ABSTRACT
IN the course of past chapters we have seen how the simple topological notions with which the child begins to construct the concept of space were transformed concurrently into projective and euclidean concepts. The first of these, embracing perspective, sections, projections and plane rotations, results from the co-ordination of viewpoints, while the second derives from the conservation of straight lines, parallels, angles, and lastly, general co-ordinate systems. Although we have not yet had occasion to make a detailed study of euclidean metrics, 2 it is nevertheless already clear that the concepts of projective and euclidean space develop together and are mutually interdependent. This conclusion was confirmed afresh by the findings of the last chapter. These showed that the construction of physical reference frames, the final stage in the evolution of basic euclidean concepts, proceeded side by side with the general co-ordination of viewpoints, the salient feature of projective space (see Chapter VIII).
