Each circular celestial motion is physically the motion of a single body.The fixed stars, planets, sun, and moon, as we see them, may be thought of as knots or pimples that occur on some of the celestial spheres. The model that Eudoxos produces to satisfy (1) - (5) has each motion being physically the rotation of a celestial sphere. Again, we have no way of knowing whether Aristotle's justifications for (5), that the element of the celestial bodies has a natural motion in a circle about the center of the universe, has any bearing on the thought of Eudoxos. True, the earth is kept as the center of the motion of the first stars, and the general area where the earth is located contains the centers of the principal motions of the the stars with the earth also inside those motions yet, other motions are later introduced which do not even have the earth within them (epicycles). Nonetheless, it was the first to be rejected by Greek astronomers, probably some time in the late 3rd or early 2nd century BCE. However, it might well be grounded in a view that (1) is meaningless without (5). The basis for principle (5) is harder to discern. So any geometrical theory of somewhat circular motion would have to be resolved into regular circular motion if it were to be treated mathematically with any reasonable depth. It should also be kept in mind, however, that regular, circular motion is mathematically more tractable than any alternative available in the fourth century BCE. Certainly, such a view may be found in the justification for such principles in the writings of his junior contemporary and colleague, Aristotle. Most historians have seen a more fundamental metaphysical principle in making celestial motion regular and circular, that the universe is perfect and that this is the simplest and most perfect motion. There is no way of knowing why Eudoxos adopted these five principles. It would have been implicit in the astronomy of Eudoxos. The qualification in (4) is significant only in the context of Ptolemy's later introduction of models which distinguish the center of the motion from the center of the path of the motion. In other words, the models must preserve or save the phenomena. The apparent irregular and non-circular motions of celestial bodies is a result of the combinations of real, circular motions that satisfy principles (1) - (5).This means constructing the apparent motions as combinations of circular motions, the basic idea behind most subsequent Greek mathematical astronomy and the basis of mathematical astronomy from Ptolemy up to Kepler. Since the apparent motion of all celestial bodies is neither circular nor regular, though it is about the earth, Eudoxos needed to construct models that preserved the five principles and the appearances. The center of all celestial motion is the center of the universe.The center of the path of any celestial motion is the same as the center of its motion.The earth is the center of the universe.The first to present a general, geometrical model of celestial motion, Eudoxos started with five basic principles. CE), although the last is our principal source for his astronomical models. Our principal sources for his astronomy are Aristotle, Aratus (3rd cent. However, his most important work was in geometry, the theory of proportion, and astronomy. A polymath, he made important contributions to geography, metaphysics, and ethics. Return to Vignettes of Ancient MathematicsĮudoxos of Knidos was born approximately 395-390 BCE and lived 53 years. Eudoxos of Knidos (Eudoxus of Cnidus): astronomy and homocentric spheres©.
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