Menelaus of Alexandria

Alexandria

Alexandria is the second-largest city of Egypt, with a population of 4.1 million, extending about along the coast of the Mediterranean Sea in the north central part of the country; it is also the largest city lying directly on the Mediterranean coast. It is Egypt's largest seaport, serving...

(c. 70–140 CE

Common Era

Common Era ,abbreviated as CE, is an alternative designation for the calendar era originally introduced by Dionysius Exiguus in the 6th century, traditionally identified with Anno Domini .Dates before the year 1 CE are indicated by the usage of BCE, short for Before the Common Era Common Era...

) was a Greek

Greeks

The Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....

  mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and astronomer

Astronomer

An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...

, the first to recognize geodesics on a curved surface as natural analogs of straight lines.

Life and Works

Although very little is known about Menelaus's life, it is supposed that he lived in Rome

Rome

Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...

, where he probably moved after having spent his youth in Alexandria

Alexandria

Alexandria is the second-largest city of Egypt, with a population of 4.1 million, extending about along the coast of the Mediterranean Sea in the north central part of the country; it is also the largest city lying directly on the Mediterranean coast. It is Egypt's largest seaport, serving...

. He was called Menelaus of Alexandria by both Pappus of Alexandria

Pappus of Alexandria

Pappus of Alexandria was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection , and for Pappus's Theorem in projective geometry...

 and Proclus

Proclus

Proclus Lycaeus , called "The Successor" or "Diadochos" , was a Greek Neoplatonist philosopher, one of the last major Classical philosophers . He set forth one of the most elaborate and fully developed systems of Neoplatonism...

, and a conversation of his with Lucius, held in Rome, is recorded by Plutarch

Plutarch

Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...

.

Ptolemy

Ptolemy

Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

 (2nd century CE

Common Era

Common Era ,abbreviated as CE, is an alternative designation for the calendar era originally introduced by Dionysius Exiguus in the 6th century, traditionally identified with Anno Domini .Dates before the year 1 CE are indicated by the usage of BCE, short for Before the Common Era Common Era...

) also mentions, in his work Almagest

Almagest

The Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths. Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt,...

(VII.3), two astronomical observations made by Menelaus in Rome in January of the year 98. These were occultation

Occultation

An occultation is an event that occurs when one object is hidden by another object that passes between it and the observer. The word is used in astronomy . It can also refer to any situation wherein an object in the foreground blocks from view an object in the background...

s of the stars Spica

Spica

Spica is the brightest star in the constellation Virgo, and the 15th brightest star in the nighttime sky. It is 260 light years distant from Earth...

 and Beta Scorpii

Beta Scorpii

Beta Scorpii is a star system in the constellation Scorpius. It has the traditional names Acrab, Akrab or Elacrab, all come from al-'Aqrab, the Scorpion, for the whole constellation, as well as Graffias, a name it shares with Xi Scorpii...

 by the moon, a few nights apart. Ptolemy used these observations to confirm precession

Precession

Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

 of the equinox

Equinox

An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...

es, a phenomenon that had been discovered by Hipparchus

Hipparchus

Hipparchus, the common Latinization of the Greek Hipparkhos, can mean:* Hipparchus, the ancient Greek astronomer** Hipparchic cycle, an astronomical cycle he created** Hipparchus , a lunar crater named in his honour...

 in the 2nd century BCE

Common Era

Common Era ,abbreviated as CE, is an alternative designation for the calendar era originally introduced by Dionysius Exiguus in the 6th century, traditionally identified with Anno Domini .Dates before the year 1 CE are indicated by the usage of BCE, short for Before the Common Era Common Era...

.

Sphaerica is the only book that has survived, in an Arabic

Arabic language

Arabic is a name applied to the descendants of the Classical Arabic language of the 6th century AD, used most prominently in the Quran, the Islamic Holy Book...

 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

Menelaus' theorem

Menelaus' theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, and a transversal line that crosses BC, AC and AB at points D, E and F respectively, with D, E, and F distinct from A, B and C, thenThis equation uses signed lengths of...

 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

Francesco Maurolico

Francesco Maurolico was a Greek mathematician and astronomer of Sicily. Throughout his lifetime, he made contributions to the fields of geometry, optics, conics, mechanics, music, and astronomy...

.

The lunar crater Menelaus

Menelaus (crater)

Menelaus is a young lunar impact crater located on the southern shore of Mare Serenitatis near the eastern end of the Montes Hæmus mountain range. The crater was named after the jilted king of Sparta from the Iliad. To the southwest is the small crater Auwers, and to the southwest is the even...

is named after him.