21. Ceva's And Menelaus's Theorems menelaus of alexandria (about 100 AD , not to be confused with Menelaus of Sparta)wrote a treatise called Sphaerica in which he used a certain property of a http://www.math.uci.edu/~mathcirc/math194/lectures/advanced3/node2.html

Next: Homework problems Up: Advanced Geometry III Previous: The nine-point circle Ceva's and Menelaus's Theorems The line segment joining a vertex of a triangle to any given point on the opposite side is called a cevian . Thus, if X Y and Z are points on the respective sides BC CA and AB of triangle ABC , the segments AX BY and CZ are cevians. This term comes from the name of the Italian mathematician Giovanni Ceva, who published in 1678 the following very useful theorem: Ceva's Theorem If three cevians AX BY and CZ , one through each vertex of a triangle ABC , are concurrent, then Conversely, if this equation holds for points X Y and Z on the three sides, then these three point are concurrent. (We say that three lines or segments are concurrent if they all pass through one point) Figure 2: Ceva's theorem Proof. Given the concurrence we can use that the areas of the triangles with equal altitudes are proportional to the bases of the triangles. Referring to Figure , we have Similarly, Now, if we multiply these, we find Conversely, suppose that the first two cevians meet at

22. Cylic Quadralerals As to Menelaus theorem, however, he probably took it without acknowledgement fromthe Spherics of menelaus of alexandria, an astronomer of about a generation http://www.pballew.net/cycquad.html

Back to MathWords and Other Words Cyclic Quadrangles A cyclic quadrangle or cyclic quadrialteral is a quadrilateral for which a single circle passes through all four vertices. We say that the quadrangle is inscribed in the circle, or that the circle circumscribes the quadrangle. In the figure shown, quadrangle ABCD is circumscribed by a circle with center at O. The area of a quadrilateral can be found by an extension of Heron's formula , that is often credited to the Indian Mathematician, Brahamagupta. If the lengths of the four sides are given as a, b, c and d; and the semiperimeter (half the perimeter), s = (a+b+c+d)/2, of the polygon, then the area of the cyclic quadrangle is given by the formula It is often possible to make several quadrangles with the same length sides, but of all the possible quadrangles with the given sides, the inscribed quadrilateral has the largest area. The length of the two diagonals of a cyclic quadrilateral are related to the four sides in Ptolemy's Theorem which states (using m and n for the diagonals lengths) mn=ac+bd. In words, the product of the diagonals is equal to the sum of the products of the oppsite sides.

23. The History Of Mathematics - Library Center For E-courses Andrews. menelaus of alexandria The Mac TutorHistory of Mathematics Archive, University of St. Andrews. http://lib.haifa.ac.il/www/mesila/math/sites.htm

The History of Mathematics Trinity College, Dublin:á åôñàðù íåçúá íéøúà David R. Wilkins éãé ìò The History of Mathematics David R. Wilkins : é"ò êøòð History of mathematics resources Indexes of Biographies MacTutor History of Mathematics archive:êåúî Mathematicians of the Seventeenth and EigHteenth Centuries Mathematics Genealogy Project Mathematical Journey through Time The Mactutor History of Mathematics archive University of st Andrews Scotland,School of Mathematics and Statistics:êåúî Philosophy and History of Science Kyoto University World of Scientific Biography Erics Treasure Trove of Scientific Biography Arabic mathematics : forgotten brilliance? Doubling the cube History Topics: Babylonian mathematics History Topics: Ancient Egyptian mathematics ... udoxus of Cnidus The Mac Tutor History of Mathematics Archive, University of St. Andrews êåúî Eudoxus of Cnidus An Introduction to the works of Euklid with an Emphasis on the Elements Euclid of Alexandria The Mac Tutor History of Mathematics Archive University of St. Andrews:êåúî

24. Who Was Who In Roman Times: Data On Persons: Menelaus Of Alexandria Sponsored links Data on Persons. menelaus of alexandria. Function ScientistImportant year 98 AD Sex Male, Synonym(s) Menelaus. No parents found. http://www.romansonline.com/Persns.asp?IntID=1006&Ename=Menelaus of Alexandria

25. Egypt Math Web Sites Died about 125 in Not known. 6 menelaus of alexandria Born about 70in (possibly) Alexandria, Egypt. Died about 130 in Not known. http://showcase.netins.net/web/rmozzer/Egypt.html

Egypt math web sites Serenus Born: about 300 in Antinoupolis, Egypt Died: about 360. Serenus wrote On the Section of a Cylinder and On the Section of a Cone . He also wrote a commentry on Apollonius's Conics which is lost. Ahmed ibn Yusuf 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

26. History Of Mathematics: Greece c. 62 CE) (Hero); Theodosius of Tripoli (c. 50? CE?); menelaus of alexandria(c. 100 CE); Nicomachus of Gerasa (c. 100); Theon of Smyrna (c. 125); http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

27. Menelaus Of Alexandria - Information An online Encyclopedia with information and facts menelaus of alexandria Information, and a wide range of other subjects. menelaus of alexandria. http://www.book-spot.co.uk/index.php/Menelaus_of_Alexandria

Menelaus of Alexandria - Information Home Mathematical and natural sciences Applied arts and sciences Social sciences and philosophy ... Interdisciplinary categories Menelaus of Alexandria (born ca. ; died ca. ) was a mathematician and astronomer External links Menelaus of Alexandria This article is a http://www.wikipedia.org/wiki/Perfect_stub_article " class='external' title="">stub . You can help Wikipedia by http://www.wikipedia.org/wiki/Find_or_fix_a_stub " class='external' title="">expanding it sl:Menelaj All text is available under the terms of the GNU Free Documentation License (see for details). . Wikipedia is powered by MediaWiki , an open source wiki engine.

28. Gods02 *. Helen of Troy. m1. menelaus of alexandria, King of Lacedaemon below. m2. b. Menelausof Alexandria, King of Lacedaemon. m. Helen of Troy (dau of Zeus) above. http://www.stirnet.com/HTML/genie/ancient/gods/gods02.htm

Index links to: Top Section Uploaded: / Updated: This page is by no means complete but will be worked on and added to from time to time. It mainly follows the Greek Myths but some Roman name equivalents have been added Until the page has 'settled down', we will not number Zeus's issue but instead list them all with a double asterisk (**). The wives/mistresses are presently listed in alphabetical order. Zeus, Lord of Heaven = Jupiter m/p*. Aegina (a nymph) Aeacus m. Endeis (dau of Sciron or Chariclo) p. Psamathe (dau of Nereus) m/p*. Alcmene (wife of Amphitryon Heracles or Hercules, the Hero m/p*. Antiope (dau of Nycteus) issue - Amphion, Zethus m/p*. Callisto (nymph of the Hunt) Arcas m. Meganira (dau of Amyclas) p. Erato (a nymph) m/p/. Danae (dau of Acrisius, King of Argos) Perseus m. Andromeda (dau of Cepheus) m/p*. Demeter (dau of Cronus, his sister) Persephone = Proserpina m/p*. Dione

29. Abraham which is a work on the geometry of the sphere by Autolycus, Apollonius s Conics,and the later contributions by Heron of Alexandria and menelaus of alexandria. http://homepages.compuserve.de/thweidenfeller/mathematiker/Abraham.htm

Abraham bar Hiyya Ha-Nasi Born: 1070 in Barcelona, Spain 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

30. Mathematiker Mit Mm Translate this page Maxwell James Clerk (1831 - 1879, Edinburgh). menelaus of alexandria (70- 130, Alexandria). Mersenne Marin (1588 - 1648, Paris). Minkowski http://homepages.compuserve.de/thweidenfeller/mathematiker/m.html

M Macaulay Francis Sowerby (1862 - 1937, Witney) MacDonald Hector Munro (1865 - 1935, Edinburgh) MacMahon Percy Alexander (1854 - 1929, Malta) Mandelbrot Bernoit (1924 - , Warschau) ... zurück

31. Re: Menelaus By Samuel S. Kutler S. Kutler skutler@sjca.edu Date Mon, 1 Feb 1999 084248 -0500 Jenny Hereis a piece of personal information about menelaus of alexandria from Heath s http://mathforum.org/epigone/math-history-list/kandpreldstend/v01540b01b2db151a3

Re: Menelaus by Samuel S. Kutler reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Re: Menelaus Author: s-kutler@sjca.edu Date: The Math Forum

32. Re: Ceva's Theorem By Samuel S. Kutler Menelaus Theorem. The former is attributed to Giovanni Ceva in 1678, the latter to menelaus of alexandria around 100 AD. Some sources http://mathforum.org/epigone/math-history-list/shanspinquah/v01540b00ae1bbe6b5e2

Re: Ceva's Theorem by Samuel S. Kutler reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Re: Ceva's Theorem Author: s-kutler@sjca.edu Date: The Math Forum

33. History Of Geometry Mechanics. menelaus of alexandria (70130 AD) developed sphericalgeometry in his only surviving work Sphaerica (3 Books). In http://geometryalgorithms.com/history.htm

History Home Overview [History] Algorithms Books Gifts Web Sites 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 these links for recommended: Greek Medieval Modern History Books ... History Web Sites Ancient Geometry (2000 BC - 500 BC) Babylon Egypt 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 India (1500 BC - 200 BC) The Sulbasutras Baudhayana (800-740 BC) Apastamba (600-540 BC) Greek Geometry (600 BC - 400 AD) Time Line of Greek Mathematicians Major Greek Geometers (listed cronologically) [click on a name or picture for an expanded biography].

34. Ancient Greeks On The Moon MENELAUS crater 16.3N – 16.0E 26 km diameter menelaus of alexandria, (c. 98)AD Geometer, Astronomer. METON crater 73.6N – 18.8E 130 km diameter (? http://www.mlahanas.de/Greeks/Moon.htm

Ancient Greeks on the Moon Apollo Belvedere on an Apollo 17 mission patch of the last and most successful mission to the Moon in December 1972 Craters on the moon named after ancient Greeks. The area of these craters combined is larger than that of the area of Modern Greece!! AGATHARCHIDES crater km diameter Agatharchides (?-150) BC Geographer AGRIPPA crater km diameter Agatharchides (c. 92) AD Astronomer ALEXANDER crater km diameter Alexander the Great (356-323) BC ANAXAGORAS crater 50 km diameter 2350 mt height walls In the northern lunar regions Anaxagoras (500-428) BC Astronomer ANAXIMANDER crater 7 km diameter 2800 mt height walls North - west lunar region ANAXIMENES crater km diameter Anaximenes (585-528) BC Astronomer APOLLONIUS crater 53 km diameter 1700 mt height walls Southern of Crisium sea Apollonius of Perga 3 rd century BC, mathematician ARATUS crater km diameter Anaximenes (315-248) BC Astronomer ARCHIMEDES crater km diameter 2060 mt height walls N - 4W East of Imbrium sea and below this crater ARCHIMEDES rima From Archimedes crater to southern hilly region The other two craters are Aristillus and Autolycus Archimedes (287-212) BC ARCHYTAS crater 31 km diameter 2350 mt height walls Northern of Frigoris sea Archytas, (428-347) BC

35. Ancient Greece Mathematics Timeline geometry. About 110 menelaus of alexandria writes Sphaerica which dealswith spherical triangles and their application to astronomy. http://www.mlahanas.de/Greeks/TLMathematics.htm

Timeline Ancient Greece Mathematics Around 600 BC the Cretan poet Epimenides is attributed to have invented the linguistic paradox with his phrase "Cretans are ever liars" - the Liar's Paradox. 2500 years later, the mathematician Kurt Gödel invents an adaptation of the Liar's Paradox that reveals serious axiomatic problems at the heart of modern mathematics. About 600 BC Thales of Miletus , He brings Babylonian mathematical knowledge to Greece and uses geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. About 530 BC Pythagoras no common rational measure is discoverable About 480 BC Parmenides of Elea founded the Eleatic School where he taught that 'all is one,' not an aggregation of units as Pythagoras had said, and that to arrive at a true statement, logical argument is necessary. Truth "is identical with the thought that recognizes it" (Lloyd 1963:327). Change or movement and non-being, he held, are impossibilities since everything is 'full' and 'nothing' is a contradiction which, as such, cannot exist. "Parmenides is said to have been the first to assert that the Earth is spherical in shape...; there was, however, an alternative tradition stating that it was Pythagoras" (Heath 1913:64). Corollary to Parmenides' rejection of the existence of 'nothing' is the Greek number system which, like the later Roman system, refused to use the Babylonian positional number system with its marker for 'nothing.' Making no clear distinction between nature and geometry, "mathematics, instead of being a science of possible relations, was to [the Greeks] the study of situations thought to subsist in nature" (Boyer 1949:25). Moreover, "almost everything in [Greek] philosophy became subordinated to the problem of change.... All temporal changes observed by the senses were mere permutations and combinations of 'eternal principles,' [and] the historical sequence of events (which formed part of the 'flux') lost all fundamental significance" (Toulmin and Goodfield 1965:40).

36. List Of Mathematicians - Reference Library Jerrold E. Marsden (USA, ; Lorenzo Mascheroni (Italy, 1750 1800); CurtisT. McMullen (USA, 1958 - ); menelaus of alexandria (Egypt ca 70- ca 140); http://www.campusprogram.com/reference/en/wikipedia/l/li/list_of_mathematicians.

Reference Library: Encyclopedia Main Page See live article Alphabetical index List of mathematicians The famous mathematicians are listed below in English alphabetical transliteration order (by surname A B C ... Z A Niels Henrik Abel (Norway, Ralph H. Abraham (USA, University of California, Santa Cruz Wilhelm Ackermann (Germany, Maria Gaetana Agnesi (Italy, Lars Valerian Ahlfors , (Finland, Ahmes , (Egypt, roughly around 17th century BC Jean le Rond d'Alembert (France, Abu Ja'far Muhammad Ibn Musa Al-Khwarizmi (Persia, Alexander Anderson (Scotland, André-Marie Ampere , (France, Apollonius of Perga (Asia Minor, 265 B.C 170 B.C Archimedes (Syracuse, 287 B.C 212 B.C Aristotle (Greece, 384 B.C 322 B.C Vladimir Arnol'd (Russia, Emil Artin (Austria, Michael Francis Atiyah (Britain, B Charles Babbage (United Kingdom, John Baez Alan Baker (Britain, Stefan Banach (Poland, Grigory Isaakovich Barenblatt (Russia, USA, Isaac Barrow (England, Thomas Bayes (England, Eric Temple Bell (Scotland, USA, Jakob Bernoulli (Switzerland, Johann Bernoulli (Switzerland, Joseph Louis Francois Bertrand (France

37. Greek Trigonometry . century. BC) e menelaus of alexandria (III century BC), both authorsof the volumes known under the title of Sphaerica. But the http://www.math.unifi.it/archimede/archimede_inglese/trigonometria/trigonometria

The Garden of Archimedes A Museum for Mathematics Brief history of trigonometry Greek 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

38. Theorems Of Menelaus And Ceva menelaus of alexandria was born about 70 AD, while Giovanni Ceva lived between 1647and 1734. In our discussion here, we will only briefly state the theorems. http://www.math.sunysb.edu/~scott/mat360.spr04/cindy/MenelausCeva.html

The Theorems of Menelaus and Ceva 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.

39. 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

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

History of Astronomy Persons History of Astronomy: Persons (M) Deutsche Fassung Mac Laurin, Colin: see Maclaurin, Colin MacDonnell, William John (1842-1910) Short biographical data and archival sources Mach, Ernst (1838-1916) Very short biography and references (Or see German version Very short biography (Eric Weisstein's Treasure Trove) Maclaurin [Mac Laurin], Colin (1698-1746) Short biography and references (MacTutor Hist. Math.) Short biography (Eric Weisstein's Treasure Trove) Short biography (in French) Very short biography (infoplease.com) Family history Family history (under construction) Find more about Maclaurin with Alta Vista Biographical data (in Estonian) Madsen, Hans Frandsen (1843-1937) Short biographical data and reference Very short biography (under construction) Biography of his son John Percival Vissing Madsen (1879-1969) and briefly about himself Maestlin, Michael (1550-1631) Biographical data and references Short biography Maffei, Francesco Scipione (1675-1755) Short biography and references From the Catholic Encyclopedia, 1913

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

Page 2     21-40 of 94    Back | 1  | 2  | 3  | 4  | 5  | Next 20