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**Eutocius of Ascalon** (/juːˈtoʊʃəs/; Greek: Εὐτόκιος ὁ Ἀσκαλωνίτης; c. 480s – c. 520s) was a Palestinian-Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian *Conics*.

Little is known about the life of Eutocius. He was born in Ascalon, then in Palestina Prima. 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.^{[1]} He traveled to the greatest scientific centers of his time, including Alexandria, to conduct research on Archimedes' manuscripts.

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.^{[2]} - Commentaries
^{[3]}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.

- the
- An introduction to Book I of the
*Almagest*by Ptolemy^{[4]}

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.^{[5]}

**^**Watts, p. 233-234**^**"Conica".*whistleralley.com*. Retrieved 2021-02-25.**^***Eutocii Ascalonitae commentarius*. 1401–1500.`{{cite book}}`

: CS1 maint: date format (link)**^**"Eutocius - Biography".*Maths History*. Retrieved 2021-10-27.**^**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.

- Watts, Edward J. (2006).
*City and School in Late Antique Athens and Alexndria*. University of California Press. ISBN 978-0-520-25816-7.

- O'Connor, John J.; Robertson, Edmund F., "Eutocius of Ascalon",
*MacTutor History of Mathematics archive*, University of St Andrews