MATHEMATICIAN, ASTRONOMER, PHYSICIST

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.

"Elements of geometry": 3 books. Lost.

Menelaus discovered a special curve that he called "paradoxical". His theorem on the relation between plane and spherical triangles is still called Menelaus' theorem.