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.
37.2 An abstractive class which is prime in respect to the formative condition of 'covering all the elements and abstractive classes constituting some assigned punct' is called an 'absolute prime.'
Evidently the condition satisfied by an absolute prime is regular for primes. The abstractive element deduced from an absolute prime is called an 'event-particle.' An event-particle is the route of approximation to an atomic event, which is an ideal satisfied by no actual event.
An abstractive class which is antiprime in respect to the formative condition of 'being a member of some assigned punct' is evidently an absolute prime. In fact this set of antiprimes is identical with the set of absolute primes.
An event-particle is an instantaneous point viewed in the guise of an atomic event. The punct which an event-particle covers gives it an absolute position in the instantaneous space of any moment in which it lies. Event-particles on a rect lie in the order derived from the puncts which they cover.
[37.3] The complete set of event-particles inhering in an event will be called the set 'analysing' that event. A set of event-particles can only analyse one event, and an event can be analysed by only one set of event-particles.