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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 quantiti…

Nicomachus

(1,669 words)

Author(s): Schmitz, Winfried (Bielefeld) | Zimmermann, Bernhard (Freiburg) | Hoesch, Nicola (Munich) | Nesselrath, Heinz-Günther (Göttingen) | Albiani, Maria Grazia (Bologna) | Et al.
(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 404, evading his …

Helicon

(372 words)

Author(s): Freitag, Klaus (Münster) | Folkerts, Menso (Munich) | Hurschmann, Rolf (Hamburg)
(Ἑλικών; Helikṓn). [German version] [1] Mountain range in central Greece Mountain range in central Greece, dividing the Copais Basin and the upper Cephissos Valley from the Gulf of Corinth (cf. Str. 9,2,25; Paus. 9,28,1-31,7). The western part of the H. belonged to Phocis and the eastern part to Boeotia. The highest elevation is the peak of the Palaiovouno (1,748 m). Few passes lead over the H., which is rich in springs and forests and was famed for its herbs. The H. has large areas that were used in anti…

Hero

(1,389 words)

Author(s): Folkerts, Menso (Munich) | Waldner, Katharina (Berlin)
[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…

Leon

(1,337 words)

Author(s): Welwei, Karl-Wilhelm (Bochum) | Cobet, Justus (Essen) | Schmitz, Winfried (Bielefeld) | Engels, Johannes (Cologne) | Folkerts, Menso (Munich) | Et al.
(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 1 M. Meier, Aristokraten und Damoden, 1998. [German version] [2] Tyrant of Phlius, 6th cent. BC Tyran…

Division of angles and circles

(923 words)

Author(s): Folkerts, Menso (Munich)
[German version] I. Ancient Orient see  Mathematics I Folkerts, Menso (Munich) II. Classical Antiquity [German version] A. Division of circles The division of circles, i.e. the division of the circumference of a circle into any number of arcs of equal length, is directly correlated to the regular polygons: if a regular n-gon is inscribed in a circle, the circumference of the circle is divided into n sections and the angle at the centre belonging to the side of the n-gon has the value 360°/ n . The Pythagoreans ( Pythagoras [2]) were already interested in the regular polygons a…

Diophantus

(1,146 words)

Author(s): Nesselrath, Heinz-Günther (Göttingen) | Strothmann, Meret (Bochum) | Folkerts, Menso (Munich)
(Διοφαντός; Diophantós). [German version] [1] Writer of comedies Author of comedies, dates unknown; one fragment and the title of one play (Μετοικιζόμενος) have been preserved. Nesselrath, Heinz-Günther (Göttingen) Bibliography 1 PCG V, 42. [German version] [2] Commander under Mithridates VI Eupator From Sinope, son of Asclepiodotus, commander to Mithridates VI Eupator. In 110 BC he provided skilful military and diplomatic support to the inhabitants of the city of Chersonesus and thus enabled them to withstand the Scythians (Str. 7,3,1…

Aristarchus

(2,018 words)

Author(s): Meier, Mischa (Bielefeld) | Pressler, Frank (Heidelberg) | Folkerts, Menso (Munich) | Montanari, Franco (Pisa)
(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 Tragedi…

Serenus

(635 words)

Author(s): Touwaide, Alain (Madrid) | Schmidt, Peter Lebrecht | Folkerts, Menso (Munich)
[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 died at the beginning of the 3rd cent. AD). The collection (dating between the 2nd and 4th cents. AD) cannot be chronologically ordered with any accuracy. It is written in hexameters and contain…

Hippocrates

(5,685 words)

Author(s): Patzek, Barbara (Wiesbaden) | Stein-Hölkeskamp, Elke (Cologne) | Folkerts, Menso (Munich) | Potter, Paul (London, Ontario) | Gundert, Beate (London, Ontario) | Et al.
(Ἱπποκράτης; Hippokrátēs). [German version] [1] Father of Peisistratus, from Brauron Father of  Peisistratus. H. is presumed to have come from Brauron, the later deme of Philaidai, and traced his ancestry back to Neleus (Hdt. 1,59; 5,65; Plut. Solon 10; 30). Patzek, Barbara (Wiesbaden) Bibliography Traill, PAA 538385. [German version] [2] Son of Megacles from Athens, approx. 6th cent. BC Son of the Alcmaeonid ( Alcmaeonids)  Megacles from Athens, born around 560 BC, H. was the brother of Cleisthenes, the father of  Megacles and Agariste [2] and thus th…

Nicon

(255 words)

Author(s): Beck, Hans (Cologne) | Bäbler, Balbina (Göttingen) | Günther, Linda-Marie (Munich) | Folkerts, Menso (Munich)
(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) Bibliography 1 PCG 7, 1989, 38. [German version] [3] Co-founder of the anti-Roman alliance of…

Theon

(2,323 words)

Author(s): Hoesch, Nicola (Munich) | Bäbler, Balbina (Göttingen) | Ameling, Walter (Jena) | Damschen, Gregor (Halle/Saale) | Folkerts, Menso (Munich) | Et al.
(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 understanding were meant to be stimulated at the same time by means of the artistic phantasía (Lat. ingenium, 'image creation'; Phantasia), so that the viewer might imagine e…

Number

(5,221 words)

Author(s): Cancik-Kirschbaum, Eva (Berlin) | I.A. | Folkerts | Folkerts, Menso (Munich) | Crubellier, Michel (Villeneuve d'Ascq) | Et al.
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 count…

Apollonius

(7,446 words)

Author(s): Ameling, Walter (Jena) | Fantuzzi, Marco (Florence) | Hunter, Richard (Cambridge) | Pressler, Frank (Heidelberg) | Hidber, Thomas (Berne) | Et al.
(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 period A. found himself responsible for the economy of the kingdom of the Ptolemies, adapting the fiscal system to the monetary economy of the Lagids, for which purpose he was entrusted with the management of finances and the co…

Menaechmus

(496 words)

Author(s): Meister, Klaus (Berlin) | Folkerts, Menso (Munich) | Neudecker, Richard (Rome)
(Μέναιχμος/ Ménaichmos). [German version] [1] M. of Sicyon Greek historian and antiquary, 4th cent. BC Greek historian and antiquary of the 4th cent. BC. Author of a Pythian history ( Pythikós), which was superseded by a list of victors of the Pythian Games at Delphi composed by Aristotle (T 3) and therefore must have existed in the early 330s (cf. Syll.3 275). A history of Alexander, ( Historía hē katá ton Makedóna Aléxandron) is entirely lost (T 1), while only fragments remain of a local history of Sicyon ( Sikyōniká). Fragments of a treatise ‘On Artists ( Perí technítōn, F 3-6; 9) deal pr…

Nicomedes

(1,542 words)

Author(s): Welwei, Karl-Wilhelm (Bochum) | Schottky, Martin (Pretzfeld) | Folkerts, Menso (Munich) | Eck, Werner (Cologne)
(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…

Mesolabium

(99 words)

Author(s): Folkerts, Menso (Munich)
[German version] (μεσολάβιον; mesolábion). A mechanical device invented by Eratosthenes [2] to establish graphically the two geometric means x and y between two given lines a and b (as in the relationship a: x = x: y = y: b). The mesolabium enabled the mechanical solution of the problem of the duplication of the cube (‘Delian problem’): if b = 2 a, then x is the desired solution of the equation for the duplication of the cube ( x3 = 2a3 ). Hippocrates [5] of Chios Folkerts, Menso (Munich) Bibliography mes T. L. Heath, A History of Greek Mathematics, Vol. 2, 1921, 258-260.

Geminus

(723 words)

Author(s): Folkerts, Menso (Munich) | Albiani, Maria Grazia (Bologna)
(Γέμινος; Géminos) [I]. [German version] [1] Astronomer and mathematician Astronomer and mathematician from the school of Posidonius. Almost nothing is known about his life. The height of his creativity was around 70 BC. It is generally accepted that he lived in Rhodes. The only fully extant treatise by G. is the ‘Introduction to Astronomy’ (Εἰσαγωγὴ εἰς τὰ φαινόμενα). It is in the tradition of  Eudoxus and  Aratus [4]. Similarly to the later writing by  Cleomedes, it is an elementary textbook on astrono…

Dositheus

(947 words)

Author(s): Schwemer, Anna Maria (Tübingen) | Folkerts, Menso (Munich) | Ego, Beate (Osnabrück) | Rist, Josef (Würzburg) | Gatti, Paolo (Trento)
(Δωσίθεος; Dōsítheos). [German version] [1] Jewish apostate Son of Drimylos, Jewish apostate. He is supposed to have saved the life of Ptolemy IV Philopator before the battle at Raphia (217 BC)(3 Macc. 1,3). Around 240 BC he was one of the two leaders of the royal secretariat and accompanied Ptolemy III in 225-24 on a trip in Egypt; he held the highest priestly office in Hellenistic Egypt around 222 as the priest of Alexander [4] the Great and the deified Ptolemies. PP 1/8,8; 3/9,5100. Schwemer, Anna Maria (Tübingen) Bibliography V. Tcherikover, A. Fuks, Corpus Papyrorum Judaicarum…

Sporus

(279 words)

Author(s): Folkerts, Menso (Munich) | Eck, Werner (Cologne)
[German version] [1] Mathematician, c. AD 200 (Σπόρος; Spóros) or Porus (Πόρος; Póros). It is unclear whether the two individuals of this name living around AD 200 are in fact the same person (v. [5]). S. or Porus wrote a (lost) compilation, Κηρία ( Keria), with extracts on the quadrature of the circle and the duplication of the cube [4. 226]. He criticized Archimedes' [1] approximation of the number pi (thus [1. 258,22]), provided his own solution to the problem of the duplication of the cube [1. 76-78; 4. 266-268] and rejected the Quadratrix of Hippias [5] of …
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