Ménélaüs of Alexandria

Ménélaos or Ménélaüs of Alexandria (fine of the 1st century) is a Mathématicien and Greek Astronome . By analogy with the property that the lines in the plan have, to determine the shortest way between two points, it introduced the concept of Géodésique on the sphere.

Biography

One knows by a dialog of Plutarque, Of facie in sphere lunæ , that Menelaüs passed part of its life to Rome, but Pappus and Proclus implies that he had studied in his youth with Alexandria.

Ptolémée, at the second century of our era, also known as in its Almageste (chap. VII.3), that Ménélaüs observed two screenings of the stars α Virginis (Spica) and β Scorpii by the Moon in Rome in January 98, only a few days of interval. For Ptolémée, they confirmed the Précession of the equinoxes, a phenomenon discovered by Hipparque at the second front century J.C.

Spherical the is the only treaty of Ménélaüs which arrived to us, and that by an Arab translation. These three books treat geometry of the sphere and its applications to astronomy. It is this treaty which defines the spherical triangle as formed by three arcs of large circles, the trilateral , and which contains the following theorem, known as Théorème of Ménélaüs , extended to the spherical triangles.

This theorem states that, the three points C, D, E belonging respectively to the right (BF), (AF), (AB), while being distinct from has, B, and F, it is equivalent to say:

$\ tfrac {\ overline {D has}} {\ overline {D F}} \ times \ tfrac {\ overline {C F}} {\ overline {C B}} \ times \ tfrac {\ overline {E B}} {\ overline {E has}} =1$
C, D, E are aligned

One calls transverse triangle ABF any line which, like here CDE, cuts three lines (BF), (AF), (AB) without intercepting the tops has, B, F.

Works

One knows by an indirect tradition the titles of some treaties of Ménélaüs:

spherical the in three books, translated into Arabic by Ishaq Ben Hunain into 910. This treaty was translated into Latin by Gerard de Crémone, then Francesco Maurolico and finally by Edmund Halley.
Of the cords in the circle , in six books, was known of Théon of Alexandria
Éléments of geometry in 3 books, translated into Arabic by Thabit ibn Qurra
Of cognitione quantitatis discretæ corporum permixtorum contained, according to the Arab tradition, of the experiments of weighing with a hydrostatic balance.
Menelaüs perhaps also held a Catalog of stars.

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