Euthumene ̄s of Massalia (ca 550 – 510 BCE?)
Wrote a periplous of the Atlantic coast of Africa, describing the mouth of the Senegal
river, and its fauna, and suggested that the reflux of the Ocean up its estuary drove the rise
of the Nile; cf. H 2.20–21 and M P.
BNP 5 (2004) 235, K. Brodersen.
PTK
E A ⇒ D P
Eutokios of Askalo ̄n (ca 510 – 530 CE)
Wrote commentaries (extant) on A’ Sphere and Cylinder (inSC), Plane Equilibria and
Measure of the Circle, and A’ Ko ̄nica (inCo), the latter conceived together with a new
edition of the first four books of Apollo ̄nios (inCo 176.17–22). Eutokios’ scholia on P-
’s Almagest (inCo 218.11–12 Heiberg) are lost. He most probably worked in Alexandria
under A whom he may have succeeded among the late Neo-Platonist commen-
tators on A (Decorps-Foulquier 65). A T, named as a com-
panion, was Eutokios’ perhaps younger contemporary (inCo 168.5 Heiberg). Some have
speculated that Eutokios may have studied under I M (the elder), but
evidence shows only that the anonymous pupil of Isido ̄ros (see I M’
), who may also be responsible for part of pseudo-E Elements Book XV,
edited Eutokios’ commentary (Jones 170–172; Decorps-Foulquier 62 n.8, contra Cameron
1990).
Eutokios claimed to have been the first in his time to write a “valuable treatise” on
Archime ̄de ̄s (inSC 2.2–3 Heiberg), seemingly regarding the following:
- Clarity (saphe ̄neia) by which Eutokios either refers to clarifying difficult points or elliptic
explanations, or to rewriting, correcting or selecting manuscript readings considered
better according to his mathematical judgment. - Authority of classical authors: Eutokios attributes his “clearer” discovered or
reconstructed versions to recognized authors, so that his attempts to clarify often renovate
their past lessons. By contrast, his opinion of the intermediate tradition of textual
transmission is often poor. - Invention (heuresis): Eutokios emphasizes in his foreword to inSC that reading Archime ̄de ̄s
requires both precision and imagination. He twice provides his reader a detailed list
of constructions and demonstrations both filling a gap in Archime ̄de ̄s’ explanations
in SC II, and displaying the method of invention (tropos heureseo ̄s) of their inventors
(inSC 66.2–126.3, 152.3–208.6), whereby Eutokios displays his own talent as their
imitator.
Eutokios’ fidelity to late Neo-Platonist principles of philosophical and mathematical
exegesis, recalled in his foreword to inSC, may plausibly explain these characteristics. Euto-
kios both appeals to divine inspiration and to Ammo ̄nios’ episte ̄monike ̄ theo ̄ria as the ultimate
guarantee of his commentary’s value. Again, in his brief allusion to the kinship of arith-
metic and geometry as part of “mathematics” in general and the use of proportions in
particular (inCo 220.18–25), he probably refers to the late Neo-Platonist emphasis on
“general mathematics” and its specific contents, as found in Ammo ̄nios’ mentor P
or in M N.
EUTHUMENE ̄S OF MASSALIA