Theon of Smyrna

Theon of Smyrna (Greek Θέων; † after 132) was an ancient Greek philosopher ( Platonist ), mathematician and astronomer from Smyrna (now Izmir in Turkey, port city on the Aegean coast). He lived under the Emperor Hadrian.

Identity

The identity of the philosopher Theon quoted with the mathematician of that name, the Claudius Ptolemy in his syntaxis ( Almagest ) and Theon of Alexandria in the 4th century in his Almagest commentary called the "old Theon " was doubted earlier. Today, however, it is considered very likely. Ptolemy mentioned Theon's observations of Venus and Mercury in the period 127-132. Otherwise, there is nothing recorded about Theon's life, but its appearance is due to a known bust that left his son of the same make (now in the Capitoline Museum, Rome ).

Works

From Theon's writings only one survives, the work on the mathematical knowledge for reading Plato's Quick. It is a general introduction to the mathematics, music theory and astronomy for the needs of Plato readers. It contains valuable quotes from a lost older literature. Theon mentions numerous authors from whom he derives his knowledge, and reports on their views, which he can often be contradictions, without seeking a cleanup or take a stand. In the first part he deals with the arithmetic and the music and gives details of the Pythagorean Tetraktys. In the second, more extensive part he deals with astronomy. Topics include, among other proofs of the sphericity of the earth, the determination of the circumference of the earth, the planetary orbits and the explanation of solar and lunar eclipses. Also on the harmony of the spheres is a Theon, but lacks a repeatedly announced for the end separate treatment of this topic, which gives rise to the assumption that the work is incompletely preserved.

In addition, Theon wrote two other works: a review of Plato's dialogue Politeia, which has not been preserved, and a record of the order in which you should read the works of Plato, and their titles. This document, probably an introduction to Plato's works, was in the 10th century the scholar Ibn an- Nadim, who used it in his al - Fihrist kitāb. It is only fragmentarily preserved in Arabic translation. Theon was concerned in this work with the tetralogy order, the division of Plato's works in groups of four; presumably it also contained a biography of Plato, have been handed down from the passages in Arabic translation.

Philosophy

Theon compares the depression in the Platonic philosophy adopted by him five stages of initiation into the mysteries of Eleusis. The first stage of the cleaning; it happens " from a child " by practicing the mathematical lessons that prepare them to Philosophy ( propaedeutic ). Among the " mathematical sciences " means Theon, Plato remarks in the Republic following, arithmetic, geometry ( ie planimetry ), solid geometry, music theory and astronomy. The second stage, in the mysteries of the reception of consecration, is in Platonism in the statement of philosophical teachings of Plato ( logic, political philosophy, natural philosophy). The third stage of the Mysteries, the "Look " ( epopteía ) corresponds, in the Platonists employment with the ideas, which is also seen as a show. The fourth stage is in the mysteries applying the bandages and the head crowning, which is expressed that the initiate can pass on the received orders. It corresponds in Platonism the acquisition of the ability to teach philosophy, whereby the other show is made possible. The fifth and final stage is apparent both in the Mysteries as well as in philosophy eudaimonia ( happiness ). It is obtained in the mysteries by the now ways to deal with the gods, in Platonism - as expressed by Theon with a formulation of Plato - through the " alignment with God, so far as it is possible." Theon's scheme of recording rites of the Mysteries at Eleusis, however, deviates from the actual course.

Mathematics

In his work on the mathematical knowledge for reading Plato Useful Theon describes a mathematical method, which is to its diagonal, suitable for determining the ratio of " Page Numbers " and " diagonal numbers ", namely the side of the square. First, he notes that the unit (1 ) is the origin of all numbers both side and diagonal. He comes to the first approximation: Number of pages 1 and diagonal number is also 1 Then he takes two units, one side and a diagonal unit. There is a new page is formed by adding to the page unit adding the diagonal unit, and a new diagonal, by adding to the diagonal unit twice the side unit: 1 1 = 2, 1 2 = 3. the new page number is therefore 2, the new diagonal number 3 for the next page number to the previous page number and the previous diagonal number is added, ie 2 3 = 5, and for the next diagonal number the previous diagonal number and twice the previous number, so 3 2 x 2 = 7

This method provides for an approximation, respectively, if the diagonal number is divided by the associated page number. The quotient approach the value by providing a lower and an upper limit for the root alternately. The method can be easily generalized for the calculation of any square roots. It is in English " Theon 's Ladder " ( Theon's manager) called; each quotient forms a rung of the "ladder".

The starting point was Plato's considerations about the "wedding number" in the Republic of Theon. It also later tied Proclus in his commentary on Politeia, where he quotes the same procedure as Theon.

Theon describes only the method, but offers no proof.

Astronomy

Theon mentions that he has constructed a model of the celestial spheres on the basis of Plato's information. He is convinced that a proper astronomical theory not only allows calculations that are consistent with the observation results, but also the physical reality reflects truthfully. When comparing the Babylonian and Egyptian astronomy with the Greek, he points out that only the Greek " Physiology" inclusive, so producing a relation between the calculations and the physical basis of astronomy.

Reception

In the Islamic world in the Middle Ages Theon was now lost work on the order in which you should read the works of Plato, and still available on its title. It was used in the 10th century by Ibn an- Nadim and later by ibn al - Qifṭī ( 1172-1248 ).

After Theon Theon of lunar crater is named senior.

Text editions and translations

• Jean Dupuis (ed.): Theon de Smyrne philosophe Platonicien, exposure of connaissances utiles Mathématiques pour la lecture de Platon. Paris 1892, reprint 1966 Bruxelles (Greek text and French translation )
• Eduard Hiller (ed.): Theonis Smyrnaei philosophical Platonici expositio rerum mathematicarum ad legendum Platonem utilium. Leipzig 1878, reprint Teubner, Stuttgart 1995, ISBN 3-519-01853-5 (Greek text; online)
• Robert Lawlor, Deborah Lawlor ( Translator ): Theon of Smyrna, Mathematics Useful for Understanding Plato. Wizards Bookshelf, San Diego, 1979 ( English translation)