Search

…

Folkerts, Menso (Munich) [German version] A. Introduction (CT) Taking their point of departure from the mathematical accomplishments of the Egyptians and Babylonians, the Greeks remodelled mathematics into a deductive system based on a theory of proof. For the Greeks, unlike for their predecessors, mathematics was a science practiced for its own sake, which also investigate…

…

(Λεωδάμας; Leōdámas). [German version] [1] Athenian orator, c. 400 BC The Athenian L. of Acharnae, a skilful orator (Aristot. Rh. 2,23,25 1400a 31-35), was rejected at his dokimasia of 382 BC to assess his candidacy for the eponymous archonship ( Archontes) because of his political role prior to 403 (Lys. 26,13f.). Engels, Johannes (Cologne) Bibliography PA 9076 Davies 13921, p. 523 LGPN 2, s.v. Leodamas (2) Traill, PAA 605085. [German version] [2] Athenian rhetor, 4th cent. BC Son of Erasistratus of Acharnae, outstanding Athenian rhetor, student of Isocrates (Plut. Mor…

…

Epithet of many gentilicia [1]. Famous persons: the jurist Salvius I. [1]; the doctor I. [2]; the emperor I. [11], called ‘Apostata’; the bishops I. [16] of Aeclanum and I. [21] of Toledo. [German version] [1] L. Octavius Cornelius P. Salvius I. Aemilianus Roman jurist, 2nd cent. AD Jurist, born about AD 100 in North Africa, died about AD 170; he was a student of  Iavolenus [2] Priscus (Dig. 40,…

(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…

(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 irra…

(Νικόμαχος/ Nikómachos). [German version] [1] Healing hero See Gorgasus and Nicomachus Schmitz, Winfried (Bielefeld) [German version] [2] Athenian official, 410-404 BC Allegedly the son of a slave and only later accepted as an Athenian citizen. In 410-404 BC, N. led the commission for recording the laws ( anagrapheîs tôn nómōn). Exiled under the Thirty ( triákonta ), he returned in 403 and again became anagrapheús. In 399/8 BC, N. was accused of manipulating the laws, thus e.g. contributing to the sentencing of the demagogue Cleophon [1] in…

(Ἑλικών; Helikṓn). [German version] [1] Mountain range in central Greece Mountain range in central Greece, dividing the Copais Basin and the upper Cephissos Vall…

[German version] [1] Of Alexandria, mathematician and engineer, 1st cent. AD (Ἥρων; Hḗrōn). [German version] A. Life H. of Alexandria, mathematician and engineer. No details of his life are known. He lived after  Archimedes [1], whom he quotes, and before  Pappus, who quotes him. In the Dioptra, ch. 35, H. describes a method for determining the time difference between Rome and Alexandria by observing the same eclipse of the moon at both locations. It is quite likely that this eclipse occurred in AD 62 and that H. probably observed it himself in Alexandria [10. 21-24]. Folkerts, Menso (Mu…

(Λέων; Léōn). Cf. also Leo. Byzantine emperor Leo [4-9]. Sicilian place name L. [13]. [German version] [1] Spartan king, 6th cent. BC Spartan king, Agiad ( Agiads), grandfather of Cleomenes [3] I (Hdt. 5,39); is said to have been successful in war together with his fellow king Agasicles in the early 6th cent. BC, but to have been defeated by Tegea (Hdt. 1,65). Sparta is said to have already achieved eunomía (‘good order’) before his time [1. 45ff.]. Welwei, Karl-Wilhelm (Bochum) Bibliography …

[German version] I Greek (Θεοδόσιος/ Theodósios). [German version] [I 1] Greek mathematician and astronomer,…

[German version] (Δεινόστρατος; Deinóstratos) D. is mentioned in Eudemus' list of mathematicians as the brother of Menachmus, who was a pupil of Eudoxus (Procl. in primum Euclidis elementorum librum comm., p. 67,11 Friedlein). He therefore lived in the middle of the 4th cent. BC  Pappus of Alexandria reports (4,30, p. 250,33-252,3 Hultsch) that to square the circle D. used a curve that was accordingly called the quadratrix (τετραγων…

(Αὐτόλυκος; Autólykos). [German version] [1] Son of Hermes and Chione Son of Hermes and Chione (or Philonis, who also bore the singer  Philammon to Apollo, Hes. fr. 64,14). He was included in various mythical family circles, as the father of  Odysseus' mother Anticlea (Hom. Od. 11,85), of  Jason's mother Polymede (Apollod. 1,107) and of Aesimus, the father of  Sinon. He gives the newborn Odysseus his name, and it is whilst hunting with his sons on Mount Parnassus that Odysseus receives the wound in his th…

[German version] (Θυμαρίδας; Thymarídas). Mathematician from Paros; according to Iamblichus (v. P. 104), T. was an early Pythagorean (Pythagorean School). He defined 'unity' (μονάς/ monás; i.e. the One that generates all the natural numbers) as περαίνουσα ποσότης ( peraínousa posótēs, 'limiting quantity'; Iambl. in Nicomachi arithmeticam introductionem 11,2-5) and called prime numbers εὐθυγραμμικός ( …

(Κάρπος; Kárpos). [German version] [1] Son of Zephyrus and a certain Hore Handsome youth, son of Zephyrus and of a certain Hore ( Horae). H…

[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 …

(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…

[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 …

[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…

(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 amon…

(Πάππος Ἀλεξανδρεύς; Páppos Alexandreús). [German version] I. Life Eminent Greek mathematician. Based on his calculation of a partial solar eclipse for the year AD 32…

(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). T…

(Ζηνόδωρος/ Zēnódōros). …

[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, weigh…

(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…

(Ἄτταλος; Áttalos). [German version] [1] Frie…

(Ἀρίσταρχος; Arístarchos). [German version] [1] Athenian politician (end of the 5th cent. BC) Athenian politician, in 411 BC the most embittered opponent of the demos among the 400 Oligarchs in Athens (Thuc. 8,90,1). A. participated in the fortification of  Eetioneia when he was strategos (Xen. Hell. 2,3,46). After the regime was toppled, he betrayed the border fortification Oenoe to the Boeotians (Thuc. 8,98), for which he was executed in 406 (?) (Lycurg. Leocr. 115; PA, 1663; Traill PAA, 164155). Meier, Mischa (Bielefeld) [German version] [2] of Tegea Tragedian, 5th cent. BC Tragedian, contemporary of Euripides, supposedly lived more than 100 years, author of 70 tragedies, two victories (Suda α 3893); first Dionysian victory maybe in 453 (DID D 3); according to Suda (ibid.) he brought drama to its current μῆκος ( mêkos; maybe related to Aristot. Poet. 1449b 12 ff., 1450b 21 ff.). Some tragedies by Ennius follow A. (Gloss. Lat. I 568 Lindsay and [1.161 ff.]). Preserved titles: Asklepios, Tantalos, Achilleus. Pr…

[German version] [1] Quinctius S. Sammonicus Author of a collection of recipes (also Quintus Serenius). Author of the Liber Medicinalis, a collection of therapeutic recipes which can be neither dated nor identified; Q. has at times been identified with S. [2] Sammonicus or with his son (Septimius [II 6] S. Sammonicus; both di…

(Ἱπποκράτης; Hippokrátēs). [German version] …

(Νίκων; Níkōn). [German version] [1] Theban military leader, 413 BC Theban leader of 300 Boeotian hoplites who, together with some Spartan units, crossed over to Sicily in 413 BC in order to defend Syracuse (Thuc. 7,19,3). Beck, Hans (Cologne) [German version] [2] Comedy writer, 4th/3rd cent. BC Comedy writer of the 4th or 3rd cent. BC; there is a preserved fragment of a play Kitharōdós, in which apparently the direct speech of a non-Greek slave is quoted (fr. 1). Bäbler, Balbina (Göttingen) …

(Θέων; Théōn). [German version] [1] Greek painter from Samos, 300 BC and after T. of Samos was a Greek painter of the Hellenistic Period, who was active around and after 300 BC. His skill as a creator of images and the successful way in which his paintings were composed were praised in handbooks of rhetoric (e.g. Quint. Inst. 12,10,6) as examples to be followed. The viewer's creative imagination and intuitive underst…

I. Mesopotamia [German version] A. Numerical systems Before systems for representing numbers in writing were (further) developed, counting stones, known as calculi or tokens, were used in arithmetic. As first-order representations they enabled operations such as increasing, decreasing, combining, separating, and distributing. Their relationship to the numerical notations recorded in the oldest ‘texts’ ( c. 3300 BC; Uruk) is still discussed [2]. The numerical signs in these texts do not represent absolute numbers but context-dependent units of counting or measurement. They are tied  in fixed relationships (sexagesimal, bisexagesimal) within linear systems of number signs. Hitherto, six basic systems and numerous variants have been identified (Uruk, Ǧamdat Naṣr, beginning of the 3rd millennium). Some of the signs are semantically ambiguous, with numerical values varying according to (metrological) context. A numerical notation in Mesopotamia consisted of a series of individual signs ordered in accordance with fixed rules. Multiples of a basic quantity were represented by iteration of the basic sign ( = 1;  = 2 etc.). Higher-value signs replaced groups of individual signs (e.g.  = 10), following fixed rules of combination. From the 2nd millennium BC the apocopated form  ( mē, from meat, ‘hundred’) accompanying the ordinary numbers from 1 to 9 was often used to express hundreds. The sign for 1,000 () is a ligature of the signs for the numbers 10 and 100, thus 10 × 100 = 1,000. Hundreds of thousands are expressed by sequences like ‘2 hundred (and the sign for) thousand’. In addition to quantity, number signs contain information about the subject (that is counted) or about the metrological system (e.g. various measuring units for areas and volumes).

(Ἀπολλώνιος; Apollṓnnios). [German version] [1] Dioiketes of Ptolemy II (259-245 BC) Of Caria, possibly Ptolemaic o ikonomos there in 267 BC. Was dioiketes of Ptolemy II from April /May 259 until the end of 245; in 252 escorted Berenice to her wedding to Antiochus II. At a critical transition p…

(Μέναιχμος/ Ménaichmos). [German version] [1] M. of Sicyon Greek historian and antiquary, 4th cent. BC …

(Νικομήδης; Nikomḗdēs). [German version] [1] Spartan commander, 458 or 457 BC Member of the Spartan royal family of the Agiadae, son of Cleombrotus [2], brother of Pausanias, the victor of Plataeae. In 458 or 457 BC, N. led a Spartan army as the guardian of his underage nephew Pleistoanax to support the inhabitants of the Doris region against the Phocians and on the return march defeated the Athenians near Tanagra (Thuc. 1,107,2-108,1; Diod. Sic. 11,79,4-80,6; Plut. Cimon 17,4-9; Plut. Pericles 10,1-4). Welwei, Karl-Wilhelm (Bochum) [German version] [2] N. I of Bithynia King from 280 BC S…