will be called 'an associated matrix for
,' and it is called 'the matrix including' that straight line.
A matrix is an associated matrix for many time-systems, but it is the matrix including only one straight line in each corresponding space. The family of time-systems for which a given matrix is an associated matrix is called a 'collinear' family. A whole family of parallel matrices are associated matrices for the same collinear family of time-systems, if any one matrix of the family is thus associated. In the space of any one time-system the straight lines included by a family of parallel associated matrices are said to be parallel.
46.3 A matrix intersects a moment in a rect. If the moment belong to a time-system with which the matrix is associated, this rect in the moment corresponds to the straight line included by the matrix in the sense that it has one particle occupying each of its points. A rect thus associated with a straight line will be said to 'occupy' it.
Thus the event-particles on a matrix
associated with a time-system
can be exhaustively grouped into mutually exclusive subsets in two distinct ways: (i)They can be grouped into the points of