Eutocius of Ascalon

Eutocius (Greek Εὐτόκιος Eutocius ) was a late ancient Greek mathematician and philosopher ( Neoplatonist ). His life falls into the late 5th century and the first half of the 6th century. He is often referred to by his hometown " Eutocius of Ascalon ". Since he belonged to the school of philosophers of Alexandria, he is also known as " Eutocius of Alexandria ".

Life

Very little is known about the life of Eutocius. He came from the city of Ashkelon in Israel today. According to a research opinion he was a pupil of the architect Isidore of Miletus and mathematician ( the Elder ). This assumption is based on four mentions in comments Isidore of Eutocius, including three endorsements, according to which " our teacher, the engineer Isidore of Miletus " a text verification is performed. How is this to be understood, however, is controversial. One can interpret it so that Eutocius the author of the notes and that he wanted to tell his teacher Isidore had the text of the works that commented Eutocius checked. According to an alternative interpretation of the four mentions of Isidore are not authentic, but have been added by an anonymous disciple of Isidore later in the text of the Eutocius. Then say the notes that Isidore revised the text of the comments of the Eutocius. If so, is the assumption that Isidore was Eutocius ' teachers obsolete. Sometimes Eutocius is mistaken for a same soldiers of Thracian origin, who had received the citizenship of Ashkelon.

A work of Eutocius contains a dedication to " Ammonius, the best of the philosophers ." Therefore, it can be assumed that Eutocius was a student of the famous philosopher Ammonius Hermeiou, who taught at the Neoplatonist school of philosophy of Alexandria. Since Ammonius was born around 440 and died probably after 517, the lifetime of the Eutocius falls into the second half of the 5th century and the first half of the 6th century. After completing his training Eutocius has continued to lived in Alexandria and granted at the local school of philosophy lessons. His students included the Neoplatonists David.

Ammonius was apparently a publicly salaried teacher of philosophy. In research, it has been suggested that Eutocius was his successor at this point and has led the school of philosophy. There are, however, no evidence.

Works

Four comments on mathematical and mathematical-physical fonts that can Eutocius be attributed with certainty, have been preserved:

• A commentary on the first four books of the Konika ( " conics " ) of the famous mathematician Apollonius of Perga. Eutocius dedicated this work to the mathematician and architect Anthemius of Tralles. He also created an annotated edition of the work. From the care of his procedure is shown by his text-critical work: He compared the present him different versions of Konika, and where they offered different readings, he tried to determine the best text version, but also noted variations which he rejected. The best version was, in his view, the clearest, most practical didactic, not like for a modern editor that presumably original. Because it mattered to him on the methodological cleanliness mathematical demonstration and on the quality of teaching, he did not hesitate before major surgery back in the text; what seemed to him superfluous, he had just gone. Only the first four of the eight books of the Konika have been preserved in Greek, and only in the edited version of Eutocius. Three other books are available only in a medieval Arabic translation, the eighth book is lost.
• A commentary on the treatise Peri sphaíras kai kylíndrou ( " On the Sphere and Cylinder" ) of Archimedes. The first book of this commentary devoted his teacher Ammonius Eutocius.
• A commentary on Archimedes ' writing Kýklou métrēsis ( " circle measurement ").
• A commentary on Archimedes ' treatise Epipédōn isorrhopíai ( " The Balancing Planes ").

None of the comments contain original discoveries of Eutocius. However, they are valuable sources for the history of ancient mathematics. Eutocius shares solutions with geometric problems that earlier mathematicians had found and which are consigned to supply only for him.

In the commentary on the Konika Eutocius scholia mentioned for the first book of Mathematike SYNTAXIS of Claudius Ptolemy, which he apparently ( the wording is ambiguous ) himself has written. In the annotated document, it is the famous astronomical work of Ptolemy, which is known as the Almagest today. Joseph Mogenet has proposed to identify the alleged lost comment Eutocius with an anonymous traditional mathematical introduction to the first book of the Almagest, but this hypothesis was refuted.

In the area of ​​philosophy itself Eutocius dealt with the logic of Aristotle. He wrote a commentary on the Neoplatonist Porphyry Isagoge the (3rd century), an introduction to Aristotelian logic. The philosopher Elias ( 6th century ) mentions that Eutocius treated the Isagoge in his classes. Material from the Isagoge - comment Eutocius is preserved in scholia, the Aretha of Caesarea compiled or transcribed.

Furthermore Eutocius wrote an astrological treatise, probably the title Astrologoumena ( " Astrological " ) wore. A comprehensive, accurate elaborate horoscope, which refers to 28 October 497 and was created in Alexandria, is ascribed in one of the three surviving manuscripts Eutocius.

Reception

In the 9th century, the Arabic translator of Apollonius ' Konika compared the edited text of Eutocius with an older version. According to the conventional opinion research he put his translation of the text in the Eutocius basis, but Roshdi Rashed has shown that this is not true.

In 1269 William of Moerbeke translated Eutocius ' Comments on " On the Sphere and Cylinder" and " The Balancing Planes " into Latin. Moerbeke friend Vitelo had access to his translations; Traces of a Eutocius reception can be seen with him. The French mathematician Johannes de Muris Moerbeke used in the 14th century translation of the Commentary on " On the Sphere and Cylinder". Around 1450, translated Jacobus Cremonensis by order of Pope Nicholas V all Archimedes Comments Eutocius into Latin.

A part of Eutocius ' Archimedes commentary was translated into Arabic in the Middle Ages. Several Arabic manuscripts of the Commentary on " On the Sphere and Cylinder", which, however, contain only fragments have been preserved. In the late Middle Ages, a Hebrew translation of the first book of the comment was to " On the Sphere and Cylinder" produced, of which only a single manuscript is received that does not contain the entire text of the book.

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

Text editions (some with translations)

• Johan Ludvig Heiberg (ed.): Apollonii Pergaei quae Grace exstant cum commentariis antiquis. Volume 2, Teubner, Stuttgart 1974, ISBN 3-519-01052-6 ( reprint of the edition Leipzig 1893), pp. 168-361 ( critical edition of Eutocius ' commentary on the Konika with a Latin translation of the publisher ).
• Charles Mugler (ed.): Archimede. Volume 4: Commentaires d' Eutocius et fragments. Les Belles Lettres, Paris, 1972 ( critical edition of the Greek text and French translation ).
• Catalogus codicum astrologorum Graecorum, Volume 1, ed. Alessandro Olivieri. Lamertin, Bruxelles 1898, pp. 170-171 (Edition of the beginning of 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 de ArchiMedis spera et chylindro, pp. 339-355, 420 - 422, 561-574: Euthocii Ascalonite rememoracio in libros de Archymedis equerepentibus; critical editions ).

Modern

• Reviel: 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 ( includes an English translation of pp. 243-368 Eutocius 'commentary on Archimedes ' " On the Sphere and Cylinder" ).