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## Division of angles and circles

(923 words)

*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…

**Source:**Brill’s New Pauly

## Diophantus

(1,146 words)

*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…

**Source:**Brill’s New Pauly

## Land surveying

(895 words)

*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…

**Source:**Brill’s New Pauly

## Polyidus

(381 words)

*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…

**Source:**Brill’s New Pauly

## Attalus

(2,358 words)

*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 …

**Source:**Brill’s New Pauly

## Aristarchus

(2,018 words)

*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…

**Source:**Brill’s New Pauly

## Serenus

(635 words)

*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…

**Source:**Brill’s New Pauly

## Hippocrates

(5,685 words)

*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…

**Source:**Brill’s New Pauly

## Nicon

(255 words)

*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…

**Source:**Brill’s New Pauly

## Theon

(2,323 words)

*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…

**Source:**Brill’s New Pauly

## Number

(5,221 words)

*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…

**Source:**Brill’s New Pauly

## Quadrature of the circle

(1,369 words)

*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…

**Source:**Brill’s New Pauly

## Theudius

(210 words)

*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…

**Source:**Brill’s New Pauly

## Eutocius

(168 words)

*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]…

**Source:**Brill’s New Pauly

## Gnomon

(272 words)

*gnomon*describes the shape of an angle bar that remains when a smaller square is removed from a larger square. The Pythagoreans represented arithmetic series with geometrically arranged dots (pebbles) in the form of figures, so t…

**Source:**Brill’s New Pauly

## Philo

(5,673 words)

*Phíl*

*ōn*). [German version] [I 1] Athenian politician Athenian from Acharnae who was exiled by the Oligarchic regime in 404 BC (Triakonta). During the civil war, he lived as a

*metoikos*(resident without Attic citizenship) in Oropos awaiting the outcome of events. Following his return, when he applied to join the

*boulḗ*he was accused of cowardice and other misdemeanours at a dokimasia investigation (Dokimasia) (Lys. 31; possibly 398 BC). Walter, Uwe (Cologne) Bibliography Blass, vol.1, 480f. Th.Lenschau, A. Raubitschek, s.v. P. (2), RE 19, 2526f. …

**Source:**Brill’s New Pauly

## Mechanical method

(255 words)

*Éphodos*) of Archimedes [1] is our source for his mechanical method from which he derived geometric formulas. To compare the surfaces of two figures, he disassembled each into an infinite number of parallel lines and balanced them on a scale. On one side of the scale, one surface is hung up at one point, i.e., as a whole. On the other side, the surface is hung up along the entire arm, i.e., each layer remains where it is and acts with a different leverage. When ea…

**Source:**Brill’s New Pauly

## Axiom

(143 words)

**Source:**Brill’s New Pauly

## Mathematics

(3,425 words)

**Source:**Brill’s New Pauly

## Hermotimus

(132 words)

**1**P. Briant, Histoire de l'empire perse de Cyrus à Alexandre, 1996, 283-288

**2**P. Guyot, Eunuchen als Sklaven und Freigelassene, 1980, Register s.v. [German version] [2] Mathematician from Colophon of Colophon, mathematician. He continued …

**Source:**Brill’s New Pauly