61. Stanley Wong's CU Ceva’s Theorem, described below, picked up on the work of menelaus of alexandria(AD 70120) who contributed greatly to the world of mathematics and science. http://www.unm.edu/~abqteach/math2002/02-02-11.htm

Return to Math Index Page Heron, Pythagoras, Euler, Ptolemy and Ceva: Some Contributions to Euclidean Geometry Stanley Wong The Academic Setting This unit will be used at Del Norte High School in Albuquerque, New Mexico. It is designed with my Honors Geometry class in mind. Students can be freshman or sophomores. The freshman are recommended by their eighth grade Algebra I teachers if they have exhibited a strong aptitude for mathematics. Math teachers from our feeder schools (Cleveland and McKinley Middle Schools) have been briefed on these recommendations. The sophomores are those who have successfully completed Honors Algebra I as freshman or who have shown great promise in regular Algebra I and who have been recommended by their teacher. Students in Honors Geometry will study, in greater depth, the concepts, techniques, and theory of the regular geometry course. Both acceleration and enrichment are integral components of the curriculum. This is the second course in the Honors/Advanced Placement Program in Mathematics and students will earn a weighted grade in this course. (Albuquerque Public Schools 16.0)

62. HighBeam Research: ELibrary Search: Results keenly interested in classical astronomy (he made outstanding translations of theConics of Apollonius and the Sphaerica of menelaus of alexandria), and having http://www.highbeam.com/library/search.asp?FN=AO&refid=ency_refd&search_dictiona

63. PORCELAINia/Alexandria/817 Site Map " menelaus" alexandria. Series. Height. 4.3 in. Mass. 390 g. Fired. Bisque. Glaze. Clear. Started. 6/15/97. Finished. 5/19/98. Style. Cambria. Series. alexandria This piece is named for http://www.porcelainia.com/817.html

PORCELAINia HOME PROCESS SERIES STYLE ... Site Map "Menelaus" Alexandria Series Height 4.3 in Mass 390 g Fired Bisque Glaze Clear Started Finished Style Cambria Series Alexandria This piece is named for the great geometer, Menelaus (70 AD to 130 AD). Menelaus's only surviving book, "Sphaerica" was the most important early contribution to spherical trigonometry, essential to both astronomy and navigation. He was the first to write down the definition of a spherical triangle and identify its geometric properties.

64. Pharos1 The island, menelaus made clear, offered a good harbour where one could its exposedsituation winter storms can be violent at alexandria - clearly suggests http://www.greece.org/alexandria/pharos/

Literary references Back to Alexandria Home Page There is a story reported by Plutarch in his Life Of Alexander, which says that the conqueror, being so taken by Egypt decided to found: "a large and populous Greek city which should bear his name, and by the advice of his architects was on the point of measuring off and enclosing a certain site for it. Then, in the night, as he lay asleep, he saw a wonderful vision. A man with very hoary locks and of a venerable aspect appeared to stand by his side and recite these verses:- 'Now there is an island in the much-dashing sea, In front of Egypt; Pharos is what men call it.' " Alexander knew his Homer and these brief lines were enough to call to mind the long passage from Book IV of The Odyssey where Menelaus tells Telemachus how he was stranded on the shores of Egypt. The island, Menelaus made clear, offered a good harbour where one could pull ships up onto the shore and take on water. So, continues Plutarch, the Macedonian set himself before the isle of Pharos and judging the situation to be very suitable "he said he saw that Homer was not only admirable in other ways, but also a very wise architect, and ordered the plan of the city to be drawn in conformity with this site." Alexander did not stay long enough to witness the construction of the city and could not have known that the little island of Pharos would be the site of and give its name to the seventh Wonder of the World.

65. The Lighthouse Of Alexandria wrongly thought to originally be marble), the Pharos of alexandria was built legendtells of the beautiful Helen visiting the island with her husband menelaus. http://www.ptahhotep.com/articles/Lighthouse.html

The Lighthouse of Alexandria by Francesca Jourdan © 1998, Francesca Jourdan After years of marching and fighting, Alexander, later to become Alexander the Great (356 BC -323 BC), finally entered Egypt in 332 BC after defeating Darius III in 333 BC. According to a myth, it is said that Alexander may have been the only natural son, not of Philip II, but of Nectanebo II (360-343 BC), the last of the native pharaohs, his mother Olympia having had an affair with him [Clayton, 1995]. Once in Egypt, he went to the Oasis of Siwa, where a priest apparently saluted him as the son of the god. Plutarch (45 AD - 125 AD) writes that the priest wished to address Alexander in Greek as “Paidion” (my child) but that the word actually came out as “Paidios” (son of Zeus). Alexander, from then on, saw himself as the son of Zeus-Amon. Soon, the great monarch planned to found a new city. His actual intentions are barely mentioned by early sources. According to tradition, the city was founded in January 331 AD [Empereur, 1998]. Plutarch mentions in Alexander’s Life that a prophet visited the king in a dream and apparently convinced Alexander of having found the right spot.

66. Planetenkunde.de / Mond - Namen - Rimae Menelaus (Menelaus-Rillen) Translate this page menelaus-Rillen Benennung (IAU) im Jahr 1978 Benannt nach dem benachbarten Krater» menelaus Namensgeber menelaus von alexandria Griechischer Astronom und http://www.astrolink.de/p012/p01204/p01204150087.htm

Missionen Adressen Missionsziele Shops Sonnensystem Mondkunde ^Übersicht Merkur Venus Erde Mars Jupiter Saturn Uranus Neptun Pluto Asteroiden Kometen ^Übersicht Geschichte Mond-Phasen Entstehung Entwicklung Geologie Oberfläche Wasser Erde-Mond Karten Namen Fakten MoFis SoFis Web-Links Tipps AstroLink.de ShuttleLink.de Planetenkunde RedShift.de Suche, etc. Impressum Mondkunde Geschichte Mond-Phasen Entstehung Entwicklung Geologie Oberfläche Wasser Erde-Mond Karten Namen Übersicht Landeplatz Landegebiet Krater Kraterkette Meer Ozean See Sumpf Bucht Ebene Albedostruktur Berg Gebirge Kap Tal Furche, Riss Rille, Rillengruppe Fakten MoFis SoFis Web-Links Tipps Mond Namen Rille (Rima), Rillengruppe (Rimae) Rimae Menelaus Rimae Menelaus Mission Mond Koordinaten: Mittl. Durchmesser: 131,0 km Dt. Bezeichnung: Menelaus-Rillen Benennung (IAU) im Jahr Benannt nach dem benachbarten Krater Menelaus Namensgeber: Menelaus von Alexandria Griechischer Astronom und Mathematiker (ca. 70 - 130) Weiter: Rimae Mersenius CD-ROM Tipps Mission Mond Aufbruch ins All Die erste CD-ROM auf Basis der neuen AstroLink Datenbank! 2 CD-ROMs, Windows, 29,90 €

67. Menelaus, Greek Mythology Link. For it is said that menelaus, returning with five ships, came first to Sunium in helost his pilot Canobus, after whom the city east of alexandria was named. http://homepage.mac.com/cparada/GML/Menelaus.html

By Carlos Parada, author of Genealogical Guide to Greek Mythology Menelaus Menelaus Relevant links SONGS OF TROY Agamemnon Helen Paris ... The Last days of Troy Map: The Returns Orestes 2 Andromache Telemachus Menelaus in GROUPS ACHAEAN LEADERS SUITORS OF HELEN WOODEN HORSE Free counter "Look to my affairs, and to the household, and to our guest from Troy [Menelaus to Helen . Ovid, Heroides Menelaus is the king of Sparta who was robbed of his sweet wife Helen by a guest he received in his palace. For his sake, a fleet of unprecedented size sailed to Troy in order to demand, by persuasion or by force, the restoration of Helen and the Spartan property that the seducer Paris , breaking all laws of hospitality, had stolen. Youth King Atreus of Mycenae , having a serious feud with his brother Thyestes 1, decided to arrest him. For this purpose he sent his sons, Agamemnon and Menelaus, who seized him in

68. TEOREMA DE MENELAUS Translate this page . 1 menelaus de alexandria, terá nascido cerca do ano 70 (depoisde Cristo) e falecido cerca do ano 130. Supõe-se que terá http://www.mat.uc.pt/~bebiano/menelaus_t.htm

TEOREMA DE MENELAUS Consideremos um triângulo [ABC]. Sejam X, Y e Z, respectivamente, pontos sobre as rectas AB, BC e CA, suportes dos lados do triângulo. É condição necessária e suficiente para que os pontos X, Y e Z sejam colineares que Demonstração . Se são colineares os pontos X, Y e Z, respectivamente sobre as rectas AB, BC e AC, então Sejam X Y e Z pontos colineares, como ilustrado nas figuras anteriores. Sejam ainda h h e h as medidas dos segmentos de perpendicular traçados de respectivamente , A B e C , para a recta XY e designemos os pés dessas perpendiculares, respectivamente, por A’ B’ e C’ . Por semelhança de triângulos, por exemplo, entre [ AA’Z ] e [ CC’Z ], podemos concluir que De modo análogo se concluiria que, dada a semelhança entre os triângulos [ AA’X ] e [ BB’X e também por semelhança entre os triângulos [ CC’Y ] e [ BB’Y ], se tem Podemos assim concluir que Se , com X, Y e Z pontos respectivamente sobre as rectas AB, BC e CA, suportes dos lados dum triângulo [ABC], então X, Y e Z são pontos colineares. Nas condições da primeira parte da demonstração, consideremos a recta

69. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï BC in Alopeconnesus (near Cyzicus) (now Turkey) Died about 320 BC menelaus, menelausof alexandria Born about 70 in (possibly) alexandria, Egypt Died about http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=M

70. History Of Alexandria: The Ptolemaic Legacy developed his theories, and wrote Elements at the alexandria Mouseion during the Later,Pappus wrote his Collection, menelaus studied spherical triangles, and http://ce.eng.usf.edu/pharos/Alexandria/History/legacy.html

The Ptolemaic Legacy The Mouseion / Library When Ptolemy Soter assumed power, he asked Demitrius Phalerus , a follower of Aristotle , to found a library system at Alexandria that would rival that of Athens. The Alexandrian Mouseion , however, far superseded its Greek prototype to become an intellectual and scientific institution; a university system rather than a bibliotheca. It was here, in the third century BC, that Archimedes invented the pump still in use today and known as Archimedes' screw , and, in the second century BC, that Hypsicles first divided the circle of the zodiac into 360 degrees. Ancient historians claim that the library's 500,000 book collection was so comprehensive that no manuscript was available in any library worldwide that was not available in Alexandria. Mathematics Have you ever heard of Euclidean Geometry? Did you know that Euclid lived, developed his theories, and wrote Elements at the Alexandria Mouseion during the reign of Ptolemy II Philadelphus? In his Elements , Euclid provided a comprehensive analysis of geometry, proportions, and theory of numbers. His other notable contribution

71. La Base De Données Expérimentale Mertens-Pack3 menelaus ( alexandria) (page 1/1, 1-1). 1324.24, menelaus( alexandria) (?), Traité sur une théorie planétaire. P.Oxy. http://promethee.philo.ulg.ac.be/cedopal/getPack.asp?_auteur=556

72. Clement Of Alexandria: The Instructor, Book 3 Clement of alexandria on Early Christian Writings. Loving, departed, carrying awayher he loved, Helen, to the folds of Ida, having found that menelaus was away http://www.earlychristianwritings.com/text/clement-instructor-book3.html

THE INSTRUCTOR. BOOK III. CHAP. I.ON THE TRUE BEAUTY. IT iS then, as appears, the greatest of all lessons to know one's self. For if one knows himself, he will know God; and knowing God, he will be made like God, not by wearing gold or long robes, but by well-doing, and by requiring as few things as possible. Now, God alone is in need of nothing, and rejoices most when He sees us bright with the ornament of intelligence; and then, too, rejoices in him who is arrayed in chastity, the sacred stole of the body. Since then the soul consists of three divisions; the intellect, which is called the reasoning faculty, is the inner man, which is the ruler of this man that is seen. And that one, in another respect, God guides. But the irascible part, being brutal, dwells near to insanity. And appetite, which is the third department, is many-shaped above Proteus, the varying sea-god, who changed himself now into one shape, now into another; and it allures to adulteries, to licentiousness, to seductions. "At first he was a lion with ample beard."

73. Clement Of Alexandria: Stromata, Book 7 Clement of alexandria on Early Christian Writings. The Stromata, orMiscellanies. Book VII. For instance, the tragedy says menelaus. http://www.earlychristianwritings.com/text/clement-stromata-book7.html

The Stromata, or Miscellanies Book VII CHAPTER I THE GNOSTIC A TRUE WORSHIPPER OF GOD, AND UNJUSTLY CALUMNIATED BY UNBELIEVERS AS AN ATHEIST. It is now time to show the Greeks that the Gnostic alone is truly pious; so that the philosophers, learning of what description the true Christian is, may condemn their own stupidity in rashly and inconsiderately persecuting the [Christian] name, and without reason calling those impious who know the true God. And clearer arguments must be employed, I reckon, with the philosophers, so that they may be able, from the exercise they have already had through their own training, to understand, although they have not yet shown themselves worthy to partake of the power of believing. The prophetic sayings we shall not at present advert to, as we are to avail ourselves of the Scriptures subsequently at the proper places. But we shall point out summarily the points indicated by them, in our delineation of Christianity, so that by taking the Scriptures at once (especially as they do not yet comprehend their utterances), we may not interrupt the continuity of the discourse. But after pointing out the things indicated, proofs shall be shown in abundance to those who have believed. But if the assertions made by us appear to certain of the multitude to be different from the Scriptures of the Lord, let it be known that it is from that source that they have breath and life; and taking their rise from them, they profess to adduce the sense only, not the words. For further treatment, not being seasonable, will rightly appear superfluous. Thus, not to look at what is urgent would be excessively indolent and defective; and "blessed, in truth, are they who, investigating the testimonies of the Lord, shall seek Him with their whole heart." And the law and the prophets witness of the Lord.

74. Literaturliste Der Autoren Mit Dem Familiennamen Costard, KVK-Ergebnisanzeige notes 8 menelaus, of alexandria / Menelai Sphaericorum libri III 9 Costard http://members.aol.com/teleaxel/buecher.htm

Main Business Park htmlAdWH('7002182', '234', '60'); KVK-Ergebnisanzeige COPAC Costard, George. / A letter to Martin Folkes, esq; President of the Royal Society, Histoire de Fortunatus et de ses enfans. / [By Jean Castilhon] . 1770 Costard, George. / The use of astronomy in history and chronology exemplified in an Sly, Costard / Sayings and doings at the Tremont House, in the year 1832 Costard, George. / A further account of the rise and progress of astronomy amongst the Costard, George. / A letter ... concerning the rise and progress of astronomy amongst the Caimo, Norberto / Voyage d'Espagne, fait en l'annee 1755 : avec des notes Menelaus, of Alexandria / Menelai Sphaericorum libri III Costard, George, 1710-1782 / A further account of the rise and progress of astronomy amongst the Costard, George, 1710-1782 / The history of astronomy, with its application to geography, history, Sly, Costard, pseud. / Sayings and doings in America Young, Edward, 1683-1765 / Quatrieme, douzieme et quinzieme nuits d'Young Costard, George, 1710-1782 / A letter to Nathaniel Brassey Halhead, Esquire : Containing some

75. Clement Of Alexandria: 05 GREEKS AS PILFERERS OF BARBARIAN PHILOSOPHY EXCERPTS FROM CLEMENT OF alexandria. it is easy to perceive that Solomon, who livedin the time of menelaus (who was during the Trojan war), was earlier by many http://www.geocities.com/zuigga/l05.htm

GREEKS AS PILFERERS OF THE BARBARIAN PHILOSOPHY EXCERPTS FROM CLEMENT OF ALEXANDRIA EXCERPTS FROM EARLY CHURCH FATHERS Against unsound teachings and impiety Concerning the false gods 02. On pagan unblushing shamelessness. 03. Concerning the Hellenic philosophy. 04. Prominent pagan figures discredited. 05. Greeks as pilferers of the Barbarian philosophy. 06. Heathens and their corrupt customs. 07. Scientific explanations. 05. GREEKS AS PILFERERS OF THE BARBARIAN PHILOSOPHY. As Scripture has called the Greeks pilferers of the Barbarian philosophy, it will next have to be considered how this may be briefly demonstrated. For we shall not only show that they have imitated and copied the marvels recorded in our books; but we shall prove, besides, that they have plagiarized and falsified (our writings being, as we have shown, older) the chief dogmas they hold, both on faith and knowledge and science, and hope and love, and also on repentance and temperance and the fear of God, -a whole swarm, verily, of the virtues of truth (Stromata 2.1). Let the philosophers, then, own as their teachers the Persians, or the Sauromatae, or the Magi, from whom they have learned the impious doctrine of

76. Menelaus Name menelaus. Occupation From alexandria. Son of Occupation Datesfl. AD 100. Brief biography Contemporaries Works Domitian http://www.swan.ac.uk/classics/staff/ter/grst/People/Menelaus.htm

Name Menelaus Occupation: From Alexandria Son of: Occupation: Dates fl . AD 100 Brief biography Contemporaries Works Domitian commissioned Menelaus’ work on specific gravities; it exists in Arabic. References DSB 9.296-302 and I Bulmer-Thomas DSB Supp.1.420-1. T E Rihll Last modified: 11 March 2003

77. JMM HM DICIONÁRIO Translate this page Nicomedes (c. -220) Osíris, Menaechmus Nicomachus, Menaechmos Menelaos NicomachosNicomedes, Menaechmus menelaus Nicomachus Nicomedes, Papo de alexandria (c. 320 http://phoenix.sce.fct.unl.pt/jmmatos/HISTMAT/HMHTM/HMDIC.HTM

Bibliografia Recursos na rede bem vindos em latim Anaximandro (-611-545) Antifonte Aristarco de Samos (-310-230?) Aristeo (c. -330) Arquimedes de Siracusa (-287?-212) Arquitas de Tarento (c. -375) Apollonius Archimedes Boetius Apollonios of Perga Aristarchos Aristaeus Aristotle Archimedes of Syracuse Archytas Apollonius of Perga Aristarchus Aristaeus Aristotle Archimedes of Syracuse Archytas Boethius Apollonios Diofanto de Alexandria (c. 250) Diophantus Democritos Dinostratos Diophantos Diocles Democritos Dinostratus Diophantus Diocles Diogenes Laertius Euclides de Alexandria (c. -300) Filolaos Endemus Eudoxus Philolaus Eratosthenes Euclid of Alexandria Endemos Eudoxos of Cnidos Eratosthenes Euclid of Alexandria Endemus Eudoxus of Cnidos Philolaus Euclide Hiparco de Alexandria (-190-120) Hipasos Hipsicles Herodotus Hipparchus Hero Herodotos Hypatia Hipparchos Hippocrates of Chios hekat Heron Herodotus Hypatia Hipparchus Hippocrates of Chios Iamblichus Iamblichos Iamblichus Menecmo (c. -350)

78. Menelaus Returning with five ships, menelaus came first to Sunium in Attica, but was driven helost his pilot Canobus, after whom the city east of alexandria was named. http://www.greekmyth.org/Laurent/Menelaus.htm

Menelaus is most well known as the king of Sparta who was robbed of his wife Helen by a guest he received in his palace. For his sake, a fleet of unprecedented size sailed to Troy in order to retrieve Helen. The story behind Menelaus begins with King Atreus of Mycenae, having a serious feud with his brother Thyestes, he decided to arrest him. Atreus had Agamemnon and Menelaus, who seized him in Delphi, brought him to Mycenae, and cast him into prison, where Atreus attempted to murder him. However, because of his misjudgments, Atreus was killed by Thyestes’s son Aegisthus, who then gave the throne to his father. As a result, Agamemnon and Atreus were forced into exile. The former stayed with King Polyphides of Sicyon, and latter stayed with King Oeneus of Calydon. They eventually returned with intent to dethrone Thyestes; and with assistance from King Tyndareus of Sparta, they drove Thyestes away to Cythera, an island off the southern coast of the Peloponnesus. Having thus seized power, the two married the daughters of Tyndareus: Agamemnon wedded Clytaemnestra, and became king in Mycenae; and Menelaus, united to Helen, and would later inherit the kingdom. Helen’s father, Tyndareus, following Odysseus' advice, exacted an oath from her many suitors (kings and princes of Hellas), stipulating that they would defend and protect he who was chosen as Helen's husband against any wrong done against him in regard to his marriage. This was the agreement, and Menelaus was the suitor chosen.

79. The Library Of Alexandria Later, Pappus wrote his Collection, menelaus studied spherical triangles, and Sporus,Heron For alexandria, whose lifeblood was export of grain and papyrus to http://www.societasviaromana.org/Collegium_Artium/library.htm

The Library of Alexandria by Ti. Dionysius Draco The Founding of the Museum and the Library The Museum was founded by Demetrius Phalerus, under the patronage of Ptolemy I, Ptolemy Soter. The establishment of the Library was handed down to Ptolemy II, Ptolemy Philadelphus, in 283 B.C., and it was during his reign that the monarch began the practice of attracting scholars, housing and funding them in the Museum, and collecting the vast Library. The idea of a formal institution for scholars of all kinds, complete with a library, was a new one, and the Museum was modelled on the Lyceum of Aristotle in Athens; Demetrius himself, an exiled tyrant of Athens, was one of Aristotle's followers. A second "daughter" library, the Serapeion, was soon established in the temple of Serapis, a popular god invented by the Ptolemies as a synthesis of Zeus, Pluto, Osiris, and the Apis bull. This library, found in the Rhakotis or Egyptian sector, was open to all, not just to royally pensioned scholars, and had copies of many of the Museum's scrolls. The Function of the Museum and the Library The Museum was a shrine built for the glorification of the Muses, and from the outset contained lecture halls, laboratories, observatories, living quarters, colonnades for ambulatory discussions, a dining hall, a garden, a zoo, the shrine itself, and, presumably, the Library, which most archaeologists and scholars conclude was housed within the shrine and not in a separate building. An estimated 30-50 scholars were probably permanently housed there, probably fed and funded first by the royal family, and later, according to an early Roman papyrus, by public money. The administrator of the Museum was a priest, appointed by the Pharaoh and was ,together with a separate Librarian, responsible for the whole collection.

80. Library Of Alexandria collections of records are the dim ancestor of the Library of alexandria and other andwhen he speaks of the great halls of Odysseus and menelaus, there s no http://www.justpacific.com/bits'n'pieces/alexandrialib.html

http://www.abc.net.au/rn/arts/ling/stories/s336540.htm Australian Broadcasting Corporation. Radio National. Lingua Franca. Saturday 28/07/01 On this week's LINGUA FRANCA: THE LIBRARY OF ALEXANDRIA AND WHAT CAME BEFORE LIONEL CASSON Author of LIBRARIES IN THE ANCIENT WORLD/YALE UNIVERSITY PRESS Founded by Ptolemy I at the beginning of the third century BC, THE LIBRARY OF ALEXANDRIA is the most famous library of the ancient world. In his slim history LIBRARIES IN THE ANCIENT WORLD, American classicist LIONEL CASSON devotes a chapter to it - the third chapter. What preceded it? The beginnings have been found in palace archives - hoards of clay tablets inscribed in cuneiform - in Mesopotamia: the ancient Near East. But critical to the development in the Hellenic world of the library as we know it were the adoption of the alphabet and the use of papyrus scrolls. Details or Transcript: THEME Jill Kitson: Welcome to Lingua Franca, I'm Jill Kitson. The Library of Alexandria, founded by Ptolemy I at the end of the 4th century BC is the most famous library of the ancient world. Its collection of papyrus scrolls, said to have numbered nearly half a million, drew intellectuals from all over the Greek speaking world. It survived Julius Caesar's torching of the nearby dockyards in 50 BC to last beyond the era of the Ptolemys well into the 3rd century of the Christian era, when it was destroyed in a local uprising. In many respects, the Library of Alexandria was like any of our great modern public libraries: it sought to be comprehensive, to hold authoritative texts on all subjects; works were catalogued and stored in alphabetical order by subject. The Library was open to all scholars. In other ways, it was like a research school and a scholarly publishing house: its scholars compared and analysed texts, translated them, wrote commentaries, and undertook lexicography and the study of grammar.

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