
Review of Short Phrases and Links 
This Review contains major "Eudoxus" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Eudoxus was the first person known to have recognized that the Earth rotates around the Sun.
 Eudoxus was the founder of the first known observatory.
 Eudoxus was the first to propose a model whereby the apparently complex motions of the heavenly bodies did indeed result from simple circular motion.
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 Eudoxus was the first Greek to make a map of the stars.
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 Eudoxus was the most reknown astronomer and mathematician of his day.
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 On returning to Cnidus, Eudoxus completed his studies.
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 The people sent a request to Eudoxus to write a constitution for a new government.
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 According to Aristotle, Eudoxus held pleasure to be the chief good, for all creatures sought it and all attempted to escape its opposite, pain.
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 He was taught for a while by Philolaus and he was a teacher of mathematics to Eudoxus of Cnidus.
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 We know that Callippus was a student in the School of Eudoxus.
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 These errors are partly to be attributed to Eudoxus himself, and partly to the way in which Aratus has used the materials supplied by him.
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 The original work of Eudoxus has been lost.
 The theory of proportions discovered by Eudoxus is here expounded masterfully by Euclid.
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 Since all his own works are lost, our knowledge of Eudoxus is obtained from secondary sources.
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 Aryabhatta independently concluded that the planets rotate around the Sun but, unlike Eudoxus, realized the orbits were ellipses rather than circles.
 Eudoxus also visited Sicily, where he studied medicine with Philiston, before making his first visit to Athens in the company of the physician Theomedon.
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 Theaetetus is also thought to be the author of the theory of proportion which appears in Eudoxus 's work.
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 From the school of Greek mathematics, Eudoxus (c.
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 Ptolemy appointed Eudoxus of Cyzicus, who made two voyages from Egypt to India.
 In the second or first century BC, Eudoxus of Cyzicus was the first Greek to cross the Indian Ocean.
 To explain the complex motion of Mars, Eudoxus had the second sphere rotate in roughly the opposite direction to the first, and at the same speed.
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 Retrograde motion was only first addressed almost a century after Philolaus by Eudoxus.
 In his Metaphysics, Aristotle developed a philosophical cosmology of spheres, based on the mathematical astronomy of Eudoxus and Callippus.
 Firstly there was a treatise by Eudoxus (unfortunately now lost) in which he named and described the constellations.
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 In the fourth century, Eudoxus of Cnidus wrote a book on the fixed stars.
 The basis of both integral and differential calculus, it was first applied by Eudoxus and later expanded by Archimedes.
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 On returning to Asia Minor, Eudoxus established his own school in Cyzicus.
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 He studied the works of all the great philosophers and geographers of the ancient world: Aristotle, Dicaearchus, Eudoxus, Ephorus, Cleon.
 According to Aristotle, Eudoxus explained the motions of all celestial bodes in terms of concentric spheres, with the earth at the center.
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 Aristotle was aware of the important discoveries of Eudoxus which affected profoundly the exposition of the Elements by Euclid.
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 Eudoxus had paved the way for Archimedes’ later study of volumes and surfaces in his work On the sphere and cylinder.
 Aratus 's poem on astronomy is based on a work of Eudoxus, and possibly also Theodosius of Bithynia's Sphaerics.
 Book V is an exposition of the work of Eudoxus, and is considered to be the greatest achievement of Euclidean geometry.
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 The first documented systematic technique capable of determining integrals is the method of exhaustion of Eudoxus (ca.
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 Eudoxus rigorously developed Antiphon 's method of exhaustion, which was used in a masterly way by Archimedes.
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 This trend was reinforced by Plato, the teacher of Eudoxus, who regarded geometry as the model of certain reasoning.
 The twosphere model devised by Plato and Eudoxus conceives of the heavens and the earth as a pair of concentric spheres.
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 Euclid must have studied in Plato's Academy in Athens to have learnt of the geometry of Eudoxus and Theaetetus of which he was so familiar.
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 Euclid changed the proofs of several theorems in this book so that they fitted the new definition of proportion given by Eudoxus.
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 Euclid proves these theorems using the "method of exhaustion" as invented by Eudoxus.
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 Hipparchus's Commentary on Aratus and Eudoxus was written in three books as a commentary on three different writings.
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 Only one work by Hipparchus has survived, namely Commentary on Aratus and Eudoxus and this is certainly not one of his major works.
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 Only one of his works, a commentary on the work of Aratus and Eudoxus, survives.
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 Hipparchus quoted from the text of Eudoxus in his commentary on Aratus.
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 Hipparchus is believed to have died on the Phaenomena of Eudoxus and Aratus").
 The Phaenomena of Aratus is a poetical account of the astronomical observations of Eudoxus.
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 Previously, Eudoxus of Cnidus in the 4th century BC had described the stars and constellations in two books called Phaenomena and Entropon.
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 This theory predated Ptolemy (it was first devised by Eudoxus of Cnidus; by the time of Copernicus it was associated with Averroes).
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 Eudoxus of Cnidus (410 or 408 BC – 355 or 347 BC) was a Greek astronomer, mathematician, scholar and student of Plato.
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Eudoxus
 Hipparchus' only preserved work is Toon Aratou kai Eudoxou Fainomenoon exegesis ("Commentary on the Phaenomena of Eudoxus and Aratus").
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 This is a critical commentary in two books on a popular poem by Aratus based on the work by Eudoxus.
 Aratus wrote a poem called Phaenomena which was based on the treatise by Eudoxus and proved to be a work of great popularity.
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Categories
 Cnidus
 Aratus
 Science > Mathematics > Number Theory > Euclid
 Exhaustion
 Commentary

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