For example, Desargues Theorem says that if corresponding sides of two triangles meet in three points lying on a straight line, then corresponding vertices lie on three concurrent lines. This illustrates a fact about incidences and has nothing to say about measurements, which is characteristic of pure projective geometry.
Projective geometry regards parallel lines as meeting in an ideal point at infinity.
A brief definition of projective geometry, by the author of an honours dissertation covering ideas from the areas of projective geometry and group theory. Construction exercises and a Geometer's Sketchpad file to download. This discussion of Pascal's theorem in terms of projective geometry includes an interactive application that lets you specify points on a conic and see how the theorem applies to them. From a course in Computer Graphics and Imaging. The classification includes quartic models of the projective plane, ruled cubics, and quadric surfaces.