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[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 sect…

(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 (Göttinge…

[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.

(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…

(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 I, 1957, 230-236, no. 127 M. Hengel, Juden, Griechen und Barbaren, in: SBS 76, 1976, 55, 125. [German version] [2] Officer, fought on the side Judas Maccabaeus Officer, fought on the side of  Judas Maccabaeus. Together with Sosipater, he destroyed a Syrian garrison left in eastern Jordan by Timotheus (2 Macc. 12,19). Timotheus himself fell into the hands of D.'s people, but he was set free (2 Macc. 12,24f.); he is probably identical t…

[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 …

(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 Rhombus see Rhombus

Almost all we know about the mathematics of the pre-Greek cultures of the Ancient Near East, essentially Mesopotamian and Egyptian mathematics, originates from written sources. These are mainly from the scribal…

(Διονυσόδωρος; 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.…

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[German version] (νεῦσις/ 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 …

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(Μενέλαος/Menélaos, Attic Μενέλεως/Menéleos; Latin Menelaus). [German version] [1] Ruler of Sparta, married to Helena A significant character in the cycle of myths about the Trojan War ( Troy: Cycle of myths). A younger brother of Agamemnon, who ruled the most significant power centre in Greek myth, Mycene, by marriage to Zeus's daughter Helen ( Helene [1]; their only child was a daughter, Hermione) M.…

(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 Autonoe, a daughter of Cadmus (Hes. Theog. 977)…

(ὁ τοῦ κύκλου τετραγωνισμός/ ho toû kýklou tetragōnismós, Latin quadratura circuli). …

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[German version] (Eυτόκιος; 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] ( …

[German version] [1] see Groma see  Groma (surveying) Folkerts, Menso (Munich) [German version] [2] see Clocks see  Clocks (time measurement) Folkerts, Menso (Munich) [German version] [3] Arithmetic technical term Arithmetic technical term from Greek numerical theory. The term was adopted from geometry, where the 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…

[German version] I Greek (Φίλων/ 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. …

[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…