41. Eudoxus eudoxus of cnidus. Born 408 BC in Cnidus (on Resadiye peninsula), AsiaMinor (now Turkey) Died 355 BC in Cnidus, Asia Minor (now Turkey). http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/dxs.htm

Eudoxus of Cnidus Born: 408 BC in Cnidus (on Resadiye peninsula), Asia Minor (now Turkey) Died: 355 BC in Cnidus, Asia Minor (now Turkey) Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Eudoxus studied at Plato 's Academy and was a student of Archytas of Tarentum. He spent over a year in Egypt and then, on his return, established a school that competed with Plato . There is ample evidence to suggest that Eudoxus had little respect for Plato 's analytic ability. Eudoxus proposed a geocentric system for the solar system in which the sun moon and planets moved on spheres centred on the earth.. Other important contributions were to the theory of proportion, where he made a definition of equal ratios similar to cross multiplying, and early work on integration with the theory of exhaustion. His theory of irrational numbers which appears in Book 5 of Euclid 's Elements , anticipated the 19th Century work of Dedekind The kampyle curve was studied by Eudoxus also in relation to the classical problem of duplication of the cube. Eudoxus found formulas for measuring pyramids cones and cylinders. Books V and XII of Euclid 's Elements are attributed to Eudoxus by some experts.

42. EUCLID eudoxus of cnidus, mathematician and astronomer, who studied at Plato sacademy, and lived for some times in Egypt. He advanced 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

43. History Of Ancient World Mathematics Page eudoxus of cnidus (408 355 BC). Eudoxus was born in Cnidus where hespent his youth in poverty like many of his fellow mathematicians. http://www.roma.unisa.edu.au/07305/ancmm.htm

Ancient World Mathematics Written by Paul Dickson (University of South Australia, 1996) Thales of Miletus (640 - 546 BC) Thales was born in Miletus in 640 BC and became a merchant as soon as his skills allowed, actual history concerning Thales is scarce but some stories about him have filtered down through the ages, whether they are true or not..... no one really knows. Thales' major mathematical contribution is believed to be the theory of a triangle inscribed within a semi-circle being right angled at the corner touching the arc if one side is the diameter of the circle. Figure 1: A Triangle inscribed in a Semi-circle makes a right angle. Thales and the Salt Caravan It is believed that while transporting salt which was loaded on mules, one of the animals slipped in a stream. The mule's load of salt was slightly dissolved by the water and it's load became lightened. This mule being smart at ways to get out of work rolled over at the next ford it came to and found it's load lighter again. Whether these mules were Thales or not is unclear bu the was consulted and came up with a plan to break the mule of this bad habit. The mule was loaded with sponges and rags, which when the mule rolled over, absorbed the water and made the load heavier. This eventually cured the mule of it's troublesome habit. Thales and the Olive Oil Empire In the ancient world of the mediterranean Olive Oil was an important commodity, as important as wheat or sugar is in todays. The Olive crop was a bumper havest one year and fearing that supply would outgrow demand for the coming Olive Oil production Thales quietly bought all the Olive presses he could afford to (no small task considering he was a very wealthy merchant by this time). Thus Thales controlled most of the Olive Oil production and 'cornered the market' of Olive Oil, a man much before his time Thales therefore became the first recorded man at about 600 BC to create a monopoly.

44. Online Book 1990). This page is part of Eric Weisstein s World of Scientific Biography.eudoxus of cnidus eudoxus of cnidus (ca. 400ca. 347 http://www.cox-internet.com/ast305/all1.html

Ancient Astronomy A Brief Introduction to Archaeoastronomy The study of the astronomical practices, celestial lore, mythologies, religions and world-views of all ancient cultures we call archaeoastronomy. America's Stonehenge Along with it's astronomical alignments, America's Stonehenge continues to be one of the most fascinating archaeological discoveries of the century. Ancient Astronomy Links Some selected links to pages with information on Ancient Astronomy Calendars and Ancient Astronomy in Egypt, India, Maya, and Mesopotamia. Ancient Astronomy Timeline A timeline of ancient astronomy from 4000 B.C. to around 140 A.D. Ancient Mesopotamia: Astronomy and Calendry Part of a history of astronomy course with links to photographs and explanations. Babylonian Planetary Theory and the Heliocentric Concept Gathered ideas regarding the view of the cosmos by ancient Babylonians as well as new interpretations are on display here. With data on periods and planetary motions. Chinese Astronomy Astronomy truly is an ancient science in China. In fact, mankind's first record of an eclipse of the Sun was made in China in 2136 BC. Egyptian Estimates of the Size and Shape of the Earth How did ancient Egyptians measure the size of the Earth?

45. Hipparchus On A Poem eudoxus of cnidus (c. 390c. 340 BC) produced a work known as the Phenomena, inwhich he described a calendar with references to the risings and settings of http://www.hps.cam.ac.uk/starry/hipppoem.html

Links Hipparchus Tour (Next) Previous Hipparchus Pages Hipparchus Astrology Calendars and Weather Prediction Mathematical Techniques ... Index Hipparchus on a Poem Title page of Aratus and Eudoxus Image by kind permission of the Master and Fellows of Trinity College Cambridge. Large image (78K). Very large image (4.2M). The sole surviving work of Hipparchus (who flourished during the second half of second century BC) is known as the Commentary on the Phenomena of Aratus and Eudoxus. Eudoxus of Cnidus (c. 390-c. 340 BC) produced a work known as the Phenomena, in which he described a calendar with references to the risings and settings of constellations. Aratus (c. 315 - before 240 BC) produced an enormously popular poem, also known as the Phenomena , which utilised Eudoxus' work. Although he wrote many other poems, Aratus' Phenomena is his only extant work. The Phenomena quickly became one of the most widely read poems in the ancient world, after the Homeric poems, the Iliad and the Odyssey.

46. Web Hosting, Domain Name, Free Web Site, Email Address Web Hosting The term, magnitude,was created by the great Greek mathematician, eudoxus of cnidus(c.408355 BC), a pupil of Archytas of Tarentum (c. 425-350 BC), a follower http://members.fortunecity.com/jonhays/puzzle.htm

web hosting domain names email addresses THE PUZZLE MORPHED BY "The Candy Miser" Without the solution to this puzzle, we would be living in medieval villages; with technology more primitive than that of the Amish of Pennsylvania; slavery AND semi-slavery wouldbe widespread; women and girls would be repressed, often abused, superstitution widespread. Whatwas the puzzle? The SQUAREGATE PUZZLE seemed to say, "You can apply ARITHMETIC to the SIDES of THE SQUARE, butyou cannot apply ARITHMETIC to its DIAGONAL. So only GEOMETRY describes THE SQUAREGATE." The term, magnitude ,was created by the great Greek mathematician, Eudoxus of Cnidus (c.408-355 B.C.), a pupil of Archytas of Tarentum (c. 425-350 B.C.), a follower of Pythagoras.As a teacher in the Academy of Plato (427-327 B.C.), Eudoxus applied the notion of magnitudeto the composition of lines, angles, volumes in geometry and also to time. This restriction of time to geometry led to the notion that "motion is geometry set to time". Hence, the four beliefs developed in the Academy: the diagonal of the square (in geometry) is not a magnitude describable by number (in arithmetic);

47. LUNATIC REORGANIZES HEAVENS Some lunatic named eudoxus of cnidus, (there have been whisperings from the oracleat Delphi that Cnidus will one day be called Turkey), thinks that the http://www.rainbowkids.de/unterhaltung/Geschichten/AWinghaven/lunatic.htm

LUNATIC REORGANIZES HEAVENS! (This article is written as though it were being published in the days of Eudoxus.) Some lunatic named Eudoxus of Cnidus, (there have been whisperings from the oracle at Delphi that Cnidus will one day be called Turkey), thinks that the planets are carried on spheres. He claims that these spheres are nested around the earth in mountings like compass gimbals. "Rotations on these explain observed motions of stars," says Eudoxus. He also says that the solar year is six hours longer than three hundred and sixty five days. He has been a pupil of the Greek philosopher Archytas and also has studied under Plato. Eudoxus is a Greek geometer and astronomer; Now he has founded a school at Cyzicus. The priests of Helios are outraged. They say that we should stick to the proper ways of reckoning the movements of the heavens, which is that Helios, the sun, mounts his glowing chariot after Eos, the dawn goddess, opens the gates of morning, and rides across the sky to light the day. Then at night Selene, or Diana, the moon goddess comes out to bring the moon to

48. Plato And Platonism eudoxus of cnidusauthor of the doctrine of proportion expounded in Euclid s Elements,inventor of the method of finding the areas and volumes of curvilinear http://www.msu.org/ethics/content_ethics/texts/plato/plato_eb.htm

Plato and Platonism "Plato and Platonism: Bibliography" Britannica Online. http://www.eb.com:180/cgi-bin/g?DocF=macro/5005/10/28.html Plato and his thought LIFE Plato was born, the son of Ariston and Perictione, in Athens, or perhaps in Aegina, 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.

49. Winter Constellations: Asterisms And Constellations The first complete description of the constellations was by eudoxus of cnidus in366 BC Most people think Eudoxus writings are the main source of the legends http://members.aol.com/ckckside/reports/constellation/astrob.htm

ASTERISMS AND CONSTELLATIONS What is the difference between asterisms and constellations? Many people get them confused with each other. They are similar, but they are also different. Asterisms are groups of stars that make a shape or form of something. The Big Dipper is an example of an asterism. It is made of seven stars, four make up the bowl and three are the handle. Constellations are a group of stars that often include asterisms. They are usually outlined by some imaginary line for them to have a shape. The Big Dipper is an asterism in the constellation Ursa Major. Often it is easier to find the asterism in the constellation than it is to find the constellation itself. For instance, I can find the Big Dipper very easily. Once I find the Big Dipper, then I can see Ursa Major. But if I tried to find Ursa Major without seeing the Big Dipper, I might not ever find Ursa Major. Since constellations include other asterisms, star clusters, nebulae and meteorites, their outline is not as clear as the asterisms which have fewer objects. A nuclear reaction something like the hydrogen bomb causes stars to shine. Hydrogen is transformed into helium and about one percent of its mass is transferred into heat energy. This energy keeps the temperature at the center of the star at millions of degrees.

50. History Of Geometry eudoxus of cnidus (408355 BC) foreshadowed algebra by developing a theory of proportionwhich is presented in Book V of Euclid s Elements in which Definitions http://geometryalgorithms.com/history.htm

History Home Overview [History] Algorithms Books Gifts Web Sites A Short History of Geometry Ancient This is a short outline of geometry's history, exemplified by major geometers responsible for it's evolution. Click on a person's picture or name for an expanded biography at the excellent: History of Mathematics Archive (Univ of St Andrews, Scotland) Also, Click these links for recommended: Greek Medieval Modern History Books ... History Web Sites Ancient Geometry (2000 BC - 500 BC) Babylon Egypt The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations. They knew how to compute areas, and even knew the "Pythagorian Theorem" 1000 years before the Greeks (see: Pythagoras's theorem in Babylonian mathematics ). But there is no evidence that they logically deduced geometric facts from basic principles. Nevertheless, they established the framework that inspired Greek geometry. A detailed analysis of Egyptian mathematics is given in the book: Mathematics in the Time of the Pharaohs India (1500 BC - 200 BC) The Sulbasutras Baudhayana (800-740 BC) Apastamba (600-540 BC) Greek Geometry (600 BC - 400 AD) Time Line of Greek Mathematicians Major Greek Geometers (listed cronologically) [click on a name or picture for an expanded biography].

51. Eudoxus Eudoxus. See eudoxus of cnidus (ca.408 BC ca.347 BC) Greek astronomerand mathematician. Eudoxus of Cyzicus (fl.130 BC) Greek navigator. http://www.fact-index.com/e/eu/eudoxus.html

Main Page See live article Alphabetical index Eudoxus 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 article is from Wikipedia . All text is available under the terms of the GNU Free Documentation License

52. My Favoriate Mathematicians: Eudoxus Eudoxus. 408 BC355 BC eudoxus of cnidus solved the foundational crisis arisingfrom the existence of irrational numbers (perhaps uncovered by Hippasus). http://homepages.feis.herts.ac.uk/~nehaniv/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

53. NOTES ON ARISTOTLE'S HEAVENLY SPHERES 4.EudoxusAristotle refers here to eudoxus of cnidus who lived from 408 to355BCE. Like Aristotle, Eudoxus had studied under Plato at the Academy. http://condor.stcloudstate.edu/~physcrse/astr106/spheresn.html

Notes on Aristotle's Heavenly Spheres 1.movements: Astronomy from Aristotle's time through the time of Copernicus largely concerned itself with the movements of celestial objects - the daily rotation of the sky that caused the sun, moon, and stars to rise and set, as well as the motion of the sun, moon, and planets through the Zodiac in a manner different for each body. 2. substance which is perceptible but eternal: Aristotle classified substances by their natural movements. Every thing under the sphere of the moon, that is, in the earth environment was composed of a mixture of the four elements: earth, water, air, and fire. These elements had the property of heaviness or lightness , whereby there natural motions were either falling down towards the center of the earth or rising upwards towards the heavens. Since the natural motion of the heavens was circular motion rather than straight up or straight down, the heavens had to be composed of a fifth element, termed aither, was thought to be eternal, perfect, and unchanging 3.more than one movement: The sun, moon, and planets share with the stars the daily rotation of the sky, which makes these objects rise and set. But in addition to the western rotation of the sky, the sun, moon, and planets also move eastward through the zodiac.

54. Ancient Greek Mathematics been preserved. Euclid is known for his `Elements , much of whichwas drawn from his predecessor eudoxus of cnidus. The `Elements http://www.crystalinks.com/greekmath.html

Ancient Greek Mathematics Ancient Greek scholars were the first people to explore pure mathematics, apart form practical problems. The Greeks made important advances by introducing the concept of logical deduction and proof in order to create a systematic theory of mathematics. The Ancient Greeks had a tremendous effects on modern mathematics. Much that was written by the mathematicians Euclid and Archimedes has been preserved. 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. From Archimedes several treatises have come down to the present. Among them are `Measurement of the Circle', in which he worked out the value of pi; `Method Concerning Mechanical Theorems', on his work in mechanics; `The Sand-Reckoner'; and `On Floating Bodies'. Platonic Solids - Plato. The physician Galen, in the history of ancient science, is the most significant person in medicine after Hippocrates, who laid the foundation of medicine in the 5th century BC . Galen lived during the 2nd century AD. He was a careful student of anatomy, and his works exerted a powerful influence on medicine for the next 1,400 years.

55. Plato eudoxus of cnidus author of the doctrine of proportion expounded in Euclid s Elements,inventor of the method of finding the areas and volumes of curvilinear http://www.kat.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.

56. Universal Library writings of, for example, Herodotus, Plato (esp. Phaedo and Timaeus),Theophrastus (Athen.2. 42b) and eudoxus of cnidus (DL 8. 8690). http://www.greece.org/alexandria/library/library1.htm

The Ancient Library Home A Universal Library Alexander the Great the Conquests as a source of knowledge The Founding of the Library and the Mouseion ... References The Modern Library BIBLIOTHECA ALEXANDRINAThe revival of the Ancient Library of Alexandria Back to Alexandria Home Page The institution of libraries and archives was known to many ancient civilisations in Egypt, Mesopotamia, Syria, Asia Minor and Greece; but all and sundry were of a local and regional nature, primarily concerned with the conservation of their own respective national tradition and heritage. The idea of a universal library, like that of Alexandria, had to wait for historic changes that would help to develop a new mental outlook which could envisage and encompass the whole world. We owe it primarily to the inquisitive Greek mind, which was impressed by the achievements of its neighbours and which led many Greek intellectuals to explore the resources of Oriental knowledge. This mental attitude among the Greeks, and the emergence of the concept of a universal culture, was given full expression in due course when Alexander embarked on his global expedition. We are familiar with a Greek literary tradition that preserved a vague memory of eminent Greeks - both legendary and historical - who made the journey to Egypt in the quest of learning (Diod. I. 98. 1-4). In many cases, the accounts are either fictitious or exaggerated, but during the century prior to Alexander's campaign, there is concrete evidence of Greek individuals visiting Egypt in particular, to acquire knowledge; this is reflected in the surviving writings of, for example, Herodotus, Plato (esp.

57. 46 Lessons In Early Geometry, Part 4/10 This would be done for them by eudoxus of cnidus ; they were not, however tosuppose that it was this the god desired, but rather that he was ordering the http://www.seshat.ch/home/geom04.htm

46 Lessons in Early Geometry, part 4/10 / provisional version in my own freestyle English / a corrected version will follow in March, April or May (hopefully) / Franz Gnaedinger / February 2003 / www.seshat.ch early geometry 1 early geometry 2 early geometry 3 / early geometry 4 / early geometry 5 early geometry 6 early geometry 7 early geometry 8 ... early geometry 10 Lesson 15 The Babylonians used an excellent value for the square root of 2, found on the clay tablet YBC 7289 from around 1650 or 1700 BC: YBC 7289 exact value How did the Babylonians possibly find this value? Divide 1393 by 985 and you obtain 1;24,51,10,3,2... Leave out the small numbers ...3,2... and keep the value 1;24,51,10. Archimedes used the ratios 265/153 and 1351/780 as boundaries for the square root of 3. Lesson 16 Victor J. Katz, A HISTORY OF MATHEMATICS, Addison-Wesley 1998, page 46, The Beginnings of Mathematics in Greece 'A report from a visit to Egypt with Plato by Simmias of Thebes in 379 B.C.E. (from a dramatization by Plutarch of Chaeronea (first/second century C.E.)): "On our return from Egypt a party of Delians met us ... and requested Plato, as a geometer, to solve a problem set them by the god in a strange oracle. The oracle was to this effect. The present troubles of the Delians and the rest of the Greeks would be at an end when they had doubled the altar at Delos How did Eudoxus solve the problem? He is known for a ladder of numbers that allows to double the square:

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

EnchantedLearning.com is a user-supported site. As a bonus, site members have access to a banner-ad-free version of the site, with print-friendly pages. Click here to learn more. (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. If the astronomy term you are looking for is not in the dictionary, please e-mail us 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.

59. 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.

60. Chapter 16: Archimedes many of the irrationals. In Plato s own time, the two greatest wereTheaetetus of Athens and eudoxus of cnidus. And at the Lyceum 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

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