21. Synoptic Chronology Of Greek Thinkers And Writers The writers and thinkers shown are Æschylus, Anaxagoras, Anaximenes, Anaximander,Antisthenes the Cynic, archytas of tarentum, Aristippus of Cyrene, http://plato-dialogues.org/tools/synopsis.htm

Bernard SUZANNE Last updated January 3, 1999 Plato and his dialogues : Home Biography Works and links to them History of interpretation New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author Synoptic chronology of Greek Thinkers and Writers This synopsis presents a visual chronology of some of the Greek writers and thinkers that preceeded, were contemporaries of, and followed Socrates and Plato, allowing to quickly see in what order they lived and who was contemporary of whom. It also includes for context some of the most prominent political leaders of the time. The dates are associated with the Olympiad numbers that were used as reference by the Greek themselves. The reader must be warned that many of the dates of birth and death here provided are only tentative, and may differ in different sources, sometimes (such as with Parmenides, for instance) by several years. The purpose of this synopsis is not to pretend to utmost accuracy, or to suggest new datings, but to provide a feel for who might have been contemporary of whom. Accordingly, the dates used were those available from widely available history books or encyclopediae, and I didn't try to ascertain these before using them. To get a more "concrete" feel for this chronology, a

22. Philosophy: Philosophers: A: Archytas-of-tarentum Spirit And Sky archytas of tarentum. Brief biography from the Thessaloniki Museum of Technology.(Added Thu Jan 01 2004) ID 112605 http://www.spiritandsky.com/philosophy/philosophers/a/archytas-of-tarentum/

Home philosophy philosophers a : archytas-of-tarentum Web www.spiritandsky.com Home Search Suggest a Site Submission Guidelines ... a : archytas-of-tarentum Links: Archytas Archytas Life and work of fourth century BC Greek mathematician, political leader and philosopher; from the Stanford Encyclopedia by Carl Huffman. (Added: Thu Jan 01 2004) ID 112604 Archytas Archytas Biography of Archytas (428BC-350BC) from the MacTutor History of Mathematics Archive. (Added: Thu Jan 01 2004) ID 112606 Archytas of Tarentum Archytas of Tarentum Brief biography from the Thessaloniki Museum of Technology. (Added: Thu Jan 01 2004) ID 112605 Home philosophy philosophers a : archytas-of-tarentum Home Search Suggest a Site Submission Guidelines ... About The Artist permission from spiritandsky.com is strictly prohibited.

23. EpistemeLinks.com: Website Results For Philosopher Archytas Of Tarentum General website search results for archytas of tarentum including brief biographies,link resources, and more. Provided by EpistemeLinks.com. http://www.epistemelinks.com/Main/Philosophers.aspx?PhilCode=Arc2

24. EpistemeLinks.com: Encyclopedia Entries For Philosopher Archytas Of Tarentum Encyclopedia entry search results for archytas of tarentum. Provided byEpistemeLinks.com. archytas of tarentum. Related resources · Main Page http://www.epistemelinks.com/Main/EncyRefs.aspx?PhilCode=Arc2

25. EBooks.com - Archytas Of Tarentum EBook In fourthcentury Greece archytas of tarentum solved a famous mathematical puzzle,saved Plato from the tyrant of Syracuse and led a powerful Greek city http://usa2.ebooks.com/ebooks/book_display.asp?IID=228691

26. Archytas Of Tarentum: Pythagorean, Philosopher And Mathematician King By Carl A. Huffman, Cambridge Univ Pr June 2005 ISBN 0521837464. http://www.thattechnicalbookstore.com/b0521837464.htm

Home Search Browse Shopping Cart ... Help QuickSearch (Words, Author, Subject, ISBN) Publishers Email a friend about this book Archytas Of Tarentum: Pythagorean, Philosopher And Mathematician King Format Hardcover Subject Philosophy / Ancient ISBN/SKU Author Carl A. Huffman Publisher Cambridge Univ Pr Publish Date June 2005 Add to cart Price Qualified Frequent Buyer Price Ships from our store in 14 - 21 business days More delivery info here Table of Contents List of figures ix Preface xi PART ONE: INTRODUCTORY ESSAYS I Life, writings and reception Sources Chronology Family, teachers and pupils Archytas and Tarentum Archytas' private life and character The death of Archytas and Horace's "Archytas Ode" Reception Other men named Archytas Writings Archytas and Plato II The philosophy of Archytas Archytas as a mathematician Archytas and his predecessors Archytas on the value of the sciences Logistic as the fundamental science Optics and mechanics Conclusion: Archytas, Plato and Aristotle III The authenticity question PART TWO: GENUINE FRAGMENTS I Fragment 1 II Fragment 2 III Fragment 3 IV Fragment 4 PART THREE: GENUINE TESTIMONIA I Testimonia for Archytas' life, writings and reception (A1 A6, B5-B8)

27. Happy Time With EnjoyEbook! archytas of tarentum is one of the three most important philosophers in thePythagorean tradition, a prominent mathematician, who gave the first solution to http://www.enjoyebook.com/Eng/User/Book/book_viw.asp?bKey=29037&odr=6&type=PDF

28. Encyclopaedia Britannica Entry archytas of tarentum. Flourished 400 350 BC, Tarentum, Magna Graecia nowTaranto, Italy. Greek scientist, philosopher, and major Pythagorean http://www.aam314.vzz.net/EB/Archytas.html

Archytas of Tarentum Flourished: 400 - 350 BC, Tarentum, Magna Graecia [now Taranto, Italy] Greek scientist, philosopher, and major Pythagorean mathematician, who is sometimes called the founder of mathematical mechanics. Plato, a close friend, made use of his work in mathematics, and there is evidence that Euclid borrowed from him for Book viii of his Elements . Archytas was also an influential figure in public affairs, and he served for seven years as commander in chief of his city. A member of the second generation of followers of Pythagoras, the Greek philosopher who stressed the significance of numbers in explaining all phenomena, Archytas sought to combine empirical observation with Pythagorean theory. In geometry, he solved the problem of doubling the cube by constructing a three-dimensional model. The conclusions that he then drew concerning continued proportions, expressed as a b b c c d , he applied to musical harmony. Thus, he was able to discern intervals of pitch in the enharmonic scale in addition to those already known in the chromatic and the diatonic scales. Rejecting earlier views that the pitch of notes sounded on a stringed instrument is related to the length or tension of the strings, he proposed instead that pitch is related to the movement of vibrating air. Incorrectly, however, he asserted that the speed at which the vibrations travel to the ear is a factor in determining pitch. Archytas' reputation as a scientist and mathematician rests on his achievements in geometry, acoustics, and music theory, rather than on his extremely idealistic explanations of human relations and the nature of society according to Pythagorean number theory. Nonmathematical writings usually attributed to him, including a fragment on legal justice, are most likely the work of other authors.

29. Archytas archytas of tarentum, son of Mnesagoras, or of Hestius, according to Aristoxenus,also was a Pythagorean. It was he who, by a letter, saved Plato from the http://www.csun.edu/~hcfll004/archytas.html

ARCHYTAS of Tarentum Diogenes Laertes Life of Archytas: Archytas of Tarentum, son of Mnesagoras, or of Hestius, according to Aristoxenus, also was a Pythagorean. It was he who, by a letter, saved Plato from the death threatened by Dionysus. He possessed all the virtues, so that, being the admiration of the crowd, he was seven times named general, in spite of the law which prohibited reelection after one year. Plato wrote him two letters, in response to this one of Archytas: Greetings: It is fortunate for you that you have recovered from your illness, for I have heard of it not only from you, but also from Lamiscus. I have busied myself about those notes, and took a trip into Lucania, where I met descendants of Ocellus. I have in my possession the treatises On Law and On Kingship On Sanctity , and On the Origin of All Things , and I am sending them to you. The others could not be discovered. Should they be found, they will be sent to you. Plato answered: Greetings: I am delighted to have received the works which you have sent me, and I acknowledge a great admiration for him who wrote them. He seems to be worthy of his ancient and glorious ancestors, who are said to be from Myra, and among the number of those Trojans who emigrated under the leadership of Laomedon, all worthy people, as the legend proves. Those works of mine about which you wrote me are not in a sufficient state of perfection, but I send them such as they are. Both of us are in perfect agreement on the subject of protecting them. No use to renew the request. May your health improve.

30. Plato: Chronology but Plato refused to participate. With the intervention of archytas of tarentum,Plato is allowed to return to Athens (summer, 360). http://www.csun.edu/~hcfll004/platochron.html

[Archonship of Diotimus] Plato born in Athens, the son of Ariston (son of Aristokles, direct descendant of Solon's brother Exekestiades); his mother was Periktione (sister of Charmides and cousin of Kritias). Plato had two brothers and a sister. His mother married a second time, to Pyrilampes, a member of the Periclean group. The Great Peloponnesian War (Part I). Young Plato received a musical and gymnastic education; he wrote juvenile epigrams and tragedies, but burned them once he became associated with Socrates. Great Peloponnesian War (Part II). He was active politically ( Letter 7 ). His uncle and cousin were among the Thirty Tyrants (404/3), who terrorized the Athenian state after Athens lost the war to Sparta in 404. Conservative coup d' état (The 400), followed later in the summer by a democratic restoration led by Alcibiades. Trial and execution of Socrates. Plato was present at the trial, but not allowed to speak. Plato and other disciples removed themselves to Megara, next door to Athens. There was later a 'Megarean School' of Socratic philosophy: Elkleides of Megara (author of a Crito, Eroticus, Aeschines, Alcibiades

31. ANF07. Fathers Of The Third And Fourth Centuries. (iii.iii.xviii) archytas of tarentum is praised, who, when he had found everything ruined 1759on his estate, rebuking the fault of his bailiff, said, “Wretch, http://www.ccel.org/ccel/schaff/anf07.iii.iii.xviii.html

ANF07. Fathers of the Third and Fourth Centuries. Chap. XVIII.—Of the punishment of faults, that it cannot take place without anger Chap. XVIII.—Of the Punishment of Faults, that It Cannot Take Place Without Anger. What need is there, they say, of anger, since faults can be corrected without this affection? But there is no one who can calmly see any one committing an offence. This may perhaps be Archytas of Tarentum is praised, who, when he had found everything ruined Plato says) no prudent man punishes because there is an offence, but to prevent the occurrence of an offence, it is evident how evil an example this wise man put forth. For if slaves shall perceive that their master uses violence when he is not angry, and abstains from violence when he is angry, it is evident that they will not commit slight offences, lest they should be beaten; but will commit the greatest offences, that they may arouse the anger of the perverse man, and escape with impunity. But I should praise him if, when he was enraged, he had given space to his anger, that the excitement of his mind might calm down through the interval of time, and his chastisement might be confined within moderate limits. Therefore, on account of the magnitude of the anger, punishment ought not to have been inflicted, but to have been delayed, lest it should inflict upon the offender pain greater than is just, or occasion an outburst of fury in the punisher. But how, how is it equitable or wise, that any one should be punished on account of a slight offence, and should be unpunished on account of a very great one? But if he had learned the nature and causes of things, he never would have professed so unsuitable a forbearance, that a wicked slave should rejoice that his master has been angry with him. For as God has furnished the human body with many and various senses which are necessary for the use of life, so also He has assigned to the soul various affections by which the course of life might be regulated; and as He has given desire for the sake of producing offspring, so has He given anger for the sake of restraining faults. Â

32. Cod.3.70141 archytas of tarentum. Pythagorean, Philosopher and Matematician King. archytas of tarentum is one of the three most important philosophers in the http://www.lerma.it/Editore/Promozione/2005_07/cod_30070141.htm

Offerta Speciale - Special Offer Carl A. Huffman Archytas of Tarentum. Pythagorean, Philosopher and Matematician King. Indice - Index 1. Life, writings and reception; 2. The philosophy of Archytas; 3. The authenticity question; Part II. Genuine Fragments: 1. Fragment 1; 2. Fragment 2; 3. Fragment 3; 4. Fragment 4; Part III: Genuine Testimonia: 1. Life and writings (A1-A6, B5-B8); 2. Moral philosophy and character; 3. Geometry: the duplication of the cube (A14 and A15); 4. Music; 5. Metaphysics; 6. Physics; 7. Miscellaneous testimonia; Appendix: Spurious writings and testimonia; Appendix: Archytas name. Abstract Archytas of Tarentum is one of the three most important philosophers in the Pythagorean tradition, a prominent mathematician, who gave the first solution to the famous problem of doubling the cube, an important music theorist, and the leader of a powerful Greek city-state. He is famous for sending a trireme to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361 BC. This is the first extensive study of Archytas' work in any language. It contains original texts, English translations and a full commentary for all the fragments of his writings and for all testimonia concerning his life and work. In addition there are introductory essays on Archytas' life and writings, his philosophy, and the question of authenticity. Carl A. Huffman presents a new interpretation of Archytas significance both for the Pythagorean tradition and also for fourth-century Greek thought, including the philosophies of Plato and Aristotle.

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34. List Of Scientists By Field archytas of tarentum. archytas of tarentum. archytas of tarentum. Arduino, Giovanni.Aretaeus of Cappadocia. Arfvedson, Johann August. Argand, Émile http://www.indiana.edu/~newdsb/a.html

Abailard, Pierre Abano, Pietro d' Abano, Pietro d' Abano, Pietro d' Abano, Pietro d' Abbe, Cleveland Abbe, Ernst Abel, John Jacob Abel, John Jacob Abel, John Jacob Abel, Niels Henrik Abel, Othenio Abetti, Antonio Abich, Otto Hermann Wilhelm Abney, William de Wiveleslie Abney, William de Wiveleslie Abraham, Max Abreu, Aleixo de Accum, Friedrich Christian Achard, Franz Karl Achard, Franz Karl Acharius, Erik Achillini, Alessandro Achillini, Alessandro Adam of Bodenstein Adam of Bodenstein Adams, Frank Dawson Adams, John Couch Adams, John Couch Adams, Leason Heberling Adams, Leason Heberling Adams, Roger Adams, Walter Sydney Adanson, Michel Adanson, Michel Addison, Thomas Adelard of Bath Adelard of Bath Adet, Pierre-Auguste Adrain, Robert Aepinus, Franz Ulrich Theodosius Aepinus, Franz Ulrich Theodosius Agardh, Carl Adolph Agardh, Jacob Georg Agassiz, Alexander Agassiz, Alexander Agassiz, Jean Louis Rodolphe Agassiz, Jean Louis Rodolphe Agathinus, Claudius Agnesi, Maria Gaetana Agol, Izrail' Iosifovich Agol, Izrail' Iosifovich Agricola, Georgius Agricola, Georgius

35. ªüº¸§Æ¶ð´µ¡£Archytas Of Tarentum¡¤ 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/3/3_78.htm

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36. Archytas (428-347 B.C.) A biography of the ancient philosopher archytas of tarentum. ARCHYTAS ofTarentum, the last and greatest of the scientific thinkers belonging to the http://www.usefultrivia.com/biographies/archytas_001.html

ARCHYTAS ARCHYTAS Aristotle wrote a treatise, which has not come down to us, on the philosophy of Archytas. Such fragments of his philosophy as survive are too slight, and their authenticity is too uncertain, to enable us to estimate their value. But researchers have brought into prominence the importance of Archytas as a mathematical discoverer. His solution of what was known as the Problem of Delos the insertion between two given quantities of two mean proportionals proves great original power and the possession of a large stock of geometrical knowledge. We see that he was familiar with the generation of cylinders and cones, and had also clear ideas on the interpenetration of surfaces; he had, moreover, a clear conception of geometrical loci, and of their application to the determination of a point by means of their intersection. It is to be added, that Archytas was the teacher of Eudoxus of Cnidus, the most important name in mathematics between Pythagoras and Archimedes. Find more articles on Archytas Purchase books on Archytas This biography is reprinted from The New Calendar of Great Men . Ed. Frederic Harrison. London: Macmillan and Co., 1920.

37. Dupcubfin.html archytas of tarentum s Solution The most interesting and complex of the solutionsto the Delian Problem is the solution developed by archytas of tarentum. http://www.ms.uky.edu/~carl/ma330/projects/dupcubfin1.html

Duplication of the Cube : Darrell Mattingly, Cateryn Kiernan The ancient Greeks originated numerous mathematical questions, most of which they learned to solve using simple mathematical tools, such as the straight edge and the collapsable compass. Three of these problems persist today, challenging students in contemporary classrooms. This triology of problems, the trisection of a given angle, the squaring of a circle, and the duplication of the cube, have since been proved impossible using exclusively the straight edge and the compass. In the quest to solve these problems using those specific tools, however, mathematicians developed numerous alternate solutions using other mathematical tools. The last problem of the trilogy is the focus of this discussion, and it challenged mathematicians for centuries, due to the restriction of using only the aforementioned tools. Origin of the Problem Proof that NO Platoic Solution Exists for the "Delian" Problem After centuries of mathematicians had worked on this problem, a proof developed that it could not be done using exclusively the straight edge and compass. This proof is based on theorems about the powers of degrees of subfields generated by the x and y coordinates of the side of the cube to be duplicated. Although the desired point can be approximated, it cannot in fact be found based on these theorems.

38. History Of Mathematics: Greece archytas of tarentum (of Taras) (c. 428c. 347); Plato (427-347); Theaetetus ofAthens (c. 415-c. 369); Leodamas of Thasos (c. 380); Leon (fl. c. 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)

39. History Of Mathematics: Chronology Of Mathematicians archytas of tarentum (of Taras) (c. 428c. 347) *SB *MT; Plato (427-347) *SB *MT;Theaetetus of Athens (c. 415-c. 369) *MT; Leodamas of Thasos (fl. c. http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *MT 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

40. Automata History archytas of tarentum made a wooden pigeon suspended from the end of a pivot whichwas rotated by a jet of water or steam. The pigeon simulated flight. http://www.automata.co.uk/History page.htm

The following is a short description of the history of automata. It can be broken down into 3 rough time frames, Ancient History, 15th-19th Century and Modern times. ANCIENT HISTORY The first Automata was created by GOD. According to Talmundic tradition, Adam was created in 5 hours. In the first, his dust was gathered from all parts of the world; In the second, it was kneaded into a shapeless mass (Golem); In the third, his limbs were shaped; In the fourth, a soul was infused into him; In the fifth, he arose and stood on his feet. "And God formed man of the dust of the ground and breathed into his nostrils the breath of life; and man became a living soul." Genesis. Chapter II. Mythology has many stories about automata, some a wild and fanciful, others may have been based on fact. We can not say for sure what is fact or fiction, so what follows is a description of some of the more exciting reference to mythological automata which are based on accounts from the Ancient Greeks. Prometheus was reputed to have made the first man and women on earth, with clay animated by fire and stolen from heaven.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

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