  We study the domain of validity of Perturbation Theory (PT), by comparing its
predictions for the reduced skewness, s_3, and kurtosis, s_4, of the projected
cosmological density field, with the results of N-body simulations. We
investigate models with different linear power spectra and consider as physical
applications both angular galaxy catalogues and weak lensing surveys. We first
find that the small-angle approximation for the predicted skewness provides a
good match to the exact numerical PT results. On the other hand, results from
non-linear simulated catalogues agree well with PT results on quasi-linear
angular scales, which correspond to scales larger than about 1 degree in the
applications we have considered. We also point out that, on smaller scale, the
projection effects tend to attenuate the effects of the strong nonlinearities
in the angular skewness and kurtosis.
