Daryn LehouxHippasios of E ̄lis (before ca 400 CE?)
Author of a remedy for horses or cows preserved in the Hippiatrika (Hippiatrica Parisina 1148
= Hippiatrica Berolinensia 130.160). The remedy is attributed to Hippasios in the treatise of
H. Hippasios is called “E ̄leios”; according to S B there
were three cities called E ̄lis.
CHG v.1; McCabe (2007) 227.
Anne McCabe
Hippasos of Metapontum (520 – 480 BCE)
Student of P. Evidence of his natural philosophical doctrines is very scanty; if
he put them in writing this book was lost very early. Hippasos made fire the first principle
(18 A7 DK), regarded soul as fiery (A9) and the kosmos as finite and ever moving (A1).
The doxographical tradition frequently combines philosophical doctrines of Hippasos and
H, therefore it is difficult to say what exactly belongs to whom. Hippasos’
principle was reflected in P’ theory, who made all heavenly bodies rotate around
the Central Fire. Hippasos discovered irrational magnitudes, which left a profound trace in
Greek mathematics (the legend that he “disclosed” this Pythagorean secret arose from a
double meaning of the word arre ̄tos: “inexpressible in numbers” and “secret”). In solid
Ptolemy’s version of Hipparkhos’ model for solar motion © Lehoux and Massie.
With the Earth at the center of the kosmos, E, and looking out at the four cardinal divisions of
the heavens (vernal equinox at A, summer solstice at B, autumnal equinox at G, and winter
solstice at D), we know that the Sun takes different times to travel through each of the seasons
(viz., 94 ½ days from A to B, 92 ½ days from B to G, 88 1/8 days from G to D, and 90 1/8 days
from D back to A again). The problem then becomes how to model this mathematically. The
elegant solution adopted by Hipparkhos is to assume that the Sun does not actually move on circle
ABDG, but in fact moves uniformly on a different circle (QKLM), one that is not centered on the
Earth but is instead centered on Z. Looking out from the Earth at E, what was an apparent
motion of the Sun from A to B is actually a real motion from Q to K on the Sun’s own smaller
circle, and this should obviously take longer than the motion from L to M (since arc QK is longer
than arc LM), as it in fact does. (Adapted from Toomer, Ptolemy’s Almagest (1984) 154.)
HIPPASOS OF METAPONTUM