ABSTRACT
THE whole of this volume has been concerned with Euclidean notions and with measurement. That study has now been the subject of fourteen chapters in this book and of chs. XIII and XIV in C.C.S., where we analysed the growth of reference systems and coordinates. In conclusion, we will try to outline the construction of Euclidean space at the level of representation. The last chapter of C.C.S. (ch. XV) contains an attempt to classify the various kinds of operation entering into the elaboration first of topological, then of projective and finally of Euclidean notions. But metric operations as such are only touched on in that chapter. Hence the need to describe their evolution in brief synoptic outline. The details of the many operations involved need not detain us any longer, and instead we will concentrate our attention on operations involved in the two fundamental mechanisms of Euclidean thinking as revealed throughout the present work: the conservation of size and its measurement.
