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.

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 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.

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.[4]

References

Watts, p. 233-234

"Conica". whistleralley.com. Retrieved 2021-02-25.

Eutocii Ascalonitae commentarius. 1401–1500.

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.

Watts, Edward J. (2006). City and School in Late Antique Athens and Alexndria. 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.

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Ancient Greek and Hellenistic mathematics (Euclidean geometry)

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 Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides 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) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner

Problems

Angle trisection Doubling the cube Squaring the circle Problem of Apollonius

Concepts/definitions

Circles of Apollonius

Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center

Results

In Elements

Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon

Apollonius

Apollonius's theorem

Other

Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Cyrene Library of Alexandria Platonic Academy

Other

Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

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