geometry he is connected with a construction of the dodecahedron. Along with Pythagoras,
Hippasos was one of the founders of mathematical harmonics; he developed the theory of
proportions in its application to harmonics (A14–15) and carried out acoustic experiments
(A12–13). To already known harmonious intervals (octave, fifth and fourth) he added a
double octave (4:1) and a twelfth (3:1). Hippasos, probably, was the first to connect the pitch
of a sound with frequency of vibration (A13).
DK 18; K. von. Fritz, “The discovery of incommensurability by Hippasos of Metapontum,” Annals of
Mathematics 46 (1945) 242–264; van der Waerden (1979); Zhmud (1997); Zhmud (2006).
Leonid Zhmud
Hippias of E ̄lis (440 – 400 BCE)
Best known to us from P’s dialogues, where he is represented as a pretentious poly-
math, public performer, and “sophist.” It appears from Plato’s Protagoras (318d7–e5) that
Hippias taught what came to be called the quadrivium (arithmetic, geometry, astronomy, and
music). Most scholars have accepted that P refers to this Hippias when he says that
some people have carried out angle trisection on the basis of the quadratices (tetrago ̄nizousai
grammai) of Hippias and N (In Eucl. p. 272.1–10 Fr.) and that Hippias gave the
characterizing feature (sumpto ̄ma) of the same curve (356.6–11). The name “quadratix”
derives from the use of the curve to square a circle, but it has a simpler application to
dividing an angle in a given ratio. Scholars disagree about whether Hippias of E ̄lis used the
quadratix for squaring the circle as well as for dividing an angle in a given ratio and about
whether he knew anything about the quadratix under any name. There is no other known
Hippias to whom such knowledge can be ascribed.
DK 86; R.K. Sprague, ed., The Older Sophists (1972) 94–105; DSB 6.405–410, I. Bulmer-Thomas;
Knorr (1986) 80–86.
Ian Mueller
Hippobotos (200 – 180 BCE)
Wrote two books on ancient philosophers. Most of the fragments are preserved in
D L and offer biographical information. Non-biographical information
seems to come from his On the Sects, dealing only with Hellenistic ethical thought. (For the
rare name compare only LGPN 2.237.)
M. Gigante, “Frammenti di Ippoboto. Contributo alla storia della storiografia filosofica,” Ommagio a
Piero Treves (1983) 151–193; Mejer (1978) passim.
Jørgen Mejer
Hippokrate ̄s (Veterin.) (before ca 500 CE?)
Wrote on the medical treatment of horses, mules, and other beasts of burden; one of the
seven principal sources of the Hippiatrika. Concealed behind the famous name, his identity is
elusive, but apparently distinct from the Hippokrate ̄s to whom A addresses two
letters, the Hippokrate ̄s cited by Ibn al-Awwa ̄m, and the so-called “Ipocras Indicus,” and
certainly from the Hippokrate ̄s to whom, along with G, the Epitome ̄ of the Hippiatrika is
attributed in MSS. Although he does not name any sources, the author of the Hippokrate ̄s-
extracts in the Hippiatrika apparently drew upon the C D-Mago ̄n tradition,
HIPPIAS OF E ̄LIS