  We demonstrate that the aperture mass as a measure for cosmic shear closely
approximates (to better than ~5%) the scaled and shifted power spectrum of the
projected mass density. This cosmological weak-lensing information can thus be
used to directly infer the projected matter power spectrum with high accuracy.
As an application, we show that aperture-mass observations can be used to
constrain the cosmic density parameter and the power-spectrum amplitude. We
show that, for a particular example, it should be possible to constrain Omega_0
to within ~ +/- 27%, and sigma_8 to within ~ +/- 8% using weak-shear data on a
square-shaped field of 8 degrees side length.
