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Menelaus Of Alexandria:     more detail

Roman Alexandria: Roman-Era Alexandrians, Hero of Alexandria, Hypatia, Menelaus of Alexandria, Hesychius of Alexandria, Pamphilus of Alexandria 70s Births: 70 Births, 71 Births, 72 Births, 75 Births, 76 Births, 78 Births, 79 Births, Hadrian, Zhang Heng, Menelaus of Alexandria 140 Deaths: Menelaus of Alexandria, Pope Hyginus, Caius Bruttius Praesens, Mithridates Iv of Parthia, Saint Pausilypus Menelai Sphæricorum libri III. Quos olim, collatis MSS. Hebræis & Arabicis, ... Præfationem addidit G. Costard, A.M. (Latin Edition) by of Alexandria Menelaus, 2010-05-27 Menelai Sphaericorum Libri Iii. (Latin Edition)

lists with details

41. Cut The Knot!
    menelaus of alexandria worked in the 1st century AD Giovanni Ceva (16481734)was an Italian engineer and geometer who lived some 16 centuries later.  
    http://www.maa.org/editorial/knot/CevaPlus.html
    
    Extractions: by Alex Bogomolny October 1999 I have a recollection. Years ago, a childhood friend of mine, Boris, shared with me with excitement an unusual experience he had on a visit to the Tretj'yakov Art Gallery in Moscow. He was accompanied by a professional painter, a good acquaintance of his older sister. While Boris was making a round in one of the halls, he observed that the painter remained all that time on the same spot studying a certain picture. Curious, my friend asked the painter what was it about the picture that kept him interested in it for so long. According to Boris, the painter did not reply directly, but, instead, stepped over to the picture and covered a spot on the picture with a palm of his hand. "Have a look at the picture and think of what you see," he requested. After a while, he uncovered the spot, stepped back and asked Boris to have another look. Well, almost 4 decades later, with the names of the painter and the picture long forgotten, I still vividly remember Boris' excitement when he told me of how entirely different, deeper and more beautiful, the picture appeared to him then. This recollection is haunting me. In retrospect, I regret to have never arranged with Boris to visit the gallery and learn how to really

42. Ceva's Theorem: A Matter Of Appreciation
    menelaus of alexandria worked in the 1st century AD, Giovanni Ceva (16481734)was an Italian engineer and geometer who lived some 16 centuries later.  
    http://www.cut-the-knot.com/Generalization/CevaPlus.shtml
    
    Extractions: by Alex Bogomolny October 1999 I have a recollection. Years ago, a childhood friend of mine, Boris, shared with me with excitement an unusual experience he had on a visit to the Tretj'yakov Art Gallery in Moscow. He was accompanied by a professional painter, a good acquaintance of his older sister. While Boris was making a round in one of the halls, he observed that the painter remained all that time on the same spot studying a certain picture. Curious, my friend asked the painter what was it about the picture that kept him interested in it for so long. According to Boris, the painter did not reply directly, but, instead, stepped over to the picture and covered a spot on the picture with a palm of his hand. "Have a look at the picture and think of what you see," he requested. After a while, he uncovered the spot, stepped back and asked Boris to have another look. Well, almost 4 decades later, with the names of the painter and the picture long forgotten, I still vividly remember Boris' excitement when he told me of how entirely different, deeper and more beautiful, the picture appeared to him then.

43. History Of Geometry
    menelaus of alexandria (70130 AD) developed spherical geometry in his onlysurviving work Sphaerica (3 Books). In Book I, he defines spherical triangles  
    http://geometryalgorithms.com/history.htm
    
    Extractions: Home Overview [History] Algorithms Books Web Sites Gift Shop A Short History of Geometry Ancient This is a short outline of geometry's history, exemplified by major geometers responsible for it's evolution. Click on a person's picture or name for an expanded biography at the excellent: History of Mathematics Archive (Univ of St Andrews, Scotland) Also, Click the following links for recommended: Books about Geometry History Web Sites about Geometry History Greek Medieval ... The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations. They knew how to compute areas, and even knew the "Pythagorian Theorem" 1000 years before the Greeks (see: Pythagoras's theorem in Babylonian mathematics ). But there is no evidence that they logically deduced geometric facts from basic principles. Nevertheless, they established the framework that inspired Greek geometry. A detailed analysis of Egyptian mathematics is given in the book: Mathematics in the Time of the Pharaohs . One of the few surviving documents was written by: Ahmes 1680-1620 BC)

44. Egypt Math Web Sites
    6 menelaus of alexandria Born about 70 in (possibly) Alexandria, Egypt. Diedabout 130 in Not known. Of Menelaus s many books only Sphaerica has survived.  
    http://showcase.netins.net/web/rmozzer/Egypt.html
    
    Extractions: Born: 835 in Baghdad (now in Iraq) Died: 912 in Cairo, Egypt. Ahmed ibn Yusuf wrote on ratio and proportion and it was translated into Latin by Gherard of Cremona. The book is largely a commentary on, and expansion of, Book 5 of Euclid's Elements . Ahmed ibn Yusuf also gave methods to solve tax problems which appear in Fibonacci's Liber Abaci . He was also quoted by Bradwardine, Jordanus and Pacioli. Abu Kamil Shuja ibn Aslam ibn Muhammad ibn Shuja Born: about 850 in (possibly) Egypt. Died: about 930. Abu Kamil Shuja is sometimes known as al'Hasib and he worked on integer solutions of equations. He also gave the solution of a fourth degree equation and of a quadratic equation with irrational coefficients. Abu Kamil's work was the basis of Fibonacci's books. He lived later than al'Khwarizmi and his biggest advance was in the use of irrational coefficients. Theon of Alexandria Born: about 335 in (possibly) Alexandria, Egypt. Died: about 395. Theon was the father of Hypatia and worked in Alexandria as a professor of mathematics and astronomy. He produced commentaries on many works such as Ptolemy's Almagest and works of Euclid. Theon was a competent but unoriginal mathematician. Theon's version of Euclid's Elements (with textual changes and some additions) was the only Greek text of the Elements known, until an earlier one was discovered in the Vatican in the late 19

45. Stanley Wong's CU
    described below, picked up on the work of menelaus of alexandria (AD The theorems of Menelaus and Ceva go together since the former gives the  
    http://www.unm.edu/~abqteach/math2002/02-02-11.htm
    
    Extractions: 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)

46. Engineering Database
    110, menelaus of alexandria writes Sphaerica which deals with spherical trianglesand their application to astronomy. 150, Ptolemy produces many important  
    http://www.diracdelta.co.uk/science/source/t/i/timeline/source.html
    
    Extractions: A brief overview of the major milestones in science and engineering. Palaeolithic peoples in central Europe and France record numbers on bones. Early geometric designs used. Sheep are domesticated in the Middle East. Corn is domesticated in the Oaxaca Valley. Wheat is domesticated in Mesopotamia. Cattle are domesticated in Mesopotamia. Copper artifacts are common in the Middle East. Barley is domesticated in Egypt. Potatoes are domesticated in Peru and Bolivia. Light wooden plows are used in Mesopotamia. Kiln-fired bricks and pots are made in Mesopotamia. Potter's wheel used in Mesopotamia. Pyramids are built in Egypt. Bronze is developed in Mesopotamia. Horse drawn vehicles are used in Egypt. Horse riding is developed on the Eurasia steppes. Copper is smelted in China. Rice paddies are developed in China. Iron working is developed in the Middle East.

47. APO Contents
    4133 menelaus of alexandria (?), Treatise on planetary theory; 4134 Proceduretext for planet? 4135 Procedure text for Venus; 4136 Procedure text for the  
    http://www.chass.utoronto.ca/~ajones/oxy/papindex.html
    
    Extractions: Return to Astronomical Papyri from Oxyrhynchus Table of Papyri I. Theoretical and Instructional Texts Menelaus of Alexandria (?), Treatise on planetary theory Procedure text for planet? Procedure text for Venus Procedure text for the moon Predictions of lunar eclipses, A.D. 56 and 57 On eclipse prediction Treatise on eclipse prediction Treatise on lunar periods Tabulated lunar phenomena On latitudes of a planet Instructions for Ptolemy's Handy Tables Instructions for Ptolemy's Handy Tables Treatise on kinematic models Procedure text Procedure text Procedure text II. Primary Tables Epochs of the sun, A.D. 161-237 Epochs of the moon, A.D. 96-166 Epochs of the moon, A.D. 187-198, and template Epochs of the moon, A.D. 217-254 Epochs of Mercury Epochs of Mercury, A.D. 206-215 Epochs of Mercury Epochs of Mercury Epochs of Mercury Epochs of Mercury Epochs of Mercury Epochs of Venus Epochs of Venus, A.D. 106-121 Epochs of Mars, A.D. 271-325 Epochs of Mars, A.D. 225-235 Epochs of Mars, A.D. 101-133 Epochs of Jupiter, A.D. 57-80 Epochs of Jupiter, A.D. 6-13

48. Theorems Of Menelaus And Ceva
    However, the theorem of Menelaus is about 1600 years older than Ceva s theorem.menelaus of alexandria was born about 70 AD, while Giovanni Ceva lived  
    http://www.math.sunysb.edu/~scott/mat360.spr04/cindy/MenelausCeva.html
    
    Extractions: The Theorem of Menelaus and Ceva's Theorem are very closely related. Both concern the products of ratios of lengths involving lines cutting off parts of a triangle. However, the theorem of Menelaus is about 1600 years older than Ceva's theorem. Menelaus of Alexandria was born about 70 AD, while Giovanni Ceva lived between 1647 and 1734. In our discussion here, we will only briefly state the theorems. For more details and proofs, see the very nice discussion at Cut The Knot and/or your textbook. This page requires a java-enabled browser for correct functioning. You can drag the points labelled A, B, C, P, and Q around with the mouse, and the rest of the picture will change accordingly. Theorem of Menelaus Let three points X, Y, and Z, lie respectively on the sides AC, BC, and AB of triangle ABC. Then the points are collinear if and only if AZ/ZB * CX/XA * BY/YC = -1 Note that these distances are signed, so if Z lies beyond B, the ratio AZ/ZB will be negative because ZB goes in the opposite direction from AZ. In the applet at right, it wasn't possible to calculate signed distances, so the product is positive.

49. Islamic Astronomy By Owen Gingerich
    The method Ptolemy used to solve spherical triangles was a clumsy one devisedlate in the first century by menelaus of alexandria.  
    http://faculty.kfupm.edu.sa/phys/alshukri/PHYS215/Islamic astronomy.htm
    
    Extractions: 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.")

50. Menelaus - Columbia Encyclopedia® Article About Menelaus
    Menelaus. Information about Menelaus in the Columbia Encyclopedia®. Menelaus crater menelaus of alexandria Menelaus theorem Menelaus theorem  
    http://columbia.thefreedictionary.com/Menelaus
    
    Extractions: Click the link for more information. . He was the husband of Helen Helen, in Greek mythology, the most beautiful of women; daughter of Leda and Zeus , and sister of Castor and Pollux and Clytemnestra . While still a young girl Helen was abducted to Attica by Theseus and Polydeuces, but Castor and Pollux rescued her. Later, when she was courted by the greatest heroes and chieftains of Greece, her foster father, Tyndareus, fearful of their jealousies, demanded that each suitor swear to defend the rights of the man Helen chose.

51. Greek Trigonometry .
    BC) e menelaus of alexandria (III century BC), both authors of the volumes knownunder the title of Sphaerica. But the biggest part of the information  
    http://www2.math.unifi.it/~archimede/archimede_inglese/trigonometria/trigonometr
    
    Extractions: of trigonometry The invention of trigonometry can be associated with certainty to the studies of astronomy of the geometric school of Alexandria. The Egyptian city of Alexandria, which bears the name of A LEXANDER T HE G REAT who founded it in the III century B.C. was the capital of the Hellenic kingdom of the P TOLEMY until the Romans conquered it. It had a central position in the Mediterranean world of antiquity and an enlightened cultural policy on the part of the rulers, who equipped it with a library famous for over a millennium, one of the seven beauties of the world. They made of Alexandria the centre of Greek mathematics almost until the Arab conquest, and the "bridge" that allowed classic geometry to reach modern times through the Arab tradition. One of the trends of Alexandrine mathematics, together with the studies of pure mathematics that continued vigorously for various centuries, was constant attention to scientific and technological applications, and consequently to quantitative Mathematics, through which the theoretical results of classic geometry could find their equivalent in the natural sciences. Thus a series of new disciplines developed, together with traditional mathematical ones, that today we would call "applied mathematics", ranging from optics to pneumatics, from mechanics to geodetics. This new point of view found a particularly fertile ground in astronomy, where a prevalently cosmological investigation, aiming at looking into the structure of the universe and the causes of the celestial motion, with its greatest example in the works of Aristotle, and in particular the

52. MSN Encarta - Mathematics
    In the meantime, methods were developed for solving problems involving planetriangles, and a theorem—named after the astronomer menelaus of alexandria—was  
    http://uk.encarta.msn.com/encyclopedia_761578291/Mathematics.html
    
    Extractions: Related Items more... Further Reading Editors' choice for Mathematics Encarta Search Search Encarta about Mathematics Editors' Choice Great books about your topic, Mathematics ... Click here Advertisement Encyclopedia Article Multimedia 12 items Article Outline Introduction Ancient Mathematics Medieval and Renaissance Mathematics Western Renaissance Mathematics ... Current Mathematics I Print Preview of Section Mathematics , study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry , or of numbers, as in arithmetic , or the generalization of these two fields, as in algebra . Towards the middle of the 19th century mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions. This latter view encompasses mathematical or symbolic logic—the science of using symbols to provide an exact theory of logical deduction and inference based on definitions, axioms, postulates, and rules for transforming primitive elements into more complex relations and theorems. This brief survey of the history of mathematics traces the evolution of mathematical ideas and concepts, beginning in prehistory. Indeed, mathematics is nearly as old as humanity itself: evidence of a sense of geometry and interest in geometric pattern has been found in the designs of prehistoric pottery and textiles and in cave paintings. Primitive counting systems were almost certainly based on using the fingers of one or both hands, as evidenced by the predominance of the numbers 5 and 10 as the bases for most

53. Menelaus And Ceva
    menelaus of alexandria (circa 100 AD) was among the first to clearly recognizegeodesics on a curved surface as the natural analogs of straight lines on a  
    http://www.mathpages.com/home/kmath442/kmath442.htm
    
    Extractions: Menelaus and Ceva Menelaus of Alexandria (circa 100 AD) was among the first to clearly recognize geodesics on a curved surface as the natural analogs of straight lines on a flat plane.  Earlier mathematicians had considered figures on a spherical surface, but it was Menelaus who had the insight to construct a complete geometry of the sphere with great circle arcs taking the place of line segments.  For example, he defined "spherical triangles" as figures comprised of three great circle arcs, and developed a family of trigonometric relations for such figures.  The most famous of these is still known as Menelaus' Theorem, although it's commonly presented only in the planar version (which was probably known to Euclid ).  In this form the theorem gives the necessary and sufficient condition for three points on the extended edges of a plane triangle to be co-linear.  Consider the triangle shown below Letting [xy] denote the distance between points x and y, the Theorem of Menelaus states that the points a,b,c located on the (extended) edges BC, AC, AB of a triangle ABC are colinear if and only if To prove this, consider a rectangular coordinate system xy with respect to which the coordinates of the vertices A,B, and C are (0,0), (

54. List Of Ancient Greeks: Information From Answers.com
    Menedemus (Cynic) Cynic philosopher; Menelaus (sculptor) - sculptor;menelaus of alexandria - mathematician; Menestor - botanical writer  
    http://www.answers.com/topic/list-of-ancient-greeks
    
    Extractions: showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping list of ancient Greeks Wikipedia list of ancient Greeks This an alphabetical list of ancient Greeks . These include ethnic Greeks and Greek language speakers from Greece and the Mediterranean world up to about 200 AD. Contents: Top A B C ... Related articles Acacius of Caesarea - bishop of Caesarea Acestorides - tyrant of Syracuse Achaeus - general Achaeus of Eretria - poet Achermus - sculptor Achilles Tatius - writer Acron - writer Acrotatus - King of Sparta Acusilaus - scholar Adeimantus - Corinthian general Adrianus - sophist Aedesius - philosopher Aeimnestus - Spartan soldier Aelianus Tacticus - military writer Aelius Aristides - orator and writer Aeneas Tacticus - writer Aenesidemus - Sceptic philosopher Aeropus I of Macedon - king Aeropus II of Macedon - king Aeschines Socraticus - Socratic philosopher Aeschines - Athenian orator Aeschylus - playwright Aesop - author of fables Aetion - painter Aetius - philosopher Agarista - two; wife of Megacles, mother of Pericles

55. History Of Astronomy: Persons (M)
    menelaus of alexandria Menelaos von Alexandria (ca. 70 ca. 130). Short biographyand references (MacTutor Hist. Math.) Find more about Menelaus and  
    http://www.astro.uni-bonn.de/~pbrosche/persons/pers_m.html

56. The History Of Mathematics - Library Center For E-courses
    menelaus of alexandria The Mac Tutor History of Mathematics Archive, menelaus of alexandria Amy Bowman adn Micha Christensen ? ?  
    http://lib.haifa.ac.il/www/mesila/math/sites.htm

57. Ah Need Good Wiccan Cooking Recipies Fur The Refugees - Above Top Secret Conspir
    Dioscorides Sextus Julius Frontinus Nicomachus of Gerasa menelaus of alexandriaMenodotus of Nicomedia Tiberius Claudius Herodes Atticus Valerius Flaccus  
    http://www.abovetopsecret.com/forum/last25
    
    Extractions: Above Top Secret 4.0 Conspiracies in Religions Welcome to the AboveTopSecret.com conspiracy discussion board. Use this board to engage in collaborative discussion and debate on a broad range of conspiracy, extraterrestrial, secret project, government agency, and other alternative topics. Within this board, our staff will be diligent in keeping the tone and style of the boards polite and congenial.

58. Abraham
    a work on the geometry of the sphere by Autolycus, Apollonius s Conics, andthe later contributions by Heron of Alexandria and menelaus of alexandria.  
    http://homepages.compuserve.de/thweidenfeller/mathematiker/Abraham.htm
    
    Extractions: Died: 1136 in Provence, France Abraham bar Hiyya was a Spanish Jewish mathematician and astronomer. His name is Hebrew for 'the prince' but he is also known by the Latin name Savasorda which comes from his 'job description' showing that he held an official position in the administration in Barcelona. Abraham bar Hiyya is famed for his book Hibbur ha-Meshihah ve-ha-Tishboret (Treatise on Measurement and Calculation), translated into Latin by Plato of Tivoli as Liber embadorum in 1145. This book is the earliest Arab algebra written in Europe. It contains the complete solution of the general quadratic and is the first text in Europe to give such a solution. Rather strangely, however, 1145 was also the year that al-Khwarizmi 's algebra book was translated by Robert of Chester so Abraham bar Hiyya's work was rapidly joined by a second text giving the complete solution to the general quadratic equation. It is interesting to see the areas of mathematics and the mathematicians with which Abraham was familiar. Of course he knew geometry through the works of Euclid , but he also knew the contributions to geometry from other Greek texts such as Theodosius 's Sphaerics in three books

59. Webpage
    Conics, and the later contributions by Heron of Alexandria and menelaus of alexandria.Abraham had also studied some of the important works on algebra by  
    http://www.k12.nf.ca/discovery/curriculum/math/famous/pageone.htm

60. The Foundations Of Christianity
    Ptolemy (Claudius Ptolemaeus) wrote the astronomical masterpiece the Almagest inAlexandria. (0.1). menelaus of alexandria wrote on mathematics. (0)  
    http://members.iinet.net.au/~quentinj/Christianity/EarlyWriters.html
    
    Extractions: The first one-and-a-half centuries of Christianity. There is a list found in many places on the Internet, citing authors who lived at the time of Jesus or within a century of him. This list apparently comes from John E. Remsburg's The Christ: A Critical Review and Analysis of the Evidence of His Existence . This page is inspired by that list and my wish to see it expanded, updated and corrected. I present a chronological listing of the writers from the Roman and Greek world of the first century and a half after the alleged crucifixion. Colour and font size provides a simple classification: Surprising failures of contemporary writers to mention Jesus (weight 5). Authors who could reasonably be expected to at least mention Jesus (weight 4 or 3). Plain coloured text indicates authors who were in a position to mention or describe Jesus (weight 2 or 1 or even 0.5). I have also included some astronomers who failed to mention the Star of Bethlhem or the crucifixion darkness with weight of 0.1 Non-supporting or suspect or uncertain references sometimes cited as evidence for Jesus (weight 0).

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