ABSTRACT
AS distinct from elementary topological relations which are concerned simply with the object as a thing in itself and with its various features taken in turn, we have shown that projective concepts imply a comprehensive linking together of figures in a single system, based on the co-ordination of a number of different viewpoints. But side by side with the development of this organized complex of viewpoints there also takes place a co-ordination of objects as such. This leads ultimately to the idea of euclidean space, the concepts of parallels, angles and proportion providing the transition between the two systems. Such a co-ordination of objects naturally assumes the conservation of distance, together with the evolution of the notion of ‘displacement’ or congruent transformation of spatial figures, culminating in the construction of systems of reference, or co-ordinates.
