribute as much advancement as has been made possible by the additional time between those people and ourselves.
--Ptolemy, Almagest (trans. Toomer, 37)
Here Ptolemy acknowledged two critical factors that supported his scholarship: the foundational work of his predecessors, and the amount of elapsed time since then, in which enough astronomical data was collected to permit him to create his model.
From all this we concluded: that the first two divisions of theoretical philosophy should rather be called guesswork than knowledge, theology because of its completely invisible and ungraspable nature, physics because of the unstable and unclear nature of matter; hence there is no hope that philosophers will ever be agreed about them; and that only mathematics can provide sure and unshakable knowledge to its devotees, provided one approaches it rigorously. For its kind of proof proceeds by indisputable methods, namely arithmetic and geometry.
--Ptolemy, Almagest
Almagest: A massive work on mathematical astronomy by Ptolemy
Tetrabiblos: One of the most complete works in astrology written by Ptolemy.
equant: A Noncentral point around which the planets move uniformly; a geometrical construction modifying the eccentric and epicycle-deferent models.
eccentric circle: A model of the Sun's orbit with the Earth a distance from the center; note that the circle is not realy eccentric, it is only descibed as eccentric with respect to the Earth.
epicycle-on-deferent model: A model of planetary orbits with the planet making a small circle called an epicycle, where the center of the epicycle moves along the deferent.
cartography: The study and practice of making representations of the Earth on a flat surface.