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1. Abel
no photo available. menelaus of alexandria. (70 AD 103 AD). Dover Publications,1953.Pages603, 606, 615. Internet menelaus of alexandria.
http://www.forestcity.k12.ia.us/Pages/FCHS/Site/menelaus.htm
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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.

 2. Encyclopædia Britannica Encyclopædia Britannica. menelaus of alexandria. Encyclopædia Britannica Articlehttp://www.britannica.com/eb/article?eu=53302

3. Menelaus - Wikipedia
http://www.wikipedia.org/wiki/Menelaus
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Menelaus
From Wikipedia, the free encyclopedia. Menelaus , 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

4. PORCELAINia/Alexandria/817
List of items from Encarta Encyclopedia. 3. menelaus of alexandria role in ancient Greek mathematics
http://www.porcelainia.com/817.html
 PORCELAINia HOME PROCESS SERIES STYLE ... Site Map "Menelaus" Alexandria Series Height 4.3 in Mass 390 g Fired Bisque Glaze Clear Started Finished Style Cambria Series Alexandria This piece is named for the great geometer, Menelaus (70 AD to 130 AD). Menelaus's only surviving book, "Sphaerica" was the most important early contribution to spherical trigonometry, essential to both astronomy and navigation. He was the first to write down the definition of a spherical triangle and identify its geometric properties.

5. Menelaus
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.

6. 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
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 14th 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.

7. Menelaus
Biography of Menelaus (70130) menelaus of alexandria. Born about 70 in (possibly) Alexandria, Egypt
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Menelaus.html
Menelaus of Alexandria
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 14th 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
http://www-history.mcs.st-andrews.ac.uk/history/References/Menelaus.html
• 9. TMTh:: MENELAUS OF ALEXANDRIA
Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ARTISTS ASTRONOMERS BIOLOGISTS BOTANISTS CHEMISTS ENGINEERS GEOGRAPHERS INVENTORS MATHEMATICIANS METEOROLOGISTS PHARMACOLOGISTS PHYSICIANS PHYSICISTS MATHEMATICIAN, ASTRONOMER, PHYSICIST
http://www.tmth.edu.gr/en/aet/1/68.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.

10. TMTh:: MENELAUS OF ALEXANDRIA
MATHEMATICIAN, ASTRONOMER, PHYSICIST menelaus of alexandria (fl. 1st centuryAD) Life Menelaus was the founder of spherical trigonometry
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.

11. References For Menelaus
References for the biography of Menelaus M F Aintabi, Arab scientific progress and menelaus of alexandria, in Actes XIIe Congrès Internat.
http://www-history.mcs.st-and.ac.uk/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
http://www-history.mcs.st-andrews.ac.uk/history/References/Menelaus.html
• 12. TMTh:: Ancient Greek Technologists
OF RHODES HIPPASUS OF METAPONTUM HYPATIA, HYPSICLES OF ALEXANDRIA IAMBLICHUS OF CHALCEDONMARINOS OF TYRE MENAECHMCUS OF THRACE menelaus of alexandria METON OF
http://www.tmth.edu.gr/en/aet/1.html
 Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ARTISTS ASTRONOMERS ... ZENO OF ELEA Read about the life and Work of Ancient Greek Scientists. Choose the desired category from the list on the left and the desired scientist from the list on the right Based on the Greek book: K. Georgakopoulos, "Ancient Greek Scientists", Athens, 1995 Contact the Technology Museum

13. A.htm
M. menelaus of alexandria. Mobius, August F. Monge, Gaspard. MacLaurin.For a different list click the letter below or click here to go home.
http://www.forestcity.k12.ia.us/pages/FCHS/Site/m.htm
Here is the current list of Mathematicians that we have on our page whose last name begins with the letter: M
MacLaurin
For a different list click the letter below or click here to go home.
A B C ... Z If you have any other mathematicians that you feel we should add to our list, please feel free to cantact me. Daniel Meyer

 14. Encyclopædia Britannica menelaus of alexandria University of St Andrews Biography of this Greek mathematicianwhose surviving work, Sphaerica, deals with spherical triangles andhttp://www.britannica.com/search?query=philo of alexandria&fuzzy=N&ct=igv&start=

15. 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
• 16. Re: Menelaus By Samuel S. Kutler
0500 Jenny Here is a piece of personal information about menelaus of alexandria from Heath's History Ptolemy quotes an
http://mathforum.com/epigone/math-history-list/kandpreldstend/v01540b01b2db151a3
Re: Menelaus by Samuel S. Kutler
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Subject: Re: Menelaus Author: s-kutler@sjca.edu Date: The Math Forum

17. The History Of Mathematics - Library Center For E-courses
Andrews. menelaus of alexandria The Mac TutorHistory of Mathematics Archive, University of St. Andrews.
http://www-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

18. 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)

As to Menelaus' theorem, however, he probably took it without acknowledgement fromthe Spherics of menelaus of alexandria, an astronomer of about a generation
Back to MathWords and Other Words
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.

20. 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
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

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