says that some people used the quadratices of Nikome ̄de ̄s and Hippias (usually thought to
be H E ̄) to trisect an angle. The bibliography lists three different accounts of
Deinostratos’ treatment of the quadratix.
Heath (1921) 1.225–230; DSB 4.103–105, I. Bulmer-Thomas; Knorr (1986) 80–86.
Ian Mueller
De ̄markhos (300 BCE – 100 CE)
C A, Chron. 1.140 (CML 6.1.1, p. 512), lists him, among other “ancients”
(P to T), as having propounded ineffective cures for epilepsy.
Fabricius (1726) 136.
PTK
De ̄me ̄trios (Math.) (250 – 300 CE)
Platonic geometer who discussed the properties of odd and even numbers; teacher of
P (P, in Plat. Remp. 2.23.14 Kroll), who met at Athens with C
L, Porphurios, and others, to celebrate P’s birthday (E, Pr. Ev.
10.3.1). Chronology and similarity of interests suggest, though not definitively, that our
De ̄me ̄trios may be identifiable with D (M).
PLRE 1 (1971) 247.
GLIM
De ̄me ̄trios (Music) (before ca 300 CE)
Author of a Peri logou sunaphe ̄s (perhaps On the Composition of Ratio, if it was a mathematical
treatise), of which only the title survives, cited by P in his commentary on
P’s Harmonics (92.25–26). Porphurios mentions De ̄me ̄trios several times in a discus-
sion on the correct use of the terms “ratio” (logos), “excess” (huperokhe ̄, i.e. the amount by
which the greater term exceeds the lesser) and “interval” (diaste ̄ma). He calls De ̄me ̄trios a
mathematical scientist (mathe ̄matikos), and names him in a list of writers who used the term
“interval” to mean “ratio,” just as P did when he referred to hemiolic, epitritic and
epogdoic intervals (rather than ratios) at Timaeus 36a–b. The list also includes P
Y, A, D ( H?), E, “and many other
canonic theorists (kanonikoi).”
RE 4.2 (1901) 2487 (#110), C. von Jan; Düring (1932).
David Creese
De ̄me ̄trios (Pythag.) (200 – 100 BCE)
Authored a treatise wherein he explained why the number four, one of He ̄rakle ̄s’ preroga-
tives (herculaneus numerus quaternaries), is particularly important for the healing art (P
28.64). Evidence is too meager to consider him a physician.
RE 4.2 (1901) 2850 (#119), Fr. Hultsch.
Bruno Centrone
DE ̄MARKHOS