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Updated: June 2, 2025
Eudoxus discovered the method of exhaustion for measuring curvilinear areas and solids, to which, with the extensions given to it by Archimedes, Greek geometry owes its greatest triumphs.
But when Aratus wrote, the practice of separating the constellations from each other had been adopted; in fact, he derived his knowledge of them chiefly from Eudoxus, the astronomer and mathematician, who certainly would not have allowed the constellations to be intermixed.
Florio, the Name of the young Heir that lived with Leontine, though he had all the Duty and Affection imaginable for his supposed Parent, was taught to rejoice at the Sight of Eudoxus, who visited his Friend very frequently, and was dictated by his natural Affection, as well as by the Rules of Prudence, to make himself esteemed and beloved by Florio.
Hanno, the Carthaginian Herodotus visits Egypt, Lybia, Ethiopia, Phoenicia, Arabia, Babylon, Persia, India, Media, Colchis, the Caspian Sea, Scythia, Thrace, and Greece Pytheas explores the coasts of Iberia and Gaul, the English Channel, the Isle of Albion, the Orkney Islands, and the land of Thule Nearchus visits the Asiatic coast, from the Indus to the Persian Gulf Eudoxus reconnoitres the West Coast of Africa Cæsar conquers Gaul and Great Britain Strabo travels over the interior of Asia, and Egypt, Greece, and Italy.
I should have told my reader, that whilst Florio lived at the house of his foster-father, he was always an acceptable guest in the family of Eudoxus, where he became acquainted with Leonilla from her infancy. His acquaintance with her by degrees grew into love, which, in a mind trained up in all the sentiments of honour and virtue, became a very uneasy passion.
Eudoxus and Archytas had been the originators of this far-famed and highly prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as a means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams.
Lastly, Archimedes tells us that Democritus was the first to state, though he could not give a rigorous proof, that the volume of a cone or a pyramid is one-third of that of the cylinder or prism respectively on the same base and having equal height, theorems first proved by Eudoxus.
II Now Eudoxus thought Pleasure to be the Chief Good because he saw all, rational and irrational alike, aiming at it: and he argued that, since in all what was the object of choice must be good and what most so the best, the fact of all being drawn to the same thing proved this thing to be the best for all: "For each," he said, "finds what is good for itself just as it does its proper nourishment, and so that which is good for all, and the object of the aim of all, is their Chief Good."
E. of Eudoxus are two short crossed clefts, and on the N. a long cleft of considerable delicacy running from N.E. to S.W. It was in connection with this formation that Trouvelot, on February 20, 1877, when the terminator passed through Aristillus and Alphonsus, saw a very narrow thread of light crossing the S. part of the interior and extending from border to border.
In astronomy Eudoxus is famous for the beautiful theory of concentric spheres which he invented to explain the apparent motions of the planets and, particularly, their apparent stationary points and retrogradations. The theory applied also to the sun and moon, for each of which Eudoxus employed three spheres.
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