  We derive the star formation histories of eight dwarf spheroidal (dSph) Milky
Way satellite galaxies from their alpha element abundance patterns. Nearly 3000
stars from our previously published catalog (Paper II) comprise our data set.
The average [alpha/Fe] ratios for all dSphs follow roughly the same path with
increasing [Fe/H]. We do not observe the predicted knees in the [alpha/Fe] vs.
[Fe/H] diagram, corresponding to the metallicity at which Type Ia supernovae
begin to explode. Instead, we find that Type Ia supernova ejecta contribute to
the abundances of all but the most metal-poor ([Fe/H] < -2.5) stars. We have
also developed a chemical evolution model that tracks the star formation rate,
Types II and Ia supernova explosions, and supernova feedback. Without metal
enhancement in the supernova blowout, massive amounts of gas loss define the
history of all dSphs except Fornax, the most luminous in our sample. All six of
the best-fit model parameters correlate with dSph luminosity but not with
velocity dispersion, half-light radius, or Galactocentric distance.
