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Topic: Eudoxus of Cnidos

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	Eudoxus of Cnidus (Site not responding. Last check: 2007-09-20)
		Eudoxus of Cnidus (Greek Eυδοξοσ) (circa 408 BC - circa 347 BC) was a Greek astronomer mathematician physician scholar and friend of Plato.
		Eudoxus invented the method of exhaustion which used in a masterly way by Archimedes.
		The work of Eudoxus and Archimedes precursors of calculus was only exceeded in mathematical sophistication rigour by Newton himself.
	www.freeglossary.com /Eudoxus_of_Cnidos (175 words)

	Eudoxus of Cnidus
		Eudoxus was born in Cnidos, on the Black Sea.
		Eudoxus was the most reknown astronomer and mathematician of his day.
		Eudoxus also demonstrated that the ratios of the volumes of two spheres is as the cube
	www.math.tamu.edu /~don.allen/history/eudoxus/eudoxus.html (759 words)

	Eudoxus
		Finally after traveling back to his home land of Cnidos, he died at the age of 53 in 355 B.C.E. He had written a book on practical astronomy, and the Eudemian Summary credits him with the authorship of the first five propositions of Book XIII of the Elements.
		On the basis of this and similiarly ambiguous evidence, it is widely believed Eudoxus was the creator of the so-called "method of exhaustion" that one finds in proofs about volumes and areas in ancient Greek texts.
		It is said that Eudoxus invented a curve called the hippopede ('horse-fetter'), which resembles the present-day symbol for infinity.
	www.math.sfu.ca /histmath/Europe/Euclid300BC/eudoxus.html (324 words)

	Eudoxus' Method: Introduction
		While the result is certainly important in the development of the ideas we have been discussing here, what is even more important for our later work in calculus is the method he uses in his argumentation.
		Eudoxus was the first to employ the method of exhaustion in the quadrature problem, a method that later geometers would return to again and again.
		The basic idea is this: to show that region R has the same area as region S, we use the logical device of the double reductio ad absurdum to structure an indirect proof.
	cerebro.xu.edu /math/math147/02f/eudoxus/eudoxusintro.html (635 words)

	Jeff’s Space and Time » Blog Archive » Almost Real (Site not responding. Last check: 2007-09-20)
		Eudoxus allowed two ratios to be compared even if the magnitude had no number (such as length in some unit) attached to it.
		Eudoxus would say we can conclude that Dedekind’s width-to-height ratio is greater than Euclid’s, even though we never measured the dimensions of the stamps.
		Eudoxus was the author of a number of astronomical works, including a star calendar and a treatise on the eight-year luni-solar cycle.
	jefflindstrom.com /blog/2006/03/27/almost-real (6301 words)

	Diogenes Laertius: Life of Eudoxus, from Lives of the Philosophers, translated by C.D. Yonge
		BY DIOGENES LAERTIUS, TRANSLATED BY C.D. Eudoxus was the son of Aeschines, and a native of Cnidos.
		One of his pupils was Chrysippus, of Cnidos, son of Erineus, who learnt of him all that he knew about the Gods, and the world, and the heavenly bodies; and who learnt medicine from Philistion the Sicilian.
		We also find another, who was a physician of Cnidos, who is mentioned by this Eudoxus, in his Circuit of the World, where he says that he used to warn people to keep constantly exercising their limbs in every kind of exercise, and their senses too.
	classicpersuasion.org /pw/diogenes/dleudoxus.htm (797 words)

	Ancient Greek literature - Wikipedia, the free encyclopedia
		Aratus wrote the 'Phaenomena', a poetic version of a treatise on the stars by Eudoxus of Cnidos, who had lived in the 4th century.
		Euclid is known for his 'Elements', much of which was drawn from his predecessor Eudoxus of Cnidus.
		The 'Elements' is a treatise on geometry, and it has exerted a continuing influence on mathematics.
	en.wikipedia.org /wiki/Ancient_Greek_literature (3630 words)

	Eudoxus
		I died in my home of Cnidos when I was fifty-three.
		I was the most renowned astronomer and mathematician of the day for advancing number theory, giving the first systematic explanation of the motions of the sun, moon, and planets, and introducing geometry into science.
		Before leaving, Eudoxus informed us that his plans for the rest of eternity include discovering how far pi goes and debates with other mathematical legends.
	www.3villagecsd.k12.ny.us /wmhs/Departments/Math/OBrien/eudoxus.html (560 words)

	Search Results for Aristotle
		Another passage recalls the fundamental assumption on which Eudoxus based his 'method of exhaustion' for measuring areas and volumes; and, of course, Aristotle was familiar with the system of concentric spheres by which Eudoxus and Callippus accounted theoretically for the independent motions of the sun, moon, and planets.
		Eudoxus may have regarded his system simply as an abstract geometrical model, but Aristotle took it to be a description of the physical world..
		The dialectical puzzles of the fifth-century Eleatics, sharpened by Plato and Aristotle in the fourth century, are complemented by the invention of precise methods of limits, as applied by Eudoxus in the fourth century and Euclid and Archimedes in the third.
	www-gap.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Aristotle&CONTEXT=1 (9198 words)

	Search Results for Plato
		There is some evidence to suggest that Eudoxus had little respect for Plato's analytic ability and it is easy to see why that might be, since as a mathematician his abilities went far beyond those of Plato.
		Plato reproached the disciples of Eudoxus, Archytas and Menaechmus for resorting to mechanics and instrumental means for resolving the problem of duplication of volume; for in their desire to find in some fashion, two mean proportionals, they resorted to a method that was irrational.
		W R Knorr, Plato and Eudoxus on the planetary motions, J. T Koetsier, Negation in the development of mathematics : Plato, Lakatos, Mannoury and the history of the intermediate-value theorem in analysis, in Perspectives on negation (Tilburg, 1995), 105-121.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Plato&CONTEXT=1 (7213 words)

	Lecture 3 (Site not responding. Last check: 2007-09-20)
		Mathematician, Eudoxus of Cnidos (c.400 - c.347 BCE), developed a system to bring some order to the complexities of planetary motion.
		Eudoxus treated each celestial body as a separate mathematical problem, but he tackled each of these problems in the same way.
		In his system, the motion of each planet (Mercury, Venus, Mars, Jupiter, and Saturn) was governed by a set of four nested concentric spheres—one to govern its daily motion, one to govern its motion through the zodiac, and two to account for the looping appearance of its retrograde motion.
	eee.uci.edu /clients/bjbecker/ExploringtheCosmos/lecture3.html (1018 words)

	Euclid, His Works and His Influences
		He also discussed the distinction between ideal circles and hand-drawn circles and that geometry has not yet been fully discovered.
		Eudoxus of Cnidos (408 - 355 B.C.E.) was famous for not only his mathematical skills, but also as a medical man, astronomer, philosopher and geographer.
		Euclid also wrote several mathematical books which were more advanced than the Elements.
	www.math.sfu.ca /histmath/Europe/Euclid300BC?C=N;O=D (401 words)

	Aristotle (Site not responding. Last check: 2007-09-20)
		Aristotle was aware of the important discoveries of Eudoxus which affected profoundly the exposition of the Elements by Euclid.
		One allusion clearly shows that Aristotle knew of Eudoxus's great Theory of Proportion which was expounded by Euclid in his Book V, and recognised the importance of it.
		by which Eudoxus and Callippus accounted theoretically for the independent motions of the sun, moon, and planets.
	idcs0100.lib.iup.edu /AncGreece/aristotle.htm (11448 words)

	ARISTOTLE biography
		On Aristotle’s arrival, Eudoxus of Cnidos (408-355 BC) was leading the school, a teacher in his own right, who had formed a successful school in Cyzicus of northwest Asia Minor.
		Apart from his study under Plato, Eudoxus had a Pythagorean education and a special interest in mathematics and astronomy.
		Plato was away to Syracuse (367/366-365 BC), in an effort to educate its young new ruler Dionysius II, and try to make reality of his political ideals.
	www.stenudd.com /myth/greek/aristotle/aristotle-04-athens.htm (6767 words)

	Dictionary of Greek and Roman Biography and Mythology, page 701 (v. 1) (Site not responding. Last check: 2007-09-20)
		Of Cnidos, has sometimes been confounded with the celebrated Stoic philosopher of the same name, who, however, lived about a century later.
		6), a pupil of Eudoxus of Cnidos and Philistion (Diog.
		Fabric.) He accompanied his tutor Eudoxus into Egypt (Diog.
	www.ancientlibrary.com /smith-bio/0710.html (836 words)

	A - Glossary for the British Library Catalogue of Illuminated Manuscripts (Site not responding. Last check: 2007-09-20)
		Manuscripts on the subject of astronomy or astrology often contain images associated with the constellations (such as Orion the hunter and Aquarius the water bearer) or diagrammatic representations of the universe and its components.
		Some of the major astronomical texts to appear in illuminated copies include: Cicero's Aratea, written in the first century B.C., a Latin translation of a third-century B.C. Greek verse text by Aratus, in turn based on a prose treatise, the Phoenomena, written by Eudoxus of Cnidos a century earlier; Ptolemy's Almagest (c.
		From the twelfth century, Arabic learning, which had preserved aspects of classical knowledge in astronomy and astrology as well as other subjects, increasingly influenced the West.
	prodigi.bl.uk /illcat/GlossA.asp (1621 words)

	Term paper on A History of the Development of Trigonometry
		Those astronomers had applied the trigonometry to the study of sky.
		B.C.) is called the founder of trigonometry although spherical geometry had been discussed by Eudoxus of Cnidos and Euclid from Alexandria.
		Theodosius of Tripoli and Menelaus of Alexandria had contributed fundamentally towards spherical trigonometry.
	www.termpapergenie.com /ahistory.html (2529 words)

	Man's Place in the Universe, by Alfred Russel Wallace
		Empedocles (444 B.C.) is said to have been the first who separated the planets from the fixed stars, by observing their very peculiar motions, while Pythagoras and his followers determined correctly the order of their succession from Mercury to Saturn.
		No attempt was made to explain these motions till a century later, when Eudoxus of Cnidos, a contemporary of Plato and of Aristotle, resided for some time in Egypt, where he became a skilful astronomer.
		In the same way, each of the five planets had four spheres, two moving like the first two of the moon, another one also moving in the ecliptic was required to explain the
	www.wku.edu /~smithch/wallace/S728-1.htm (10852 words)

	Diogenes Laertius Lives of the Philosophers: Thales, translated by C.D. Yonge
		And Alexander the Myndian agrees with him in the ninth book of his Traditions.
		(He is the man whom Eudoxus places among the seven wise men instead of Cleobulus ; but Plato inserts his name instead of Periander.) The God accordingly made this reply concerning him:
		The person who went to the temple to ask the question was Anacharsis ; but again Daimachus the Platonic philosopher, and Clearchus, state that the goblet was sent by Croesus to Pittacus, and so was carried round to the different men.
	classicpersuasion.org /pw/diogenes/dlthales.htm (2321 words)

	Schiller Institute—The Truth About Temporal Eternity
		Next, double repeatedly, at an equal speed, the number of sides of each of these respectively inscribed and circumscribed polygons.
		At that point in the lesson, our attention must be turned to the famous "method of exhaustion" associated with a mathematician of Plato's Academy of Athens, Eudoxus.
		Let the class ask itself: What is the relationship between the circular perimeter and the perimeters of the polygons when the n of 2
	www.schillerinstitute.org /fid_91-96/943-1_temp_eternity.html (11423 words)

	Astrology and Religion Among the Greeks and Romans: Lecture II. Babylon and Greece
		Now, about the period when Philip of Opus published or wrote the Epinomis, another pupil
		of Plato, the astronomer Eudoxus of Cnidos, declared: "No credence should be given to the Chaldeans, who predict and mark out the life of every man according to the day of his nativity."
		But like Eudoxus, Theophrastus, a little later, spoke of it in his treatise on "Celestial Signs": he regarded with surprise the claim of the Chaldeans to be able to predict from these signs the.
	www.sacred-texts.com /astro/argr/argr07.htm (5461 words)

	Alchemy Forum 1451-1500
		Does anyone know if the following 'Eudoxus' is the one to whom the "Six
		"Eudoxus of Cnidos: The greatest of all Greek astronomers, a contemporary
		No writings of Eudoxus survive -- his ideas have been pieced together
	www.levity.com /alchemy/frm1500.html (15260 words)

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