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 Menelaus Of Alexandria:     more detail

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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

Extractions: no photo available (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 Article
http://www.britannica.com/eb/article?eu=53302

3. Menelaus - Wikipedia
http://www.wikipedia.org/wiki/Menelaus

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

Extractions: 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

Extractions: 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,

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

Extractions: 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

Extractions: 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

Extractions: 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

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

Extractions: 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. "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.

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

Extractions: 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. "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.

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

Extractions: 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

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

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

Extractions: Here is the current list of Mathematicians that we have on our page whose last name begins with the letter: M 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 and
http://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

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

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

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

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

As to Menelaus' theorem, however, he probably took it without acknowledgement fromthe Spherics of menelaus of alexandria, an astronomer of about a generation