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Accordingly no moment can intersect a point-track more than once, and every moment intersects a point-track in one event-particle. Anyone who at the successive moments of α should be at the event-particles where those moments intersect a given point of α will be at rest in the timeless space of time-system α.
Let the time-system be named α, and let the moment of time-system α to which our quick perception of nature approximates be called M. Any straight line r in space α is a locus of points and each point is a point-track which is a locus of event-particles.
Namely, a straight line in the space of time-system β is the locus of those points of β which all intersect some one point-track which is a point in the space of some other time-system. Thus each point in the space of a time-system α is associated with one and only one straight line of the space of any other time-system β.
Each moment of α will intersect a point-track in one and only one event-particle. This property of the unique intersection of a moment and a point-track is not confined to the case when the moment and the point-track belong to the same time-system. Any two event-particles on a point-track are sequential, so that they cannot lie in the same moment.
A point-track is a locus of event-particles. It is defined by reference to one particular time-system, α say. Corresponding to any other time-system these will be a different group of point-tracks. Every event-particle will lie on one and only one point-track of the group belonging to any one time-system.
Also every duration which is part of a given duration intersects the stations of the given duration in loci which are its own stations. By means of these properties we can utilise the overlappings of the durations of one family that is, of one time-system to prolong stations indefinitely backwards and forwards. Such a prolonged station will be called a point-track.
The first axiom of congruence is that the opposite sides of any parallelogram are congruent. This axiom enables us to compare the lengths of any two segments either respectively on parallel rects or on the same rect. Also it enables us to compare the lengths of any two segments either respectively on parallel point-tracks or on the same point-track.
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