41. Re: [HM] An Ancient Greek Library By George L. McDowell, Jr. Iamblichus 28.. Isadorus of Miletus 29.. Marinus 30.. menelaus of alexandria31.. Nichomachus of Gerasa 32.. Nicomedes 33.. Pappus of Alexandria 34.. http://mathforum.org/epigone/historia_matematica/merpreezan/009501c19c80$c7b37b6

Re: [HM] An ancient Greek library by George L. McDowell, Jr. reply to this message post a message on a new topic Back to messages on this topic Back to Historia-Matematica Discussion Group Subject: Re: [HM] An ancient Greek library Author: geomcd@erols.com Date: The Math Forum

42. Biography-center - Letter M doctor.cfm/2069.html; menelaus of alexandria, wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Menelaus.html;Menger, Karl www http://www.biography-center.com/m.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish M 749 biographies www-history.mcs.st-and.ac.uk/~history/Mathematicians/Meray.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Mobius.html MacArthur, Douglas www.pbs.org/wgbh/pages/amex/macarthur/peopleevents/pandeAMEX106.html Macarthur, Elizabeth www.abc.net.au/btn/australians/macarthu.htm MacArthur, Mary P.H. www.pbs.org/wgbh/pages/amex/macarthur/peopleevents/pandeAMEX109.html Macaulay, Francis www-history.mcs.st-and.ac.uk/~history/Mathematicians/Macaulay.html Macaulay, Eunice www.nfb.ca/e/highlights/eunice_macaulay.html MacBride, Seán www.nobel.se/peace/laureates/1974/macbride-cv.html Macció, Rómulo www.proa.org.ar/exhibicion/maccio/exhibi-fr.html MacCullagh, James www-history.mcs.st-and.ac.uk/~history/Mathematicians/MacCullagh.html MacCurtain, Margaret

43. Astron-astrol summarised and advanced these techniques and Hipparchus and menelaus of alexandriaproduced tables of what would today be called values of the sine function. http://www.nd.edu/~dharley/HistIdeas/astron-astrol.html

Ideas in Society, 1500-1700 Astronomy and astrology Galileo's horoscope for his daughter Virginia Mathematics is and always has been of central importance to astronomy. As soon as observations became quantified the possibility for calculation and prediction based on observations was open to astronomers. Mathematical developments were both applied to and motivated by astronomical calculations, and many of the most famous astronomers were also mathematicians and vice versa. Although techniques have become increasingly complex, the majority of mathematical astronomical techniques are concerned with positioning and calculation of relative distances of heavenly bodies. The basis of this is spherical trigonometry, which allows calculations on the celestial sphere based on observations taken from an observer on earth. The projection of the celestial sphere onto a flat surface allowed the construction of instruments such as the astrolabe and the mapping of the heavens. Techniques for increasingly accurate calculation were crucial to the development of

44. Free-TermPapers.com - History Of Math methods were developed for solving problems involving plane triangles, and a theoremnamedafter the astronomer menelaus of alexandria-was established for http://www.free-termpapers.com/tp/28/mdg17.shtml

Can`t find essay here? Order custom written term paper. We offer high quality and quick writing for only $12.95 per page! Top 25 Essay Sites Top 50 Essay Sites Top 100 Essay Sites Quick Links: 1. GoldenEssays.com FreeEssays.cc Free-Essays-Free-Essays.com Essays.cc ... Can`t find essay here? Order custom written term paper. We offer high quality and quick writing for only $12.95 per page!

45. Islamic Astronomy By Owen Gingerich The method Ptolemy used to solve spherical triangles was a clumsy onedevised late in the first century by menelaus of alexandria. http://users.kfupm.edu.sa/phys/alshukri/PHYS215/Islamic astronomy.htm

Islamic astronomy by Owen Gingerich Scientific American , April 1986 v254 p74(10) Historians who track the development of astronomy from antiquity to the Renaissance sometimes refer to the time from the eighth through the 14th centuries as the Islamic period. During that interval most astronomical activity took place in the Middle East North Africa and Moorish Spain. While Europe languished in the Dark Ages, the torch of ancient scholarship had passed into Muslim hands. Islamic scholars kept it alight, and from them it passed to Renaissance Europe. Two circumstances fostered the growth of astronomy in Islamic lands. One was geographic proximity to the world of ancient learning, coupled with a tolerance for scholars of other creeds. In the ninth century most of the Greek scientific texts were translated into Arabic, including Ptolemy's Syntaxis , the apex of ancient astronomy. It was through these translations that the Greek works later became known in medieval Europe . (Indeed, the Syntaxis is still known primarily by its Arabic name, Almagest, meaning "the greatest.")

46. Self-Service Science Forum Message elliptic geometry. Spherical geometry was studied by menelaus of alexandriaabout AD 100 and by the Arabs about 1000. Its most famous http://www2.abc.net.au/science/k2/stn/february2000/posts/topic40063.shtm

From: bart Subject: straight lines post id: 40063 If I travelled in a straight line forever would I come back to where I was? This forum is un-moderated. The views and opinions expressed are those of the individual poster and not the ABC. The ABC reserves the right to remove offensive or inappropriate messages. From: bart Subject: re: straight lines post id: 40066 and if I do come back to the place I start, do straight lines exist? This forum is un-moderated. The views and opinions expressed are those of the individual poster and not the ABC. The ABC reserves the right to remove offensive or inappropriate messages. From: mark Subject: re: straight lines post id: 40068 id say yes. This forum is un-moderated. The views and opinions expressed are those of the individual poster and not the ABC. The ABC reserves the right to remove offensive or inappropriate messages. From: Chris Mann Subject: re: straight lines post id: 40070 mathematically, no. The mathematic definition for a straight line (in Euclidean space) is a circle of infinite radius. R = inf therefore Circumferece = inf: Infinite length. However, because space is curved by gravity, and depending on how you draw your straight line, you may just end up where you started, because

47. Greek Mathematics Mechanics. menelaus of alexandria (70130 AD) is the first to treatspherical triangles, ie triangles in Spherical Geometry. He 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.

48. Maths Thesaurus Medium. meg, Mega, Megabyte, Megametre, Member. Member of, Memory,Menelaus, menelaus of alexandria, Menelaus' theorem. Mensuration,Mental http://thesaurus.maths.org/dictionary/map/indices/M

M (255 terms) m M M of I Maclaurin series ... Möbius

49. Publications Page 1. menelaus of alexandria; Oenopides of Chios; Pappus of Alexandria; Ptolemy;Thales of Miletus; Theon of Alexandria; Xenocrates of Chalcedon; Zenodorous http://www.angelfire.com/jazz/onslow/writing/pubs.html

H O M E P A G E T E A C H I N G W R I T I N G R A D I O ... M I S C . Last updated March 2003 by david.tulloch @paradise.net.nz P U B L I C A T I O N S Magazine Articles 'Spinning Web Tales', North and South , December 2001. 'Weird, Wild, Wacky', North and South , October 2001, p.29. 'Web Pets', North and South , August 2001, p.28. 'List Lurkers', North and South , April 2001, p.29 'Web Radio', North and South , March 2001, p.25 'Unreal Estate', North and South , October, 2000, p.35 Fiction 'Just the Bright Stars', in Coastlines, prose and poetry from Wellington to Foxton , Selected by Dame Kate Harcourt, Greater Otaki Library Trust, December, 2001. Textbook Essays 'The Video recorder', and 'Fractal Theory and Benoit Mandelbrot', in Science and Its Times 1950-1999: Understanding the Social Significance of Scientific Discovery , Vol. 7, Gale Group Publishers, Farmington Hills, Michigan, 2000. 'Lebesgue's Development of the Theory of Measure', and 'Wolfgang Pauli's Exclusion Principle' in Science and Its Times 1900-1949 , Vol. 6, 2000. 'The Phlogiston Theory of Fire', 'Genesis versus Geology', and 'Abraham Gottlob Werner's Neptunist Stratigraphy', in

50. Precursors menelaus of alexandria (c AD 70 130) Greeks using Geometry to understand theStars Ancient Greek Astronomy Greek Astronomy, which presents Aristotle http://idcs0100.lib.iup.edu/scirev/SciRev_precursors.html

Precursors Home Up [ Precursors ] Anatomists Philosophers Aristotle Ptolemy ... Roger Bacon WHO "The Symposium," Pietro Testa, 1648 THE PRECURSORS The World by Observation and Logic PYTHAGORAS (c. 580-c. 500 BC) While universally noted for the Pythagorean Theorem, Pythagoras left little to allow a definition of his thought. Pythagoras, a mystic, emphasized knowledge and science as a path to salvation. He and his followers studied mathematics and harmony. Plato used the number mysticism of the Pythagoreans to establish an idealistic ontology with mathematics as the prototype of reality. to Pythagoras' page Life and Times Resume Historical Import ARISTOTLE (384-322 BC) After Aristotelian thought was fused and reconciled with Christian doctrine it was ironically used to impeded observational science. Scholasticism, the philosophical system developed during the 12th Century Renaissance, criticized any ideas if they had not been accepted as part of the Aristotelian corpus. to Aristotle's page Life and Times Resume Historical Import PTOLEMY (A.D. c. 100-c. 170)

51. ENC: Curriculum Resources: A History Of Mathematics (ENC-017351, Full Record) trigonometry and mensuration Early trigonometry Aristarchus of Samos Eratosthenesof Cyrene Hipparchus of Necaea menelaus of alexandria Ptolemy's Almagest The http://www.enc.org/resources/records/full/0,1240,017351,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Advanced Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. A history of mathematics ENC#: ENC-017351 Edition: Second edition. Publisher: John Wiley and Sons, Inc Date: Ordering Information Grades: 6 7 8 9 10 11 12 Post-secondary Abstract: This text presents a chronological look at the development of mathematics. It starts with the concept of number, which is the foundation of mathematics. The book then describes how each layer of mathematical knowledge was added and how various cultures contributed to the general mathematical knowledge over the centuries. In many instances, the development of a concept took place in more than one geographical location, such as the idea of logarithms. John Napier of Scotland was the first to publish a work on logarithms, but Jobst Burgi of Switzerland developed a similar idea at about the same time. A chronological table, beginning with the origin of the sun and ending with 1980, places important mathematical developments in relation to historical world wide events. Forty pages of references are included. (Author/JAR) User Comments: None currently available.

52. 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)

53. 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.

54. Pharos1 Illustrated history by Colin Clement of the ancient Egyptian lighthouse built c.290 BC and destroyed Category Arts Architecture Lighthouses Pharos of alexandria...... 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/

55. La Base De Données Expérimentale Mertens-Pack3 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

56. 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

57. Literaturliste Der Autoren Mit Dem Familiennamen Costard, KVK-Ergebnisanzeige Translate this page amongst the 7 Caimo, Norberto / Voyage d'Espagne, fait en l'annee 1755 avec desnotes 8 menelaus, of alexandria / Menelai Sphaericorum libri III 9 Costard http://members.aol.com/TeleAxel/buecher.htm

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 Costard, George / The history of astronomy : with its application to geography, history

58. Daniel 11 menelaus retaliated by complaining to Andronicus, who then put Onias to death. brotherof Ptolemy VI Philometor, began to reign in alexandria after Antiochus http://members.aol.com/gparrishjr/d11.html

Daniel 11 This chapter contains the prophecy of the progression and conflict between the kings who ruled to the north of Israel and the kings who ruled to the south. Daniel received this vision from one called "a man" sometime around the year 536 BCE. - Daniel 10:1. Vs. 1 - The man speaks of his previous activities during the first year of Darius the Mede. Vs. 2 - Three kings, Cambyses II (529 - 523 BCE), Gaumata (523 BCE -522 BCE), and Darius I (522 - 485 BCE). Vs. 3 - Alexander the Great 336 - 323 BCE. Vs. 4 - The four winds were Alexander's generals, Cassander, Lysimachus, Seleucus Nicator, and Ptolemy Lagus. Vs. 5 - Ptolemy I Soter, the son of Lagus, king of Egypt in 306 BCE. One of his princes, Seleucus I Nicator, rose to power in the north (Syria). Vs. 6 - Verse six begins with the expression "at the end of years," which means after some time. Ptolemy I died in 250 BCE. His son, Ptolemy II Philadelphia ruled Egypt, and sent his daughter, Berenice, to Antiochus II, who had become king of Syria. Berenice and her son, by Antiochus II, were murdered by Antiochus' first wife, Laodice, whom he had divorced to marry Berenice. Vs. 7

59. Encyclopædia Britannica menelaus's theorem. Farnsworth, Philo Taylor American pioneer in the developmentof television. View Article Index Entry. alexandria city, seat of Douglas http://search.britannica.com/search?query=philo of alexandria&ct=eb&fuzzy=N&show

60. Menelaus' And Ceva's Theorems And Their Many Applications Theorems involving menelaus' theorem and some applications of menelaus' theorem to geometry problems.Category Science Math Geometry...... menelaus was a mathematician from alexandria who was born around 70 AD and diedin 120 AD. He contributed greatly to the world of mathematics and science. http://hamiltonious.virtualave.net/essays/othe/finalpaper4.htm

Matchmaker.com: Sign up now for a free trial. Date Smarter! Introduction Proof of Menelaus Theorem Diagram 1 In this instance, triangle ABC is cut by transversal LN, and the three segments having no common end are NC, MA, and BL. The three other segments are AN, BM, and FL. Since their products are equal, it is easy to conclude that if the product of one of the two groups of three segments becomes the numerator in a fraction with the other product as the denominator, the fraction would be equal to 1, hence the equation in the above figure. There is more than one proof of Menelaus, but the more elegant proof is the one that will be discussed in this paper. To start with, have any triangle ABC cut by transversal LN. (Refer to diagram 1) Extend BC such that it intersects with L and label the other two points of intersection M (on segment BA) and N (on segment CA.) After that, construct perpendicular segments p (A to MN), q (C to LN), and r (B to LM.) (Diagram 2) Diagram 2 It can be concluded: Therefore: 1) Triangle XMB := Triangle YMA. (AA Theorem)

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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