Menelaus of Alexandria

Menelaus of Alexandria (/ˌmɛnɪˈleɪəs/; Greek: Μενέλαος, Menelaos; c. 70 – 140 CE) was a Greek^[1] mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines.

Life and works

Sphaericorum libri tres

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.

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.

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 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

↑ Encyclopaedia 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)."

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.

External links

Ancient Greek astronomy

Astronomers	Acoreus Aglaonice Agrippa Anaximander Andronicus Apollonius Aratus Aristarchus Aristyllus Attalus Autolycus Bion Callippus Cleomedes Cleostratus Conon Eratosthenes Euctemon Eudoxus Geminus Heraclides Hicetas Hipparchus Hippocrates of Chios Hypsicles Menelaus Meton Oenopides Philip of Opus Philolaus Posidonius Ptolemy Pytheas Seleucus Sosigenes of Alexandria Sosigenes the Peripatetic Strabo Thales Theodosius Theon of Alexandria Theon of Smyrna Timocharis

Works	Almagest (Ptolemy) On Sizes and Distances (Hipparchus) On the Sizes and Distances (Aristarchus) On the Heavens (Aristotle)

Instruments	Antikythera mechanism Armillary sphere Astrolabe Dioptra Equatorial ring Gnomon Mural instrument Triquetrum

Concepts	Callippic cycle Celestial spheres Circle of latitude Counter-Earth Deferent and epicycle Equant Geocentrism Heliocentrism Hipparchic cycle Metonic cycle Octaeteris Solstice Spherical Earth Sublunary sphere Zodiac

Influences	Babylonian astronomy Egyptian astronomy

Influenced	Medieval European science Indian astronomy Medieval Islamic astronomy

Ancient Greek mathematics

Mathematicians	Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus

Treatises	Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Elements (Euclid) On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) The Sand Reckoner

Problems	Problem of Apollonius Squaring the circle Doubling the cube Angle trisection

Centers	Cyrene Library of Alexandria Platonic Academy

Timeline of Ancient Greek mathematicians

Authority control	WorldCat Identities VIAF: 3272146 LCCN: nr93024514 ISNI: 0000 0003 8162 5645 GND: 119043874 SUDOC: 099055902 BNF: cb12191815z (data)

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