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EUDOXUS studied geometry under Archytas the Pythagorean. When a young man he visited Athens, and remained there two months with the view of hearing the lectures of Plato and others: but he entered into no intimate relations with Plato. Then he travelled in Egypt, and here composed his Octaëteris, a work on the correspondence of solar and lunar revolutions. Ultimately he took up his abode in Cyzicus, where he founded a school of geometry and astronomy. At the height of his reputation he paid a second visit to Athens, accompanied by many of his pupils. Here he may probably have seen Aristotle, who, in the Ethics, speaks in high terms of his moral character. Thence he returned to his native city, Cnidus, in Asia Minor, where he was received with every sign of respect. The tower from which he made astronomical observations was pointed out to travellers for many generations afterwards.
The titles of two of his astronomical works, the Mirror and the Phenomena, have been preserved. Their substance has been preserved, though not perhaps with great accuracy, in the poem of Aratus, a commentary on which is the first work of Hipparchus. In this work Eudoxus endeavoured to frame a map of the stars, and of the times of their rising and setting, with a view to determine the precise relation of the sun's path in the heavens to the equator. To represent the apparent motion of the sun and the planets, he devised a complicated system of spheres moving simultaneously with unequal velocities. For this he has been derided: but the method, developed and modified afterwards by Apollonius, Hipparchus, and Ptolemy, is strictly scientific in principle.
As a geometer, Eudoxus holds a very important place. Proclus tells us, in speaking of Euclid, that he arranged much of what Eudoxus had discovered. Archimedes, in one of his letters, expressly states that Eudoxus proved that the pyramid was the third part of the prism, and the cone the third part of the cylinder, of the same base and altitude; and further, that these theorems were discovered by a method similar to that which led to his own discovery of the quadrature of the parabola--that is, by the Method of Exhaustions indicated by Euclid, and developed in the 12th book. There is good reason also to attribute to Eudoxus the accurate doctrine of proportions contained in the 5th definition of the 5th book, as contrasted with the 21st proposition of the 7th book, which only applies to commensurable magnitudes. In dealing with this subject he developed the analytical method: proving that every solution greater or less than the one considered issued in contradiction.
The work of Eudoxus is mentioned by Comte as the point of definite separation between philosophy and science. Indeed, after his time the two sciences of mathematics and astronomy were usually pursued by different thinkers.
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| This biography is
reprinted from The New Calendar of Great Men. Ed. Frederic
Harrison. London: Macmillan and Co., 1920. |
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