1. Menelaus Of Alexandria --  Encyclopædia Britannica MLA style " menelaus of alexandria." Encyclopædia Britannica. 2004 APA style menelaus of alexandria. Encyclopædia Britannica. Retrieved May 10, 2004, from Encyclopædia http://www.britannica.com/eb/article?eu=53302

2. Abel no photo available. menelaus of alexandria. ( 70 A.D. 103 A.D.) Written and Researched by Amy Bowman and Micah Christensen. One of the greatest mathematicians was Menelaus. He was born about 70 A.D. in Alexandria, Egypt. Dover Publications 1953.Pages 603, 606, 615. Internet menelaus of alexandria. http://www.forestcity.k12.ia.us/Pages/FCHS/Site/menelaus.htm

no photo available Menelaus of Alexandria (70 A.D. - 103 A.D.) Written and Researched by Amy Bowman and Micah Christensen One of the greatest mathematicians was Menelaus. He was born about 70 A.D. in Alexandria, Egypt. Menelaus wrote many books but only Sphaerica has survived. In this book he deals with spherical triangles and their application to astronomy. He was the first to write down the definition of a sperical triangle. In Book One of Sphaerica , he set up the basics for treating spherical triangles as Euclid treated plain triangles. This marked a turning poin in the development of spherical trigonometry. Book Two applies spherical trigonometry to astronomy. Book Three deals with spherical trigonometry and includes Menelaus' theorem. This diagram shows the theorem. (See below) A point lying on a side line of a triangle, but not coinciding with a vertex of the triangle, is called a Menelaus point of the triangle for this side. Menelaus also wrote a six book treatise on chords in a circle. He also estimated that the moon moves 1 degree per century. Menelaus died in 103 A.D. It is not known what part of the world that he died in, but it is believed to be near the Middle East, possibly Egypt.

3. Menelaus Menelaus' Thm. Menelaus's Theorem is very similar to Ceva's Theorem The theorem is named for menelaus of alexandria, who lived around the end of the first century http://www.pballew.net/menelaus.html

Menelaus' Thm  Menelaus's Theorem is very similar to Ceva's Theorem .  The theorem states that if a straight line intersects all three sides of a triangle (one or all three intersections may be on the extended legs) then the  sides must be cut into proportions that multiply to make one.  Using the figure, triangle ABC is cut by the line at A', B', and C' on the opposite sides of the trinangle and so  . The theorem is also written in the equivalent form,  The theorem is named for Menelaus of Alexandria, who lived around the end of the first century.  You can find more about his life at the St Andrews University web site.   Menelaus also proved a spherical version of the same theorem.  If the triangle and the cutting line are all formed by great circle arcs on a sphere, then the formula states that  HOEHN'S THM Almost 1900 years after Menelaus (1995) a mathematician named Hoehn published a similar looking theorem about Pentagons in Mathematics Magazine.  In it he stated that the product of all the red segments equals the product of all the blue segments.

4. TMTh:: MENELAUS OF ALEXANDRIA MATHEMATICIAN, ASTRONOMER, PHYSICISTmenelaus of alexandria( fl. 1st century AD) Life. Menelaus was the founder of spherical trigonometry and the first to treat it as a branch of http://www.tmth.edu.gr/en/aet/4/68.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN, ASTRONOMER, PHYSICIST MENELAUS OF ALEXANDRIA (fl. 1st century AD) Life Menelaus was the founder of spherical trigonometry and the first to treat it as a branch of mathematics distinct from stereometry and astronomy. He lived in Rome, where he made astronomical observations in 98 AD. He conducted experiments into specific gravity. Menelaus is cited by Ptolemy and Plutarch. One of the craters on the moon has been named "Menelaus" in his honour. Work Menelaus worked on developing mathematical methods for use in astronomical calculations. "Sphaerica": Survives in Arabic and Hebrew translation. 3 books. Book I deals with the geometry of the sphere; it introduces for the first time the concept of the spherical triangle (a triangle formed by three arcs of great circles on the surface of a sphere). Book II covers the application of spherical geometry and trigonometry to astronomical measurements and calculations. Book III concentrates on spherical trigonometry and introduces "Menelaus's Theorem", modifying the theorem on plane triangles and extending it to spherical triangles. This theorem became of fundamental importance in spherical trigonometry and astronomy, and was used by later geographers and astronomers, e.g. Ptolemy in the 2nd century. He named spherical triangles "trilaterals", and described their properties. "On the calculation of the chords in a circle": 6 books. Lost.

5. Menelaus And Ceva Menelaus and Ceva. menelaus of alexandria (circa 100 AD) was among the first to clearly recognize geodesics on spherical surface, but it was Menelaus who had the insight to construct http://www.mathpages.com/home/kmath442/kmath442.htm

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), (

6. The Beginnings Of Trigonometry History of Mathematics). Both Pappus and Proclus call him menelaus of alexandria (Heath 260), so we may assume which was mentioned by Theon of Alexandria, but those books have all http://www.math.rutgers.edu/~cherlin/History/Papers2000/hunt.html

The Beginnings of Trigonometry Joseph Hunt History of Mathematics Rutgers, Spring 2000 The ancient Greeks transformed trigonometry into an ordered science. Astronomy was the driving force behind advancements in trigonometry. Most of the early advancements in trigonometry were in spherical trigonometry mostly because of its application to astronomy. The three main figures that we know of in the development of Greek trigonometry are Hipparchus, Menelaus, and Ptolomy. There were likely other contributors but over time their works have been loss and their names have been forgotten. "Even if he did not invent it, Hipparchus is the first person of whose systematic use of trigonometry we have documentary evidence." (Heath 257) Some historians go as far as to say that he invented trigonometry. Not much is known about the life of Hipp archus. It is believed that he was born at Nicaea in Bithynia. (Sarton 285) The town of Nicaea is now called Iznik and is situated in northwestern Turkey. Founded in the 4th century BC, Nicaea lies on the eastern shore of Lake Iznik. He is one of the g reatest astronomers of all time. We know from Ptolemy's references that he made astronomical observations from 161 to 127 BC. (Sarton 285) Unfortunately, nearly all of his works are lost, and all that remains is his commentary on the Phainomena of Eudoxos of Cnidos, and a commentary on an astronomical poem by Aratos of Soloi. (Sarton 285) Most of what we know about Hipparchus comes from Ptolemy's

7. Menelaus menelaus of alexandria. Very little else is known of Menelaus s life, exceptthat he is called menelaus of alexandria by both Pappus and Proclus. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Menelaus.html

Menelaus of Alexandria Born: about 70 in (possibly) Alexandria, Egypt Died: about 130 Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Although we know little of Menelaus of Alexandria 's life Ptolemy records astronomical observations made by Menelaus in Rome on the 14 th January in the year 98. These observation included that of the occultation of the star Beta Scorpii by the moon. He also makes an appearance in a work by Plutarch who describes a conversation between Menelaus and Lucius in which Lucius apologises to Menelaus for doubting the fact that light, when reflected, obeys the law that the angle of incidence equals the angle of reflection. Lucius says (see for example [1]):- In your presence, my dear Menelaus, I am ashamed to confute a mathematical proposition, the foundation, as it were, on which rests the subject of catoptrics . Yet it must be said that the proposition, "All reflection occurs at equal angles" is neither self evident nor an admitted fact. This conversation is supposed to have taken place in Rome probably quite a long time after 75 AD, and indeed if our guess that Menelaus was born in 70 AD is close to being correct then it must have been many years after 75 AD.

8. References For Menelaus Articles MF Aintabi, Arab scientific progress and menelaus of alexandria,in Actes XIIe Congrès Internat. d Histoire des Sciences http://www-gap.dcs.st-and.ac.uk/~history/References/Menelaus.html

References for Menelaus Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: T L Heath, A History of Greek Mathematics (2 Vols.) (Oxford, 1921). O Neugebauer, A history of ancient mathematical astronomy (New York, 1975). Articles: M F Aintabi, Arab scientific progress and Menelaus of Alexandria, in III ( Paris, 1971), 7-12. O Schmidt, On the theorems of Ptolemy and Menelaus (Danish), Nordisk Mat. Tidskr. G Yussupova, Commentaries to Menelaus' Spherics by al-Tusi and al-Yazdi (Russian), Izv. Akad. Nauk USSR Ser. Fiz.-Mat. Nauk G Yussupova, Zwei mittelalterliche arabische Ausgaben der 'Sphaerica' des Menelaos von Alexandria, Historia Math. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR April 1999 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Menelaus.html

9. Menelaus Biography of Menelaus (70130) menelaus of alexandria. Born about 70 in (possibly) Alexandria, Egypt Although we know little of menelaus of alexandria's life Ptolemy records astronomical observations made by http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Menelaus.html

Menelaus of Alexandria Born: about 70 in (possibly) Alexandria, Egypt Died: about 130 Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Although we know little of Menelaus of Alexandria 's life Ptolemy records astronomical observations made by Menelaus in Rome on the 14 th January in the year 98. These observation included that of the occultation of the star Beta Scorpii by the moon. He also makes an appearance in a work by Plutarch who describes a conversation between Menelaus and Lucius in which Lucius apologises to Menelaus for doubting the fact that light, when reflected, obeys the law that the angle of incidence equals the angle of reflection. Lucius says (see for example [1]):- In your presence, my dear Menelaus, I am ashamed to confute a mathematical proposition, the foundation, as it were, on which rests the subject of catoptrics . Yet it must be said that the proposition, "All reflection occurs at equal angles" is neither self evident nor an admitted fact. This conversation is supposed to have taken place in Rome probably quite a long time after 75 AD, and indeed if our guess that Menelaus was born in 70 AD is close to being correct then it must have been many years after 75 AD.

10. Alexandria --  Britannica Student Encyclopedia Alexandria Britannica Student Encyclopedia. To cite this page MLA style Alexandria. Britannica Student Encyclopedia. 2004. Encyclopædia http://www.britannica.com/ebi/article?eu=340864&query=menelaus of alexandria&ct=

11. Menelaus Of Alexandria menelaus of alexandria. menelaus of alexandria (born around 70; diedaround AD 140) was a mathematician. http//wwwgroups.dcs.st http://www.fact-index.com/m/me/menelaus_of_alexandria.html

Main Page See live article Alphabetical index Menelaus of Alexandria Menelaus of Alexandria (born around 70; died around A.D. 140) was a mathematician http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Menelaus.html This article is from Wikipedia . All text is available under the terms of the GNU Free Documentation License

12. Me 163 Komet Mendota, Illinois Mendota, Minnesota Mendota Heights, Minnesota Mendoza ProvinceMenedemus Menegroth Menehune Menelaus menelaus of alexandria Meneldil Menelik http://www.fact-index.com/m/me/

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13. Menelaus - Wikipedia, The Free Encyclopedia During this period Menelaus and his brother, Agamemnon took refuge with Tyndareus, king of Sparta, whose See also menelaus of alexandria ( about 70 about 140), mathematician http://en2.wikipedia.org/wiki/Menelaus

Menelaus From Wikipedia, the free encyclopedia. Menelaus (also transliterated as Meneláos ), in Greek mythology , was a king of Sparta and son of Atreus and Aerope Atreus was murdered by his brother, Aegisthus , who took possession of the throne of Mycenae and ruled jointly with his father Thyestes . During this period Menelaus and his brother, Agamemnon took refuge with Tyndareus , king of Sparta, whose daughters Clytemnestra and Helen they respectively married. Helen and Menelaus had one daughter, Hermione Menelaus succeeded Tyndareus (whose only sons, Castor and Polydeuces became gods), and Agamemnon, with his brother's assistance, drove out Aegisthus and Thyestes, and recovered his father's kingdom. He extended his dominion by conquest and became the most powerful prince in Greece. When it was time for Helen, Tyndareus' daughter, to marry, many Greek kings and princes came to seek her hand or sent emissaries to do so on their behalf. Among the contenders were Odysseus Menestheus Ajax the great Patroclus and Idomeneus , but Menelaus was the favorite though, according to some sources, he did not come in person but was represented by his brother Agamemnon. All but Odysseus brought many and rich gifts with them. Tyndareus would accept none of the gifts, nor would he send any of the suitors away for fear of offending them and giving grounds for a quarrel. Odysseus promised to solve the problem in a satisfactory manner if Tyndareus would support him in his courting of

14. Encyclopedia: Menelaus Of Alexandria Updated Mar 20, 2004. Encyclopedia menelaus of alexandria. menelaus of alexandria(born ca. 70; died ca. External links. menelaus of alexandria {{msgstub}}. http://www.nationmaster.com/encyclopedia/Menelaus-of-Alexandria

Supporter Benefits Signup Login Sources ... Pies Factoid #14 If you like kids, then Uganda might be the place for you. Half the population is under 15 Interesting Facts Make your own graph: Hold down Control and click on several. Compare All Top 5 Top 10 Top 20 Top 100 Bottom 100 Bottom 20 Bottom 10 Bottom 5 All (desc) in category: Select Category Agriculture Crime Currency Democracy Economy Education Energy Environment Food Geography Government Health Identification Immigration Internet Labor Language Manufacturing Media Military Mortality People Religion Sports Taxation Transportation Welfare with statistic: view: Correlations Printable graph / table Pie chart Scatterplot with ... * Asterisk means graphable. Added May 21 Mortality stats Multi-users ½ price Catholic stats Top Graphs Richest Most Murderous Most Populous Most Militaristic ... More Stats Categories Agriculture Background Crime Currency ... Welfare Updated: Mar 20, 2004 Encyclopedia : Menelaus of Alexandria Menelaus of Alexandria (born ca. ; died ca. ) was a mathematician and astronomer. External links Menelaus of Alexandria The Wikipedia article included on this page is licensed under the GFDL Usage implies agreement with terms

15. Encyclopedia: Menelaus I often grieve, as I sit here in my house, for one and all of them. See alsomenelaus of alexandria (about 70 - about 140), mathematician. Related Stats. http://www.nationmaster.com/encyclopedia/Menelaus

Supporter Benefits Signup Login Sources ... Pies Factoid #27 Nearly 1% of Montserrations are police Interesting Facts Make your own graph: Hold down Control and click on several. Compare All Top 5 Top 10 Top 20 Top 100 Bottom 100 Bottom 20 Bottom 10 Bottom 5 All (desc) in category: Select Category Agriculture Crime Currency Democracy Economy Education Energy Environment Food Geography Government Health Identification Immigration Internet Labor Language Manufacturing Media Military Mortality People Religion Sports Taxation Transportation Welfare with statistic: view: Correlations Printable graph / table Pie chart Scatterplot with ... * Asterisk means graphable. Added May 21 Mortality stats Multi-users ½ price Catholic stats Top Graphs Richest Most Murderous Most Populous Most Militaristic ... More Stats Categories Agriculture Background Crime Currency ... Welfare Updated: Apr 30, 2004 Encyclopedia : Menelaus Menelaus (also transliterated as '''Menel os'''), in Greek mythology , was a king of Sparta and son of Atreus and Aerope Atreus was murdered by his brother, Aegisthus , who took possession of the throne of Mycenae and ruled jointly with his father Thyestes . During this period Menelaus and his brother

16. MenelausTheorem Lithuanian Polish Slovak JavaMenelaus Theorem. Menelaus' theorem en) Intersection of lines ( en) menelaus of alexandria ( en) Ratio http://www.thesaurus.maths.org/dictionary/map/word/2327

Home Preferences Help User Guides ... Forum thesaurus.maths.org alphabetical galleries topics For Quick Reference: drag this m-button to your links toolbar Find word or phrase containing matching starting with ending with in English English Danish German Spanish ... Menelaus Theorem Menelaus' theorem (English) Search for " Menelaus' theorem " in NRICH PLUS maths.org Google Definition level 1 If we have a triangle ABC, and we extend the lines AB, BC, CA to infinity and draw a new line L which cuts BC, CA, AB at X, Y, Z, then BX XC CY YA AZ ZB Show graph Requires Java Relations broader: (en) Theorem references: (en) Intersection of lines (en) Menelaus of Alexandria (en) Ratio (en) Triangle Funded by: EU Socrates Minerva, HeyMath!, Cambridge University Press

17. MenelausOfAlexandria menelaus of alexandria Menelaus (English). Search for menelaus of alexandria OR Menelaus in NRICH PLUS maths.org Google. Definition level 1. http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=2893&langcod

18. NebulaSearch Encyclopedia Mendham Township, New Jersey---Menelaus Of Alexandria Mendham Township, New Jerseymenelaus of alexandria. Mendham_Township,_New_Jersey;Mendip; Mendip_Hills; Mendip_hills; Mendocino,_California; http://www.nebulasearch.com/encyclopedia/contents/155673-155698-Mendham_Township

NebulaSearch Top Encyclopedia Top NebulaSearch Encyclopedia Index Main Index Mathematical_table..................Menuridae Memorial_of_the_Propagation_in_China_of_the_Lumino..................Menuridae Mendham Township, New Jersey-Menelaus of Alexandria Mendip Mendocino,_California Mendon,_Illinois Mendon,_Massachusetts ... Menehune NebulaSearch Directory

19. Menelaus Of Alexandria - Encyclopedia Article About Menelaus Of Alexandria. Free Menelaus encyclopedia article about Menelaus. Free access, no I often grieve, as I sit here in my house, for one and all of them. . Seealso menelaus of alexandria (about 70 - about 140), mathematician. http://encyclopedia.thefreedictionary.com/Menelaus of Alexandria

Dictionaries: General Computing Medical Legal Encyclopedia Menelaus of Alexandria Word: Word Starts with Ends with Definition Menelaus of Alexandria This page is about Alexandria in Egypt. For other uses see Alexandria (disambiguation). Alexandria (in Arabic, Iskenderia) is a city and chief seaport in Egypt on the Mediterranean Sea. It is the capital of the Al Iskandariyah governate. It was named after Alexander the Great, who founded the city, and was the home of Euclid. For over a thousand years from its foundation it was the capital of the country, the seat of the Ptolemaic dynasty, and quickly became one of the greatest cities of the Hellenistic world, and has remained one of the largest and most important cities of Egypt ever since; nowadays it is the nation's second largest city and still an important center of Hellenism. Click the link for more information. (born ca. Alternate uses, see Number 70 Centuries: 1st century BC - 1st century - 2nd century Decades: 20s 30s 40s 50s 60s - Years: 65 66 67 68 69 - Events The building of the Colosseum starts (approximate date).

20. Encyclopedia4U - Menelaus Of Alexandria - Encyclopedia Article Menelausmenelaus of alexandria. Born about 70 in (possibly)Alexandria, Egypt Died about 130 in Not known. http://www.encyclopedia4u.com/m/menelaus-of-alexandria.html

ENCYCLOPEDIA U com Lists of articles by category ... Encyclopedia Home Page SEARCH : Menelaus of Alexandria Menelaus of Alexandria (born around 70; died around A.D. 140) was a mathematician http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Menelaus.html Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities. Privacy This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article " Menelaus of Alexandria

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