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 Encyclopædia Britannica "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 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 obse ...

, 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, 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. Ptolemy (2nd century CE) also mentions, in his work ''

Almagest The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canon ...

'' (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 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 t ...

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 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 o ...

. ''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; Walte ...

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

Notes

References

* Ivor Bulmer-Thomas. "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