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Updated: June 2, 2025
As our eye falls upon Asia Minor and its outlying islands, we reflect that here were born such men as Thales, Anaximander, Anaximenes, Heraclitus, Pythagoras, Anaxagoras, Socrates, Aristarchus, Hipparchus, Eudoxus, Philolaus, and Galen. From the northern shores of the aegean came Lucippus, Democritus, and Aristotle.
Eudoxus and Archytas were the first who began to treat of this renowned science of mechanics, cleverly illustrating it, and proving such problems as were hard to understand, by means of solid and actual instruments, as, for instance, both of them resorted to mechanical means to find a mean proportional, which is necessary for the solution of many other geometrical questions.
The method of exhaustion is seen in operation in Eucl. XII. 1-2, 3-7 Cor., 10, 16-18. Props. 3-7 Cor. and Prop. 10 prove that the volumes of a pyramid and a cone are one-third of the prism and cylinder respectively on the same base and of equal height; and Archimedes expressly says that these facts were first proved by Eudoxus.
To conclude, the happy Pair were married, and half Eudoxus's Estate settled upon them. Leontine and Eudoxus passed the remainder of their Lives together; and received in the dutiful and affectionate Behaviour of Florio and Leonilla the just Recompence, as well as the natural Effects of that Care which they had bestowed upon them in their Education. No. 124. Monday, July 23, 1711. Addison.
About 368 years before Christ, Eudoxus, of Cnidus, whose desire of studying astronomy induced him to visit Egypt, Asia, and Italy, who first attempted to explain the planetary motions, and who is said to have discovered the inclination of the moon's orbit, and the retrograde motion of her nodes, is celebrated as having first applied geographical observations to astronomy; but he does not appear to have directed his researches or his conjectures towards the figure or the circumference of the earth, or the distances or relative situations of any places on its surface.
That observer had said that the obliquity corresponded to the side of a pentadecagon, or fifteen-sided figure, which is equivalent in modern phraseology to twenty-four degrees of arc. But so little is known regarding the way in which Eudoxus reached his estimate that the measurement of Eratosthenes is usually spoken of as if it were the first effort of the kind.
Eudoxus of Cnidus, endeavouring to account for the fact that the planets, during every apparent revolution round the earth, come to rest twice, and in the shorter interval between these "stationary points," move in the opposite direction, found that he could represent the phenomena fairly well by a system of concentric spheres, each rotating with its own velocity, and carrying its own particular planet round its own equator, the outermost sphere carrying the fixed stars.
Florio was no sooner arrived at the great House that stood in his Neighbourhood, but Eudoxus took him by the Hand, after the first Salutes were over, and conducted him into his Closet. He there opened to him the whole Secret of his Parentage and Education, concluding after this manner: I have no other way left of acknowledging my Gratitude to Leontine, than by marrying you to his Daughter.
During the whole Course of his Studies and Travels he kept up a punctual Correspondence with Eudoxus, who often made himself acceptable to the principal Men about Court by the Intelligence which he received from Leontine. In order to this, they both of them married much about the same time.
Its schools were empty, its teachers silent; but the houses in which Plato and his friend Eudoxus were said to have dwelt and studied were pointed out to the traveller, to warm his love of knowledge and encourage him in the pursuit of virtue. Memphis was the second city in Egypt, while Thebes and Abydos, the former capitals, had fallen to the size and rank of villages.
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