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	Ancient Greek Mathematics - Crystalinks (Site not responding. Last check: 2007-10-13)
		Greek mathematics, as that term is used in this article, is the mathematics developed from the 6th century BC to the 5th century AD around the shores of the Mediterranean.
		Mathematical developments took place in Greek-speaking centers as far apart as Sicily and Egypt, and with a high estimation of the intellectual and cultural status of mathematics (for example in the school of Plato).
		Among the foremost modern historians of Greek mathematics was Thomas Heath.
	www.crystalinks.com /greekmath.html (305 words)

	Greek mathematics - Wikipedia, the free encyclopedia
		Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean.
		Greek mathematics studied from the time of the Hellenistic period onwards (from 323 BC) refers to all mathematics of those who wrote in the Greek language, since Greek mathematics was now not only written by Greeks but also non-Greek scholars throughout the Hellenistic world, which was spread across the Eastern end of the Mediterranean.
		Greek mathematics constitutes a major period in the history of mathematics, fundamental in respect of geometry and the idea of formal proof.
	en.wikipedia.org /wiki/Greek_mathematics (631 words)

	Aristotle and Mathematics > Aristotle and Greek Mathematics (Stanford Encyclopedia of Philosophy)
		The problem must be as old as Greek mathematics, given that the problem marks a transition from Egyptian to Greek style mathematics.
		Greek mathematicians wisely avoided non-uniform magnitudes which could not be reduced to uniform magnitudes.
		With the possible exception of this theorem, all of Aristotle's original mathematics may be found in his arguments against infinity and on motion in the Physics iii-vii and De caelo i, many of which use proportion theory.
	plato.stanford.edu /entries/aristotle-mathematics/supplement4.html (1716 words)

	Aristotle and Mathematics (Stanford Encyclopedia of Philosophy)
		Mathematical examples: ‘line’ is in the definition of triangle, ‘point’ is in the definition of line.
		The objects studied by mathematical sciences are perceptible objects treated in a special way, as a perceived representation, whether as a diagram in the sand or an image in the imagination.
		The parts of a mathematical object which do not occur in the definition of the object, e.g., acute angle is not in the definition of right angle, but is a part of it and so is a non-perceptible material part of the angle (Metaphysics vii.10, 11).
	plato.stanford.edu /entries/aristotle-mathematics (9432 words)

	¥±. The Greek Mathematics : Demonstrative Geometry
		In the 600 B.C. Mathematics was focused as a study and a science in the ancient Greek as a matter of course in China, India and Babylonia and to learn Geometry in Egypt.
		However, Greek mathematics was remarkable theoretically, but unremarkable in the field of number and calculus.
		The Pythagoreans found that for strings under the same tension, the lengths should be 2 to 1 for the octave 3 to 2 for the fifth, and 4 to 3 for the fourth.
	library.thinkquest.org /22584/emh1200.htm (2214 words)

	Greek For Euclid: Contents
		Mathematics, as what is taught in schools is wrongly called, is not calculation but an exercise in reason, and Euclid does it with words.
		Greek geometry traditionally begins with Thales of Miletus (624-547 BC), one of the Seven Wise Men of the ancient world (to people of the classical world), who is said to have brought the rudiments from Egypt.
		Greek is a living language with a continuous tradition of three millennia, which has been subject to constant evolution in that time, so there cannot be a single 'correct' authority.
	www.du.edu /~etuttle/classics/nugreek/contents.htm (3319 words)

	Greek Mathematics and its Modern Heirs
		Shown here are the inscriptions of an icosahedron (a solid composed of twenty equilateral triangular faces) in a cube, and of a cube in an octahedron (a solid of eight equilateral triangular faces).
		This is the holograph of his translation of the greatest Greek mathematician, Archimedes, with the commentaries of Eutocius.
		The translations were made in 1269 at the papal court in Viterbo from two of the best Greek manuscripts of Archimedes, both of which have since disappeared.
	www.ibiblio.org /expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.html (628 words)

	Mathematics (Rome Reborn: The Vatican Library & Renaissance Culture)
		The mathematics and astronomy of the Greeks had been known in medieval western Europe only through often imperfect translations, some of them made from Arabic intermediary texts rather than the Greek originals.
		One of the most powerful creations of Greek science was the mathematical astronomy created by Hipparchus in the second century B.C. and given final form by Ptolemy in the second century A.D. Ptolemy's work was known in the Middle Ages through imperfect Latin versions.
		George Trebizond, one of the notable Greek scholars who came to Italy in the early fifteenth century, made a new translation of the Almagest from the Greek for Pope Nicholas V between March and December of 1451.
	www.loc.gov /exhibits/vatican/math.html (2972 words)

	Mathematics - Wikipedia, the free encyclopedia
		Mathematics (colloquially, maths, or math in American English) is the body of knowledge centered on concepts such as quantity, structure, space, and change, and the academic discipline which studies them; Benjamin Peirce called it "the science that draws necessary conclusions".
		Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method.
		Mathematical logic is concerned with setting mathematics on a rigid axiomatic framework, and studying the results of such a framework.
	en.wikipedia.org /wiki/Mathematics (4093 words)

	Greek Demonstration: The Return of Odysseus and the Elements of Euclid
		In the first half of the fifth century Greek mathematics incorporates the formal logical techniques of Eleatic ontology into its theoretical structure, and this structure, which was now both axiomatic and deductive, is essentially unchanged as it appears in the Elements of Euclid.
		The evidentiary force of such a sign in Greek mathematics was seen first in the Elements of Euclid in the procedure of superposition by which the side-angle- side criterion for triangle equality is established.
		The greek word for "point" in geometry is semeion, a special form of the noun sema, which in the Odyssey names the sign of the olive trunk at the center of Penelope's bed.
	ccat.sas.upenn.edu /~awiesner/gkdem.html (13693 words)

	>The Origins of Greek Mathematics
		The Greeks settled in Asia Minor, possibly their original home, in the area of modern Greece, and in southern Italy, Sicily, Crete, Rhodes, Delos, and North Africa.
		The ancient Greek civilization lasted until about 600 B.C. The Egyptian and Babylonian influence was greatest in Miletus, a city of Ionia in Asia Minor and the birthplace of Greek philosophy, mathematics and science.
		In actual fact, our direct knowledge of Greek mathematics is less reliable than that of the older Egyptian and Babylonian mathematics, because none of the original manuscripts are extant.
	www.math.tamu.edu /~don.allen/history/greekorg/greekorg.html (1554 words)

	Ancient Greek Mathematics
		Greeks obtained Geometry as an art of measuring the land from the Egyptians as Herodotus describes.
		A characteristic Greek discovery that the square root of 2 is not a rational number is for me one of the best examples that Greeks were interested in true science.
		, Greek Geometry from Thales to Euclid (Conics)
	www.mlahanas.de /Greeks/GreekMathematics.html (834 words)

	Ancient Greek Mathematics - History for Kids!
		Instead, Greek mathematicians were more focused on geometry, and used geometric methods to solve problems that you might use algebra for.
		The Greeks in general were very interested in rationality, in things making sense and hanging together.
		History of Greek Mathematics: From Aristarchus to Diophantus, by Thomas L. Heath (1921, reprinted 1981).
	www.historyforkids.org /learn/greeks/science/math/index.htm (391 words)

	Mathematics
		Greek is one of many Indo-European languages with singular, dual, and plural numbers (though of course the dual was nearly dead by New Testament times).
		Greek math was obviously relevant to the New Testament, and Hebrew math -- which in turn was influenced by Egyptian and Babylonian -- may have influenced the thinking of the NT authors.) The above is mostly by way of preface: It indicates something about how numbers and numeric notations evolved.
		There is only one Greek mathematical work which survives from the period before Euclid, and it is at once small and very specialized -- and survived because it was included in a sort of anthology of later works.
	www.skypoint.com /~waltzmn/Mathematics.html (19195 words)

	Greek sources I
		The truth, however, is not nearly so simple and we will illustrate the way that Greek mathematical texts have come down to us by looking first at perhaps the most famous example, namely Euclid's Elements.
		It was not used by the Greeks, however, until around 450 BC for earlier they had only an oral tradition of passing knowledge on through their students.
		The survival of the library of the Metochion of the Holy Sepulchre in Istanbul could not be guaranteed amid the fighting, and head of the Greek Orthodox Church requested that the books from the library be sent to the National Library of Greece to ensure their safety.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Greek_sources_1.html (2711 words)

	AllRefer.com - Euclid, Greek mathematician (Mathematics, Biography) - Encyclopedia
		Little is known of his life other than the fact that he taught at Alexandria, being associated with the school that grew up there in the late 4th cent.
		The great contribution of Euclid was his use of a deductive system for the presentation of mathematics.
		Although Euclid's system no longer satisfies modern requirements of logical rigor, its importance in influencing the direction and method of the development of mathematics is undisputed.
	reference.allrefer.com /encyclopedia/E/Euclid.html (334 words)

	Read This: The Mathematics Of Plato's Academy
		The early Pythagoreans based their mathematics on commensurable magnitudes (or on rational numbers, or on common fractions m/n), but their discovery of the phenomenon of incommensurability (or the irrationality of the square root of 2) showed that this was inadequate.
		On later Greek mathematics, Fowler basically only comments on what is relevant to the reconstruction of the early material.
		A modern mathematician moves almost effortlessly from a definition of proportion ("A is to B as C is to D") to the definition of ratio as a kind of equivalence class.
	www.maa.org /reviews/mpa.html (2046 words)

	ANCIENT GREEK MATHEMATICS
		If you are interested in learning more about Greek mathematics, you can browse this website or chat (below) with others about the influence of Greek mathematics on western civilization.
		The ancient Greek architects who calculated the measurements that would be used in the construction of the Parthenon, used mathematics to come up with their designs.
		Greek mathematics has made an astonishing impact on our world.
	www.angelfire.com /me/Huffamoose (221 words)

	Basic Ideas in Greek Mathematics
		In fact, the Greeks managed to prove (it can be done with elementary algebra) that pairs of numbers can be added indefinitely, and their ratio gives a better and better approximation to the square root of 2.
		It is clear from the above discussion that the Greeks laid the essential groundwork and even began to build the structure of much of modern mathematics.
		This level of mathematical analysis attained by Archimedes, Euclid and others is far in advance of anything recorded by the Babylonians or Egyptians.
	galileo.phys.virginia.edu /classes/109N/lectures/greek_math.htm (4334 words)

	A Manual of Greek Mathematics
		This concise but thorough history encompasses the enduring contributions of the ancient Greek mathematicians whose works form the basis of most modern mathematics.
		Written by a distinguished scholar and mathematician, the well-written, nontechnical text is geared toward high school, college, and graduate students, teachers, and those seeking a historical perspective on mathematics.
		Topics include Pythagorean arithmetic, Plato's use and philosophy of mathematics, an in-depth analysis of Euclid's "Elements," the beginnings of Greek algebra and trigonometry, and other mathematical milestones.
	store.doverpublications.com /0486432319.html (172 words)

	Diane's Mathematics Page
		CRC This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas, published in late 1995 by CRC press.
		Greek Diagrams: their Use and their Meaning Reviel Netz, Cambridge gives a talk on diagrams in greek manuscripts.
		Earliest Uses of Mathematical Symbols the names of the individuals who first used various common mathematical symbols, and the dates the symbols first appeared.
	www.geocities.com /Athens/Academy/9468/mathematics.htm (1036 words)

	Proofs and Pythagoras - Greek Mathematics
		The Greeks were the first people of the ancient world who systematically studied geometry, which is the study of the size and shape of an object.
		The Greeks got the idea for an alphabet from the Phoenicians, a seafaring people who lived around 1500 BC along the coast of Syria.
		The Greek alphabet had twenty-seven letters, so the first nine letters represented the digits 1 through 9; the second nine letters represented the tens, and the last nine letters represented the hundreds.
	www.edhelper.com /ReadingComprehension_35_195.html (602 words)

	Ancient Greek Mathematics (Site not responding. Last check: 2007-10-13)
		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.
	members.tripod.com /~JFrazz9/math.html (48 words)

	The Shaping of Deduction in Greek Mathematics - Cambridge University Press
		It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science.
		A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae.
		Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521622794 (320 words)

	TCA's Greek Too!
		It is, indeed, disturbing to notice that the APA standards for Latin teacher training fails to even mention Greek as an ancillary subject for prospective Latin teachers (APA Newsletter, vol.
		To encourage more Latin teachers to invest some effort in acquainting their students with the basics of Greek and to offer a resource for teachers of Greek in schools, the TCA has set up a this mini-site in conjunction with the TCA website specifically to promote Greek at the school level.
		It is hoped that Latin teachers and especially interested Hellenists at the university level will contribute ideas for promoting and developing Greek in schools, reviews of teaching material, and short articles for the web page.
	www.txclassics.org /greek.htm (367 words)

	Introduction to the works of Euclid
		The former work also exhibits the ``classical'' Greek form -- discussed in section III below -- found in all of Euclid's treatises, demonstrating that this style of presentation was not original with Euclid, but was established before his time.
		The Greeks made a clear distinction between logistic, which Plato identifies as ``the art of calculation,'' and arithmetic, which is known today as number theory.
		Secondly, since Euclid bases his entire geometry on points, straight lines, and circles (and thus construction by straight-edge and compass alone), the so-called three famous problems of Greek mathematics -- squaring the circle, doubling the cube, and trisecting the angle -- are not to be found in the work.
	www.obkb.com /dcljr/euclid.html (9104 words)

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