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	Eudoxus (Site not responding. Last check: 2007-10-06)
		Eudoxus made important contributions to the theory of proportion, where he made a definition allowing possibly irrational lengths to be compared in a similar way to the method of cross multiplying used today.
		Eudoxus may have regarded his system of spheres simply as an abstract geometrical model, but Aristotle took it to be a description of the physical world.
		Eudoxus wrote about Egypt and the religion of that country with particular authority and it is clear that he learnt much about that country in the year he spent there.
	www.stetson.edu /~efriedma/periodictable/html/Xe.html (525 words)

	Eudoxus (Site not responding. Last check: 2007-10-06)
		Eudoxus was born in 408 B.C. in Cnidus.
		Eudoxus studied at Plato's Academy and was a student of Archytas of Tarentum.
		Eudoxus also devised a theory of planets carried on glassy spheres that were nested around the Earth in mountings like compass gimbals: rotations on these explained observed motions.
	www.angelfire.com /ca5/ancientgreecescience/eudoxus (169 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)

	TMTh:: EUDOXUS OF CNIDUS (Site not responding. Last check: 2007-10-06)
		Archimedes notes that Eudoxus was the first to prove that the cone and the pyramid are one-third respectively of the cylinder and prism with the same base and height.
		Eudoxus calculated that the ratio of the length to the width of the world was 2:1.
		Eudoxus was particularly interested in the climate in various parts of the world, and in the zones of the terrestrial globe with similar astronomical data (appearance of the night sky, length of longest day, etc.).
	www.tmth.edu.gr /en/aet/1/46.html (970 words)

	Eudoxus (Site not responding. Last check: 2007-10-06)
		Eudoxus of Cnidus was the son of Aischines.
		The proofs of these results are attributed to Eudoxus by Archimedes in his work On the sphere and cylinder and of course Archimedes went on to use Eudoxus's method of exhaustion to prove a remarkable collection of theorems.
		One argument in favour of thinking that Eudoxus believed in the spheres only as a computational device is the fact that he appears to have made no comment on the substance of the spheres nor on their mode of interconnection.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Eudoxus.html (2288 words)

	References for Eudoxus (Site not responding. Last check: 2007-10-06)
		L Corry, Eudoxus' theory of proportions as interpreted by Dedekind (Spanish), Mathesis 10 (1) (1994), 1-24.
		V E Thoren, Anaxagoras, Eudoxus, and the regression of the lunar nodes, J.
		I Yavetz, On the homocentric spheres of Eudoxus, Arch.
	www-gap.dcs.st-and.ac.uk /~history/Printref/Eudoxus.html (415 words)

	EUDOXUS - LoveToKnow Article on EUDOXUS (Site not responding. Last check: 2007-10-06)
		The Phaenomena of Aratus is a poetical account of the astronomical observations of Eudoxus.
		2), Eudoxus held that pleasure was the chief good, because (1) all beings sought it and endeavoured to escape its contrary, pain; (2) it is an end in itself, not a relative good.
		Aristotle, who speaks highly of the sincerity of Eudoxuss convictions, while giving a qualified approval to his arguments, considers him wrong in not distinguishing the different kinds of pleasure and in making pleasure the summum bonum.
	www.1911encyclopedia.org /E/EU/EUDOXUS.htm (290 words)

	Eudoxus Systems - Biography of Eudoxus
		Eudoxus of Cnidus (c.408 - c.355 BC) was one of the greatest Greek mathematicians.
		Eudoxus did not invent these, but carried them over from an earlier civilisation, most probably the Babylonians of c.
		It is close to the Greek islands of Cos and Rhodes and the city of Halicarnassus, where King Mausolus's tomb, the Mausoleum, was one of the seven wonders of the ancient world.
	www.eudoxus.com /eudoxus.html (302 words)

	Eudoxus (Site not responding. Last check: 2007-10-06)
		Proclus says that he invented the theory of proportions explained in Book V. Archimedes credits Eudoxus with the proof by mean of a certain Lemma (perhaps Book X 1) of the propositions that any pyramid is one-third of a prism sharing a common base and altitude (Book XII 7 Cor.
		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 (322 words)

	eudoxus
		Eudoxus studied mathematics from Archytas, who was Pythagoras' follower.
		One of the questions that Eudoxus was interested in was the problem of duplicating the cube.
		One of the most interesting and important contributions to mathematics by Eudoxus is his work on the theory of proportion.
	www.mathsisgoodforyou.com /people/eudoxus.htm (300 words)

	Eudoxus, of Cnidus (Site not responding. Last check: 2007-10-06)
		Work attributed to Eudoxus includes methods to calculate the area of a circle and to derive the volume of a pyramid or a cone.
		Probably Eudoxus regarded the celestial spheres as a mathematical device for ease of computation rather than as physically real, but the idea was taken up by Aristotle and became entrenched in astronomical thought until the time of Tycho Brahe.
		In mathematics Eudoxus' early success was in the removal of many of the limitations imposed by Pythagoras on the theory of proportion.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/E/Eudoxus/1.html (189 words)

	Eudoxus of Cnidus
		Eudoxus of Cnidus (Εύδοξος ο Κνίδιος), (408-355 BC) son of Aeschines, Greek mathematician, astronomer, geographer and philosopher, whose genius was apparent from a very young age.
		Archimedes notes in a letter to Eratosthenes that Eudoxus was the first to prove that the cone and the pyramid are one-third respectively of the cylinder and prism with the same base and height and that the formula was known to Democritus was he could not provide a proof.
		Eudoxus is considered to have found the Hippopede (Horse Foot) curve which in today terms can be written as a special form of the polar equation r
	www.mlahanas.de /Greeks/Eudoxus.htm (1506 words)

	[35.01] The Latitude and Epoch for the Origin of the Astronomical Lore of Eudoxus (Site not responding. Last check: 2007-10-06)
		Eudoxus reports on many astronomical lore items such as that the head of Draco skims the northern horizon and that Orion sets when Scorpius rises.
		Many of these lore items have their validity depend on the latitude and epoch of the observations on which the lore is based, so for example the two lore items just quoted will each yield rather fuzzy simultaneous constraints on the latitude and epoch of the observer.
		My results are; (1) All lore reported by Eudoxus were based on observations from the year 1130 ±80 BC and at a latitude of 36.0 ± 0.9 degrees north.
	www.aas.org /publications/baas/v35n5/aas203/345.htm (355 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)

	Eudoxus of Cnidus
		Eudoxus, born in the city of Cnidus in southern Asia Minor, in the last years of the Vth century B. C., is one of the great mathematicians of all times, and probably the greatest of ancient Greece's mathematicians.
		" Eudoxus, with the method of exhaustion he developed in geometry, is one of the fathers of integral calculus.
		He is also the inventor in astronomy of a scheme to account for the mouvement of planets based on concentric spheres turning within one another, a method that was to be complexified later by Aristotle, and he can thus be viewed as the father of scientific astromony.
	plato-dialogues.org /tools/char/eudoxus.htm (607 words)

	Eudoxus of Cnidus
		Eudoxus, of Cnidus, Greek savant, flourished about the middle of the 4th century BC.
		Several works have been attributed to him, but they are all lost; some fragments are preserved in the extant work of the astronomer Hipparchus.
		According to Aristotle's Ethics, Eudoxus held that pleasure was the chief good, because (1) all beings sought it and endeavored to escape its contrary, pain; (2) it is an end in itself, not a relative good.
	www.nndb.com /people/658/000096370 (313 words)

	Euclidís Elements, by far his most famous and important work, is a comprehensive collection of the mathematical ... (Site not responding. Last check: 2007-10-06)
		Eudoxus’ theory of proportion provides a necessary foundation, but it is Euclid’s use of Eudoxus’ method of exhaustion that is the key element to providing rigorous proofs.
		The method of exhaustion is a modern term that came into use during the seventeen century and refers to the approximation of a figure using a sequence of inscribed figures within it.
		Eudoxus, through his work in extending the theory of proportion and inventing the method of exhaustion, played a significant role in Euclid’s development of the Elements, considered to be one of the greatest works in history.
	jwilson.coe.uga.edu /emt668/EMAT6680.F99/Wise/essay7/essay7.htm (1902 words)

	Learn more about Eudoxus of Cnidus in the online encyclopedia. (Site not responding. Last check: 2007-10-06)
		Eudoxus of Cnidus (Greek Eυδοξοσ) (circa 408 BC - circa 347 BC) was a Greek astronomer, mathematician, physician, scholar and friend of Plato.
		The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Newton himself.
		An algebraic curve (the Kampyle of Eudoxus) is named after him
	www.onlineencyclopedia.org /e/eu/eudoxus_of_cnidus.html (237 words)

	Eudoxos Hippopede Machine (Site not responding. Last check: 2007-10-06)
		Horse training paths were typically laid out in a figure 8, which is the kind of retrograde motion suggested by this model.
		Its only fault is that the inner ring tends to oscillate whereas it should always rotate in a fixed plane.
		Eudoxus, Plato's pupil, figured that you only needed 26 simultaneous uniform motions to account for the motions of all seven celestial bodies.
	www.fas.harvard.edu /~scdiroff/lds/AstronomyAstrophysics/EudoxosHippopedeMachine/EudoxosHippopedeMachine.html (317 words)

	Astronomer (from Eudoxus of Cnidus) -- Encyclopædia Britannica
		Astronomer (from Eudoxus of Cnidus) -- Encyclopædia Britannica
		In two works, Phaenomena and Mirror, Eudoxus described constellations schematically, the phases of fixed stars (the dates when they are visible), and the weather associated with different phases.
		The city was an important commercial centre, the home of a famous medical school, and the site of the observatory of the astronomer Eudoxus.
	www.britannica.com /eb/article-2182 (810 words)

	Eudoxus (407-354 B.C.)
		In this work Eudoxus endeavoured to frame a map of the stars, and of the times of their rising and setting, with a view to determine the precise relation of the sun's path in the heavens to the equator.
		There is good reason also to attribute to Eudoxus the accurate doctrine of proportions contained in the 5th definition of the 5th book, as contrasted with the 21st proposition of the 7th book, which only applies to commensurable magnitudes.
		The work of Eudoxus is mentioned by Comte as the point of definite separation between philosophy and science.
	www.usefultrivia.com /biographies/eudoxus_001.html (414 words)

	Eudoxus and Aristotle (Site not responding. Last check: 2007-10-06)
		Eudoxus’ attempted to explain the cosmos with “elemental” geometrical concepts
		However, Eudoxus believed in the spheres only as a computational device is the fact that he appears to have made no comment on the substance of the spheres nor on their mode of interconnection
		Eudoxus may have regarded his system simply as an abstract geometrical model, but Aristotle took it to be a description of the physical world...
	www.d.umn.edu /~aroos/ptolemy/tsld008.htm (68 words)

	Spectator, July 21, 1711
		The Wife of Eudoxus, knowing that her Son could not be so advantageously brought up as under the Care of Leontine, and considering at the same time that he would be perpetually under her own Eye, was by degrees prevailed upon to fall in with the Project.
		For it seems Eudoxus was so filled with the Report of his Son's Reputation, that he could no longer withhold making himself known to him.
		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.
	tabula.rutgers.edu /spectator/text/july1711/no123.html (1368 words)

	Sample Chapter for Dolling, L.M., Statile, G.N., Gianelli, A.F.,: The Tests of Time: Readings in the Development of ...
		Blending careful observation with sophisticated mathematical constructs, Eudoxus sought to describe the motions of the heavens in terms of a series of concentric spherical shells, with the earth geometrically at the center of those shells.
		Since the axes of the spheres were in different planes and since the spheres could transmit their motions to one another through the axes, Eudoxus was able to "account" for the rather complicated motions that had been observed--for example, the retrograde motions of Mars, Jupiter, and Saturn.
		The shells of Eudoxus became hollow transparent spheres that carried the sun, moon, and five planets around the earth.
	www.pupress.princeton.edu /chapters/i7432.html (4915 words)

	Eudoxus of Cnidus -- Encyclopædia Britannica
		More results on "Eudoxus of Cnidus" when you join.
		Epicurus' predecessors were in physics Leucippus and Democritus and in ethics Antiphon Sophista, Aristippus of Cyrene, and Eudoxus of Cnidus, a geometer and astronomer.
		Epicurus differed from all of these in his systematic spirit and in the unity that he tried to give to every part of philosophy.
	www.britannica.com /eb/article-9033194 (734 words)

	Chapter A Story of an Heir of A Story of an Heir by Joseph Addison
		Eudoxus, at his first setting out in the world, threw himself into a court, where by his natural endowments and his acquired abilities he made his way from one post to another, till at length he had raised a very considerable fortune.
		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.
		They were both of them fathers about the same time, Eudoxus having a son born to him, and Leontine a daughter; but to the unspeakable grief of the latter, his young wife (in whom all his happiness was wrapt up) died in a few days after the birth of her daughter.
	www.bibliomania.com /0/5/91/338/8575/1.html (676 words)

	Plato
		One of his first disciples to distinguish himself in science was Eudoxus (409-356 B.C.) of Cnidus, the founder of observational cosmology.
		His most influential contribution was his view that the heavenly bodies move on a series of concentric spheres, of which the center is Earth, itself a sphere.
		Eudoxus had observed the irregularities in the movements of the planets.
	iweb.tntech.edu /chem281-tf/Hellen1.htm (2494 words)

	History of Geometry
		Eudoxus also did early work on integration using his method of exhaustion by which he determined the area of circles and the volumes of pyramids and cones.
		He was the first to show that ellipses, parabolas, and hyperbolas are obtained by cutting a cone in a plane not parallel to the base.
		He perfected integration using Eudoxus' method of exhaustion, and found the areas and volumes of many objects.
	geometryalgorithms.com /history.htm (2539 words)

	The Hutchinson Dictionary of Scientific Biography: Eudoxus (c. 408-c. 353 BC)@ HighBeam Research (Site not responding. Last check: 2007-10-06)
		Himself a great influence on contemporary scientific thought, Eudoxus was the author of several important works.
		Many of his theories have survived the test of centuries; work attributed to Eudoxus includes methods to calculate the area of a circle and to derive the volume of a pyramid or a cone.
		He also devised a system to demonstrate the motion of the known planets when viewed from the...
	www.highbeam.com /library/doc0.asp?DOCID=1P1:99916234&refid=ip_encyclopedia_hf (200 words)

	Eudoxus of Cnidus Biography / Biography of Eudoxus of Cnidus Main Biography
		Eudoxus of Cnidus Biography / Biography of Eudoxus of Cnidus Main Biography
		Eudoxus was born in Cnidus, a Greek colony in Asia Minor, into a family of physicians; he studied at the medical school there.
		Each Biography is written by a biographical expert or professional educator and is a complete resource on the individual.
	www.bookrags.com /biography-eudoxus-of-cnidus (260 words)

	Eudoxus' Planetary Model (Site not responding. Last check: 2007-10-06)
		Eudoxus of Critus devised an astronomical system, which lines among the most notable products of Greek genius.
		This is a simulation of the planetary model which he devised.
		Web pages are provided as a privilege to OU students to enhance their life long learning experience, and the opinions expressed herein are not necessarily those of the institution or its student body.
	students.ou.edu /S/Mohammad.I.Shaikh-1/EudoxusPlanetaryModel.html (231 words)

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