1. Greek Mathematics And Its Modern Heirs greek mathematics and its Modern Heirs. Classical Roots of the Scientific Revolution. 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

2. History Of Mathematics: Greece A history of greek mathematics. Two volumes. Clarendon Press, Oxford, 1921 Translation The beginnings of greek mathematics, tr. by A 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)

3. Greek Mathematics - History For Kids! H4K Lesson Plans. for Teachers. Parents' Corner. H4K Crafts and Projects. greek mathematics. Because the Greeks had only very clumsy ways of writing down numbers, they didn't like algebra. architecture, and so did mathematics. Some famous Greek mathematicians were Pythagoras, Aristotle http://www.historyforkids.org/learn/greeks/science/math

China India West Asia Greece ... Religion The Web Just H4K H4K Lesson Plans for Teachers Parents' Corner H4K Crafts and Projects Greek Mathematics Because the Greeks had only very clumsy ways of writing down numbers , they didn't like algebra. They found it very hard to write down equations or number problems. Instead, Greek mathematicians were more focused on geometry, and used geometric methods to solve problems that you might use algebra for. Greek mathematicians were also very interested in proving that certain mathematical ideas were true. So they spent a lot of time using geometry to prove that things were always true, even though people already knew that they were true most of the time anyway. The Greeks in general were very interested in rationality , in things making sense and hanging together. They wanted to tie up the loose ends. They liked music, because music followed strict rules to produce beauty. So did architecture , and so did mathematics.

4. Wonders Of Ancient Greek Mathematics Please note These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. Wonders of Ancient greek mathematics. ( and maybe some not so wonderful but http://www.perseus.tufts.edu/GreekScience/Students/Tim/Contents.html

Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library . We do not have contact information for the authors. Please keep that in mind while reading these papers. Wonders of Ancient Greek Mathematics (and maybe some not so wonderful but still cool stuff) By Timothy Reluga Look at the comments on this paper. Preface Enigma's of the Past Squaring the Circle Doubling the Cube Trisecting the Angle Elegant Proofs and Methods of Ancient Ones Pythagorus's Theorem The Golden Section Splitting the prism and the Method of Exhaustions Archimede's Spiral Technical References Glossary may or may not be helpful Constructions defined Biographies of mathematicians, modern and ancient Geographic Locations and some bibliographic info on ancient Greek thinkers(everybody did everything back then) Manuscripts of Euclid and Archimedes scanned from the Vatican's display in Washington D.C.

5. Greek Mathematics Please note These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. Chris Weinkopf. greek mathematics. April 19, 1995 Order, Purpose, and Method. greek mathematics was premised on inductive reasoning http://www.perseus.tufts.edu/GreekScience/Students/Chris/GreekMath.html

Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library . We do not have contact information for the authors. Please keep that in mind while reading these papers. Chris Weinkopf Greek Mathematics April 19, 1995 Look at the comments on this paper. Table of Contents The Divisions The Pure and the Physical Order, Purpose, and Method Greek mathematics was premised on inductive reasoning. Whereas ancient historians sough to deduce facts from observations, the mathematicians sought to explore and discover truths working from a factual foundation. Theoretical mathematics also provided ancient philosophers with the tools of logic, which were thus employed in the pursuit of practical ends. The classical interpretation of mathematics, as well as the subdivision of the discipline into specific categories, demonstrates the Greeks' approach to the subject. The Divisions A fragment of Archytus , a Pythagorean friend and contemporary of Plato, explains the Quadrivivium , the four fields into which the Pythagoreans divided mathematics: arithmetic, geometry, sphaeric (astronomy), and music. Plato classified mathematics into the same categories, but included as a separate division stereometry three-dimensional geometry between geometry and sphaeric. (The Pythagoreans considered stereometry as subfield of geometry).

6. Ancient Greek Mathematics Ancient greek mathematics. Ancient Greek scholars were the first people to 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.

7. Greek Mathematics Ancient greek mathematics. Ancient greek mathematics achieve the full flower of intellectual Many of the results from greek mathematics are advanced mathematical topics still http://www.math.tamu.edu/~dallen/masters/Greek/content4.htm

Ancient Greek Mathematics Ancient Greek mathematics achieve the full flower of intellectual development on an equal par with modern levels. The brought the full flower of geometry as an axiomatic system. They also seem to have created the basis of logical argument and the axiomatic method. Probably there is no other epoch of human civilization where evidence of such fundamental and sweeping changes in though have occurred. Many of the results from Greek mathematics are advanced mathematical topics still today. As well, most mathematicians haven't a glimmer of its depth. While everyone has heard of Euclid, few know that the famous Elements was a compendium of plane geometry, number theory, and solid geometry. From this work of thirteen book, just the first two are studied in high school. As you will see the theoretical content is remarkable, exceeded perhaps only by mathematical technique as achieved by Archimedes and Apollonius. Greek Mathematics Goals Readings Problems I n most cases the readings will be presented in the form of Acrobat (PDF) documents. To read and print them you will need the Adobe Acrobat Reader.

8. Greece - Greek Math Resources on ancient greek mathematics, calculations, geometry, and on Zeno, Archimedes, and Roman numerals. Basic Ideas in greek mathematics. Michael Fowler's lecture http://ancienthistory.about.com/cs/greekmath

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About History Ancient / Classical History Ancient Greece - Greek ... Science Medicine Greek Mathematics Home Essentials Site Map - Start Here! Atlas - Myths - Timelines ... Trojan War Hero Achilles - Troy zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Atlas and Places - Where? Ancient Greece - Greek Ancient Rome - Romans ANE Egypt Persia Israel... ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Ancient / Classical History newsletter. Search Ancient / Classical History Greece - Greek Math Resources on ancient Greek mathematics, calculations, geometry, and on Zeno, Archimedes, and Roman numerals. Alphabetical Recent Up a category Euclid An Alexandrian mathematician and teacher, Euclid is most famous for his geometry with its logical deductions, axioms and postulates. The Number 60 in Distance and Time Sixty may be an arbitrary number but it approximates the numbers of days in the year and is easier to work with because it has so many factors than a decimal system. Pythagoras Mathematics From your Guide. Links to Pythagorean mathematics.

9. Mathematics 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. So you can pick any of greek mathematics. Ptolemy's Geography. Greek Astronomy http://www.ncsa.uiuc.edu/SDG/Experimental/vatican.exhibit/exhibit/d-mathematics/

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

10. 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

History Topics: Index of Ancient Greek mathematics Articles about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy ... The teaching of mathematics in Ancient Greece. Various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name below to go to that biography. Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers Al-Haytham Johann Bernoulli Cusa James Gregory ... Search Form JOC/EFR January 2004 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Greeks.html

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

How do we know about Greek mathematics? Ancient Greek index History Topics Index There are two separate articles in this archive: "How do we know about Greek mathematics?" and How do we know about Greek mathematicians? . There is a common belief that the question posed in this article, about Greek mathematics rather than Greek mathematicians, is easy to answer. Perhaps all we need to do to answer it is to read the mathematical treatises which the Greek mathematicians wrote. We might think, very naively, that although some of the origainal texts have been lost there should be plenty left for us to be able to gain an excellent picture of Greek mathematics. 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 . When we read Heath's The Thirteen Books of Euclid's Elements are we reading an English translation of the words which Euclid wrote in 300 BC? In order to answer this question we need to examine the way the Elements has reached us, and, more generally, how the writings of the ancient Greek mathematicians have been preserved.

12. Portland State's Greek Civ For Kids and how. The main idea of greek mathematics is a simple one someone observes nature and finds that certain simple forms exist. It http://www.historyforkids.org/greekciv/science/mathematics/it.htm

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. The main idea of Greek Mathematics is a simple one: someone observes nature and finds that certain simple forms exist. It should be no surprise that the Greeks were extremely successful in the area of geometry, since geometry deals with shapes and lengths. 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. Plato Bibliography Return to Science topics

13. 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

History Topics: Index of Ancient Greek mathematics Articles about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy ... The teaching of mathematics in Ancient Greece. Various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name below to go to that biography. Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers Al-Haytham Johann Bernoulli Cusa James Gregory ... Search Form JOC/EFR January 2004 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Greeks.html

14. Basic Ideas In Greek Mathematics Basic Ideas in greek mathematics. Michael Fowler. University of Virginia. http://www.phys.virginia.edu/classes/109N/lectures/greek_math.htm

Basic Ideas in Greek Mathematics Michael Fowler University of Virginia 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

15. The Origins Of Greek Mathematics next Next About this document. The Origins of greek mathematics. Though the Greeks The Sources of greek mathematics. In actual fact 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

16. Classical Greek Mathematics UP Classical greek mathematics. During the period from about 600 BC to 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.

17. History For Kids! wwwadm.pdx.edu/user/sinq/greekciv2/science/mathematics/it.html More results from www-adm.pdx.edu ?. The greek mathematics Demonstrative Geometry?. The greek mathematics Demonstrative Geometry. Characteristic of greek mathematics In greek mathematics after Euclid. One http://www-adm.pdx.edu/user/sinq/greekciv/science/mathematics/IT.html

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18. Greek History - Greek Science And Its Influence On Western Civilization Ancient greek mathematics Have you ever wondered who was responsible for making those complicated theorems that we use in geometry and algebra? http://www.hellenism.net/eng/history-math.htm

Ancient Greek Mathematics Have you ever wondered who was responsible for making those complicated theorems that we use in geometry and algebra? What about the fact that certain intersecting lines are called rectangles or triangles? Where did all of these interesting ideas come from? Most of these ideas came from the great minds of mathematicians from ancient Greece. If it wasn't for these Mathematicians, we would have a harder time solving mathematical problems. For example, modern architects would have a harder time calculating distances as they would not know that the sum of the squares of two sides of a right triangle equals the square of its hypotenuse (Pythagorean Theorem). These ideas have formed the basis for the advancement of science in western civilization. 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. Greek Influence - Main Page Ancient Greek Agriculure Ancient Greek Astronomy Ancient Greek Earth Science ... Ancient Greek Medicine For over a thousand years (from the fifth century B.C. to the fifth century A.D.) Greek mathematicians maintained a splendid tradition of work in the exact sciences: mathematics, astronomy, and related fields. Though the early synthesis of Euclid and some of the supremely brilliant works of Archimedes were known in the medieval west, this tradition really survived elsewhere. In Byzantium, the capital of the Greek-speaking Eastern empire, the original Greek texts were copied and preserved. In the Islamic world, in locales that ranged from Spain to Persia, the texts were studied in Arabic translations and fundamental new work was done.

19. Greek Mathematics FloorPlan v7 Banner 10000037. Era of greek mathematics. The Greeks are 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.

20. ¥j§Æþ¼Æ¾Ç¡]ancient Greek Mathematics¡^ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.edp.ust.hk/math/history/2/2_4.htm

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