the properties of the simplest multiple (mn:n) and epimoric ((n+1):n) ratios; (3) seven sub-
sequent propositions (10–16) wherein the properties of simple musical intervals are shown
to be analogous to those of the ratios of props.1–9; (4) two propositions (17–18) locating the
“movable” notes in the scale by the method of concordance; (5) a final two propositions
(19–20) introducing the monochord and marking on it the bridge-positions corresponding
to the notes of a two-octave scale-system.
The Sectio owes as much to 4th c. developments in acoustics and harmonics as it does to
Euclidean mathematics. In the preface, the basic assumptions of Arkhutan acoustics (e.g.,
that sound is caused by impact, ple ̄ge ̄) are adopted and modified, apparently with the aim of
allowing mathematical propositions to be demonstrated on strings, in ways that suggest the
influence of theories akin to those expressed in the A O S and the
A P (11.6, 19.12, 19.23, 19.39). The Sectio is also a polemical text;
certain propositions (e.g. 16, 18) are clearly intended to refute not only the conclusions but
also the basic assumptions of Aristoxenian harmonics.
Ed.: MSG; H. Menge, Euclides Phaenomena et scripta musica (1916).
Düring (1932); A.D. Barker, “Methods and aims in the Euclidean Sectio Canonis,” JHS 101 (1981) 1–16;
A. Barbera, “Placing Sectio Canonis in historical and philosophical contexts,” JHS 104 (1984)
157 – 161; Barker (1989); A. Barbera, The Euclidean Division of the Canon (1991); A.D. Barker, “Three
approaches to canonic division,” Apeiron 24 (1991) 49–83; A.C. Bowen, “Euclid’s Sectio canonis and
the history of Pythagoreanism,” in Bowen (1991); O. Busch, Logos Syntheseos (1998); Mathiesen
(1999); S. Hagel, “Zur physikalischen Begründung der pythagoreischen Musikbetrachtung,” WS
114 (2001) 85–93; Barker (2007) ch. 14, 364–410.
David Creese
Eude ̄mos (Methodist) (ca 21 – 31 CE)
The irony-infused episode in T, Hist. 4.3 and 11, and the gossipy notice in P
29.20 name Eude ̄mos the Methodist as a personal physician to Tiberius’ son Drusus “the
Younger” and his wife, Liuilla (Liuia Iulia). Implicated long after Drusus’ death in 23,
Eude ̄mos was put on the rack in 31, “confessing” to murder by poisoning, a charge stem-
ming from a letter written by Apicata to Tiberius after the disgrace and execution of her ex-
husband Seianus; she conveniently committed suicide once the letter was sent. Liuilla’s
adultery with Eude ̄mos, as recorded by Pliny, “... was an easy frill” (Levick, 279 n. 151).
Only Tacitus’ innuendo suggests Eude ̄mos was named in Apicata’s letter; more likely it
simply stated that Seianus and Liuia had poisoned Drusus (whose death was quite likely to
have been “natural”). “[A doctor’s] professional duties at the time of the alleged murder
would ensure that the unfortunate Eude ̄mos... stood at the head of the list of candidates
for the rack” (Seager, 156).
Eude ̄mos was T’s student (C A, Acute 2.219 [Drabkin,
p. 286; CML 6.1.1, p. 278]), and under Eude ̄mos’ name is preserved a poetic version of a
theriac invented by A VIII P (G, Antid. 2.14 [14.185– 186
K.]; Tecusan, p. 339, rough translation), perhaps indicating that Themiso ̄n, who had emi-
grated from Syria to Italy, passed along to Eude ̄mos some of Antiokhos’ detailed knowledge
of pharmacology and toxicology, especially antidotes against snake bites, scorpion stings,
and spiders (cf. Gale ̄n, Antid. 2.17 [14.201–202 K.]). Eude ̄mos was one of the first physi-
cians to write about hudrophobia, as contracted from dog bites (P, Poisonous
Animals 1.4 [CMG 10.1.1, p. 5]), but assumed that hudrophobia was the same as melankho-
lia, a diagnosis refuted by Caelius Aurelianus (Acute 3.107–108 [Drabkin, p. 368; CML 6.1.1,
EUDE ̄MOS (METHODIST)