Abstract
In the contribution, we talk about synthetic methods in the projective extension of the real plane or three-dimensional space for solving problems of projective incidence and affine geometry. We use the concept of von Staudt's "Wurf" , defined in his Beiträge zur Geometrie der Lage, and the derived property that cross-ratios are invariant under projective transformations.
The concept of choosing an infinite hyperplane is used for making hypothesis in an affine space to solve projective problems and vice-versa. Insight into the von Staudt's constructions on the projective scale is given.
The methods are shown on some examples in elementary planimetry and stereometry.