21. Plato: Chronology Probably Plato s first real attention to Pythagoreanism, which was undergoinga renaissance in South Italy under the leadership of archytas of tarentum. 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

22. Title archytas of tarentum Ca. One of the last prominent Pythagoreans, Archytas ofTarentum was a mathematician, teacher, philosopher, and military leader. http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/archytastext.html

ARCHYTAS OF TARENTUM Ca. 430 BCE to 350 BCE One of the last prominent Pythagoreans , Archytas of Tarentum was a mathematician, teacher, philosopher, and military leader. Archytas was also a contemporary and good friend of Plato , and is even credited with saving his life! Archytas' main contribution to mathematics was his work involving the harmonic mean, which he used to discover a geometric way of duplicating the cube . That is, given any cube, construct another cube with exactly double the volume. This problem is also referred to as the Delian Problem. Archytas' other major contribution to mathematics was his eminence as a teacher. Archytas was involved with teaching at Plato's Academy. Menaechmus , a student of Eudoxus , who in turn was a student of Archytas was also interested in the Delian problem and found an independent geometric solution.

23. Archytas (428-347 B.C.) archytas of tarentum, the last and greatest of the scientific thinkers belongingto the Pythagorean school, was contemporary with Plato, and is said to have 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.

24. Greciaheroica2 3. archytas of tarentum. Archytas was a disciple of Philolaus who wroteabout proportions and studied arithmetic, geometric and harmonic mean. http://descartes.cnice.mecd.es/ingles/maths_workshop/A_history_of_Mathematics/Gr

THE GREEK HEROIC AGE II History HIPPIAS OF ELIS Unlike the Pythagoreans, Hippias de Elis (460 B.C.) was a Sophist ; in other words he earned his living by teaching his disciples. This is mentioned in Plato's Dialogues , where he is described as having little substance, earning more money than his peers and somewhat proud in character. Proclus ascribed to him the invention of the first curve, which is different to the circumference , known as the trisectrix or quadratrix of Hippias, which allows the angle to be divided into three equal parts. It can also be used to square the circle although Dinostratus gave a clear demonstration of this in the following century. Hippias' trisectrix Whilst a moves around the circle at constant velocity b moves along the segment at constant velocity too. Each point on the curve represents the point where the arc and segment coincide as we move along them at the same time. In this window you can see how Hippias' trisectrix is used to trisect the angle in three equal parts.

25. Plato Plato did not expect the plan to succeed but because both Dion andarchytas of tarentum believed in the plan then Plato agreed. http://www.crystalinks.com/plato.html

http://www.crystalinks.com/plato.html Plato - (about 427-347 B.C.) Plato is probably one of the greatest philosophers of all times, if not the greatest. Plato was born to an aristocratic family in Athens. His father, Ariston, was believed to have descended from the early kings of Athens. Perictione, his mother, was distantly related to the 6th-century B.C. lawmaker Solon. When Plato was a child, his father died, and his mother married Pyrilampes, who was an associate of the statesman Pericles. Plato's original name was Aristocles, but in his school days he received the nickname Platon (meaning "broad" ) because of his broad shoulders. It was mostly in Pyrilampes' house that Plato was brought up. Aristotle writes that when Plato was a young man he studied under Cratylus who was a student of Heracleitus, famed for his cosmology which is based on fire being the basic material of the universe. It almost certain that Plato became friends with Socrates when he was young, for Plato's mother's brother Charmides was a close friend of Socrates. The Peloponnesian War was fought between Athens and Sparta between 431 BC and 404 BC.

26. The Earlier History Of Powered Flight Another tale recounts the invention of a Greek named archytas of tarentum whowas said to have made a wooden bird about four hundred years before Christ. http://www.centennialofflight.gov/essay/Prehistory/earliest_flight/PH1.htm

The Earliest Efforts at Flight In Greek mythology, Icarus flew too close to the sun Other legends about flight abound. Another early one tells of King Bladud, who ruled in Britain in the ninth century B.C.E. Bladud supposedly constructed a pair of wings with which he proposed to fly. But, according to the monk Geoffrey of Monmouth in a history of the British kings, Bladud was dashed to pieces as he landed on top of the Temple of Apollo in the town of Trinovantum. Another tale recounts the invention of a Greek named Archytas of Tarentum who was said to have made a wooden bird about four hundred years before Christ. This bird was powered by steam and supposedly flew about 50 feet (15 meters). "Flight" of Simon the Magician in Roman times Earlier, in 1010, a monk in Malmsesbury, England, attached artificial wings to his body and jumped from the top of his abbey to glide to only two broken legs upon landing. Other tower jumpers suffered death or injuries, while a few achieved some partial success with their glides. In fifteenth-century Italy, the brilliant Italian artist, scientist, and engineer Leonardo da Vinci, who understood some of the basic principles of flight as early as the 1480s, was the first to seriously study aerodynamics. He examined the way birds flew and sketched their wings and muscles in a flying position. His notebooks were filled with drawings and descriptions of birds in flight and with models that had wings like birds. Unfortunately, his ornithopter and helicopter designs could never have left the ground with them. He, and others of his time, failed to realize that human beings lacked the necessary muscle power to imitate bird flight with flapping wings. His works were rediscovered in the 19th century and had little or no influence on the history of flight technology.

27. Automata History 400 BC archytas of tarentum made a wooden pigeon suspended from the end of a pivotwhich was 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.

28. "Technology And Spiritual Progress" By Arne Wettermark" It is told of archytas of tarentum, philosopher and mathematician, contemporary ofPlato, that he had constructed a wooden dove, which by means of an ingenious http://www.theosophy-nw.org/theosnw/science/sc-wett.htm

Technology and Spiritual Progress By Arne Wettermark It is told of Archytas of Tarentum, philosopher and mathematician, contemporary of Plato, that he had constructed a wooden dove, which by means of an ingenious mechanism could fly, flap its wings and remain airborne for a considerable time. Archytas, who lived 400 B.C., is also supposed to have invented the screw, the crane and various hydraulic machines. Some time later the philosopher Aristotle relates the common use in his time of robots, which he defined as "an apparatus wherein certain parts are set in motion by an external contact with another portion of the apparatus." When Marcellus in the year 212 B.C. besieged Syracuse, the Romans suffered heavy losses through machines and instruments constructed by Archimedes: cranes armed with gigantic tongs that, from the city walls, grasped the enemy's ships, raised them in the air and then dropped them; catapults that caused a hail of gigantic rocks on the infantry. There is even said to have been a large burning glass, by means of which ships could be ignited and burnt. (Cf. Time magazine, November 26, 1973; this procedure was successfully repeated by Greek naval personnel in waters near Athens.)

29. Greek Mathematics Later, archytas of tarentum (428350 BC) used the curve to duplicate thecube. Archytas produced a piece of work on the theory of sound. 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.

30. CUBE archytas of tarentum (c. 430 Bc) solved the problems by means of sections of ahalf cylinder; according to Eutocius, Menaechmus solved them by means of the http://82.1911encyclopedia.org/C/CU/CUBE.htm

CUBE CUBE All these solutions were condemned by Plato on the ground that they were mechanical and not geometrical, i.e. they were not effected by means of circles and lines. However, no proper geometrical solution, in Platos sense, was obtained; in fact it is now generally agreed that, with such a restriction, the problem is insoluble. The pursuit of mechanical methods furnished a stimulus to the study of mechanical loci, for example. the locus of a point carried on a rod which is caused to move according to a definite rule. Thus Nicomedes invented the conchoid (q.v.); Diodes the cissoid (q.v.); Dinostratus studied the quadratrix invented by Hippias; all these curves furnished solutions, as is also the case with the trisectrix, a special form, of Pascals limaon (q.v.). These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola. In algebra, the cube of a quantity is the quantity multiplied by itself twice, i.e. if abe the quantity aXaXa(=af) is its cube. Similarly the cube root of a quantity is another quantity which when multiplied by itself twice gives the original quantity; thus ai is the cube root of a (see ARITHMETIC and ALGEBRA). A cubic equation is one in which the highest power of the unknown is the cube (see EQUATION); similarly, a cubic curve has an equation containing no term of a power higher than the third, the powers of a compound term being added together.

31. Dictionary Of The History Of Ideas and the object receives a kind of impression as a result of the compression exertedupon it by the eye and by the object.” archytas of tarentum, according to http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv3-51

32. Dictionary Of The History Of Ideas Aristotle was probably describing the views of fifth and fourth- century Pythagoreanssuch as archytas of tarentum, under whom the doctrine of a universe http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv4-05

33. Bolt Science - Historical Background To Screw Threads It is considered by some that the screw thread was invented in about400BC by archytas of tarentum (428 BC 350 BC). Archytas is http://www.boltscience.com/pages/screw2.htm

Information on Screw Threads Historical Background Bolt Science is committed to providing expertise in bolted joint technology and to this end we present the following information for education purposes. It is considered by some that the screw thread was invented in about 400BC by Archytas of Tarentum (428 BC - 350 BC). Archytas is sometimes called the founder of mechanics and was a contemporary of Plato. One of the first applications of the screw principle were in presses for the extraction of oils from olives and juice from grapes. The oil presses in Pomeii were worked by the screw principle. Archimedes (287 BC - 212 BC) developed the screw principle and used it to construct devices to raise water. The water screw may have originated in Egypt before the time of Archimedes was constructed from wood and was used for land irrigation and to remove bilge-water from ships. The Romans applied the Archimedean screw to mine drainage. The screw was described in the first century AD in Mechanica of Heron of Alexandria. The construction of the screw thread depended upon the eye and skill of the craftsman. Advances on this occurred in the eighteenth century. Antoine Thiout around 1750 introduced the innovation of equipping a lathe with a screw drive allowing the tool carriage to be moved longitudinally semi-automatically. Screws with fine pitches are essential in a wide variety of instruments - such as micrometers. To construct such a thread a lathe was essential. Jesse Ramsden in 1770 made the first satisfactory screw-cutting lathe. Using his lathes a long screw cut be cut from a carefully cut small original. Precision screws allowed precision instruments to be made to allow the construction of steam engines and machines tools. By their use in surveying instruments they assisted in the construction and development of canals, roads and bridges.

34. History Of Astronomy: What's New At This Site On April 30, 1999 BC) Crater Archimedes (lunar feature). archytas of tarentum (c. 428BC c. 350 BC) Short biography and references; Crater Archytas http://www.astro.uni-bonn.de/~pbrosche/new/new990430.html

History of Astronomy What's new History of Astronomy: What's new at this site on April 30, 1999 Some URLs have been updated. History of astronomy Persons A Abbe, Ernst ... Crater Abbe (lunar feature) , Jena, Germany (in German) Ernst-Abbe-Oberschule (Gymnasium) , Berlin, Germany (in German) Ernst-Abbe-Gymnasium , Oberkochen, Germany (in German) Abbot, Charles Greeley (1872-1973) Crater Abbot (lunar feature) Abel, Niels Henrik (1802-1829) Crater Abel (lunar feature) Abetti, Antonio (1846-1928) Crater Abetti (lunar feature) Abu'l Fida [Abu'L-fida; Abulfeda], Ismail (1273-1331) Crater Abulfeda (lunar feature) Abul Wafa [Abu'l-Wafa] Muhammad al-Buzjani (940-997) Crater Abul Wafa (lunar feature) Acosta, Cristobal (1515-c.1594) Solar system feature named after him. No other relation to astronomy known to us. Biographical data and references Crater Acosta (lunar feature) Adams, John Couch (1819-1892) Crater Adams (lunar feature) Agatharchides of Cnidus (? - c. 150 BC) Very short biography Crater Agatharchides (lunar feature) Find more about Agatharchides with Alta Vista Agrippa (fl. AD 92)

35. History Of Astronomy: What's New At This Site On June 6, 2000 Brit.). archytas of tarentum (c. 428 BC c. 350 BC) Short biography (Encycl. Brit.).Argelander, Friedrich Wilhelm August (1799-1875) Short biography (Encycl. http://www.astro.uni-bonn.de/~pbrosche/new/new000606.html

History of Astronomy What's new History of Astronomy: What's new at this site on June 6, 2000 Some URLs have been updated. Welcome / About Site map (complete Table of Contents) updated Acknowledgements updated History of astronomy Persons A Abbadie, Antoine Thompson d' (1810-1897) Very short biography (Encycl. Brit.) Abbe, Cleveland (1838-1916) Very short biography (Encycl. Brit.) Abbe, Ernst (1840-1905) Short biography (Encycl. Brit.) Abbot, Charles Greeley (1872-1973) Short biography and references (Encycl. Brit.) Abel, Niels Henrik (1802-1829) Short biography and references (Encycl. Brit.) Abney, Sir William de Wiveleslie (1843-1920) Very short biography (Encycl. Brit.) Abraham bar Hiyya Ha-Nasi [Abraham Ben Chaja [Chija]; Abraham Judaeus] (c.1065-c.1136) Short biography (Encycl. Brit.) Ab u al-Fid a ' [Abu'l Fida; Abu'L-fida; Abulfeda], Ismail (1273-1331) Short biography (Encycl. Brit.) Ab u al-Waf a ' [Abul Wafa; Abu'l-Wafa; Abul Wefa] Muhammad al-Buzjani (940-997) Short biography (Encycl. Brit.)

36. Pythagoras Pythagoras successors were Philolus of Croton (c.470390 BC) andarchytas of tarentum (fl. 400-350 BC), who was a mathematician. http://www.kirjasto.sci.fi/pythagor.htm

Choose another writer in this calendar: by name: A B C D ... Z by birthday from the calendar Credits and feedback Pythagoras (570?-495? B.C.) Greek pre-Socratic mathematician and spiritual teacher, a semi-mystical figure, whose ideas has survived, as quotations, in writings of his successors. Pythagoras himself apparently did not record his philosophy in writing, but The Golden Verses , commonly dated to the fourth century B.C. , constitute an important source of ancient Pythagoreanism. "First the Immortal Gods as ranked by law / Honor, and use an oath with holy awe. / Then honour Heroes which Mankind excell, / And Daemons of the earth, by living well. " (from The Golden Verses , trans. by John Norris) Little is known of Pythagoras' life, or what he originally said. And there so are many legends and anecdotes about him, that modern scholars have concluded that Pythagoras acted more like a religious leader than a scientist, mathematician or systematic philosopher. However, at that time these different roles were not contradictory. Pythagoras was born in Samos, Greece, about 570 B.C.

37. Pythagoreanism In the fourth century there existed a friendship between a leading Pythagoreanand archytas of tarentum, a statesman and brilliant mathematician, whose was http://www.themystica.com/mystica/articles/p/pythagoreanism.html

Back to Home Page or Contents Page or Past and present beliefs or Index Pythagoreanism An ethical, religious, and mystical system of teaching founded by Pythagoras in the sixth century BC. Those holding to such teaching were called Pythagoreans. Their first society or brotherhood was established in Croton about 530 BC. The teaching exerted political influence in Croton and in other city-states throughout the region. By the fifth century BC Pythagorean societies in southern Italy had became involved in the fierce fighting between the aristocracy and the democratic forces of government. When the democratic party gained control it fiercely turned on the Pythagoreans in their settlements and burned them. Those that survived fled back to the Greek mainland and settled around Thebes and Phlius. About this time in the fifth century BC the Pythagoreans separated into two distinct groups called the Acusmatici (from akousma , meaning "oral precept") whose members emphasized the observation of the special Pythagorean way of life taught by the master himself. The second group was the Mathematici (meaning "students of theoretical subjects"), who prsued interests in arithmetic, the theory of music, astronomy, and cosmology. The Mathematici group eventually became closely associated with the doctrine of Plato and his followers who established the Platonic Academy. The Acusmatici became wandering ascetics finally joining the Cynics of the fourth century BC.

38. Plutarch According to such principles Pericles regulated his life; so did likewisearchytas of tarentum and Dion the Syracusan and Epaminondas the Theban. http://home.uchicago.edu/~ahkissel/plutarch.html

Plutarch Excerpts from Plutarch's writings on education Adam Kissel (using Charles William Super's tr., Plutarch on Education (C. W. Bardeen: Syracuse, N.Y., 1910)) "The Education of Boys" (ps.-Plutarch) We may remark in general terms regarding virtue what we are accustomed to say concerning the arts and sciences, namely, that three factors are essential to the formation of a well rounded character: phusis logos , and ethos . By instruction I understand the acquisition and imparting of knowledge; by ethos . Natural endowments are inborn; progress is a matter of education; application, of (exercise); while the highest excellence is the result of all combined. In so far as any of these is wanting, is necessarily defective. Natural endowments without education are blind; education, where there are no natural endowments, is inefficacious; and practice apart from both is incomplete and must fail of its end. In confirmation of these views I might say that the three combined and cooperated in the psychic powers of the men of glorious memory such as Pythagoras and Socrates and Plato and all who have won imperishable renown. Fortunate and favored of the gods is every one upon whom the gods have bestowed all these gifts. If any one thinks that lack of natural endowments can not be supplied by suitable instruction and practice in virtue he is very much, yes, altogether mistaken. For disuse destroys the best natural endowments while improves even weak ones. (49-50)

39. Aviation Timeline, Indian Airforce archytas of tarentum, a Greek mathematician, scientist, and philosopher who livedin Italy, may have designed a small flying dove balanced so as to fly by http://www.geocities.com/siafdu/triviac.html

Aviation Timeline 13000 B.C, India 3,000 years ago, China The Chinese invented and flew kites at least 3,000 years ago. Kites eventually reached Europe in the 14th century. Although we think of them primarily as toys, they have been used to lift people for serious observations, for measurement or weaponry in war, and today for meteorological work. Marco Polo witnessed kites carrying humans in China in the 1300s. 400 B.C., Greece Archytas of Tarentum, a Greek mathematician, scientist, and philosopher who lived in Italy, may have designed a small flying "dove" balanced so as to fly by means of a whirling arm which provided lift. The Middle Ages (and earlier), Europe Roger Bacon, an English Franciscan monk, suggested the use of large, hollow globes of thin metal, filled with rarefied air or "Liquid fire" (perhaps hydrogen gas) to achieve flight. Most experimenters, however, just designed wings, strapped them on, and jumped. None of them worked well even as gliders; most didn't work at all. Some of the would be aviators died. Children played with flying toys with whirring blades. This may have been true of children on many continents. 1010, England

40. Math History - Pre-historic And Ancient Times About 375BC, archytas of tarentum develops mechanics. He studies the classicalproblem of doubling the cube and applies mathematical theory to music. http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MpreAndAncient.

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