Eutocius of Ascalon (; el, Εὐτόκιος ὁ Ἀσκαλωνίτης; 480s – 520s) was a Palestinian-Greek mathematician who wrote commentaries on several
Archimedean treatises and on the
Apollonian
The Apollonian and the Dionysian are philosophical and literary concepts represented by a duality between the figures of Apollo and Dionysus from Greek mythology. Its popularization is widely attributed to the work ''The Birth of Tragedy'' by Fri ...
''Conics''.
Life and work
Little is known about the life of Eutocius. He was born in
Ascalon, then in
Palestina Prima
Palaestina Prima or Palaestina I was a Byzantine province that existed from the late 4th century until the Muslim conquest of the Levant in the 630s, in the region of Palestine. It was temporarily lost to the Sassanid Empire (Persian Empire) ...
. He lived during the reign of
Justinian. Eutocius became head the
school of philosophy in Athens following
Ammonius and he was succeeded in this position by Olympiodorus, possibly as early as 525. He traveled to the greatest scientific centers of his time, including
Alexandria
Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandria ...
, to conduct research on
Archimedes' manuscripts.
He wrote commentaries on
Apollonius and on
Archimedes
Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...
. The surviving works of Eutocius are:
*A
Commentary
Commentary or commentaries may refer to:
Publications
* ''Commentary'' (magazine), a U.S. public affairs journal, founded in 1945 and formerly published by the American Jewish Committee
* Caesar's Commentaries (disambiguation), a number of works ...
on the first four books of the
''Conics'' of Apollonius.
*Commentarieson:
**the
''Sphere and Cylinder'' of Archimedes.
**the ''
Quadrature of the Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty ...
'' of Archimedes (''In Archimedis circuli dimensionem'' in
Latin
Latin (, or , ) is a classical language belonging to the 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 the power of the ...
).
**the ''Two Books on Equilibrium'' of Archimedes.
*An introduction to Book I of the ''
Almagest
The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canoni ...
'' by Ptolemy
Historians owe much of their knowledge of Archimedes' solution of a cubic by means of intersecting conics, alluded to in ''The Sphere and Cylinder'', to Eutocius and his commentaries. Eutocius dedicated his commentary on Apollonius' ''Conics'' to
Anthemius of Tralles
Anthemius of Tralles ( grc-gre, Ἀνθέμιος ὁ Τραλλιανός, Medieval Greek: , ''Anthémios o Trallianós''; – 533 558) was a Greek from Tralles who worked as a geometer and architect in Constantinople, the capit ...
, also a mathematician, and architect of the
Hagia Sophia
Hagia Sophia ( 'Holy Wisdom'; ; ; ), officially the Hagia Sophia Grand Mosque ( tr, Ayasofya-i Kebir Cami-i Şerifi), is a mosque and major cultural and historical site in Istanbul, Turkey. The cathedral was originally built as a Greek Ortho ...
patriarchal basilica in
Constantinople
la, Constantinopolis ota, قسطنطينيه
, alternate_name = Byzantion (earlier Greek name), Nova Roma ("New Rome"), Miklagard/Miklagarth (Old Norse), Tsargrad ( Slavic), Qustantiniya (Arabic), Basileuousa ("Queen of Cities"), Megalopolis (" ...
.
[Boyer, p. 193. "Eutocius (born ca. 480), commented on several Archimedean treatises and on the Apollonian ''Conics''. It is to Eutocius that we owe the Archimedean solution of a cubic through intersecting conics, referred to in ''The Sphere and Cylinder'' but not otherwise extant except through the commentary of Eutocius. The commentary by Eutocius on the ''Conics'' of Apollonius was dedicated to Anthemius of Tralles (t534), an able mathematician and architect of St. Sophia of Constantinople."]
References
Sources
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External links
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{{Authority control
480 births
540 deaths
Ancient Greek mathematicians
6th-century mathematicians
6th-century Byzantine writers
6th-century Byzantine scientists