The geometrical aberrations theory of a centered system is applied to calculate the third order aberrations of the optical system based on two spherical mirrors (the so-called Schwarzschild objective). The role of each of the third order field aberrations in the formation of the view field is analyzed. The scaling effect (i.e., the relationship between the optics' geometrical dimensions and the spatial resolution) is studied. The performance of a 21 x Schwarzschild objective (including the nonconcentric scheme) is investigated using a ray-tracing computer simulation. The tolerances of the axial and lateral alignments of the Schwarzs- child objective are found and the results are used to design a soft x-ray optical system based on multilayer mirrors to provide low geometrical aberrations (spatial resolution about 0.05 ?m) and a view field up to 300 ?m. Soft x-ray imaging microscope experiments demonstrate good accordance with the predicted performance of the optics. High resolution optics such as these can be a good basis for the optical instrumentation in soft x-ray microscopy, extreme ultraviolet lithography (EUVL), microanalysis, etc.