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## 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

## Theodosius

(3,100 words)

*Theodósios*). [German version] [I 1] Greek mathematician and astronomer, 2nd/1st cent. BC Greek mathematician and astronomer. Folkerts, Menso (Munich) [German version] I. Life and works According to Str. 12,4,9, T. was one of the most important men in Bithynia; the birthplace Tripoli given in the Suda (s. v. Θ.) may relate to another T. As Strabo also names T.’ sons as important mathematicians, T. must belong in the 2nd half of the 2nd cent. BC, or, at the latest, the 1st half of the 1st. …

**Source:**Brill’s New Pauly

## Deinostratus

(385 words)

*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 (τετραγωνίζουσα). This curve, said to have already been used by Hippias of Elis for the trisection…

**Source:**Brill’s New Pauly

## Autolycus

(734 words)

*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…

**Source:**Brill’s New Pauly

## Thymaridas

(162 words)

*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 (

*euthygrammikós*, 'rectilinear'; ibid. 27,4), because they can only be set out in one dimension. The name 'Flower of T.' (Θυμαρίδειον ἐπάνθημα,

*Thymarídeion epánthēma*) is gi…

**Source:**Brill’s New Pauly

## Carpus

(196 words)

*Kárpos*). [German version] [1] Son of Zephyrus and a certain Hore Handsome youth, son of Zephyrus and of a certain Hore ( Horae). He organizes a swimming race with Calamus, his best friend, but drowns in the event. In mourning, his friend kills himself and is turned into reeds. C. is turned into a crop of the field (Nonnus, Dion. 11,385-481). Frey, Alexandra (Basle) [German version] [2] C. of Antioch Mathematician A mathematician, who lived presumably in the 1st or 2nd cent. AD. Information on him is given in four fragments by Pappus (8,3), Proclus (in Euc…

**Source:**Brill’s New Pauly

## Theodorus

(7,286 words)

*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 …

**Source:**Brill’s New Pauly

## Ptolemaeus

(19,876 words)

*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…

**Source:**Brill’s New Pauly

## Hypsicles

(603 words)

*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…

**Source:**Brill’s New Pauly

## Archimedes

(2,119 words)

**Source:**Brill’s New Pauly

## Euclides

(2,633 words)

*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 …

**Source:**Brill’s New Pauly

## Pappus of Alexandria

(727 words)

*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…

**Source:**Brill’s New Pauly

## Duplication of the Cube

(1,109 words)

*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*32). The problem thus…

**Source:**Brill’s New Pauly

## Zenodorus

(744 words)

*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 …

**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