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Updated: September 2, 2025
He therefore placed the earth in the central position, and in succession revolved round her the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn; beyond the orbit of Saturn came the firmament of the fixed stars. As to the solid crystalline spheres, one moving from east to west, the other from north to south, these were a fancy of Eudoxus, to which Ptolemy does not allude.
EUDOXUS. A bright deep ring-plain, about 40 miles in diameter, in the hilly region between the Mare Serenitatis and the Mare Frigoris, with a border much broken by passes, and deviating considerably from circularity.
Immediate satisfaction, or relief, and those who confer it, are treated with contempt, and presented as in hostility to the perfection of the mental structure. The Stoics altered this theory by saying that only the first of the three was bonum; the others were merely praeposita or sumenda. Lastly, it was maintained by Eudoxus, one of the most estimable philosophers contemporary with Aristotle.
But Plato sent of his disciples and friends, Aristonymus to the Arcadians, to set in order their commonweal, Phormio to the Eleans, and Menedemus to the Pyrrhaeans. Eudoxus gave laws to the Cnidians, and Aristotle to the Stagirites, who were both of them the intimates of Plato. And Alexander the Great demanded of Xenocrates rules and precepts for reigning well.
This is no more the case than that the spheres of Eudoxus and Callippus were supposed to be real. Both were introduced only to illustrate the mathematical conception upon which the solar, planetary, and lunar tables were constructed.
The arguments urged by Eudoxus as proving pleasure to be the chief good, are, That all beings seek pleasure; and avoid its opposite, pain; that they seek pleasure as an end-in-itself, and not as a means to any farther end; that pleasure, added to any other good, such as justice or temperance, increases the amount of good; which could not be the case, unless pleasure were itself good.
Eudoxus brought it with him to Egypt, and subjected it to the inspection of several pilots: they pronounced it to be the prow of a small kind of vessel used by the inhabitants of Gadez, to fish on the coast of Mauritania, as far as the river Lixius: some of the pilots recognised it as belonging to a particular vessel, which, with several others, had attempted to advance beyond the Lixius, but had never afterwards been heard of.
He observed it in the ring-plain Eudoxus, crossing the southern side of the floor from wall to wall; and also in connection with the prominent cleft running from the north side of Burg to the west of Alexander, and in some other situations. He terms these phenomena Murs enigmatiques. Apparent prolongations of clefts in the form of rows of hillocks or small mounds are very common.
Eudoxus apparently approached the figure to be measured from below only, i. e. by means of figures successively inscribed to it. Archimedes approaches it from both sides by successively inscribing figures and circumscribing others also, thereby compressing them, as it were, until they coincide as nearly as we please with the figure to be measured.
Plato and Eudoxus spent thirteen years in Heliopolis for the purpose of extracting the scientific knowledge of the Egyptian priests, yet they learned but little beyond the fact that the solar year was a trifle beyond three hundred and sixty-five days. No great names have come down to us from the priests of Babylon or Egypt; no one gained an individual reputation.
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