61. Euclid zeno of sidon, about 250 years after Euclid wrote the Elements , seems to havebeen the first to show that Euclid's propositions were not deduced from the http://philosophy.ohio-state.edu/people/Faculty/tennant.9/euclid.html

Euclid of Alexandria Born: about 365 BC in Alexandria, Egypt Died: about 300 BC Euclid is the most prominent mathematician of antiquity best known for his treatise on geometry The Elements . The long lasting nature ofThe Elements must make Euclid the leading mathematics teacher of all time. Little is known of Euclid's life except that he taught at Alexandria in Egypt. Euclid's most famous work is his treatise on geometry The Elements . The book was a compilation of geometrical knowledge that became the centre of mathematical teaching for 2000 years. Probably no results in The Elements were first proved by Euclid but the organisation of the material and its exposition are certainly due to him. The Elements begins with definitions and axioms, including the famous fifth, or parallel, postulate that one and only one line can be drawn through a point parallel to a given line. Euclid's decision to make this an axiom led to Euclidean geometry. It was not until the 19th century that this axiom was dropped and non-euclidean geometries were studied. Zeno of Sidon, about 250 years after Euclid wrote the

62. "Who Was Socrates?", Part III, Pages 69-76. in behalf of Socrates at some later date, by Plato, Xenophon or pseudoXenophon,Lysias, Theodectes, Demetrius of Phalerum, zeno of sidon, Plutarch, Theo of http://www.chss.montclair.edu/english/furr/socrates/wpart3pp69to76.html

you , who fit neither of them, who under the democracy were the most violent hater of the people-and who under the oligarchy have become equally violent as a hater of oligarchical merit? I am, and always have been, Critias, an enemy both to extreme democracy and to oligarchical tyranny. I desire to constitute our political community out of those who can serve it on horseback and with / 70 / heavy armor;-I have proposed this once, and I still stand to it. I side neither with democracy nor despots, to the exclusion of the dignified citizens. Prove that I am now, or ever have been, guilty of such crime, and I shall confess myself deserving of ignominious death." Where was Socrates through all this? There can be little doubt that he was very intimate with the oligarchical leaders, many of whom he had instructed in the notion that only the good and the wise and the true should rule; that government was not an art that could be picked up at random by the "man in the street," but depended on "knowledge, knowledge of ultimate principles of the "good" and the "just,"-knowledge which could only be gained by study and a painful askesis Neither Socrates nor, for that matter, Plato made any at. tempt to conceal their criticisms of Athenian democracy, its de-/ 71 / pendence (as they thought) on the whim of the multitude and the caprice of the lot;" nor did they conceal their preference for Sparta's more aristocratic, oligarchic and servile organization of society." Moreover the essence of Socrates' teaching was, as we have seen, profoundly anti-democratic, striking at the very theoretical roots on which the democratic way of life (even in a slave-owning democracy) was founded. It is only when the logic of political struggle produces a Critias, that such men as Theramenes and Socrates draw back in virtuous horror. However much we may excuse Socrates from any responsibility or sanction of the actual violence committed, we must nevertheless realize that the instinct of the democracy was profoundly right when it saw in him the evil genius behind the scene; the

63. Epicureanism than 400 books. Much was also written by his disciple zeno of sidon,who was heard by Cicero in 79 BC in Athens. After Zeno, there http://members.tripod.com/EsotericTexts07/Epicureanism.htm

Epicureanism The Epicurean school Epicurus’ successor in the direction of the Garden was Hermarchus of Mitylene, and he was succeeded in turn by Polystratus, who was the last survivor to have heard Epicurus. Superior to both, however, were Metrodorus and Colotes, against whom a small work by Plutarch was directed. Among the Epicureans of the 2 nd century BC, mention must be made of Demetrius of Lacon, of whose works some fragments remain, and Apollodorus , who wrote more than 400 books. Much was also written by his disciple Zeno of Sidon, who was heard by Cicero in 79 BC in Athens. After Zeno, there were Phaedrus, also a teacher of Cicero, who was in Rome in 90 BC, and Patro, the head of the school until 51 BC. Already famous as an epigram writer was Philodemus of Gadara (born 110 BC). In the papyri of Herculaneum, comprising the effects of Philodemus’ library, there are sizable remains of almost all of his numerous works. Epicureanism had already been introduced in Rome, in the 2 nd century BC. The first person to spread its doctrines in Latin prose was a certain Amafinius. At the time of Cicero, Epicureanism was in fact the philosophy in vogue; and the number of Romans subscribing to it was, according to Cicero, very large. Among the greatest was Titus Lucretius Carus ( c.

64. Diogenes Laertius - Lives Of Eminent Philosophers garden, who wrote over four hundred books, is also famous; and the two Ptolemaeiof Alexandria, the one black and the other white; and zeno of sidon, the pupil http://www.epicurus.net/lives.html

Lives of Eminent Philosophers, Book X Diogenes Laertius Diogenes Laertius (3 rd Century A.D.) is the primary source for the surviving complete letters of Epicurus and for biographical and other pertinent information about him: Index: Biography of Epicurus Epicurus's followers and namesakes Epicurus's writings Overview of Epicureanism ... Epicurean ethics Biography of Epicurus Epicurus, son of Neocles and Chaerestrate, was an Athenian of the Gargettus ward and the Philaidae clan, as Metrodorus says in his book On Noble Birth . He is said by Heraclides (in his Epitome of Sotion ) as well as by others, to have been brought up at Samos after the Athenians had sent colonists there and to have come to Athens at the age of eighteen, at the time when Xenocrates was head of the Academy and Aristotle was in Chalcis. After the death of Alexander of Macedon and the expulsion of the Athenian colonists from Samos by Perdiccas, Epicurus left Athens to join his father in Colophon; for some time he stayed there and gathered students around him, then returned to Athens again during the archonship of Anaxicrates [307-306 B.C.]. For a while, it is said, he pursued his studies in common with other philosophers, but afterwards put forward independent views by founding the school named after him.

65. Epicureanism The philosophy was popular throughout the ancient world; it was spread by the successorsof Epicurus, who included Polystratus, zeno of sidon, and Philodemus http://www.slider.com/enc/18000/epicureanism.htm

SubmitWolf - Award winning Internet Software Home Encyclopeadia E Ena - Eph ... Rope Ladders Trellian WebPage Slider Search: The Web Encyclopaedia Shopping Index Help Encyclopaedia epicureanism philosophy that follows the teachings of Epicurus , who held that pleasure is the end of all morality and that real pleasure is attained through a life of prudence, honor, and justice. The philosophy was popular throughout the ancient world; it was spread by the successors of Epicurus, who included Polystratus, Zeno of Sidon, and Philodemus of Gadara. Only in later times did epicureanism come to mean devotion to extravagant pleasure. Add URL Advertise Contact Us Epicurus Rope Ladder

66. Food For Thought Biographies BC. Zeno of Elea (Greek philosopher), c.495c.430 BC. zeno of sidon(Phoenician-born Greek philosopher), c.150-c.70 BC. Zeno, Apostolo http://www.evcom.net/~tourette/bio/bio_Z.htm

67. AC/CLC2 Views Of Antiquity- Socrateses 2. 23. 13, 1399a 711), Demetrius of Phalerum (Diog. Laert. 9. 15, etc. and Plut.Aristides 1 and 27), zeno of sidon (Suda, sv) and Theon of Smyrna (Suda, sv). http://maple.cc.kcl.ac.uk/socrates/text/maxor03main.html

68. Mathem_abbrev Christophe Yunus, Abu'lHasan ibn Yushkevich, Adolph, Zariski, Oscar Zassenhaus,Hans Zeeman, Erik Zelmanov, Efim Zeno of Elea zeno of sidon, Zenodorus Zermelo http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm

Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive. Some suggestions on the historical perspective might be: (a) Any wars etc. (b) Scientific breakthroughs of the time (c) Major discoveries of the time (d) How did this mathematician change history etc.

69. A.htm name begins with the letter Z. Zeno of Elea. zeno of sidon. Fora different list click the letter below or click here to go home. http://www.forestcity.k12.ia.us/pages/FCHS/Site/z.htm

Here is the current list of Mathematicians that we have on our page whose last name begins with the letter: Z Zeno of Elea Zeno of Sidon For a different list click the letter below or click here to go home. A B C ... Z If you have any other mathematicians that you feel we should add to our list, please feel free to cantact me. Daniel Meyer

70. Famous Scientists And Mathematicians elementary particles . RETURN TO TOP. zeno of sidon Mathematician andphilosopher 150 BC 70 BC. RETURN TO TOP The Nobel Prize. NOBEL http://www.saintmarksschool.org/public/library/webliographies/scientists/

Famous Scientists and Mathematicians A B C D ... H I J K L M ... N O P Q R S T U V W X Y Z THE NOBEL PRIZE ON-LINE SUBSCRIPTIONS ... AL-BIRUNI Muslim Cartographer, Astronomer, and Mathematician. 973 - 1048 Determined earth's circumference RETURN TO TOP ARISTOTOLE Ancient Greek Philosopher, Mathematician, and Scientist. 384B.C. - 322 B.C. Aristotle's Influence on Contemporary Biology RETURN TO TOP ARCHIMEDES 287B.C. - 212 B.C. Ancient Sicilian Mathematician. RETURN TO TOP NIELS HENRIK DAVID BOHR The Nobel Prize in Physics in 1922 "for his services in the investigation of the structure of atoms and of the radiation emanating from them" NIELS HENRIK DAVID BOHR NEILS BOHR RETURN TO TOP BOOLE, GEORGE Irish mathematician and logician. 1815 - 1864 The Boolean logic used in today's comuters is based on his work RETURN TO TOP TYCHO BRAHE Danish Mathematician 1546 - 1601 TYCHO BRAHE TYCHO BRAHE RETURN TO TOP EDUARD BUCHNER The Nobel Prize in Chemistry 1907 "for his biochemical researches and his discovery of cell-free fermentation" RETURN TO TOP W RACHEL CARSON Time 100 persons of the 20th Century Author. Envionmentalist.

71. Euclid Of Alexandria zeno of sidon, about 250 years after Euclid wrote the Elements, seems to havebeen the first to show that Euclid's propositions were not deduced from the http://uk.geocities.com/magoos_universe/euclid.htm

Euclid of Alexandria Born: about 325 BC Died: about 265 BC in Alexandria, Egypt E uclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements . The long lasting nature of The Elements must make Euclid the leading mathematics teacher of all time. However little is known of Euclid's life except that he taught at Alexandria in Egypt. Proclus, the last major Greek philosopher, who lived around 450 AD wrote (see [1] or [9] or many other sources):- Not much younger than these [pupils of Plato] is Euclid, who put together the elements, arranging in order many of Eudoxus's theorems, perfecting many of Theaetetus's, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for Archimedes, who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry. He is therefore younger than Plato's circle, but older than Eratosthenes and Archimedes; for these were contemporaries, as Eratosthenes somewhere says. In his aim he was a Platonist, being in sympathy with this philosophy, whence he made the end of the whole Elements the construction of the so-called Platonic figures. There is other information about Euclid given by certain authors but it is not thought to be reliable. Two different types of this extra information exists. The first type of extra information is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. It is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors.

72. Lives_Epicurus Black, and Ptolemy the Fair. And zeno of sidon, the pupil of Apollodorus,a voluminous author; and 26. Demetrius, who was called http://www.southalabama.edu/philosophy/coker/PHL_240/Web_Hellenistic_Philosophy/

The Lives and Opinions of Eminent Philosophers Book X The Life of Epicurus by Diogenes La«rtius, written circa 230 A.D. translation by C.D. Yonge (1812 - 1891) Emendations by Coker are underlined. Some of Yonge's Sentences are broken up to reflect section numbering. [Section Numbering follows: Diogenes Laertii, Vitae Philosophorum ed. H.S. Long (Oxford: Oxford University Press, 1964)] Highlights: His Life and Times in Brief Common Misrepresentations His True Character His Will His Works Introduction to the Letters Notes on the Canon Epicurus to Herodotus Epicurus to Pythocles Opinions About the "Wise Man" Epicurus to Menœceus Epicurus on Pleasure as Compared to the Beliefs of the Cyrenaics His Fundamental Maxims; c.f.: Oates Hicks The Life of Epicurus Epicurus was an Athenian, and the son of Neocles and Chairestrate, of the burgh of Gargettus, and of the family of the Philaidae, as Metrodorus tells us in his treatise on Nobility of Birth . Some writers, and among them Heraclides, in his Abridgment of Sotion , say, that as the Athenians had Colonis and Samos, he was brought up there, and came to Athens in his eighteenth year, while Xenocrates was president of the Academy, and Aristotle at Chalcis. But after the death of Alexander, the Macedonian, when the Athenians were driven out of Samos by Perdiccas, Epicurus went to Colophon to his father.

73. Home Introduction Romans Early Christianity Greek Mythology Other 3190) No year; Zeno(2579) year 79 BC; Zeno(2580) No year; Zeno ofRhodes(2580) No year; zeno of sidon(2579) year 79 BC; Zenodorus(2581 http://education.domaindlx.com/history/Descrpt.asp?Desc=AU

74. Lebanon History zeno of sidon, A Mathematician Lebanon on EmeraldEmpire ConcoursCharles-Hélou, Quelle Francophonie pour le XXIe siècle? http://www.chez.com/walid/lebanon.htm

.Pictures of Lebanon The lebanese war ( in french! ) Personnal pages: Abdul's Lebanese-American Home Page Joseph and Henry Lebanon Page Robert Mitri's Home Page Anthony Wehbe's Website ... Lebanese Students Club , S. El Masri Lebanon Pages , B. Medawar WWW VL, Lebanon , Gh. A. Abbas Homepages and Websites of Lebanon , M. Abbas Lebanon: A Rising Star , D. Khalil Lebanon on the Web , R. Dagher Lebanon Pages , B. Chebaro Interesting Sites in Lebanon , F. Abou-Shakra Lebanon , A. Fawaz Lebanese Links , A. Aoude Lebanon Home Page , E. Jabbour Lebanon Home Page , W. Nabhane Lebanon - Liban , C. Gabril Lebanon , R. Hage Lebanon from Mexico , G.H. Badui Lebanon's WWW Sites , S.Gh. AlHajeri Religious site: The Maronite Church Catholic Churches of Lebanon St. Sharbel, Hermit of Lebanon Abraham Ecchelensis, A Learned Maronite ... Zakat Fund Politics: The Lebanese Forces Fundamentalism: Lebanon's Hezbollah Seen from Inside (Politics) Lebanese National Congress Le Rassemblement pour le Liban World Lebanese Organization Centre for Arab Unity Studies ... United Nations Interim Force in Lebanon . Another Site Lebanon on CNN's Faces of Conflict The Israel-Hezbollah war (in depth coverage) Israel-Lebanon Conflict (extended online coverage) ... Beirut Memorial, Onslow County

75. Untitled Document eg the definitions of figure and parallels); but besides these we have quotationsfrom a separate work which he wrote to controvert zeno of sidon, an Epicurean http://www.headmap.com/book/euclid/before/proclus.htm

[p. 29] CHAPTER IV. PROCLUS AND HIS SOURCES It is well known that the commentary of Proclus on Eucl. Book I. is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus. They are the more precious because the original works of the forerunners of Euclid, Archimedes and Apollonius are lost, having probably been discarded and forgotten almost immediately after the appearance of the masterpieces of that great trio. Proclus himself lived 410-485 A.D., so that there had already passed a sufficient amount of time for the tradition relating to the pre-Euclidean geometers to become obscure and defective. In this connexion a passage is quoted from Simplicius who, in his account of the quadrature of certain lunes by Hippocrates of Chios, while mentioning two authorities for his statements, Alexander Aphrodisiensis (about 220 A.D.) and Eudemus, says in one place , “As regards Hippocrates of Chios we must pay more attention to Eudemus

76. ZENO De Sidon de multiples invasions et passa sous la domination de plusieurs peuples. Zéno de sidon était un disciple dEpicure. http://coll-ferry-montlucon.pays-allier.com/zeno.htm

ZENO De Sidon Vers 150 – vers 70 av J.C. Zéno de Sidon est né dans la ville de Sidon. Cette ville était une très ancienne cité phénicienne dont la fondation remonte au troisième millénaire avant J.C. Comptoir maritime très important, elle eut à subir de multiples invasions et passa sous la domination de plusieurs peuples. Zéno de Sidon était un disciple d’Epicure. Or, il est bien connu qu’Epicure ne se souciait que de la recherche du bonheur (plaisir) et qu’il éprouvait une grande aversion pour les Mathématiques. Zéno fut un élève d’un certain Apollodorus (fervent défenseur de l’épicurisme et qui écrivit plus de 400 livres) et sur la fin de sa vie, il enseigna lui même dans le fameux « Jardin » d’Athènes qui était en fait le nom de l’Ecole fondée par Epicure dans le jardin de sa propre maison. Zéno était un homme très éclectique qui écrivit sur un nombre considérable de sujets : la Logique, l’Atomisme, la Biologie, l’Ethique, la Littérature, l’Eloquence, la Poésie, la Théorie de la connaissance et bien sûr les Mathématiques. Excepté sur ces deux derniers sujets, nous ne savons pratiquement rien de ses écrits qui ont pratiquement complètement disparu. Toute sa philosophie reposait sur sa conviction que la Connaissance « vraie » ne pouvait provenir que de l’Expérience (de la multitude des expériences humaines) et pas d’un Raisonnement « abstrait ».

77. Zeno Zenao De Sidon Translate this page Zeno/ão de sidon (150 - 70 a. C) Filósofo grego nascido na cidadede sidon,na costa do Mediterrâneo, uma das mais antigas cidades http://www.sobiografias.hpg.ig.com.br/ZenoSido.html

Zen o de Sidon (150 - 70 a. C) antes de Cristo Epicuro . Estudou com Apolodoro e deu aulas a Euclides em Os elementos . Morreu em Atenas e para alguns historiadores foi o primeiro a considerar a possibilidade da Philodemus de Gadara . Philodemus estudou com ele em Atenas e retornou a Roma (75 a. C) para trabalhar para o aristocrata Lucius Calpurnius Piso Nova B U S C A :

78. Roman Stoicism (Chapter 3: The Academy And The Porch) of Tyre and sidon, in the other as far as Athens, whence he brought back a numberof ‘Socratic books,’ which were eagerly read by the young zeno, and in http://www.geocities.com/stoicvoice/journal/0203/ea0203b1.htm

Roman Stoicism (Chapter 3: The Academy and the Porch) by E. Vernon Arnold (1857 - 1926) realist is . But just as Plato holds that general conceptions are alone true and real, so he necessarily maintains that objects perceivable by the senses are only half-real, and that the ordinary man lives in a world of illusions. Thus the thoughts of the philosopher are separated by an abyss from the world in which men live and die. The ideal State is modeled on the individual man. To the three parts of the soul correspond three classes of citizens; the rulers, whose virtue is Wisdom; the guardians, on whom Courage is incumbent; the laborers and tradesmen, who owe the State Soberness and obedience. Thus the political system to which Plato leans is that of an Aristocracy; for the middle class in his state has only an executive part in the government, and the lower orders are entirely excluded from it. Aristotle thus reinstates the credit of the common man; he it is who possesses the substance of truth and gives it habitual expression by speech, even roughly indicating the various kinds of existence by different forms of words. It is now indicated that a study of grammar is required as the foundation of logic. In the study of physics Aristotle picks up the thread which Socrates had dropped deliberately, that is, the teaching of the Ionic philosophers. Either directly from Empedocles, or from a

79. Hisamatsu: Sep Reguloj De Vimalakirti Parto 1 Nia FASSocieto emfazas rektan sidon (tanza) kiel parton de nia praktiko. aspekto en la purlanda budhismo, la pordego de forbailado en zeno estas nenio http://web.kyoto-inet.or.jp/people/nobutak/vim1.htm

Hejmen Sep Reguloj de Vimalakirti (2) de HISAMATSU Shin'ichi El Yuima Shichisoku (Sep Reguloj de Vimalakirti) (FAS-Societo, Kyoto, 1960). Originale gxi estis serio da PARTO UNU: RIPOZA SIDO Manifesti la aferojn de la ordinara homo sen forjxeti la Dharmo-Vojon Mi dezirus fari -paroladojn pri sep reguloj, kiujn mi elprenas el la Vimalakirti-Sutro . Por la unua, mi volus trakti "ripozan sidon" ( yenzuo , Jp. enza ), kiu estas predikita en la Cxapitro pri "Discxiploj." Mi decidis komencigxi per tiu cxi termino, cxar Vimalakirti priskribas gxin kiel "Manifesti la aferojn de la ordinara homo sen forjxeti la Dharmo-Vojon," esprimo menciita en mia antauxparolo. Mi kredas, ke tiu cxi esprimo estas la plej esenca en nia hodiauxa praktiko de la budha-vojo. Krome, ecx se ne temas pri la budha vojo gxi estas la plej tauxga esprimo por nia ultima estomaniero. Nia FAS-Societo emfazas "rektan sidon" ( tanza ) kiel parton de nia praktiko. Tial ni bezonas havi klaran komprenon de la vera signifo de tiu cxi rekta sido, surbaze de profunda esploro. Se ne, ni ne povus gxuste praktiki la gravan praktikon de la FAS-Societo. Malsamaj homoj havas malsamajn opiniojn koncerne al la signifo de rekta sido, kaj la budhismo dum sia longa historio efektive ne limigis sin al nur unu senco. Tial estas des pli necese por ni klarigi ties veran signifon. Se temas pri la gxusta maniero de rekta sido, ni kutime pensas pri la detalaj instruoj pri la gxusta fizika pozicio kaj mensa sinteno, kiuj trovigxas en

80. Euclides Translate this page zeno de sidon, cerca de 250 años despues de que Euclides escibió Los Elementos,parece haber sido el primero en mostrar que las proposiciones de Euclides no http://www.mat.ucm.es/deptos/am/guzman/pagjor/euclides.htm

Los Elementos comienza con axiomas, incluyendo el famoso quinto axioma de Euclides, que postula que solamente se puede dibujar una linea a traves de un punto que sea paralela a otra linea. La decision de Euclides de hacer de este un axioma llevo a la generacion de la geometria Euclidiana. No fue sino hasta el siglo XIX cuando este axioma fue derribado y otras geometrias no euclidianas empezaron a ser estudiadas. Euclides pudo no haber sido un matematico de primera clase pero la importancia de su obra lo convierte en el maestro de los matematicos de todos los tiempos. 1.-Punto, que lo define como "una cosa que no tiene parte"

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