  We present predictions for cosmological parameter constraints from combined
measurements of second- and third-order statistics of cosmic shear. We define
the generalized third-order aperture mass statistics <M_ap^3> and show that it
contains much more information about the bispectrum of the projected matter
density than the skewness of the aperture mass. From theoretical models as well
as from LCDM ray-tracing simulations, we calculate <M_ap^2> and <M_ap^3> and
their dependence on cosmological parameters. The covariances including shot
noise and cosmic variance of M_ap^2, M_ap^3 and their cross-correlation are
calculated using ray-tracing simulations. We perform an extensive Fisher matrix
analysis, and for various combinations of cosmological parameters, we predict
1-sigma-errors corresponding to measurements from a deep 29 square degree
cosmic shear survey. Although the parameter degeneracies can not be lifted
completely, the (linear) combination of second- and third-order aperture mass
statistics reduces the errors significantly. The strong degeneracy between
Omega_m and sigma_8, present for all second-order cosmic shear measures, is
diminished substantially, whereas less improvement is found for the
near-degenerate pair consisting of the shape parameter Gamma and the spectral
index n_s. Uncertainties in the source galaxy redshift z_0 increase the errors
of all other parameters.
