The Fundamentals of the Ptolemaic System
Partly on aesthetic grounds and partly because no other hypothesis suggested itself, Ptolemy generally retained the semimystical Pythagorean belief that nothing but motion at constant speed in a perfect circle is worthy of a celestial body. He combined simple circular motions to explain the complicated wanderings of the planets against the background of the fixed stars. Ptolemy explained retrograde motion by assuming that each planet moved in a circle called an epicycle, whose center was in turn carried around the earth in a circular orbit called a deferent. Thus the motion of all the planets around the earth in the Ptolemaic system was somewhat similar to the motion that modern astronomy ascribes to the moon as it revolves around the earth while the earth itself is revolving around the sun. The fact that the inferior planets (Venus and Mercury) never stray far from the sun was explained by the provision that the centers of their epicycles always had to lie on the line connecting the earth and sun.
In the final version of his system Ptolemy modified the postulate of uniform motion in order to explain the variations in the apparent speeds of the planets. He found that these variations could be reproduced most conveniently by displacing the earth from the center of the deferent to a point called the eccentric. He then assumed that the motion of the center of the epicycle along the deferent appeared uniform, not from the center of the deferent or from the eccentric, but from a third point symmetrically displaced from the eccentric, called the equant. This modification was tantamount to abandoning the postulate of uniform motion. Ptolemy considered it more important to achieve a closer agreement with the observed astronomical data than to adhere to any preconceived first principles. His work thus anticipates the positivist spirit of modern empirical science, which makes no ontological claim for its constructs but merely asserts that nature behaves "as if" these constructs lay behind appearances.
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