Geometrical Revisiting. Perspective whithout “veils”, or Cabri, Monge and Perspective

The principle of "intersection of the visual pyramid" and the basic notions of Monge's method of the double orthogonal projection are sufficient to create the system of representation which we are presenting here. Such system is rather versatile, it allows to realize both central and angular perspectives and therefore it is particularly useful for revisiting and "discovering" through the dynamism of Cabri (a software specially created for the teaching of geometry: cf. for example Pellegrino and Zagabrio 1996) some fundamental properties and characteristic concepts of perspective representation (such as vanishing points, horizon line, etc.), so as to achieve the comprehension of: – the genesis of the rules that are at the basis of various systems of perspective representation (for more information about the modes of application of such systems, see the handbooks for geometric drawing); – the origin of the concepts of improper point and improper straight line which are at the basis of perspective together with the operations of projection and section