Menelaus of Alexandria (c. 70 - 140) was a Greek^[1] mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines. Antiquity and modernity stand cheek-by-jowl in Egypts chief Mediterranean seaport For other uses, see Alexandria (disambiguation). ... This article is about the year 70. ... Events Pope Pius I succeeded Pope Hyginus. ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. ...

Life and Works

Although very little is known about Menelaus's life, it is supposed that he lived in Rome, where he probably moved after having spent his youth in Alexandria. He was called Menelaus of Alexandria by both Pappus of Alexandria and Proclus, and a conversation of his with Lucius, held in Rome, is recorded by Plutarch. Nickname: Motto: SPQR: Senatus Populusque Romanus Location of the city of Rome (yellow) within the Province of Rome (red) and region of Lazio (grey) Coordinates: Region Lazio Province Province of Rome Founded 21 April 753 BC Government  - Mayor Walter Veltroni Area  - City 1,285 km²  (580 sq mi)  - Urban 5... Nickname: Alexandria on the map of Egypt Map of Alexandria Coordinates: , Country Egypt Founded 334 BC Government  - Governor Adel Labib Population (2001)  - City 3,500,000 Time zone EET (UTC+2)  - Summer (DST) EEST (UTC+3) Twin Cities  - Baltimore  United States  - Cleveland  United States  - ConstanÅ£a  Romania  - Durban  South Africa... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... This article is about Proclus Diadochus, the Neoplatonist philosopher. ... Mestrius Plutarchus (Greek: Πλούταρχος; 46 - 127), better known in English as Plutarch, was a Greek historian, biographer, essayist, and Middle Platonist. ...

Ptolemy (2nd century CE) also mentions, in his work Almagest (VII.3), two astronomical observations made by Menelaus in Rome in January of the year 98. These were occultations of the stars Spica and Beta Scorpii by the moon, a few nights apart. Ptolemy used these observations to confirm precession of the equinoxes, a phenomenon that had been discovered by Hipparchus in the 2nd century BCE. A medieval artists rendition of Claudius Ptolemaeus Claudius Ptolemaeus (Greek: ; ca. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... Events Roman emperor Nerva succeeded by Trajan Tacitus finished his Germania (approximate date) Births Deaths January 27: Nerva, Roman emperor Apollonius of Tyana, Greek/Roman philosopher and mathematician (b. ... In this July, 1997 still frame captured from video, the bright star Aldebaran has just reappeared on the dark limb of the waning crescent moon in this predawn occultation. ... Spica (α Vir / α Virginis / Alpha Virginis) is the brightest star in the constellation Virgo, and one of the brightest stars in the nighttime sky. ... Beta Scorpii (β Sco / β Scorpii) is a star system in the constellation Scorpius. ... Precession of a gyroscope Precession refers to a change in the direction of the axis of a rotating object. ... Illumination of the Earth by the Sun on the day of equinox, (ignoring twilight). ... Precession of the equinoxes is caused by a polar motion, a change in the orientation of the Earths axis. ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ...

Sphaerica is the only book that has survived, in an Arabic translation. Composed of three books, it deals with the geometry of the sphere and its application in astronomical measurements and calculations. The book introduces the concept of spherical triangle (figures formed of three great circle arcs, which he named "trilaterals") and proves Menelaus' theorem (an extension to spherical triangles of a previously known result). It was later translated by the sixteenth century astronomer and mathematician Francesco Maurolico. Arabic ( or just ) is the largest living member of the Semitic language family in terms of speakers. ... Right spherical triangle Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. ... Menelaus theorem, case 1: line DEF passes inside triangle ABC Menelaus theorem, attributed to Menelaus of Alexandria, is a theorem about triangles in plane geometry. ... Francesco Maurolico (in Latin, Franciscus Maurolycus) (September 16, 1494-July 21 or July 22, 1575) was an Italian mathematician and astronomer. ...

Bibliography

The titles of a few books by Menelaus have been preserved:

• On the calculation of the chords in a circle, composed of six books
• Elements of geometry, composed of three books, later edited by Thabit ibn Qurra
• On the knowledge of the weights and distributions of different bodies
• He may also have written a star catalogue.

Abul Hasan Thabit ibn Qurra ibn Marwan al-Sabi al-Harrani, (826 – February 18, 901) was an Arab astronomer and mathematician. ... A star catalogue, or star catalog, is an astronomical catalog that lists stars. ...

Secondary sources

• Bulmer-Thomas, Ivor. "Menelaus of Alexandria." Dictionary of Scientific Biography 9:296-302.

External links

• Menelaus of Alexandria
• Menelaus' Theorem Interactive proof with animation and key concepts by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"