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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 …

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 …

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…

Autolycus

(734 words)

Author(s): Graf, Fritz (Columbus, OH) | Folkerts, Menso (Munich)
(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…

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…

Eudoxus

(1,483 words)

Author(s): Folkerts, Menso (Munich) | Nesselrath, Heinz-Günther (Göttingen) | Brodersen, Kai (Mannheim)
(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…

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…

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…

Mechanical method

(255 words)

Author(s): Folkerts, Menso (Munich)
[German version] The ‘Method (Ἔφοδος; 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…

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…

Aristaeus

(716 words)

Author(s): Schachter, Albert (Montreal) | Folkerts, Menso (Munich)
(Αρισταιο̃ς; 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…

Zenodorus

(744 words)

Author(s): Folkerts, Menso (Munich) | Matthaios, Stephanos (Cologne) | Bringmann, Klaus (Frankfurt/Main) | Neudecker, Richard (Rome)
(Ζηνόδωρος/ 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 …

Diocles

(2,746 words)

Author(s): Bloch, René (Berne) | Meister, Klaus (Berlin) | Hidber, Thomas (Berne) | Nutton, Vivian (London) | Folkerts, Menso (Munich) | Et al.
(Διοκλῆς; 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…

Rhombus

(103 words)

Author(s): Folkerts, Menso (Munich)
(ῥόμβος/ 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…

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…

Carpus

(196 words)

Author(s): Frey, Alexandra (Basle) | Folkerts, Menso (Munich)
(Κάρπος; 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…

Duplication of the Cube

(1,109 words)

Author(s): Folkerts, Menso (Munich)
(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). The problem thus…

Mathematics

(3,425 words)

Author(s): Folkerts, Menso (Munich)
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 investigated its own foundations; thus, practical considerations and directly numerical problems faded into the background. The main accomplish…

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…

Anthemius

(604 words)

Author(s): Leppin, Hartmut (Hannover) | Johne, Klaus-Peter (Berlin) | Folkerts, Menso (Munich)
[German version] [1] Praefectus praetorio Orientis 405-414 AD Probably sent to Persia as an envoy in AD 383, 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…
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