1. History Of Mathematics: Greece Gow, James (18541923). A short history of greek mathematics. Cambridge, 1884. TranslationThe beginnings of greek mathematics, tr. by AM Ungar. http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

2. Perseus Update In Progress greek mathematics was premised on inductive reasoning. http://www.perseus.tufts.edu/GreekScience/Students/Chris/GreekMath.html

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3. History Of Mathematics - Origins Of Greek Mathematics Profile of greek mathematics, the foundation for modern math. Learn about its major schools, including the Ionian and Pythagorean schools. The Origins of greek mathematics. Though the Greeks certainly borrowed from other civilizations, they built a culture http://www.math.tamu.edu/~don.allen/history/greekorg/greekorg.html

Next: About this document The Origins of Greek Mathematics Though the Greeks certainly borrowed from other civilizations, they built a culture and civilization on their own which is The most impressive of all civilizations, The most influential in Western culture, The most decisive in founding mathematics as we know it. Basic facts about the origin of Greek civilization and its mathematics. The best estimate is that the Greek civilization dates back to 2800 B.C. just about the time of the construction of the great pyramids in Egypt. 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. About 775 B.C. they changed from a hieroglyphic writing to the Phoenician alphabet. This allowed them to become more literate, or at least more facile in their ability to express conceptual thought. 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. From the viewpoint of its mathematics, it is best to distinguish between the two periods: the

4. Greek Mathematics And Its Modern Heirs Library of Congress. Includes articles and original document images of early Greek contributions to Category Science Math History......greek mathematics and its Modern Heirs. Classical Roots of the ScientificRevolution. This room has another display with more greek mathematics. . http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.htm

Greek Mathematics and its Modern Heirs Classical Roots of the Scientific Revolution Euclid, Elements In Greek, Ninth century Euclid's "Elements," written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. Vat. gr. 190, vol. 1 fols. 38 verso - 39 recto math01 NS.01 Archimedes, Works In Latin, Translated by Jacobus Cremonensis, ca. 1458 In the early 1450's, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' "On Conoids and Spheroids" with highly ornate, and rather curious, illumination. Urb. lat. 261 fol. 44 verso - 45 recto math02 NS.17

5. Greek Mathematics And Its Modern Heirs greek mathematics and its Modern Heirs Classical Roots of the Scientific Revolution For over a thousand yearsfrom the fifth century B.C. http://sunsite.unc.edu/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.htm

Greek Mathematics and its Modern Heirs Classical Roots of the Scientific Revolution Euclid, Elements In Greek, Ninth century Euclid's "Elements," written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. Vat. gr. 190, vol. 1 fols. 38 verso - 39 recto math01 NS.01 Archimedes, Works In Latin, Translated by Jacobus Cremonensis, ca. 1458 In the early 1450's, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' "On Conoids and Spheroids" with highly ornate, and rather curious, illumination. Urb. lat. 261 fol. 44 verso - 45 recto math02 NS.17

6. Mathematics So you can pick any of greek mathematics. Ptolemy's Geography. Greek Astronomy. http://sunsite.unc.edu/expo/vatican.exhibit/exhibit/d-mathematics/Mathematics.ht

Mathematics Ancient Science and Its Modern Fates Until recently, historians of the Scientific Revolution of the 16th and 17th centuries treated it as a kind of rebellion against the authority of ancient books and humanist scholarship. In fact, however, it began with the revival of several tremendously important and formidably difficult works of Greek science. Scholarship supported science in this world where faith and science were not yet seen as two, irreconcilable cultures. The three ancient doors to the next rooms all have signs written on them in Greek and Latin. Luckily for you we created modern metal plates with the translations, next to the doors. So you can pick any of: Greek Mathematics Ptolemy's Geography Greek Astronomy Also, someone left a note on the wall. When you have seen everything, walk back to the Main Hall

7. Greek Mathematics Index History Topics Index of Ancient greek mathematics. Articles about greek mathematics. http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Greeks.html

8. Greek Mathematics Index History Topics Index of Ancient greek mathematics. Articles about greek mathematics.Squaring the circle. How do we know about greek mathematics? http://www-gap.dcs.st-and.ac.uk/~history/Indexes/Greeks.html

9. Greek Sources I How do we know about greek mathematics? It is easy to see, therefore, why no completegreek mathematics text older than Euclid's Elements has survived. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Greek_sources_1.html

10. Perseus Update In Progress greek mathematics. Because the Greeks had only very clumsy ways of writing down numbers, they didn't like algebra. http://www.perseus.tufts.edu/GreekScience/Students/Mike/geometry.html

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11. Perseus Update In Progress Wonders of Ancient greek mathematics. (and maybe some not so wonderful but stillcool stuff). By Timothy Reluga. Look at the comments on this paper. Preface. http://www.perseus.tufts.edu/GreekScience/Students/Tim/Contents.html

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12. Greek Mathematics James J. Woeppel 3Sep-02 greek mathematics James J. Woeppel http://www.portfolio.iu.edu/jwoeppel/M110/Greekmath.htm

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13. Basic Ideas In Greek Mathematics groundwork and even began to build the structure of much of modern mathematics. ASource Book in Greek Science, MR Cohen and IE Drabkin, Harvard, 1966. http://galileoandeinstein.physics.virginia.edu/lectures/greek_math.htm

Michael Fowler UVa Physics Department Index of Lectures and Overview of the Course Link to Previous Lecture Closing in on the Square Root of 2 In our earlier discussion of the irrationality of the square root of 2, we presented a list of squares of the first 17 integers, and remarked that there were several "near misses" to solutions of the equation m n . Specifically, 3 + 1. These results were also noted by the Greeks, and set down in tabular form as follows: After staring at this pattern of numbers for a while, the pattern emerges: 3 + 2 = 5 and 7 + 5 = 12, so the number in the right-hand column, after the first row, is the sum of the two numbers in the row above. Furthermore, 2 + 5 = 7 and 5 + 12 = 17, so the number in the left-hand column is the sum of the number to its right and the number immediately above that one. The question is: does this pattern continue? To find out, we use it to find the next pair. The right hand number should be 17 + 12 = 29, the left-hand 29 + 12 = 41. Now 41 = 1681, and 29

14. Classical Greek Mathematics UP Classical greek mathematics. During the period from about 600 BCto 300 BC , known as the classical period of greek mathematics http://www.rbjones.com/rbjpub/maths/math005.htm

Classical Greek Mathematics During the period from about 600 B.C. to 300 B.C. , known as the classical period of Greek mathematics, mathematics was transformed from an ecclectic collection of practical techniques into a coherent structure of deductive knowledge. For many mathematicians, the discipline we call mathematics was founded in this period. Here we briefly survey the achievements from a logical point of view From Procedural to Declarative Knowledge The change of focus from practical problem solving methods to knowledge of general mathematical truths and the development of a body of theory transforms mathematics into a scientific discipline. Abstraction Pythagorean abstraction and Plato's "ideals" make the subject matter of mathematics out of this world Logic The cannons of deductive reasoning are systematised by Aristotle in his syllogistic logic Foundations The Greeks showed concern for the logical structure of mathematics. The Pythagorean's sought to found all of mathematics on number but were confounded by the discovery of incommensurable ratios in geometry. This prevented them from giving an account of geometric magnitudes in terms of their numbers (what we now call the natural numbers or positive integers). By the end of the Pythagorean period geometry has come to be regarded as fundamental. The problem of incommensurable ratios will remain unresolved for more than two millenia. Deduction From very early in the classical period deduction is perceived as the primary method of arriving at mathematical truths. This contrasts with (but does not entirely displace) non-deductive generalisation from particulars.

15. Real Numbers - Some History consider here. The first is the period of classical greek mathematicsin which mathematics first emerged as a deductive science. The http://www.rbjones.com/rbjpub/maths/math008.htm

Real Numbers - some history Greek beginnings building on sand back to basics There are two major periods in the historical development of the real number system which we consider here. The first is the period of classical Greek mathematics in which mathematics first emerged as a deductive science. The second is that of the rigourisation of analysis and the formalisation of mathematics which took place mostly in the 19th century. Between these periods mathematics expanded very much in areas which depended on real numbers despite weakness in the understanding of real numbers. Greek Beginnings Number in Classical Greek Mathematics The social division in classical Greece, between slaves and citizens, supported a division of practical computation and mathematical theory. Though Greek mathematics understood as numbers only what we call the natural numbers, they dealt also with whole number ratios, and with geometric magnitudes, corresponding to what we now call rationals and reals. None of these systems were treated as we would treat them today, but even geometric magnitudes were treated in Greece with greater rigour than at any subsequent period until the real number system was placed on a firm foundation in the 19th century. The Method of Exhaustion Before any of the number systems had been established to modern standards Eudoxus developed the Method of Exhaustion. This was used extensively in

16. The Helenistic Period Of Greek Mathematics Because of them, this period is sometimes called the ``golden age of greek mathematics. Inthe works of Apollonius, greek mathematics reached its zenith. http://www.math.tamu.edu/~don.allen/history/helnistc/helnistc.html

Next: About this document Aristarchus of Samos (ca. 310-230 BC) He was very knowledgeable in all sciences, especially astronomy and mathematics. He discovered an improved sundial, with a concave hemispherical circle. He was the first to formulate the Copernican hypotheses and is sometimes called the Ancient Copernican He countered the nonparallax objection by asserting that the stars to be so far distant that parallax was not measurable. Wrote On the Sizes and Distances of the Sun and Moon . In it he observed that when the moon is half full, the angle between the lines of sight to the sun and the moon is less than a right angle by 1/30 of a quadrant. From this he concluded that the distance from the earth to the sun is more than 18 but less than 20 times the distance from the earth to the moon. (Actual ). Without trigonometry he was aware of and used the fact that He also made other trigonometic estimates without trigonometry. ARCHIMEDES Apollonius of Perga (ca 262 BC - 190 BC) Apollonius was born in Perga in Pamphilia (now Turkey), but was possibly educated in Alexandria where he spent some time teaching. Very little is known of his life. He seems to have felt himself a rival of Archimedes. In any event he worked on similar problems. He was known as the ``great geometer" because of his work on conics.

17. Greek Mathematics FloorPlan v7 Banner 10000037 Era of greek mathematics. The Greeksare responsible for initial explosion of Mathematical ideas. For http://members.fortunecity.com/kokhuitan/greek.html

Era of Greek Mathematics The Greeks are responsible for initial explosion of Mathematical ideas. For several centuries, Greek mathematics reign the mathematical world, with great advances in Number Theory, the Theory of Equation, and in particular Geometry. The first great Greek mathematician is Thales of Miletus (624-547 BC). He brought the knowledge of Egyptian Geometry to the Greeks and discovered several theorems in elementary Geometry. He predicted a Solar Eclipse in 585 BC and could calculate the height of a pyramid, as well as how far a ship is from land. One of his pupils, the Greek philosopher, Anaximander of Miletus (610-546 BC), is considered the founder of Astronomy. Perhaps the most prominent Greek mathematicians is Pythagoras of Samos (569-475 BC). His ideas were greatly influenced by Thales and Anaximander. His school of thought practiced great secrecy and he (and his followers, called Pythagoreans) believe everything in the world can be reduced to numbers. This idea stemmed from Pythagoras' observations in Music, Mathematics and Astronomy. E.g. Pythagoras noticed that vibrating strings produce harmonics in which the lengths of the strings are in ratios of whole numbers. In fact, he contributed greatly to the mathematical theory of music. He had the notion of Odd and Even Numbers, Triangular Numbers, Perfect Numbers, etc. In particular, he is well known today for his Pythagoras Theorem. Although this theorem is known to the Babylonians and Chinese long before Pythagoras, he seemed to be the first person to provide a proof of it.

18. Ancient Greek Mathematics Ancient greek mathematics. Ancient Greek scholars were the first peopleto explore pure mathematics, apart form practical problems. 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.

19. Greek Mathematics greek mathematics. Allman, GJ Greek Geometry from Thales to Euclid. Selections Illustratingthe History of greek mathematics, Vol. 1 From Thales to Euclid. http://www.ericweisstein.com/encyclopedias/books/GreekMathematics.html

Greek Mathematics Allman, G.J. Greek Geometry from Thales to Euclid. Bulmer-Thomas, Ivor. Selections Illustrating the History of Greek Mathematics, Vol. 1: From Thales to Euclid. Cambridge, MA: Harvard University Press, 1980. $21.25. Bulmer-Thomas, Ivor. Selections Illustrating the History of Greek Mathematics, Vol. 2. Cambridge, MA: Harvard University Press, 1939-41. Gricke, N. Mathematik in Antike und Orient. Berlin: Springer-Verlag, 1984. 292 p. ISBN: 0387110478. $?. Gow, James. A Short History of Greek Mathematics. London: Cambridge University Press, 1884. $?. Heath, Thomas Little. A History of Greek Mathematics, Vol. 1: From Thales to Euclid. New York: Dover, 1981. $11.65. Heath, Thomas Little. A History of Greek Mathematics, Vol. 2: From Aristarchus to Diophantus. New York: Dover, 1981. $11.65. Heath, Thomas Little. A Manual of Greek Mathematics. Oxford, England: Clarendon Press, 1931. 552 p. Netz, Reviel. The Shaping of Deduction in Greek Mathematics. Cambridge, England: Cambridge University Press, 1999. 327 p. $?. Thomas, Ivor.

20. Greek Mathematics Similar pages wwwadm.pdx.edu/user/sinq/greekciv/science/mathematics/IT.html Similar pages More results from www-adm.pdx.edu historyforkids! H4K HOME. greek mathematics Because the Greeks had only very clumsyways of writing down numbers, they didn't like algebra. They http://www-adm.pdx.edu/user/sinq/greekciv2/science/mathematics/it.html

The ancient Greeks were very interested in scientific thought. They were not satisfied with just knowing the facts; they wanted to know the why and how. It should be no surprise that the Greeks were extremely successful in the area of mathematics. The mathematics we use today, and its content, are for the most part Greek. The Greeks laid down the first principles, and invented methods for solving problems. Though most people don't realize it, mathematics is a Greek science - regardless of what modern day analysis might bring. Below are some of the great mathematicians of Greece. Bibliography

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