41. Eudoxus eudoxus of cnidus. Born 408 BC in Cnidus, now Knidos, Turkey, died 355 BC in Cnidus.Eudoxus studied mathematics from Archytas, who was Pythagoras follower http://www.mathsisgoodforyou.com/people/eudoxus.htm

Eudoxus home courses topics theorems ... timeline Eudoxus of Cnidus Born 408 BC in Cnidus, now Knidos, Turkey, died 355 BC in Cnidus 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. He was also interested in number theory and the theory of music. Another of his interests was geography, and he wrote a book called Tour of the Earth , but there is no surviving copy of it. One of the most interesting and important contributions to mathematics by Eudoxus is his work on the theory of proportion. He looked at various types of lengths and where others have come to a standstill in front of a problem of how to compare lengths which could be measured by rational and irrational numbers, Eudoxus came to a solution: he made a definition allowing possibility of using irrational lengths and comparing them with the rational by using the method of cross multiplication. As we know, irrational numbers are those which cannot be written or expressed as a fraction of two rational numbers. They occur in nature and in mathematics quite often - Pi is an irrational number, as is Eudoxus' theory appears in Euclid's Elements , Book V, definition 4: it states that "magnitudes are said to have a ratio to one another which is capable, when a multiple of either may exceed the other."

42. Math Lessons - Eudoxus Of Cnidus Math Lessons eudoxus of cnidus. eudoxus of cnidus. Another article treatsof Eudoxus of Cyzicus. eudoxus of cnidus (Greek E?d?s) (410 or 408 BC http://www.mathdaily.com/lessons/Eudoxus_of_Cnidus

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Ancient mathematicians Eudoxus of Cnidus Another article treats of Eudoxus of Cyzicus Eudoxus of Cnidus Greek or 408 BC or 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.

43. Eudoxus- Germantown Academy Mathematical Biographies Eudo Its eudoxus of cnidus, and you are very welcome. eudoxus of cnidus Dictionary of Scientific Biography Volume Three New York, New York, http://www.germantownacademy.org/academics/US/Math/Millar/Eudoxus/Beer.htm

"Edoxus of Cnidus " by Mitchell Beer '00 Mitch of Springfield : Pleasure to speak with you today Eudoxus. Eudoxus of Cnidus Mitch: Please we all don't speak ancient Greek here. Eudoxus: Sorry about that, it is a pleasure to have returned from the grave to speak with you today Mitch. Mitch: Firstly before we start Eudoxus, can I call you Eudo? Eudo : No. Mitch: Well then Eudo, how about we start with you and Cnidus. Eudo: I said you couldn't call me Eudo, but Cnidus is a quaint little town on the Resadiye peninsula in Asia Minor. I was born in 408, not a particularly interesting year. Actually the only reason it is interesting is because I was born then. Died in the same place too in 355. Mitch: How about your daddy. He too had a strange name. Eudo: What do you expect; we were ancient Greeks. He was Aischines. Mitch: A pleasant name as well. Let's now move to your travels and studies throughout your life. Were did you go? What and whom did you know? Eudo: I have been to a plethora of places throughout my philosophical career, most notable being Tarentum and Athens and Sicily, as well as Heliopolis in Egypt. I started with Tarentum, where I studied the mathematics of geometry under the beneficent Archytas, who studied under the great Pythagoras. Archytas's interest in the Duplication of the Cube led me to be interested in it as well. Mitch: Fascinating.

44. Eudoxus Of Cnidus Biography eudoxus of cnidus biography and related resources. http://www.biographybase.com/biography/Eudoxus_of_Cnidus.html

Biography Base Home Link To Us Search Biographies: Browse Biographies A B C D ... Z Eudoxus of Cnidus Biography Eudoxus of Cnidus 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 1500s, 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. An algebraic curve (the Kampyle of Eudoxus) is named after him Eudoxus of Cnidus Resources Contact Us Sitemap This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article Eudoxus of Cnidus

45. Chapter 15, Golden Mean 8 Perhaps the most gifted geometer to study there was eudoxus of cnidus, who finallybroke the deadlock of the irrationals, and freed geometry for the great http://www.anselm.edu/homepage/dbanach/pyth4.htm

Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell) 15. THE GOLDEN AGE AND THE GOLDEN MEAN The second half of the 5th century B.C. was the Golden Age of Greece. This was the period of her most beautiful art and architecture, and some of her wisest thinkers besides. Both owed much to the popular new study of geometry. By the start of the next century, geometry itself was entering its own classic age with a series of great developments, including the Golden Mean. The times were glorious in many ways. The Persian invaders had been driven out of Hellas forever, and Pericles was rebuilding Athens into the most beautiful city in the world. At his invitation, Greek mathematicians from elsewhere flocked into the new capital. From Ionia came Anaxa- goras, nicknamed "the mind." From southern Italy and Sicily came learned Pythagoreans and the noted Zeno of Elea. And their influence was felt over all Athens. High on the hill of the Acropolis rose new marble temples and bronze and painted statues. Crowds thronged the vast new open-air theater nearby, to hear immortal tragedies and comedies by the greatest Greek playwrights. These splendid public works were completed under the direction of the sculptor Phidias and several architects, all of whom knew and used the principles of geometry and optics. "Success in art," they insisted, "is achieved by meticulous accuracy in a multitude of mathematical proportions." And their buildings had a dazzling perfection never seen before-the beauty of calculated geometric harmony.

46. Chapter 16: Archimedes Menaechmus, who had studied with Plato and Eudoxus, was trying to teach Alexandersome the two greatest were Theaetetus of Athens and eudoxus of cnidus. http://www.anselm.edu/homepage/dbanach/arch.htm

Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell) 16. A ROYAL ROAD, AFTER ALL During the 4th century B.C., Greek geometry burst its bonds and went on to the tremendous discoveries of the "age of giants." And Greek culture, too, burst from the mainland of Hellas and spread to most of the eastern Mediterranean. Both developments were connected with the romantic figure of Alexander the Great. After Plato's time, teachers and alumni from the Academy had gone on to found schools of their own. In particular, Plato's most famous associate, the great philosopher Aristotle, had set up the Lyceum in Athens, and started the systematic classification of human knowledge. And Aristotle's most renowned pupil was the warrior king Alexander of Macedon, who tried to conquer the world. In thirteen years, Alexander extended his rule over Greece proper, and Ionia, Phoenicia, Egypt, and the vast Persian domains as far as India. Then he died, and his empire broke up. But throughout those far-flung lands, he had founded Greek cities and planted the seeds of Greek civilization-the Greek language, Greek art, and, of course, Greek mathematics. Mathematicians traveled with his armies. And there is even a

47. Eudoxus Of Cnidus The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://episte.math.ntu.edu.tw/people/p_eudoxus/

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48. EUCLID EUDOXUS c.408 c.355 BC Greek Mathematician. eudoxus of cnidus, mathematicianand astronomer, who studied at Plato s academy, and lived for some times in http://www.hyperhistory.com/online_n2/people_n2/persons2_n2/eudoxus.html

EUDOXUS c.408 - c.355 BC Greek Mathematician Eudoxus of Cnidus, mathematician and astronomer, who studied at Plato's academy, and lived for some times in Egypt. He advanced subsantially number theory, and constructed a model of 27 spheres to explain the motions of the Moon, stars, and planets. www link : From the University of St. Andrews, Scotland School of Mathematics Biography

49. MESSENMESSENGER: Astronomer Biographies eudoxus of cnidus was a Greek astronomer, mathematician and philosopher, one ofthe most renowned of his day. He devised a planetary system based on spheres http://btc.montana.edu/messenger/elusive_planet/bios.htm

Eugenios Antoniadi (1870-1944) Eugenios Antoniadi 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) Aristarchus of Samos 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 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. Johann Franz Encke (1791-1865) Johann Franz Encke is known for determining the orbit of a comet that was later named for him. Using this information, he determined quite accurately the mass of the Mercury. He also studied the rings of Saturn.

50. Astronomers-Zoom Astronomy Glossary eudoxus of cnidus (408355 BC) was a Greek scholar (perhaps a student of Plato)who theorized that the Earth was at the center of the universe and that the http://www.zoomwhales.com/subjects/astronomy/glossary/Astronomers.shtml

Become a member of Enchanted Learning. Site subscriptions last 12 months. Click here for more information on site membership. $20.00/year or other amount (directly by Credit Card $20.00/year or other amount (via PayPal As a thank-you bonus, site members have access to a banner-ad-free version of the site, with print-friendly pages. (Already a member? Click here. Zoom Astronomy Astronomy Dictionary A B C D ... Z Click on an underlined word for more information on that subject. Zoom Astronomy HALL OF ASTRONOMERS An astronomer is someone who studies astronomy. The following night-owls are important astronomers, astrophysicists, mathematicians, and other scientists who have contributed greatly to our knowledge of the universe. ADAMS, JOHN C. John Couch Adams (1819-1892) was an English astronomer and mathematician who, at 24 years old, predicted the existence of the planet Neptune (Le Verrier also predicted its existence, independently). AIRY, GEORGE Sir George Bidell Airy (1801-1892) was the director of Greenwich Observatory/Astronomer Royal of England from 1835 to 1881. Airy installed a transit (a precise surveying device) at Greenwich, England, which was used to define the zero degree meridian of the Earth (zero-degrees longitude). A crater on Mars about 5 degrees south of the equator and on what is defined as Mars' prime meridian (zero-degrees longitude) is call Airy. A small crater within this crater (which is called Airy-0) is where the meridian line (zero-degrees longitude) crosses. A crater on the moon is also named for him (latitude 18.1 degrees, longitude 354.3 degrees, diameter 36 km). Airy is supposed to have stated incorrectly that Charles Babbage's new "analytical engine" (the predecessor of the computer) was "worthless," effectively ending Babbage's government funding.

51. Articles - Eudoxus Of Cnidus Another article treats of Eudoxus of Cyzicus. eudoxus of cnidus (Greek text from the article in Wikipedia, The Free Encyclopedia eudoxus of cnidus. http://www.anfolk.com/articles/Eudoxus_of_Cnidus

Another article treats of Eudoxus of Cyzicus Eudoxus of Cnidus Greek or 408 BC or 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 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 Indian Mathematician Bhaskara and later by Newton An algebraic curve (the Kampyle of Eudoxus) is named after him a x = b (x + y Also

52. CLAW-Cats In Space-Notable Humans Page One eudoxus of cnidus Our Notable Human for November Pronounced yOOdok sus, nI dus.eudoxus of cnidus , 408?–355? BC, Greek astronomer, mathematician, http://www.geocities.com/catsinspace03/notablehumans2.html

NOTABLE HUMANS SIR FRANK WATSON DYSON Our Notable Human for June 2004 English astronomer: He was astronomer royal of Scotland (1905–10) and of England (from 1910). As director (1910–33) of Greenwich Observatory he greatly expanded its research activities and inaugurated (1928) the wireless transmission of Greenwich time. Noted for his study of solar eclipses, he was an authority on the spectrum of the corona and on the chromosphere; his observations of an eclipse (in Brazil, 1919) confirmed Einstein's theory of the effect of gravity on light. Dyson plotted the motions of many previously uncharted stars. A fellow of the Royal Society from 1901, he was knighted in 1915. His publications include Astronomy: A Handy Manual (1910) and Eclipses of the Sun and Moon (with Richard Woolley, 1937). CHRISTIAN HUYGENS Our Notable Human for May 2004 Apr 14, 2004 - Dutch astronomer Christian Huygens was born on April 14, 1629; exactly 375 years ago. He was an influential astronomer who improved on Galileo's original telescope design by developing new techniques to grind and polish lenses. With his improved telescope, Huygens was able to resolve the rings of Saturn better than anyone at the time, and realize their true shape as rings. He also discovered Titan, Saturn's largest moon. He died in 1695. MADAME MARIE CURIE Our Notable Human for April 2004 Submitted by Chloe Marie Curie's Primary Accomplishment During the first years after the discovery of radioactivity, a large number of chemists and physicists were busy studying the new phenomenon. Madame Marie Sklodowska Curie, Polish born, educated in chemistry, and the wife of the French physicist, Pierre Curie, carried out an extensive test of all chemical elements and their compounds for radioactivity, and found that thorium emits radiation similar to that of uranium. Comparing radioactivity of uranium ores with that of metallic uranium, she noticed that ores are about five times more radioactive than would be expected from their uranium content. This indicated that the ores must contain small amounts of some other radioactive substances much more active than uranium itself, but, to separate them, very large amounts of expensive uranium ores were needed.

53. Index Of Ancient Greek Scientists eudoxus of cnidus (408360 BC). Greek astronomer and mathematician. Belonged tothe school of Plato. Developed the theory of proportions and the method of http://www.ics.forth.gr/~vsiris/ancient_greeks/whole_list.html

not complete Agatharchos. Greek mathematician. Discovered the laws of perspectives. Anaxagoras of Clazomenae (480-430 B.C.). Greek philosopher. Believed that a large number of seeds make up the properties of materials, that heavenly bodies are made up of the same materials as Earth and that the sun is a large, hot, glowing rock. Discovered that the moon reflected light and formulated the correct theory for the eclipses. Erroneously believed that the Earth was flat. Links: Anaxagoras of Clazomenae, MIT Anaximander (610-545 B.C.). Greek astronomer and philosopher, pupil of Thales. Introduced the apeiron (infinity). Formulated a theory of origin and evolution of life, according to which life originated in the sea from the moist element which evaporated from the sun ( On Nature ). Was the first to model the Earth according to scientific principles. According to him, the Earth was a cylinder with a north-south curvature, suspended freely in space, and the stars where attached to a sphere that rotated around Earth. Links: Anaximander, Internet Encyclopedia of Philosophy

54. The Homocentric Spheres Of Eudoxus, Callippus, And Aristotle (Note 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).

55. My Favoriate Mathematicians: Eudoxus eudoxus of cnidus solved the foundational crisis arising from the existence ofirrational numbers (perhaps uncovered by Hippasus). http://homepages.feis.herts.ac.uk/~comqcln/eudoxus.html

Eudoxus 408 BC-355 BC Eudoxus of Cnidus solved the foundational crisis arising from the existence of irrational numbers (perhaps uncovered by Hippasus ). His solution, constructing real numbers as limits of sequences of ratios of commensurables, was given a "uniqueness" part by Dedekind. Eudoxus' treatment of irrational numbers comprises Book X of Euclid, first chairman of the Mathematics Dept. at the University of Alexandria. More Links: Short Biography of Eudoxus Document by C. Nehaniv, February 2, 1996 e-mail: nehaniv@u-aizu.ac.jp

56. Hotmath Practice Problems For AOL@School is called a kampyle of Eudoxus. (Such curves were first studied by the Greekmathematician eudoxus of cnidus, born in 408 BC.) http://hotmath.school.aol.com/AOL-SCHOOL/calculus/section_3_1.html

AOL@SCHOOL Main Administrators Teachers High School Students Middle School Students Elementary School Students Primary School Students Help Order AOL@SCHOOL School Store Hotmath Practice Problems for AOL@School: Calculus Chapter 3: Derivatives If the tangent line to y f x ) at (5, 2) passes through (1, 1), find f (5) and f Sketch the graph of a function for which f f f f Describe the x -values at which f is differentiable. Write the domain of f Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function differentiable at x Determine whether the function is differentiable at x Assuming the axes have equal scales, sketch the graph of the derivative. Find the derivative of the function using the definition of derivative. State the domains of both the function and its derivative. Find the derivative of the function using the definition of derivative. State the domains of both the function and its derivative. Find the derivative of the function.

57. Plato eudoxus of cnidus, who came to Plato s Academy with his own disciple). his own school), eudoxus of cnidus, Philippus of Opus (an astronomer), http://www.omhros.gr/Kat/History/Txt/Cl/Plato/Plato.htm

Plato (427-347 B.C.) The great Greek philosopher Plato was most likely born in Athens to an aristocratic family, though little is known of his early life. He was a large, athletic, intelligent man, who could have succeeded in any number of callings — but he became a disciple of the great teacher, Socrates, and devoted himself chiefly to a life of the mind. He travelled widely, then sometime before 368 B.C. founded his own school, the Academy, at Athens, where he remained for the rest of his life, apart from a few visits to Syracuse. Plato's life of thought was captured in a series of dialogues, most of them spotlighting his master Socrates. Readers wishing to jump into the Dialogues would do well to begin with the Apology , in which Socrates defends himself against the charges of atheism and teaching controversial ideas to the youth of Athens. The trial, or course, ended unsuccessfully for Socrates, and he was sentenced to death. In Crito , Socrates explains his reasons for refusing to escape from prison. Phaedo contains a discussion of immortality, but ends with Socrates' execution and is one of the most moving short pieces of narrative ever written. Next, one should read the early dialogues. The main character is Socrates, and the main subject is the definition of moral concepts (e.g, temperance in

58. Plato eudoxus of cnidus author of the doctrine of proportion expounded in Euclid sElements, Eudoxus and Aristotle wrote laws for Cnidus and Stagirus. http://www.omhros.gr/Kat/History/Greek/Ph/Plato.htm

Plato b. 428/427 BC, Athens, or Aegina, Greece d. 348/347, Athens Ancient Greek philosopher, the second of the great trio of ancient Greeks Socrates , Plato, and Aristotle who between them laid the philosophical foundations of Western culture . Building on the life and thought of Socrates, Plato developed a profound and wide-ranging system of philosophy. His thought has logical, epistemological, and metaphysical aspects; but its underlying motivation is ethical. It sometimes relies upon conjectures and myth, and it is occasionally mystical in tone; but fundamentally Plato is a rationalist, devoted to the proposition that reason must be followed wherever it leads. Thus the core of Plato's philosophy, resting upon a foundation of eternal Ideas, or Forms, is a rationalistic ethics. Life Plato was born, the son of Ariston and Perictione, in about 428 BC, the year after the death of the great statesman Pericles . His family, on both sides, was among the most distinguished in Athens. Ariston is said to have claimed descent from the god Poseidon through Codrus, the last king of Athens; on the mother's side, the family was related to the early Greek lawmaker Solon . Nothing is known about Plato's father's death. It is assumed that he died when Plato was a boy. Perictione apparently married as her second husband her uncle Pyrilampes, a prominent supporter of Pericles; and Plato was probably brought up chiefly in his house. Critias and Charmides, leaders among the extremists of the oligarchic terror of 404, were, respectively, cousin and brother of Perictione; both were friends of Socrates, and through them Plato must have known the philosopher from boyhood.

59. 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 first astronomerto follow Plato s recommendation. Blending careful observation with http://www.pupress.princeton.edu/chapters/i7432.html

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.

60. The Ten Greatest Mathematicians borrowed from the more brilliant eudoxus of cnidus (408355 BC). about theSun was first introduced by the eudoxus of cnidus mentioned above, http://freepages.genealogy.rootsweb.com/~jamesdow/Tech/mathmen.htm

OAS_AD('Top'); The Ten Greatest Mathematicians of All Time ranked in approximate order of ``greatness.'' To qualify, the mathematician's work must have breadth depth , and historical importance. Carl F. Gauss Archimedes of Syracuse Sir Isaac Newton Leonhard Euler Pierre de Fermat Euclid of Alexandria Augustin Cauchy Bernhard Riemann Gottfried Wilhelm Leibniz These are my personal rankings, but most of the selections should have wide acceptance among mathematical historians. If the criteria were just depth and historical importance then the greats Georg Cantor (1845-1918), and (1811-1832) would be urging their names on to this list, but these are lacking somewhat in breadth , compared with the Top Ten, who each were outstanding in multiple fields. Most of the selections were easy, but choosing Riemann, Euclid and Leibniz to round out the list was difficult. Riemann was undoubtedly an outstanding genius, but several great mathematicians might be better choices based on their work's historical importance, for example (1596-1650) or Joseph-Louis Lagrange (1736-1813). Conversely Euclid's work has great historical significance, but much of it was probably borrowed from the more brilliant

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