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(604 words)

Author(s): Leppin, Hartmut (Hannover) | Johne, Klaus-Peter (Berlin) | Folkerts, Menso (Munich)
[German version] [1] Praefectus praetorio Orientis 405-414 AD Probably sent to Persia as an envoy in AD 383, comes sacrarum larg. (eastern region) in AD 400; magister officiorum (eastern region) at the latest in AD 404, cos. 405; at the latest from AD 406 patricius. A. gained considerable political influence in his role as praefectus praetorio Orientis from AD 405-414, initially under Arcadius, later under the underage Theodosius II. He was a Christian, but looked upon pagan culture with an open mind [1. 82 f.]. Through the building of walls, he took…


(124 words)

Author(s): Folkerts, Menso (Munich)
[German version] (νεῦσις/ neûsis, ‘inclination’, in the mathematical sense: ‘verging’) is a geometric operation that cannot be performed with a compass and ruler alone. It allows problems  that lead to cubic and other higher equations (for example, cube duplication, angle trisection, squaring the circle) to be solved geometrically. A neûsis construction is necessary when a straight line through a given point is supposed to intersect two given lines so that the distance between the points of intersection is equal to a certain distance. Nicomede…


(3,891 words)

Author(s): Kinzl, Konrad (Peterborough) | Riedweg, Christoph (Zürich) | Döring, Klaus (Bamberg) | Badian, Ernst (Cambridge, MA) | Bartels, Jens (Bonn) | Et al.
(Διόδωρος, Διόδορος; Diódōros, Diódoros). Well-known representatives of the name: the philosopher D. [4] Kronos, the mathematician D. [8] of Alexandria, the universal historian D. [18] Siculus, the early Christian theologian D. [20] of Tarsus. [German version] [1] Athenian fleet commander in the Peloponnesian War Athenian, fleet commander with Mantitheus at the end of 408-407 BC at the Hellespont with a sufficient number of ships, so that Alcibiades [3] was able to sail to Samos and Thrasyllus and Theramenes to Athens (Diod. Sic. 13,68,2). (Traill, PAA 329550; Develin 171). Kinzl, …


(2,514 words)

Author(s): Visser, Edzard (Basle) | Zahrnt, Michael (Kiel) | Ameling, Walter (Jena) | Wandrey, Irina (Berlin) | Folkerts, Menso (Munich) | Et al.
(Μενέλαος/Menélaos, Attic Μενέλεως/Menéleos; Latin Menelaus). [German version] [1] Ruler of Sparta, married to Helena A significant character in the cycle of myths about the Trojan War ( Troy: Cycle of myths). A younger brother of Agamemnon, who ruled the most significant power centre in Greek myth, Mycene, by marriage to Zeus's daughter Helen ( Helene [1]; their only child was a daughter, Hermione) M. became king of a region in the Eurotas valley with its capital Sparta and Amyclae [1], which was significant…


(716 words)

Author(s): Schachter, Albert (Montreal) | Folkerts, Menso (Munich)
(Αρισταιο̃ς; Aristaîos). [German version] [1] Greek rural deity Rural deity linked with sheep, the discovery of olive oil and honey, hunting, healing, prophecy and the end- ing of a period of drought on Ceos (cf. Apoll. Rhod. 2,500 ff.). In literature he is famous for the death of his bees, which occurred because he was responsible for the death of  Euridices, and he successfully searched for ways to restore the bee populations (Verg. G. 4,315-558). A. is a complex figure who can be found in Central Greece, in Arcadia, on Ceos and in Cyrene. He was the husband of Auto…

Quadrature of the circle

(1,369 words)

Author(s): Folkerts, Menso (Munich)
(ὁ τοῦ κύκλου τετραγωνισμός/ ho toû kýklou tetragōnismós, Latin quadratura circuli). [German version] I. The nature of the problem The quadrature of the circle is one of the three 'classic problems' (the other two being the trisection of an angle, cf. division of angles and circles, and the duplication of the cube) of ancient Greek mathematics. The problem is to find the side x of a square such that its area is equal to the area of a circle with radius r using a geometric procedure; that is,  to determine the value of the variable x in the equation x 2 = π r 2. Accordingly, the solution to the q…


(210 words)

Author(s): Folkerts, Menso (Munich)
[German version] (Θεύδιος; Theúdios). Mathematician and philosopher from Magnesia, probably 4th century BC. The only information about him comes from the catalogue of mathematicians in Proclus's [2] commentary on Euclid [1. 67, Z. 12-20]. T. is mentioned there after Eudoxus [1] and before Philippus of Medma, who was a pupil of Plato [1]; Therefore, T. was probably a contemporary of Aristotle [6]. According to Proclus, T., Menaechmus [3] and Deinostratus conducted research together at the Academy ( Akadḗmeia ), improved the arrangement of the 'Elements', and put many limited pr…


(168 words)

Author(s): Folkerts, Menso (Munich)
[German version] (Eυτόκιος; Eutókios) The mathematician E. of Ascalon was presumably born around AD 480; the widespread assumption that he was a pupil of the architect  Isidorus of Miletus is hardly plausible [1. 488]. He wrote commentaries on three works of  Archimedes [1] ( Perì sphaíras kaì kylíndrou, Περὶ σφαίρας καὶ κυλίνδρου, kýklou métrēsis, κύκλου μέτρησις, Perì epipédōn isorrhopiôn, Περὶ ἐπιπέδων ἰσορροπιῶν, text editions [3. 1-319]) as well as on the first four books of Apollonius' Kōniká (Κωνικά) [13] (dedicated to  Anthemius [3], text edition [4. 168-361]…


(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 …


(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, Wa…


(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…


(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…


(2,633 words)

Author(s): Rhodes, Peter J. (Durham) | Döring, Klaus (Bamberg) | Folkerts, Menso (Munich) | Zaminer, Frieder (Berlin) | Di Marco, Massimo (Fondi Latina) | Et al.
(Εὐκλείδης; Eukleídēs). [German version] [1] Athenian archon in 403/2 BC Athenian archon in 403/2 BC. During his year in office Athens made a new start following the Oligarchy of the Thirty (e.g., see And. 1,87-94) and, among others, officially adopted the Ionian alphabet (Theopomp. FGrH 115 F 155). Rhodes, Peter J. (Durham) Bibliography Develin 199 LGPN 2, Εὐκλείδης (9). [German version] [2] of Megara Student of Socrates Student of Socrates, founder of the  Megarian School; born between 450 and 435, probably died early in the 360s. In Plato's Phaedon (59c) E. is named among those …

Pappus of Alexandria

(727 words)

Author(s): Folkerts, Menso (Munich)
(Πάππος Ἀλεξανδρεύς; Páppos Alexandreús). [German version] I. Life Eminent Greek mathematician. Based on his calculation of a partial solar eclipse for the year AD 320, it is assumed that P. lived in the first half of the 4th cent. (on this and on erroneous dating in the Suda see [2. 2-4]). Folkerts, Menso (Munich) [German version] II. Works The most important surviving work is the Συναγωγή/ Synagōgḗ, customarily cited as the Collectio (ed. [1], French translation [3], edition and English translation of book 7 [2]). Of the 8 books, the first is wholly lost, the se…

Duplication of the Cube

(1,109 words)

Author(s): Folkerts, Menso (Munich)
(κύβου διπλασιασμός/ kýbou diplasiasmós according to Eratosthenes, in [1. 88,16]). [German version] I. General The duplication of the cube ─ besides the  division of angles and circles and the  squaring of the circle ─ belongs to the three classic problems in Greek  mathematics. The challenge is such: to find ─ through the use of geometry ─ for a given cube with a side-length of a (and thus the volume of a 3) the side x of another cube whose volume is twice as big as that of the given cube. The problem is therefore to find the value of x, to which applies: x 3 = 2 a 3 (that is: x = a 32). The problem thus…


(744 words)

Author(s): Folkerts, Menso (Munich) | Matthaios, Stephanos (Cologne) | Bringmann, Klaus (Frankfurt/Main) | Neudecker, Richard (Rome)
(Ζηνόδωρος/ Zēnódōros). [German version] [1] Greek mathematician, probably at the beginning of the 2nd cent. BC Greek mathematician, probably at the beginning of the 2nd cent. BC [5; 6. 604 f.]. He wrote a work 'Isoperimetric figures' (Περὶ ἰσοπεριμέτρων σχημάτων, Perì isoperimétrōn schēmátōn) in which he proved that of all figures of the same circumference the circle has the greatest area, and formulated the proposition that of all bodies of the same surface area the sphere has the greatest volume [3; 4; 7]. Substantial parts of the …

Land surveying

(895 words)

Author(s): Folkerts, Menso (Munich)
[English version] The writings of the Roman surveyors ( agrimensores) deal with their various areas of activity: measurement of areas; limitation, i.e. division by orthogonal boundaries; creation of land registers and general parceling maps; functioning as a judges or experts in land law, particularly in boundary disputes; collaboration in religious ceremonies; units of length and area, weights and determining area and volume. Mathematical questions are dealt with most notably by Balbus' work Expositio et ratio omnium formarum (ca . AD 100), the anonymous Liber podismi and a wo…


(381 words)

Author(s): Käppel, Lutz (Kiel) | Börm, Henning (Kiel) | Folkerts, Menso (Munich) | Zimmermann, Bernhard (Freiburg)
(Πολύιδος/ Polýidos, Latin Polyidus). [German version] [1] Mythical seer and miracle-worker from Corinth ('of wide learning'). Mythical seer and miracle-worker from Corinth (cf. Cic. Leg. 2,33), descendant of Melampus [1] (Pherecydes FGrH 3 F 115a; Paus. 1,43,5), spouse of Eurydameia, father of Euchenor (Hom. Il. 13,663-668; cf. Cic. Div. 1,89), Cleitus [2], Astycrateia and Manto (not identical with the seeress Manto). His powers are testified to by numerous accounts of his assitence: in Corinth, for example…


(2,358 words)

Author(s): Badian, Ernst (Cambridge, MA) | Mehl, Andreas (Halle/Saale) | Folkerts, Menso (Munich) | Dingel, Joachim (Hamburg) | Neudecker, Richard (Rome) | Et al.
(Ἄτταλος; Áttalos). [German version] [1] Friend of  Philippus, rival of Alexander the Great at the court of his father Friend of  Philippus who did not punish him for an insult inflicted on Pausanias. At the wedding of his niece Cleopatra (II) to Philippus (337 BC) he called  Alexander [4] the Great a nothos (illegitimate son) and was attacked by him, whereupon Alexander and Olympias were banned (Plut. Alex. 9 among others). With his father-in-law (Curt. 6,9,18) Parmenion, he commanded the invading army in Asia. After Philippus' death, Alexander …


(1,483 words)

Author(s): Folkerts, Menso (Munich) | Nesselrath, Heinz-Günther (Göttingen) | Brodersen, Kai (Mannheim)
(Εὔδοξος; Eúdoxos). [German version] [1] of Cnidus Ancient mathematician and astronomer One of the most important ancient mathematicians and astronomers, he was presumably born in 391/390 BC (on the problem of dating see [7. 137-139]). He studied mathematics with  Archytas [1] and medicine with  Philistion. At the age of 23 he went to Athens and it is said that, among other things, he attended lectures there with  Plato. At the expense of his Cnidian friends, presumably in 365/4 [11], E. went with a letter…
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