# Search

###
Your search for **'dc_creator:( "Folkerts, Menso (Munich)" ) OR dc_contributor:( "Folkerts, Menso (Munich)" )'**
returned **57**
results.
Modify search

### Sort Results by Relevance | Newest titles first | Oldest titles first

## Leodamas

(261 words)

*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…

**Source:**Brill’s New Pauly

## Diocles

(2,746 words)

*Dioklês*). [German version] [1] Hero in Megara Hero in Megara. He supposedly died in battle, bravely covering a youth with his shield. At his grave boys competed for who could give the sweetest kiss. This agon, which took place every spring, was called Dioclea (Schol. Pind. Ol. 7,157; 13,156a; Theoc. 12,27-33 with Schol.: Aition). Perhaps the kisses represented farewell kisses repeated in the cult of the hero ([1]; to the contrary [2]). According to Schol. Aristoph. Ach.774 the agon was founded…

**Source:**Brill’s New Pauly

## Iulianus

(4,648 words)

**Source:**Brill’s New Pauly

## Eudoxus

(1,483 words)

*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…

**Source:**Brill’s New Pauly

## Theaetetus

(1,081 words)

*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…

**Source:**Brill’s New Pauly

## Nicomachus

(1,669 words)

*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 …

**Source:**Brill’s New Pauly

## Helicon

(372 words)

*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…

**Source:**Brill’s New Pauly

## Hero

(1,389 words)

*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…

**Source:**Brill’s New Pauly

## Leon

(1,337 words)

*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…

**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

## Apollonius

(7,446 words)

*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…

**Source:**Brill’s New Pauly

## Menaechmus

(496 words)

*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…

**Source:**Brill’s New Pauly

## Nicomedes

(1,542 words)

*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…

**Source:**Brill’s New Pauly

## Mesolabium

(99 words)

*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.

**Source:**Brill’s New Pauly

## Geminus

(723 words)

*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…

**Source:**Brill’s New Pauly

## Dositheus

(947 words)

*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…

**Source:**Brill’s New Pauly

## Sporus

(279 words)

*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 …

**Source:**Brill’s New Pauly

## Rhombus

(103 words)

*rhómbos*). [German version] [1] Geometric shape In the plane, a rectangle with four sides of equal length but with unequal angles (

*i.e.*, with two acute and two obtuse angles; Euc. 1, Def. 22; Censorinus, DN 83,14 Jahn). In three dimensions, a rhombus is the solid of revolution consisting of two cones with the same base (Archim. De sphaera et cylindro 1, def. 6). Folkerts, Menso (Munich) Bibliography

**1**T. L. Heath, The Thirteen Books of Euclid's Elements, vol. 1, 21925, 189

**2**A. Hug, s.v. Ῥόμβος (

*rhombus*), RE 1 A, 1069. [German version] [2] See Top see Top [German version] [3] See Rho…

**Source:**Brill’s New Pauly

## Mathematics

(6,466 words)

**Source:**Brill’s New Pauly

## Dionysodorus

(550 words)

*Dionysódōros*). [German version] [1] Taxiarch to Theramenes c. 400 BC Taxiarch to Theramenes, betrayed to the Thirty by Agoratus (Lys. or. 13,30; 39-42). The latter was taken to court in 399/98 BC by D.'s brother and brother-in-law, Dionysius, the speaker of the 13th oration written by Lysias. Strothmann, Meret (Bochum) [German version] [2] Theban and Olympic winner, envoy and participant in the battle of Issus Theban and Olympic winner. Sent as an ambassador to Darius [3] and taken prisoner together with other Greek ambassadors by Parmenion in …

**Source:**Brill’s New Pauly

## Anthemius

(604 words)

*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…

**Source:**Brill’s New Pauly

## Neusis

(124 words)

*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…

**Source:**Brill’s New Pauly

## Diodorus

(3,891 words)

*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, …

**Source:**Brill’s New Pauly

## Menelaus

(2,514 words)

**Source:**Brill’s New Pauly

## Aristaeus

(716 words)

*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…

**Source:**Brill’s New Pauly