36.3 The essential characteristic of space is bound up in what may be termed the 'repetition property' of parallelism. This repetition property is an essential element in congruence as will be seen later; also the homogeneity of space depends on it. Examples of the repetition property are as follows: if a rect intersects any moment in one and only one punct, then it intersects each moment of that time-system in one and only one punct: if a level intersects any moment in one and only one rect, then it intersects any moment of that time-system in one and only one rect. But we must not apply the theory of repetition in parallelism mechanically without attention to the nature of the property concerned. For example, if a rect is incident in a moment, it does not intersect any other moment of the same time-system, and therefore à fortiori is not incident in any of them; and analogously for a level incident in a moment. 36.4 Puncts on a rect have an order which is derivative from the order of moments in a time-system and which connects the orders of various time-systems. The puncts on any given rect will respectively be incident in the moments of any time-system to which the rect is not parallel. Any moment of will contain one punct of , and any punct of will lie in one moment of . Thus the puncts of have derivatively the order of the moments of . Again let be another such time-system. Then the puncts of have derivatively the order of the moments of . But it is found that these two orders for puncts on are identical, namely there is only one order for the puncts on to be obtained in this way. By means of these puncts on rects the orders of moments of different time-systems are correlated. Thus the existence of order in the instantaneous spaces of moments is explained; but the theory of congruence has not yet been entered upon. 36.5 The set of puncts, rects and levels in any one moment thus form a complete three-dimensional euclidean geometry, of which the meaning of the metrical properties has not yet been investigated. It is no necessary here to enunciate the fundamental propositions [such as two puncts defining a rect, and so on] from which the whole theory can be deduced so far as metrical relations are not concerned. CHAPTER X FINITE ABSTRACTIVE ELEMENTS 37. Absolute Primes and Event-Particles. 37.1 It follows from the principles of convergence to simplicity with diminution of extent that, for exhibiting the relations between events in their utmost simplicity, abstractive elements of minimum complexity are required, that is, elements which converge towards the ideal of an atomic event. This requisite exacts that the formative condition from which the 'atomic' element is deduced should be such as to impose the minimum of restriction on convergence.