Autolycus of Pitane (; c. 360 – c. 290 BC) was a

Greek Greek may refer to: Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group *Greek language, a branch of the Indo-European language family **Proto-Greek language, the assumed last common ancestor of all kno ...

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, and

geographer A geographer is a physical scientist, social scientist or humanist whose area of study is geography, the study of Earth's natural environment and human society, including how society and nature interacts. The Greek prefix "geo" means "earth" a ...

. He is known today for his two surviving works ''On the Moving Sphere'' and ''On Risings and Settings'', both about

spherical geometry 300px, A sphere with a spherical triangle on it. Spherical geometry or spherics () is the geometry of the two-dimensional surface of a sphere or the -dimensional surface of higher dimensional spheres. Long studied for its practical applicati ...

Life

Autolycus was born in Pitane, a town of

Aeolis Aeolis (; ), or Aeolia (; ), was an area that comprised the west and northwestern region of Asia Minor (modern-day Turkey), mostly along the coast, and also several offshore islands (particularly Lesbos), where the Aeolian Greek city-states w ...

within Ionia, Asia Minor. Of his personal life nothing is known, although he was a contemporary of

Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...

and his works seem to have been completed in

Athens Athens ( ) is the Capital city, capital and List of cities and towns in Greece, largest city of Greece. A significant coastal urban area in the Mediterranean, Athens is also the capital of the Attica (region), Attica region and is the southe ...

between 335–300 BC.

Euclid Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...

references some of Autolycus' work, and Autolycus is known to have taught

Arcesilaus Arcesilaus (; ; 316/5–241/0 BC) was a Greece, Greek Hellenistic philosophy, Hellenistic philosopher. He was the founder of Academic Skepticism and what is variously called the Second or Middle or New Academy – the phase of the Platonic Acade ...

. The

lunar crater Lunar craters are impact craters on Earth's Moon. The Moon's surface has many craters, all of which were formed by impacts. The International Astronomical Union currently recognizes 9,137 craters, of which 1,675 have been dated. History The wo ...

Autolycus In Greek mythology, Autolycus (; ) was a robber who had the power to metamorphose or make invisible the things he stole. He had his residence on Mount Parnassus and was renowned among men for his cunning and oaths. Family There are a number of d ...

was named in his honour.

Work

Autolycus' two surviving works are about spherical geometry with application to

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

: ''On the Moving Sphere'' and ''On Risings and Settings'' (of stars). In

late antiquity Late antiquity marks the period that comes after the end of classical antiquity and stretches into the onset of the Early Middle Ages. Late antiquity as a period was popularized by Peter Brown (historian), Peter Brown in 1971, and this periodiza ...

, both were part of the "

Little Astronomy ''Little Astronomy'' ( ) is a collection of minor works in Ancient Greek mathematics and astronomy dating from the 4th to 2nd century BCE that were probably used as an astronomical curriculum starting around the 2nd century CE. In the astronomy o ...

", a collection of miscellaneous short works about geometry and astronomy which were commonly transmitted together. They were translated into

Arabic Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns lang ...

in the 9th century, and with the addition of a few additional works became known as the "Middle Books" (sitting between Euclid's ''Elements'' and

Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...

's ''

Almagest The ''Almagest'' ( ) is a 2nd-century Greek mathematics, mathematical and Greek astronomy, astronomical treatise on the apparent motions of the stars and planetary paths, written by Ptolemy, Claudius Ptolemy ( ) in Koine Greek. One of the most i ...

''). Both were preserved both in Greek and in Arabic, but were unknown in medieval Western Europe. They were translated from Arabic into Latin in the 12th century. Later, remaining Greek copies were also translated into Latin.

''On the Moving Sphere''

''On the Moving Sphere'' ( ) concerns the movements of points and arcs on the sphere as it rotates on an axis. While the obvious application is the diurnal motion of the stars as the

celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...

appears to rotate about an immobile Earth (as modeled at the time), Autolycus' treatise never explicitly discusses this application: its content consists entirely of elementary theorems about the arcs of

great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Discussion Any arc of a great circle is a geodesic of the sphere, so that great circles in spher ...

s and parallel

small circle In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the ''spherical radius'') from a given point on the sphere (the ''pole'' or ''spherical center''). It is ...

s on an abstract sphere. The work is simple and probably derivative of older works, but each theorem includes a clearly enunciated statement, a figure of the construction alongside its proof, and finally a concluding remark. ''On the Moving Sphere'' is believed to be the oldest mathematical treatise from ancient Greece that is completely preserved: All prior Greek mathematical works are taken from later summaries, commentaries, or descriptions of the works. It shows that by Autolycus' day there was a thoroughly established textbook tradition in geometry that is today regarded as typical of classical Greek geometry. Moreover, it gives indications of what theorems were well known in his day (around 320 BC). Two hundred years later

Theodosius Theodosius ( Latinized from the Greek "Θεοδόσιος", Theodosios, "given by god") is a given name. It may take the form Teodósio, Teodosie, Teodosije etc. Theodosia is a feminine version of the name. Emperors of ancient Rome and Byzantium ...

wrote the '' Spherics'', a treatise establishing the fundamental definitions and constructions in spherical geometry whose content is believed to have a common origin with ''On the Moving Sphere'' in some pre-Euclidean textbook, possibly written by Eudoxus. In contrast to later astronomical analyses by

Hipparchus Hipparchus (; , ; BC) was a Ancient Greek astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hippar ...

(2nd century BC) and

(2nd century AD), but similarly to the planar geometry of Euclid's ''Elements'', both Autolycus's work and Theodosius' does not involve concrete quantification or trigonometry: spherical arcs are compared in size, but not given any numerical measure.

''On Risings and Settings''

In the two-book treatise ''On Risings and Settings'' ( ), Autolycus studied the relationship between the rising and the setting of the stars throughout the year. The second book is an expansion of the first and of higher quality. He wrote that "any star which rises and sets always rises and sets at the same point in the horizon." Autolycus relied heavily on Eudoxus' astronomy and was a strong supporter of Eudoxus' theory of homocentric spheres.

Footnotes

References

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External links

Autolycus ''On The Moving Sphere'' from the Million Books Project (Greek with Latin translation)

ΠΕΡΙ ΚΙΝΟΥΜΕΝΗΣ ΣΦΑΙΡΑΣ and ΠΕΡΙ ΕΠΙΤΟΛΩΝ ΚΑΙ ΔΥΣΕΩΝ (Mogenet ed., 1950)
{{DEFAULTSORT:Autolycus of Pitane 3rd-century BC Greek writers Ancient Greek astronomers Ancient Greek geometers Ancient Greek geographers Aeolians 360s BC births 290s BC deaths 4th-century BC geographers 3rd-century BC geographers 4th-century BC Greek mathematicians 3rd-century BC Greek mathematicians 4th-century BC Greek writers