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(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…


(6,466 words)

Author(s): Høyrup, Jens (Roskilde) | Folkerts, Menso (Munich)
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 traditions, even though some sources give a glimpse of the mathematics of ‘lay’ practitioners. When scribes were concerned with the properties of mathematical objects, the purpose was always to calculate something. That is always true in professional practice, but it also holds for school texts, even when these deal with situations …


(550 words)

Author(s): Strothmann, Meret (Bochum) | Badian, Ernst (Cambridge, MA) | Folkerts, Menso (Munich) | Ameling, Walter (Jena) | Montanari, Franco (Pisa)
(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. 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 …


(272 words)

Author(s): Folkerts, Menso (Munich)
[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…


(5,673 words)

Author(s): Walter, Uwe (Cologne) | Döring, Klaus (Bamberg) | Ameling, Walter (Jena) | Knell, Heiner (Darmstadt) | Folkerts, Menso (Munich) | Et al.
[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. …

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…


(143 words)

Author(s): Folkerts, Menso (Munich)
[German version] In the same way as postulates, axioms were presumably introduced in conflict with Eleatic philosophy in order to enable the acceptance of the existence of the manifold [1. 322-325; 2; 3]. According to Aristotle, axioms are central to every branch of knowledge, particularly the law of contradiction and the principle of the excluded middle (Metaph. Γ 3,1005a19-b27); for the organization of the fundamental principles of a branch of knowledge wherein proof is sought see Aristot. An. p…


(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…


(132 words)

Author(s): Wiesehöfer, Josef (Kiel) | Folkerts, Menso (Munich)
[German version] [1] Prisoner of war from Pedasa Prisoner of war from Pedasa, who, according to Hdt. 8,104f., as a eunuch, had become one of the closest confidants of  Xerxes I and is said to have taken his revenge on the slave trader Panionius (Ath. 6,266e attests that the story was well known).  Eunuchs Wiesehöfer, Josef (Kiel) Bibliography 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 …


(261 words)

Author(s): Engels, Johannes (Cologne) | Folkerts, Menso (Munich)
(Λεωδάμας; 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…


(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…


(4,648 words)

Author(s): Giaro, Tomasz (Frankfurt/Main) | Nutton, Vivian (London) | Franke, Thomas (Bochum) | Johnston, Sarah Iles (Princeton) | Montanari, Franco (Pisa) | Et al.
Epithet of many gentilicia [1]. Famous persons: the jurist Salvius I. [1]; the doctor I. [2]; the emperor I. [11], called ‘Apostata’; the bishops I. [16] of Aeclanum and I. [21] of Toledo. [German version] [1] L. Octavius Cornelius P. Salvius I. Aemilianus Roman jurist, 2nd cent. AD Jurist, born about AD 100 in North Africa, died about AD 170; he was a student of  Iavolenus [2] Priscus (Dig. 40,2,5) and the last head of the Sabinian law school (Dig. 1,2,2,53). I., whose succession of offices is preserved in the inscription from Pupput, provi…


(3,100 words)

Author(s): Folkerts, Menso (Munich) | Frede, Michael (Oxford) | Matthaios, Stephanos (Cologne) | Berger, Albrecht (Berlin) | Groß-Albenhausen, Kirsten (Frankfurt/Main) | Et al.
[German version] I Greek (Θεοδόσιος/ 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. …


(385 words)

Author(s): Folkerts, Menso (Munich)
[German version] (Δεινόστρατος; 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…


(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…


(162 words)

Author(s): Folkerts, Menso (Munich)
[German version] (Θυμαρίδας; 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…


(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…
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