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Eutocius of Ascalon (ca. 480 – ca. 540) was a Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian Conics.


Life and work

Little is known about the life of Eutocius. 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.
    • 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 St. Sophia.[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."


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