Eudoxus Quotes

And Pythagoras is reported to have been a disciple of Sonches the Egyptian arch-prophet; and Plato, of Sechnuphis of Heliopolis; and Eudoxus, of Cnidius of Konuphis, who was also an Egyptian. [Stromata, 1.15]

Though resident much of his life in the city of Cnidus on the coast of Asia Minor, Eudoxus was a student at Plato’s Academy, and returned later to teach there. No writings of Eudoxus survive, but he is credited with solving a great number of difficult mathematical problems, such as showing that the volume of a cone is one-third the volume of the cylinder with the same base and height. (I have no idea how Eudoxus could have done this without calculus.) But his greatest contribution to mathematics was the introduction of a rigorous style, in which theorems are deduced from clearly stated axioms.

Keep this constantly in mind: that all sorts of people have died—all professions, all nationalities. Follow the thought all the way down to Philistion, Phoebus, and Origanion. Now extend it to other species. We have to go there too, where all of them have already gone: . . . the eloquent and the wise—Heraclitus, Pythagoras, Socrates . . . . . . the heroes of old, the soldiers and kings who followed them . . . . . . Eudoxus, Hipparchus, Archimedes . . . . . . the smart, the generous, the hardworking, the cunning, the selfish . . . . . . and even Menippus and his cohorts, who laughed at thewhole brief, fragile business. All underground for a long time now. And what harm does it do them? Or the others either—the ones whose names we don’t even know? The only thing that isn’t worthless: to live this life out truthfully and rightly. And be patient with those who don’t.

Heartened up by this story, I began to draw upon his more comprehensive knowledge as to the ages of the pictures and as to certain of the stories connected with them, upon which I was not clear; and I likewise inquired into the causes of the decadence of the present age, in which the most refined arts had perished, and among them painting, which had not left even the faintest trace of itself behind. "Greed of money," he replied, "has brought about these unaccountable changes. In the good old times, when virtue was her own reward, the fine arts flourished, and there was the keenest rivalry among men for fear that anything which could be of benefit to future generations should remain long undiscovered. Then it was that Democritus expressed the juices of all plants and spent his whole life in experiments, in order that no curative property should lurk unknown in stone or shrub. That he might understand the movements of heaven and the stars, Eudoxus grew old upon the summit of a lofty mountain: three times did Chrysippus purge his brain with hellebore, that his faculties might be equal to invention. Turn to the sculptors if you will; Lysippus perished from hunger while in profound meditation upon the lines of a single statue, and Myron, who almost embodied the souls of men and beasts in bronze, could not find an heir. And we, sodden with wine and women, cannot even appreciate the arts already practiced, we only criticise the past! We learn only vice, and teach it, too. What has become of logic? of astronomy? Where is the exquisite road to wisdom? Who even goes into a temple to make a vow, that he may achieve eloquence or bathe in the fountain of wisdom? And they do not pray for good health and a sound mind; before they even set foot upon the threshold of the temple, one promises a gift if only he may bury a rich relative; another, if he can but dig up a treasure, and still another, if he is permitted to amass thirty millions of sesterces in safety! The Senate itself, the exponent of all that should be right and just, is in the habit of promising a thousand pounds of gold to the capitol, and that no one may question the propriety of praying for money, it even decorates Jupiter himself with spoils'. Do not hesitate, therefore, at expressing your surprise at the deterioration of painting, since, by all the gods and men alike, a lump of gold is held to be more beautiful than anything ever created by those crazy little Greek fellows, Apelles and Phydias!

The Greek astronomer Eudoxus described the motions of the heavenly bodies by means of the celestial globe, or sphere of heaven. He concluded that the stars were fixed to a sphere that rotated at a constant speed. The earliest complete description of the constellations themselves was given in Aratus of Soli’s poem The Phenomena, (270 B.C). The Alexandrian astronomer Ptolemy (c. 137 A.D.)

He saw how the virginal circles of Eudoxus had led to a more coherent astronomy, how the conic sections of Apollonius had prefigured the spirit of universal gravitation. The world had its uses, yes; ideas could be rotated to expedient planes. It wasn’t his method to test the disposition of the physical universe but this didn’t “mean he reacted skeptically to those who drove hooks into nature. He considered the case of Archimedes, son of astronomer, floating body, lever adept, nude runner, catapulter, weigher of parabolas, tactician of solar power, sketcher of equations in sand and with fingernail on own body anointed in after-bath olive oil, killed by dreamless Romans.