  We have developed a technique to systematically discover and study
high-redshift supernovae that can be used to measure the cosmological
parameters. We report here results based on the initial seven of >28 supernovae
discovered to date in the high-redshift supernova search of the Supernova
Cosmology Project. We find a dispersion in peak magnitudes of sigma_{M_B} =
0.27 this dispersion narrows to sigma_{M_B,corr} = 0.19 after "correcting" the
magnitudes using the light-curve "width-luminosity" relation found for nearby
(z <= 0.1) type Ia supernovae from the Calan/Tololo survey (Hamuy et al. 1996).
Comparing lightcurve-width-corrected magnitudes as a function of redshift of
our distant (z = 0.35-0.46) supernovae to those of nearby type Ia supernovae
yields a global measurement of the mass density, Omega_M = 0.88^{+0.69}_{-0.60}
for a Lambda = 0 cosmology. For a spatially flat universe (i.e., Omega_M
+Omega_Lambda = 1), we find Omega_M = 0.94 ^{+0.34}_{-0.28} or, equivalently, a
measurement of the cosmological constant, Omega_Lambda = 0.06 ^{+0.28}_{-0.34}
(<0.51 at the 95% confidence level). For the more general Friedmann-Lemaitre
cosmologies with independent Omega_M and Omega_Lambda, the results are
presented as a confidence region on the Omega_M-Omega_Lambda plane. This region
does not correspond to a unique value of the deceleration parameter q_0. We
present analyses and checks for statistical and systematic errors, and also
show that our results do not depend on the specifics of the width-luminosity
correction. The results for Omega_Lambda-versus-Omega_M are inconsistent with
Lambda-dominated, low density, flat cosmologies that have been proposed to
reconcile the ages of globular cluster stars with higher Hubble constant
values.
