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Theodorus

(7,286 words)

Author(s): Knell, Heiner (Darmstadt) | Folkerts, Menso (Munich) | Baumhauer, Otto A. (Bremen) | Schmitz, Winfried (Bielefeld) | Blume, Horst-Dieter (Münster) | Et al.
[German version] I Greek (Θεόδωρος; Theódōros). [German version] [I 1] Of Samos, Greek architect, bronze sculptor and inventor, Archaic period Multitalented Greek inventor, architect, bronze sculptor and metal worker ( toreutḗs; Toreutics) of the Archaic period from Samos (for the occupational image cf. architect). His father was Telecles (Hdt. 3,41; Paus. 8,14,8; 10,38,6) or according to other sources (Diog. Laert. 2,103; Diod. Sic. 1,98) Rhoecus [3]; his name is so frequently mentioned in conjunction with the latter that …

Hypsicles

(603 words)

Author(s): Folkerts, Menso (Munich)
[German version] (Ὑψικλῆς; Hypsiklês). Hellenistic mathematician and astronomer. From the introduction to book 14 of Euclid's ‘Elements’ written by him, it follows that H. lived in Alexandria around 175 BC. It is attested by MSS that he composed what later was added as book 14 to the ‘Elements’ of  Euclides [3] (ed. [1]). Like bk. 13 it deals with the inscribing of regular bodies into a sphere and was thought of as an explanation to a lost work of  Apollonius [13] about dodecahedra and icosahedra. H. shows that the planes th…

Ptolemaeus

(19,876 words)

Author(s): Ameling, Walter (Jena) | Mehl, Andreas (Halle/Saale) | Zahrnt, Michael (Kiel) | Günther, Linda-Marie (Munich) | Schottky, Martin (Pretzfeld) | Et al.
(Πτολεμαῖος/ Ptolemaîos). Personal name meaning 'warlike' (not 'hostile'), first recorded in Hom. Il. 4,228; the name occurred in Macedonia in the 5th and 4th cents. BC, from where it spread to Thessaly, still in the 4th cent. (IG IX 2, 598). It became prominent with the Lagid dynasty, and became common, not only in Egypt, where it may at first have indicated solidarity with the dynasty, but also elsewhere. It underwent many deformations and transmutations. Ptolemies Famous persons: P. [1] I Soter, P. [6] III Euergetes; P. [22], the son of Caesar; the scientist Claudius P. [65]. Ameling, Walter (Jena) I. Dynasty of the Hellenistic kings in Egypt [German version] [1] P. I Soter (Σωτήρ; Sōtḗr). Founder of the dynasty of the Ptolemies. Born in 367/6 BC, the son of Lagus [1] (legend gives Philip II (Philippus [4] II) as the father, Curt. 9,8,22; Paus. 1,6,2) and Arsinoë [II 1], thr…

Archimedes

(2,119 words)

Author(s): Folkerts, Menso (Munich) | Degani, Enzo (Bologna)
[1] of Syracuse C. 287-232 BC [German version] A. Life A. was born in 287 BC in Syracuse, son of the astronomer Phidias. He was friends with King Hieron II, and later with his son Gelon. A. probably spent some time in Alexandria; he later sent on his writings to the mathematicians (Conon, Dositheus, Eratosthenes) who were working there. In Syracuse, A. studied problems of mathematical and physical theory, but also their practical applications; the machines and physical apparatus which he built (e.g. the s…

Division of angles and circles

(923 words)

Author(s): Folkerts, Menso (Munich)
[German version] …

Theaetetus

(1,081 words)

Author(s): Folkerts, Menso (Munich) | Albiani, Maria Grazia (Bologna)
(Θεαίτητος; Theaítētos). [German version] [1] T. of Athens, mathematician, c. 400 BC Mathematician, a native of Athens, pupil of Theodorus [2] of Cyrene and later a member of Plato's Academy ( Akadḗmeia ). In Plato's [1] dialogue named after him, T. appears (together with the aged Theodorus [2]) as about fifteen years old in 399 BC; he was therefore born c. 414. Plato describes him as gentle, courageous and quick to apprehend. After he had been wounded in the battle of Corinth, T. contracted dysentery and died in 369. T. contributed substantially to the theory of irrational quantities. He studied and classified (linearly) incommensurable magnitudes whose squares are commensurable. This classification of irrational quantities can be found in Book 10 of Euclid's (Euclides [3]) Elements, which suggests that this book could hark back to T. ([10. 271-282]; sceptical: [1. 303]). Plato (Tht. 147d-148b) describes how T. distinguished between line segments that when squared produce a square number, and those that do not; T. calls the latter δυνάμει ( dynámei = potentially, i.e. in the second power) commensurable with the former, which he describes as lengths (μῆκος, mêkos). T. expresses the following proposition: "All the lines which form the four sides of the equilateral or s…
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