Eutocius of Ascalon

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

## Contents

* 1 Life and work
* 2 References
* 3 Sources
* 4 External links

## Life and work

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 probably became the head of the Alexandrian school 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 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.
* 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]

## References

1. ↑ Watts, p. 233-234
2. ↑ "Conica". http://whistleralley.com/conics/conica/.
3. ↑ (in EN) Eutocii Ascalonitae commentarius. 1401–1500. https://gallica.bnf.fr/ark:/12148/btv1b10035288z.
4. ↑ "Eutocius – Biography" (in en). https://mathshistory.st-andrews.ac.uk/Biographies/Eutocius/.
5. ↑ 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."

## Sources

* Boyer, Carl Benjamin (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7. https://archive.org/details/historyofmathema00boye.

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

## External links

* O'Connor, John J.; Robertson, Edmund F., "Eutocius of Ascalon", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Eutocius.html .

* v
* t
* e

Ancient Greek mathematics

Mathematicians
(timeline)|

* Anaxagoras
* Anthemius
* Archytas
* Aristaeus the Elder
* Aristarchus
* Apollonius
* Archimedes
* Autolycus
* Bion
* Bryson
* Callippus
* Carpus
* Chrysippus
* Cleomedes
* Conon
* Ctesibius
* Democritus
* Dicaearchus
* Diocles
* Diophantus
* Dinostratus
* Dionysodorus
* Domninus
* Eratosthenes
* Eudemus
* Euclid
* Eudoxus
* Eutocius
* Geminus
* Heron
* Hipparchus
* Hippasus
* Hippias
* Hippocrates
* Hypatia
* Hypsicles
* Isidore of Miletus
* Leon
* Marinus
* Menaechmus
* Menelaus
* Metrodorus
* Nicomachus
* Nicomedes
* Nicoteles
* Oenopides
* Pappus
* Perseus
* Philolaus
* Philon
* Porphyry
* Posidonius
* Proclus
* Ptolemy
* Pythagoras
* Serenus
* Simplicius
* Sosigenes
* Sporus
* Thales
* Theaetetus
* Theano
* Theodorus
* Theodosius
* Theon of Alexandria
* Theon of Smyrna
* Thymaridas
* Xenocrates
* Zeno of Elea
* Zeno of Sidon
* Zenodorus

Treatises|

* Almagest
* Archimedes Palimpsest
* Arithmetica
* Conics (Apollonius)
* Elements (Euclid)
* On the Sizes and Distances (Aristarchus)
* On Sizes and Distances (Hipparchus)
* On the Moving Sphere (Autolycus)
* The Sand Reckoner

Problems|

* Problem of Apollonius
* Squaring the circle
* Doubling the cube
* Angle trisection

Centers|

* Cyrene
* Library of Alexandria
* Platonic Academy

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