  We set new constraints on a seven-dimensional space of cosmological
parameters within the class of inflationary adiabatic models. We use the
angular power spectrum of the cosmic microwave background measured over a wide
range of \ell in the first flight of the MAXIMA balloon-borne experiment
(MAXIMA-1) and the low \ell results from COBE/DMR. We find constraints on the
total energy density of the universe, \Omega=1.0^{+0.15}_{-0.30}, the physical
density of baryons, \Omega_{b}h^2=0.03 +/- 0.01, the physical density of cold
dark matter, \Omega_{cdm}h^2=0.2^{+0.2}_{-0.1}$, and the spectral index of
primordial scalar fluctuations, n_s=1.08+/-0.1, all at the 95% confidence
level. By combining our results with measurements of high-redshift supernovae
we constrain the value of the cosmological constant and the fractional amount
of pressureless matter in the universe to 0.45<\Omega_\Lambda<0.75 and
0.25<\Omega_{m}<0.50, at the 95% confidence level. Our results are consistent
with a flat universe and the shape parameter deduced from large scale
structure, and in marginal agreement with the baryon density from big bang
nucleosynthesis.
