''Sphaerics'' ( grc, Σφαιρικά) was a set of three volumes on

spherical geometry 300px, A sphere with a spherical triangle on it. Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sp ...

written by Theodosius of Bithynia in the 2nd century BC. These proved essential in the restoration of

Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...

to Western civilization, when brought back from the

Islamic world The terms Muslim world and Islamic world commonly refer to the Islamic community, which is also known as the Ummah. This consists of all those who adhere to the religious beliefs and laws of Islam or to societies in which Islam is practiced. I ...

during the

crusades The Crusades were a series of religious wars initiated, supported, and sometimes directed by the Latin Church in the medieval period. The best known of these Crusades are those to the Holy Land in the period between 1095 and 1291 that were ...

and translated back from

Arabic Arabic (, ' ; , ' or ) is a Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C. E.Watson; Walter ...

into

Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

History

Theodosius appears to have written ''Sphaerics'' as a supplement to Euclid's ''Elements'', allowing its application in

astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

. Elements had lacked spherical geometry. Sphaerics had its own shortcomings, for example

Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a 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 e ...

had already introduced

trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...

, but Theodosius makes no use of it, perhaps because he was basing it on an earlier work by Eudoxus. Theodosius' primary function in this, and other, works is to gather together existing information into one place. In the first book of Sphaerics, he carefully explains that a sphere is a shape whose surface is an equal distance, in any spot, from a central point, and then goes on to examine the geometry of spheres, extensively. The work's primary importance was in the restoration of

to European knowledge, as this, and much other technology and philosophy, had been lost to Christendom, but preserved in

translations during the

Islamic Golden Age The Islamic Golden Age was a period of cultural, economic, and scientific flourishing in the history of Islam, traditionally dated from the 8th century to the 14th century. This period is traditionally understood to have begun during the reign ...

, then brought back to Europe during the

Crusades The Crusades were a series of religious wars initiated, supported, and sometimes directed by the Latin Church in the medieval period. The best known of these Crusades are those to the Holy Land in the period between 1095 and 1291 that were ...

and translated back into Latin."Theodosius of Bithynia" at Encyclopedia.com
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References

{{Ancient Greek mathematics Ancient Greek mathematical works