Menelaus of

Alexandria Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandri ...

(; grc-gre, Μενέλαος ὁ Ἀλεξανδρεύς, ''Menelaos ho Alexandreus''; c. 70 – 140 CE) was a

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

Encyclopædia Britannica The (Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various t ...

"Greek mathematician and astronomer who first conceived and defined a spherical triangle (a triangle formed by three arcs of great circles on the surface of a sphere)."

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...

, the first to recognize

geodesics In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...

on a curved surface as natural analogs of straight lines. Menelau_de_alexandria_cropped

Life and works

Although very little is known about Menelaus's life, it is supposed that he lived in

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

, where he probably moved after having spent his youth in

. He was called ''Menelaus of Alexandria'' by both

Pappus of Alexandria Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem i ...

and Proclus, and a conversation of his with Lucius, held in Rome, is recorded by

Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for hi ...

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance ...

(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

occultation An occultation is an event that occurs when one object is hidden from the observer by another object that passes between them. The term is often used in astronomy, but can also refer to any situation in which an object in the foreground blocks ...

s of the stars

Spica Spica is the brightest object in the constellation of Virgo and one of the 20 brightest stars in the night sky. It has the Bayer designation α Virginis, which is Latinised to Alpha Virginis and abbreviated Alpha Vir or α Vir. Analys ...

and

Beta Scorpii Beta Scorpii (β Scorpii, abbreviated Beta Sco, β Sco) is a multiple star system in the southern zodiac constellation of Scorpius. It bore the traditional proper name of Acrab , though the International Astronomical Union now regards ...

by the moon, a few nights apart. Ptolemy used these observations to confirm

precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...

of the

equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...

es, a phenomenon that had been discovered by

Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equi ...

in the 2nd century

BCE Common Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the or ...

. ''Sphaerica'' is the only book that has survived, in an

Arabic Arabic (, ' ; , ' or ) is a Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C. E.Watson; Walter ...

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 Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...

(figures formed of three great circle arcs, which he named "trilaterals") and proves

Menelaus' theorem Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ''ABC'', and a transversal line that crosses ''BC'', ''AC'', and ''AB'' at points ''D'', ''E'', and ''F'' respec ...

on collinearity of points on the edges of a triangle (which may have been previously known) and its analog for spherical triangles. It was later translated by the sixteenth century astronomer and mathematician Francesco Maurolico. The lunar crater

Menelaus In Greek mythology, Menelaus (; grc-gre, Μενέλαος , 'wrath of the people', ) was a king of Mycenaean (pre- Dorian) Sparta. According to the ''Iliad'', Menelaus was a central figure in the Trojan War, leading the Spartan contingent of th ...

is named after him.

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 Thabit ( ar, ) is an Arabic name for males that means "the imperturbable one". It is sometimes spelled Thabet. People with the patronymic * Ibn Thabit, Libyan hip-hop musician * Asim ibn Thabit, companion of Muhammad * Hassan ibn Sabit (died 674 ...

* ''On the knowledge of the weights and distributions of different bodies'' * He may also have written a star catalogue.

Notes

References

Ivor Bulmer-Thomas Ivor Bulmer-Thomas CBE FSA (30 November 1905 – 7 October 1993), born Ivor Thomas, was a British journalist and scientific writer who served eight years as a Member of Parliament (MP). His career was much influenced by his conversion to the Chu ...

. "Menelaus of Alexandria." ''Dictionary of Scientific Biography'' 9:296-302. * Pedro Pablo Fuentes González, �
Ménélaos d’Alexandrie
��, in R. Goulet (ed.), ''Dictionnaire des Philosophes Antiques'', vol. IV, Paris, CNRS, 2005, p. 456-464. * Roshdi Rashed and Athanase Papadopoulos, Menelaus' Spherics. Early Translation and al-Māhānī / al-Harawī's Version. De Gruyter, Scientia Graeco-Arabica 21. xiv, 874 pages.

External links

* * {{Authority control 70 births 140 deaths 2nd-century Greek people Ancient Greek geometers Ancient Greek astronomers Roman-era Alexandrians 2nd-century mathematicians