Eutokios

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Eutokios ( Greek Εὐτόκιος Eutókios ) was a late ancient Greek mathematician and representative of the Neoplatonic philosophy . His lifetime falls in the late 5th century and the first half of the 6th century. He is often named after his hometown Eutokios of Askalon . Since he belonged to the Philosophers School of Alexandria , he is also known as Eutocios of Alexandria .

Life

Very little is known about the life of the Eutokios. He came from the city of Askalon in what is now Israel. One research suggests that he was a student of the architect and mathematician Isidorus of Miletus (the Elder). This assumption is based on four mentions of Isidore in the commentaries of Eutocios, including three notes that "our teacher, the engineer Isidorus of Miletus" carried out a text check. How this is to be understood, however, is controversial. It can be interpreted to mean that Eutokios was the author of the notes and that he wanted to inform that his teacher Isidorus had checked the text of the works on which Eutokios commented. According to an alternative interpretation, the four mentions of Isidoros are not authentic, but were added to the text of Eutokios by an unknown student of Isidoros. Then the notes say that Isidorus checked the text of Eutokios' commentaries. If so, the assumption that Isidorus was Eutokios' teacher is invalid. Sometimes Eutokios is confused with a soldier of the same name of Thracian origin, who had received the citizenship of Askalon.

A work by Eutokios contains a dedication to "Ammonius, the best of the philosophers". It can therefore be assumed that Eutokios was a student of the famous philosopher Ammonios Hermeiou , who taught at the Neoplatonic School of Philosophy in Alexandria. Since Ammonios was born around 440 and probably died after 517, Eutokios' lifetime falls in the second half of the 5th century and the first half of the 6th century. After completing his training, Eutokios continued to live in Alexandria and taught at the philosophy school there. The Neoplatonist David was one of his students .

Ammonios was apparently a publicly paid philosophy teacher. Research has suggested that Eutokios was his successor in this position and directed the school of philosophy. But there is no evidence of this.

Works

Four comments on mathematical or mathematical-physical writings that can be ascribed to Eutokios with certainty have been preserved:

  • a commentary on the first four books of the Kōniká ("conic sections") by the famous mathematician Apollonios von Perge . Eutokios dedicated this work to the mathematician and architect Anthemios von Tralleis . He also produced an edition of the annotated work. His text-critical work testifies to the diligence of his approach : he compared the different versions of the Konika available to him , and where they offered different readings , he tried to determine the best text version, but also noted variants that he rejected. From his point of view, the best version was the clearest, most didactically expedient, not the presumably original one, as for a modern editor. Since the methodological cleanliness of the mathematical demonstration and the didactic quality were important to him, he did not shy away from major interventions in the text; he simply left out what seemed superfluous. Of the eight Konika books , only the first four have been preserved in Greek, and only in the version edited by Eutokios. Three other books are only available in a medieval Arabic translation, the eighth book is lost.
  • a commentary on Archimedes' treatise Peri sphaíras kai kylíndrou ("On the sphere and cylinder ") . Eutokios dedicated the first book of this commentary to his teacher Ammonios.
  • a commentary on Archimedes' writing Kýklou métrēsis (" Circular Measurement ").
  • a commentary on Archimedes' treatise Epipédōn isorrhopíai ("The balance of flat surfaces").

None of the commentaries contain Eutokios' own discoveries. But they are valuable sources for the history of ancient mathematics. Eutokios shares solutions to geometrical problems that earlier mathematicians had found and some of which have only been handed down from him.

Commenting on the Konika Eutocius mentioned scholia to the first book of mathematike SYNTAXIS of Claudius Ptolemy , which he apparently (the wording is ambiguous) has written himself. The annotated writing is the famous astronomical work of Ptolemy, now known as Almagest . Joseph Mogenet has proposed to identify the alleged missing comment of Eutokios with an anonymously handed down mathematical introduction to the first book of the Almagest , but this hypothesis has been refuted.

In the philosophical field, Eutocius dealt with the logic of Aristotle . He wrote a commentary on the isagogue of the Neo-Platonist Porphyrios (3rd century), an introduction to Aristotelian logic. The philosopher Elias (6th century) mentioned that Eutocius in his classes Isagoge treated. Material from the Isagogue Commentary by Eutocios has come down to us in scholias that Arethas of Caesarea compiled or copied.

Furthermore, Eutokios wrote an astrological treatise, which was probably entitled Astrologoumena ("Astrological"). An extensive, carefully worked out horoscope relating to October 28, 497 and drawn up in Alexandria is ascribed to Eutocius in one of the three surviving manuscripts.

reception

In the 9th century, the Arabic translator of Apollonios' Konika compared the text edited by Eutokios with an older version. Traditional research suggests that he based his translation on the version of Eutokios, but Roshdi Rashed has shown that this is not the case.

In 1269 Wilhelm von Moerbeke translated Eutokios' comments on “On Sphere and Cylinder” and “The Balance of Flat Surfaces” into Latin. Moerbeke's friend Witelo had access to his translations; Traces of a Eutokios reception can be seen on him. In the 14th century, the French mathematician Johannes de Muris Moerbekes used the translation of the commentary on "On Sphere and Cylinder". Around 1450, on behalf of Pope Nicholas V , Jacobus Cremonensis translated all of Eutocius' commentaries on Archimedes into Latin.

Part of Eutokios' commentary on Archimedes was translated into Arabic in the Middle Ages. Some Arabic manuscripts from the commentary on “On Sphere and Cylinder”, which only contain fragments, have been preserved. In the late Middle Ages , a Hebrew translation of the first book of the commentary on “On Sphere and Cylinder” was made, of which only a single manuscript has survived, which does not contain the entire text of the book.

The humanist Giorgio Valla published in his work De expetendis et fugiendis rebus opus (Venice 1501) translated into Latin excerpts from the Konika and from the commentary of Eutokios. The first edition of the Archimedes Commentaries appeared in Basel in 1544. A Latin translation of the first four books of the Konika and the Commentary of Eutokios, made by Federigo Commandino, was printed in Bologna in 1566. The first edition of the original Greek text of this commentary was published by Edmond Halley in Oxford in 1710.

Text output (partly with translations)

  • Johan Ludvig Heiberg (Ed.): Apollonii Pergaei quae Graece exstant cum commentariis antiquis . Volume 2, Teubner, Stuttgart 1974, ISBN 3-519-01052-6 (reprint of the Leipzig 1893 edition), pp. 168-361 (critical edition of Eutokios' commentary on the Konika with a Latin translation by the editor).
  • Charles Mugler (Ed.): Archimède . Volume 4: Commentaires d'Eutocius et fragments . Les Belles Lettres, Paris 1972 (critical edition of the Greek texts and French translation).
  • Catalogus codicum astrologorum Graecorum , Volume 1, ed. Alessandro Olivieri . Lamertin, Bruxelles 1898, pp. 170–171 (edition of the beginning of the Astrologoumena ).

Translations

Medieval

  • Marshall Clagett (Ed.): Archimedes in the Middle Ages , Volume 2: The Translations from the Greek by William of Moerbeke . The American Philosophical Society, Philadelphia 1976, ISBN 0-87169-117-5 (pp. 221–285, 406–416, 486–526: Eutokii Ascalonite rememoracio in libros Archimedis de spera et chylindro ; pp. 339–355, 420– 422, 561-574: Euthocii Ascalonite rememoracio in libros Archymedis de equerepentibus ; critical editions).

Modern

  • Reviel Netz : The works of Archimedes. Translated into English, together with Eutocius' commentaries, with commentary, and critical edition of the diagrams . Volume 1: The Two Books On the Sphere and the Cylinder . Cambridge University Press, Cambridge 2004, ISBN 0-521-66160-9 (contains pages 243-368 an English translation of Eutokios 'commentary on Archimedes' “On Sphere and Cylinder”).

literature

Web links

Remarks

  1. ↑ See Alan Cameron : Isidore of Miletus and Hypatia: On the Editing of Mathematical Texts . In: Greek, Roman, and Byzantine Studies 31, 1990, pp. 103-127, here: 103-107, 115-127; Richard Goulet: Eutocius d'Alexandrie. In: Richard Goulet (ed.): Dictionnaire des philosophes antiques , Volume 3, Paris 2000, p. 393.
  2. ↑ See on this commentary and on Eutokios' edition of the Konika Jaap Mansfeld : Prolegomena mathematica , Leiden 1998, pp. 40–43; Roshdi Rashed (Ed.): Apollonius de Perge, Coniques . Volume 1.1: Livre I , Berlin 2008, pp. 10-25; Micheline Decorps-Foulquier: Eutocius d'Ascalon éditeur du traité des Coniques d'Apollonios de Pergé et l'exigence de "clarté" . In: Gilbert Argoud, Jean-Yves Guillaumin (eds.): Sciences exactes et sciences appliquées à Alexandrie , Saint-Étienne 1998, pp. 87-101, here: 87-93, 97, 99-101; Micheline Decorps-Foulquier: L'édition d'Eutocius d'Ascalon des Coniques d'Apollonius de Perge . In: Ahmad Hasnawi et al. (Ed.): Perspectives arabes et médiévales sur la tradition scientifique et philosophique grecque , Leuven and Paris 1997, pp. 49-60. For individual passages see Michel Federspiel: Notes critiques et exégétiques sur le commentaire d'Eutocius aux Coniques d'Apollonius . In: Revue des Études Grecques 117, 2004, pp. 730–743.
  3. ↑ Jaap Mansfeld: Prolegomena mathematica , Leiden 1998, p. 45f.
  4. ↑ Jaap Mansfeld: Prolegomena mathematica , Leiden 1998, p. 46f.
  5. ↑ Jaap Mansfeld: Prolegomena mathematica , Leiden 1998, p. 47.
  6. ↑ See also Wilbur Richard Knorr: Textual Studies in Ancient and Medieval Geometry , Boston 1989, pp. 165f .; Richard Goulet: Eutocius d'Alexandrie. In: Richard Goulet (ed.): Dictionnaire des philosophes antiques , Volume 3, Paris 2000, p. 394.
  7. ↑ Joseph Mogenet: L'Introduction à l'Almageste , Bruxelles 1956, pp. 13–34. For refutation, see Wilbur Richard Knorr: Textual Studies in Ancient and Medieval Geometry , Boston 1989, pp. 155–211 and Jaap Mansfeld: Prolegomena mathematica , Leiden 1998, pp. 79–81.
  8. ↑ Leendert Gerrit Westerink: Texts and Studies in Neoplatonism and Byzantine Literature , Amsterdam 1980, pp. 62, 64, 67 lines 4-6.
  9. ↑ Michael Share (ed.): Arethas of Caesarea's Scholia on Porphyry's Isagoge and Aristotle's Categories (Codex Vaticanus Urbinas Graecus 35) , Athens et al. 1994, pp. XIII-XV; Leendert Gerrit Westerink , Jean Trouillard (eds.): Prolégomènes à la philosophie de Platon , Paris 1990, p. XVI, note 26.
  10. ^ Wilhelm Gundel , Hans Georg Gundel : Astrologumena , Wiesbaden 1966, p. 247.
  11. ↑ Otto Neugebauer , Henry B. van Hoesen: Greek Horoscopes , Philadelphia 1959, pp. 152–157, 188f .; Alan Cameron: Isidore of Miletus and Hypatia: On the Editing of Mathematical Texts . In: Greek, Roman, and Byzantine Studies 31, 1990, pp. 103–127, here: 105.
  12. ↑ Roshdi Rashed (ed.): Apollonius de Perge, Coniques . Volume 1.1: Livre I , Berlin 2008, pp. 28-44.
  13. ↑ Marshall Clagett (Ed.): Archimedes in the Middle Ages , Volume 2, Philadelphia 1976, pp. 8, 16-27; Volume 4, Philadelphia 1980, pp. 73-78.
  14. ↑ Marshall Clagett (Ed.): Archimedes in the Middle Ages , Volume 3, Philadelphia 1978, pp. 19f., 29f., 48, 84.
  15. ↑ On this translation, see Marshall Clagett (Ed.): Archimedes in the Middle Ages , Volume 3, Philadelphia 1978, pp. 321–342.
  16. ^ Marshall Clagett: Archimedes in the Middle Ages , Volume 1, Madison 1964, pp. 3, 658f .; Wilbur Richard Knorr: Textual Studies in Ancient and Medieval Geometry , Boston 1989, p. 127, note 132; Richard Lorch: The Arabic Transmission of Archimedes 'Sphere and Cylinder and Eutocius' Commentary . In: Journal for the History of Arab-Islamic Sciences 5, 1989, pp. 94–114, here: 106–108, 114.
  17. ^ Marshall Clagett (Ed.): Archimedes in the Middle Ages , Volume 4, Philadelphia 1980, pp. 236-244.
personal data
SURNAME Eutokios
ALTERNATIVE NAMES Eutokios of Ascalon; Eutocios of Alexandria
BRIEF DESCRIPTION late antique Greek mathematician and philosopher (Neoplatonist)
DATE OF BIRTH 5th century
DATE OF DEATH 6th century