ABSTRACT
We have met two types of objective geometry: the geometry of succession and global resemblance, and the geometry of relations of position. There exists still a third: the geometry of simultaneity, of local similarity and of qualitative similarity. It is most interesting because it best recalls the methods of physicists. However, let us approach it indirectly. Let us first see what nature would look like were the network of simultaneities, local similarities, and qualitative similarities not isolated, but interwoven with the web of the relations of position which we have just constructed. Relations of position, in fact, actualize the maximum of an intuitive geometric order, the very ideal of an immediate apprehension and science of space. It is worth while observing all that the other adds to it, however; and later, we shall show that relations of position are self sufficient.
