61. Thales Of Miletus [Internet Encyclopedia Of Philosophy] They commence with Mamercus, who was a pupil of Thales, and include Hippias of Elis,Pythagoras, Anaxagoras, eudoxus of cnidus, Philippus of Mende, Euclid, and http://www.utm.edu/research/iep/t/thales.htm

Thales of Miletus (62?-546 BCE) Table of Contents (Clicking on the links below will take you to that part of this article) The Writings of Thales Possible Sources for Aristotle Thales says Water is the Primary Principle Thales and Mythology ... Abbreviations The Writings of Thales Doubts have always existed about whether Thales wrote anything, but a number of ancient reports credit him with writings. Simplicius (Diels, Dox. p. 475) specifically attributed to Thales authorship of the so-called Nautical Star-guide. Diogenes Laertius raised doubts about authenticity, but wrote that 'according to others [Thales] wrote nothing but two treatises, one On the Solstice and one On the Equinox ' (D.L. I.23). Lobon of Argus asserted that the writings of Thales amounted to two hundred lines (D.L. I.34), and Plutarch associated Thales with opinions and accounts expressed in verse (Plutarch, De Pyth. or. 18. 402 E). Hesychius, recorded that '[Thales] wrote on celestial matters in epic verse, on the equinox, and much else' (DK, 11A2). Callimachus credited Thales with the sage advice that navigators should navigate by Ursa Minor (D.L. I.23), advice which may have been in writing. Diogenes mentions a poet, Choerilus, who declared that '[Thales] was the first to maintain the immortality of the soul' (D.L. I.24), and in

62. Lecture 6 Eudoxus' Proof That The Ratio Of Circles Is The Ratio Of Diameter Squa The most important was eudoxus of cnidus (408 - -355), who inventedthe Method of Exhaustion , the Greek version of limits. At http://www.maths.uwa.edu.au/~schultz/3M3/L6Euclid.html

Lecture 6: Eudoxus' proof that the area of a circle is a constant times diameter squared. Classical Greek mathematics The century after Plato -320 - -220 was the classical age of Greek mathematics. There were 20 or 30 mathematicians whose names have been recorded, although their writings don't all survive. The most important was Eudoxus of Cnidus (-408 - -355), who invented the "Method of Exhaustion", the Greek version of limits. At the end of this period, the major achievments were put in textbook form by the great teacher Euclid of Alexandria, whose dates are uncertain probably around -300, (Alexander -356 - -323). His "Elements" of 13 books was in use for 2000 years, and is the second most translated book. Books 16: plane geometry Books 79: number theory Books 10 : magnitudes Books 1113: solid geometry. For a more detailed index to Euclid, click here. These books contain definitions, postulates, theorems etc, much like today's mathematical texts, which are all descended from them. Euclid did not record the names of the discoverers, but his commentators did. The text Euclid Book XII, Proposition 2.

63. Eudoxus Of Cnidus - Wikipedia, The Free Encyclopedia The Geocentric Hierarchy The geocentric school of astronomy began with eudoxus of cnidus (409356 BC), aneminent resident at the academy of Plato (427-347 BC), several decades after http://www.wikipedia.org/wiki/Eudoxus_of_Cnidus

Eudoxus of Cnidus From Wikipedia, the free encyclopedia. Another article treats of Eudoxus of Cyzicus Eudoxus of Cnidus Greek 408 BC - circa 347 BC ) was a Greek astronomer mathematician physician , scholar and friend of Plato . Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus 's poem on astronomy He was a pupil in mathematics of Archytas in Athens . In mathematical astronomy his fame is due to the introduction of the astronomical globe , and his early contributions to understanding the movement of the planets His work on proportions shows tremendous insight into numbers ; it allows rigorous treatment of continuous quantities and not just whole numbers or even rational numbers . When it was revived by Tartaglia and others in the , it became the basis for quantitative work in science for a century, until it was replaced by the algebraic methods of Descartes Eudoxus invented the method of exhaustion , which was used in a masterly way by Archimedes . The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Newton himself.

64. Spheres And Planetaria (Sources) space, was a very early invention, the first one of that kind having been constructedby Thales of Miletus, and later marked by eudoxus of cnidus (a disciple http://www.mcs.drexel.edu/~crorres/Archimedes/Sphere/SphereSources.html

S O U R C E S Back to . . . Archimedes Home Page This section . . . Introduction Sources Cicero BC De Re Publica Book I , Sections 21-22 (In this passage Cicero writes of a discussion that takes place in 129 BC among a group of learned Romans. One of them relates an incident in 166 BC in which a Roman consul, Gaius Sulpicius Gallus, is at the home of Marcus Marcellus, the grandson of the Marcellus who conquered Syracuse in 212 BC (Translation by Clinton W. Keyes in Cicero: De Re Publica, De Legibus Loeb Classical Library Harvard University Press , Cambridge, 1928.) Cicero BC Tusculan Disputations Book I , Section XXV(63) For when Archimedes fastened on a globe the movements of moon, sun and five wandering stars, he, just like Plato's God who built the world in the Timaeus, made one revolution of the sphere control several movements utterly unlike in slowness and speed. Now if in this world of ours phenomena cannot take place without the act of God, neither could Archimedes have reproduced the same movements upon a globe without divine genius. (Translation by J. E. King in

65. Models Of Planetary Motion -- McConnell The Eudoxan Solution eudoxus of cnidus (c. 390 c. 337 BC) envisioned a system ofspheres whose combined uniform motion would resemble a hippopede, a figure http://faculty.fullerton.edu/cmcconnell/Planets.html

Models of Planetary Motion from Antiquity to the Renaissance Craig Sean McConnell Assistant Professor of Liberal Studies California State University, Fullerton Contents Introduction Retrograde Motion of the Planets The Eudoxan Solution From Hippopede to Retrograde Loops ... For Further Study Introduction Since antiquity, astronomers have attempted to explain the motions they observed in the heavens with geometrical models. This web site has been designed to help students in history of astronomy courses who are encountering these models for the first time. Often, students struggle to visualize how the static drawings in their textbook relate to the complex motions of the planets. By animating these images, I hope students will be able to more completely "see" how combinations of circles and spheres produced the distinctive retrograde motions exhibited by the planets. These images are not drawn to scale; they are meant only to serve as an aid to understanding how these models account for the motions in the heavens. Though this site includes a narrative description of the elements of these astronomical models, it is not intended to serve as a complete introduction to the history of ancient astronomy. For such an introduction, please consult one of the texts recommended

66. The Homocentric Spheres Of Eudoxus, Callippus, And Aristotle However, the original mathematical model of the cosmos was developed in thefourthcentury by the geometer eudoxus of cnidus (ca. 400 -347 BC). http://www.ouc.bc.ca/phys/dkay/eudoxus.htm

The Homocentric Spheres of Eudoxus, Callippus, and Aristotle (Note: This site is under construction last updated on 30 July 99) Ever since the publication of the Principia by Isaac Newton in 1687 one of the principal goals of physics has been the construction of mathematical models to describe how nature works. However, this idea did not originate with Newton. The most famous earlier examples are the laws of planetary motion of Johannes Kepler (1571 - 1630) and the planetary systems of Claudius Ptolemy (2nd century A.D.) and Nicolas Copernicus (1473 - 1543). As Copernicus drew on the methods of Ptolemy, so too did Ptolemy draw on earlier work, particularly that of Apollonius of Perga and Hipparchus of the third and second centuries B.C., respectively. However, the original mathematical model of the cosmos was developed in the fourth-century by the geometer Eudoxus of Cnidus (ca. 400 -347 B.C.). His geometrical model for describing the motions of the planets has come to be known as the Homocentric Spheres. By the beginning of the fourth century B.C. the most widely held view of the universe was that it consisted of a spherical earth at rest in the center of a rotating "celestial sphere" carrying the fixed stars. The planets moved in the region between these two spheres. Outside the sphere of stars was nothing, not even space. The complete celestial catalog was short. There were the fixed stars, and seven "wanderers", the planets Sun, Moon, Mercury (Hermes), Venus (Aphrodite), Mars (Ares), Jupiter (Zeus), and Saturn (Kronos).

67. Sample Chapter For Dolling, L.M., Statile, G.N., Gianelli, A.F.,: The Tests Of T One of Plato s pupils, eudoxus of cnidus (409 BC356 BC), was the firstastronomer to follow Plato s recommendation. Blending careful http://pup.princeton.edu/chapters/i7432.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE The Tests of Time: Readings in the Development of Physical Theory Edited by Lisa M. Dolling, Arthur F. Gianelli, and Glenn N. Statile Book Description Endorsements Class Use and other Permissions . For more information, send e-mail to permissions@pupress.princeton.edu This file is also available in Adobe Acrobat PDF format INTRODUCTION Although Heliocentric Theory is well known, describing it without the use of unwarranted or unjustified assumptions is not easy. Simply put, the theory suggests that the earth has two motions, a rotation on an axis and an orbital motion about the sun. Further, it maintains that the sun is central to, although not exactly in the center of, the orbits of all those heavenly bodies known as the planets, of which the earth is one. The physical reference frame used to determine the motions of this "solar" system is the frame of the fixed stars, bodies that do not appear to change their positions relative to one another. In this theory the dual motions attributed to the earth are considered to be in some sense real. The Geocentric View of Eudoxus Although not really interested in astronomy, the philosopher Plato had a great influence on the course of its early history. Because he perceived the heavens to be more perfect than the earth, Plato urged astronomers to describe celestial motions in terms of the most perfect of geometrical shapes, the circle. In fact, for Plato, the most perfect motion would be uniform circular motion, motion in a circle at a constant rate of speed.

68. The Web Eudoxia. eudoxus of cnidus. Eudoxus of Cyzicus. Eudes. Eudocia. Eudocia Macrembolitissa.Eudoxia. eudoxus of cnidus. Eudoxus of Cyzicus. Eugene. Eugene III. Eugene IV. http://www.slider.com/Enc/E/Eu.htm

The Web Encyclopaedia Shopping Ah‑ha ... Index The Web Encyclopaedia Shopping Ah-ha Kanoodle Findwhat Summary Top Encyclopaedia E Eu ... Free Search Toolbar Eu Still searching the hard way? Try the Free Slider Search Toolbar and spend less time searching!! www.trellian.com Sponsored Link EU Eu Euboea Eubulides ... ‰vvoia Slider in: Espa±ol Deutsch Dansk Nederlands ... Download the FREE Slider.com Search Toolbar!

69. Eudoxus :: Online Encyclopedia :: Information Genius Eudoxus. Online Encyclopedia See eudoxus of cnidus (ca.408 BC ca.347 BC) Greekastronomer and mathematician. Eudoxus of Cyzicus (fl.130 BC) Greek navigator. http://www.informationgenius.com/encyclopedia/e/eu/eudoxus.html

Quantum Physics Pampered Chef Paintball Guns Cell Phone Reviews ... Science Articles Eudoxus Online Encyclopedia See Eudoxus of Cnidus (ca. 408 BC - ca. 347 BC ) Greek astronomer and mathematician. Eudoxus of Cyzicus (fl.130 BC) Greek navigator. This is a disambiguation page; that is, one that just points to other pages that might otherwise have the same name. If you followed a link here, you might want to go back and fix that link to point to the appropriate specific page. This content from wikipedia is licensed under the GNU Free Documentation License Power Supplies Hardware Information Law Advice

70. MESSENGER: Astronomer Biographies Encke. eudoxus of cnidus (408355 BC) was a Greek astronomer, mathematicianand philosopher, one of the most renowned of his day. http://btc.montana.edu/ceres/MESSENGER/bios.htm

Astronomer Biographies Eugenios Antoniadi (1870-1944) was a Frenchman best known for his planetary observations of the planets Mercury and Mars. Using an 83 cm refracting telescope, he produced a detailed map of the surface of Mars. So accurate was this map that most of the features on it have been confirmed by recent spacecraft missions. In 1933, he became the first to produce a detailed map of the surface of Mercury, naming some of the surface features known today. Mercury's 450 km long Antoniadi ridge is named in his honor. Aristarchus of Samos (310-230 BC) was a Greek mathematician and astronomer who was an advocate of the heliocentric model, in which all the planets orbit around the Sun. This argument was fully accepted seventeen centuries later. Aristarchus' only surviving text is his Treatise on the Sizes and Distances of the Sun and Moon Rolf Dyce , together with Gordon Pettengill, measured the spin rate of Mercury using radar pulses reflected from the planet's surface. The two researchers concluded that Mercury requires only about 59 days (two-thirds of a orbital period) to rotate once about its axis, rather than the 88 days that had been claimed by earlier observers. He is Professor Emeritus at Cornell University.

71. Biography-center - Letter E project/eudoxus/eudoxus.htm; eudoxus of cnidus, wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Eudoxus.html;Euler, Leonhard www http://www.biography-center.com/e.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish E 282 biographies Eadred, www.britannia.com/history/monarchs/mon10.html Eadwig, www.britannia.com/history/monarchs/mon11.html Eagan, Edward www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=52407 Eagles, www.hotelcal.com Eakins, Thomas www.ibiblio.org/wm/paint/auth/eakins/ Eakins, Thomas www.getty.edu/art/collections/bio/a1729-1.html Eakins, Thomas www.pbs.org/wnet/americanmasters/database/eakins_t.html Eales, Henry www.whonamedit.com/doctor.cfm/1429.html Earl of Aberdeen, www.spartacus.schoolnet.co.uk/PRaberdeen.htm Earl of Derby, www.spartacus.schoolnet.co.uk/PRderby1.htm Early, Jubal Anderson civilwarhome.com/earlybio.htm Earnhardt (Ralph), Dale www.hickoksports.com/biograph/earnhardtd.shtml Easterly, Thomas Martin

72. Title eudoxus of cnidus Ca. 410 BCE to 355 BCE Eudoxus was one of the most famousstudents of Archytas, and also studied under Plato in Athens. http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/eudoxtext.html

EUDOXUS OF CNIDUS Ca. 410 BCE to 355 BCE Eudoxus was one of the most famous students of Archytas , and also studied under Plato in Athens. As such, he was almost certainly influenced by Pythagorean ideas. Eudoxus was an excellent mathematician and astronomer. Unfortunately, none of Eudoxus' works have survived, and our information about his work comes to us indirectly through other sources. Eudoxus made two major contributions to mathematics. The first was his theory of proportions. After Theaetetus discovered irrational numbers, a crisis arose in the mathematical community because many of the Pythagorean proofs did not account for the existence of irrationals, an assumption that rendered these proofs invalid. Eudoxus' theory of proportions, well documented in Euclid 's Elements , solved this problem, thus ending the crisis of irrationals. It is not entirely clear to what extent Eudoxus got his theory of proportions from Theaetetus' work, but history has generally credited it to Eudoxus. Eudoxus' second major contribution to mathematics was his method of exhaustion. It was well known by Eudoxus' time that the circumference of a circle can be approximated by inscribing a polygon in the circle and measuring the perimeter of that polygon. Eudoxus took this idea one step further and invented the method of exhaustion. He reasoned that by adding more sides to the inscribed polygon, a better approximation of the circumference, and hence p, is possible. The method of exhaustion involves inscribing polygons with successively more sides into a circle, thereby exhausting the small area between the circle and polygon. Although there is some speculation that

73. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï 365 BC in Alexandria, Egypt Died about 300 BC Eudoxus, eudoxus of cnidus Born 408BC in Cnidus (on Resadiye peninsula), Asia Minor (now Turkey) Died 355 BC http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=E

74. Greek And Copernican Astronomy eudoxus of cnidus (409356 BC) 27 concentric spheresfour for each planet andthree for the moon and sun; only simple circular motions; model failed to http://www.msu.edu/course/lbs/492/stillwell/greekastro.html

LBS 333 Topics in the History of the Physical Sciences Spring 1998 Lecture 3: Astronomical Systems: Plato to Copernicus The Pythagorean theory: planet and fixed stars distinguished; all celestial bodies-revolve around the central fire; no precise account of the movements of heavenly bodies (number mysticism, not practical applications) PLATONIC THEORY: Two kinds of movements: (1) sphere of the fixed stars (shared by all the heavenly bodies) and (2) the independent movements of the sun, moon, and planets along the ecliptic in an opposite sense to that of the movement of the fixed stars. Plato—a Pythagorean: astronomy is geometrical problems, not just pure observations; mathematical structure of the universe. Problem of the motions of the planets: wandering planets ; Eudoxus of Cnidus (409-356 BC) 27 concentric spheresfour for each planet and three for the moon and sun; only simple circular motions; model failed to account for the observed phenomena in at least four ways. 1) Figure 8 movements not like the observed variation of planetary retrogradations ;

75. History Of Astronomy: Persons (E) Very short biography; Bibliography and WWW links. eudoxus of cnidus (c.400 BC c. 347 BC) Short biography and references (MacTutor Hist. http://www.astro.uni-bonn.de/~pbrosche/persons/pers_e.html

History of Astronomy Persons History of Astronomy: Persons (E) Deutsche Fassung Earnshaw, Thomas (1749-1829) Portrait, letter, clocks Find more about Earnshaw with Alta Vista Eaton, Etta Maine (1869-1915) Short biography Eberhard, Gustav (1867-1940) Find documents about Eberhard with Alta Vista Eckert, Wallace John (1902-1971) Short biography and references (MacTutor Hist. Math.) Very short biography Eddington, Arthur Stanley (1882-1944) Short biography, photo, references, and links (Bruce medal.) Short biography and references (MacTutor Hist. Math.) Short biography and references Short biography Short biography (Eric Weisstein's Treasure Trove) Short biography Very short biography Find more about Eddington with Alta Vista Edgeworth, Kenneth Essex (1880-1972) Kenneth Essex Edgeworth. A biographical note , by Andrew Hollis From J. Brit. Astron. Assoc., 106, 6, 1996, p.354 Edison, Thomas Alva (1847-1931) Short biography and references (Eric Weisstein's Treasure Trove) Einbu [Enebo], Sigurd (1866-1946)

76. Eudoxus, Of Cnidus eudoxus, of cnidus (c. 400c. 347 BC). Greek mathematician and astronomer.He devised the first system to account for the motions http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/E/Eudoxus/1.html

Eudoxus, of Cnidus (c. 400-c. 347 BC) Greek mathematician and astronomer. He devised the first system to account for the motions of celestial bodies, believing them to be carried around the Earth on sets of spheres. 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. Eudoxus also established a test for the equality of two ratios. The model of planetary motion was published in a book called On Rates. Further astronomical observations were included in two other works, The Mirror and Phaenomena, providing the basis of the constellation system still in use today. In a series of geographical books with the overall title of A Tour of the Earth, Eudoxus described the political, historical, and religious customs of the countries of the E Mediterranean.

77. Cnidus cnidus was also the birthplace of eudoxus, a pupil of Plato at the Academywho became one of the brightest mathematicians of ancient Greece. http://plato-dialogues.org/tools/loc/cnidus.htm

Bernard SUZANNE Last updated November 15, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. By clicking on the minimap at the beginning of the entry, you can go to a full size map in which the city or location appears. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations City of southern Asia Minor, on a peninsula between the islands of Cos and Rhodes (area 6) Cnidus, a colony of

78. Ether, In Physics And Astronomy To Everest, Mount. Alphabetic Index To Entries. Euclid of Megara. Eudes. Eudocia. Eudocia Macrembolitissa. Eudoxia. eudoxusof cnidus. eudoxus of Cyzicus. Eugene III. Eugene IV. Eugene. Eugene of Savoy. http://www.bartleby.com/65/index81.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations Respectfully Quoted English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. ether, in physics and astronomy to Everest, Mount

79. Eudoxus Definition Meaning Information Explanation definition.com . eudoxus was the name of two ancient Greeks eudoxusof cnidus (c.408 BC - c.347 BC) Greek astronomer and mathematician. http://www.free-definition.com/Eudoxus.html

A B C D ... Contact Beta 0.71 powered by: akademie.de PHP PostgreSQL Google News about your search term Eudoxus Eudoxus was the name of two ancient Greeks Eudoxus of Cnidus (c. 408 BC - c. 347 BC ) Greek astronomer and mathematician. Eudoxus of Cyzicus (fl. 130 BC ) Greek navigator. Books about 'Eudoxus' at: amazon.com or amazon.co.uk Note: This article from Wikipedia is made available under the terms of the GNU FDL Further Search within Free-Definition Link from your web site to this article with this HTML tag: top

80. EUDOXUS eudoxus, of cnidus, Greek savant, flourished about the middle of the 4th centuryBC It is chiefly as an astronomer that his name has come down to us. eudoxus. http://29.1911encyclopedia.org/E/EU/EUDOXUS.htm

EUDOXUS EUDOXUS See J. A. Letronne, Sur les ecrites et les travaux dEudoxe de Cnide, daprbs L. Ideler (1841); G. V. Schiaparelli, Le Sfere omoceniriche di Eudosso (Milan, 1876) ; T. H. Martin in Acadimie des inscriptions, 3rd of October, 1879; article in Ersch ansi Grubers Allgemeine Encyklo~adie. EUDOXIA LOPUKHINA EUGENE

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