Menelaus of Alexandria
Menelaus of Alexandria was a prominent mathematician and astronomer known for his contributions to spherical geometry, specifically the development of the geometry of spheres, which incorporates concentric arcs analogous to lines in plane geometry. Although details of his life are sparse, he is believed to have spent time in both Alexandria and Rome. Notably, he is referenced by the mathematician Ptolemy, who noted Menelaus's observations related to celestial bodies. His most significant surviving work is the book "Sphaerica," which focuses on spherical geometry, although its original Greek text has been lost and is now known through an Arabic translation. In addition to "Sphaerica," he is thought to have authored texts on mechanics, optics, basic geometry, and astronomy. Menelaus's theorem plays a critical role in both planar and spherical trigonometry and continues to have relevance in astronomy today. His work laid the groundwork for future mathematicians, particularly influencing Ptolemy, who followed him in the Alexandrian tradition.
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Subject Terms
Menelaus of Alexandria
Related civilizations: Hellenistic and Roman Greece, Egypt, Imperial Rome
Major role/position: Mathematician, astronomer
Life
Menelaus (mehn-el-AY-uhs) of Alexandria invented the geometry of spheres, in which concentric arcs are analogous to lines in the geometry of planes. Little is known of his life except that he lived for a time in Alexandria and for a time in Rome. Mathematician Ptolemy reported that Menelaus observed the proximity of the star Beta Scorpii to the Moon in 98 c.e. Plutarch reported his conversation with a certain Lucius about the angles of incidence of reflected light. Mathematical commentator Pappus of Alexandria and Neoplatonist philosopher Proclus both mentioned him. Only his book on spherical geometry, Sphaerica (first century c.e.; English translation, 1936), survives, but he is supposed to have also written books on mechanics, optics, basic geometry, and astronomy. The original Greek text of Sphaerica has been lost. The content has been preserved through an Arabic translation.
Influence
The Menelaus theorem was an important advance in both planar and spherical trigonometry and remains applicable in astronomy. In its most basic form, it says that for any triangle ABC, if AXB, AYC, BCZ, and XYZ are each lines, then (AX/XB) = (AY/YC) (CZ/BZ). Menelaus’s most immediate and significant effect was on another Alexandrian mathematician and astronomer, Ptolemy, who lived about a generation later.
Bibliography
Brunschwig, Jacques, and G. E. R. Lloyd. Greek Thought: A Guide to Classical Knowledge. Cambridge, Mass.: Harvard University Press, 2000.
Gow, James. A Short History of Greek Mathematics. New York: Chelsea, 1968.
Heath, Thomas Little. A History of Greek Mathematics. New York: Dover, 1981.
Neugebauer, Otto. A History of Ancient Mathematical Astronomy. Berlin: Springer, 1975.