Eutocius of Ascalon

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Eutocius of Ascalon (/jˈtʃəs/; Greek: Εὐτόκιος ὁ Ἀσκαλωνίτης; c. 480 – c. 540) was a Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian Conics.

Life and work[edit]

Little is known about the life of Eutocius. He was born in Ascalon, then in Palestina Prima. He wrote commentaries on Apollonius and on Archimedes. The surviving works of Eutocius are:

  • A Commentary on the first four books of the Conics of Apollonius.
  • Commentaries on:
    • the Sphere and Cylinder of Archimedes.
    • the Quadrature of the Circle of Archimedes (In Archimedis circuli dimensionem in Latin).
    • the Two Books on Equilibrium of Archimedes.

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, also a mathematician, and architect of the Hagia Sophia patriarchal basilica in Constantinople.[1]


  1. ^ 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."


  • Boyer, Carl Benjamin (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7.

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