This theorem, the theorems of 43.2 and the corresponding theorem for two families of parallel rects are examples of the repetition property of parallelism. It is evident that, given any three event-particles not on one rect or one point-track, a parallelogram can be completed of which the three event-particles are three corners, any one of the event-particles being at the junction of the adjacent sides through the three corners. In such a parallelogram opposite sides are always of the same denomination, namely both rects or both point-tracks; but adjacent sides may be of opposite denominations. 43.4 The event-particles occupying a point in the time-less space of a time-system a appear at the successive moments of as successively occupying the same point . If be any other time-system, then the point of the space of intersects a series of points of the space of in event-particles which lie on the successive moments of . These event-particles of thus occupy a succession of points of at a succession of moments of ; and we shall find that this locus of points is what is meant by a straight line in the space of . Thus the point in the space of correlates the successive points on a straight line of with the successive moments of . Thus in the space of the point of the space of appears as exemplifying the kinematical conception of a moving material particle traversing a straight line. It will appear later that, owing to the 'repetition property' of parallelism, the motion is uniform. 44. Matrices. 44.1 A level is obtained by taking a rect and an event-particle co-momental with , and by forming the locus of event-particles on rects through and intersecting , including also particles on the rect through and parallel to . The same level would be obtained by taking the particles on the rects intersecting and parallel to some one rect through which intersects . 44.2 Analogously to levels, a locus of event-particles called a 'matrix' is obtained by taking a rect and an event-particle which is not co-momental with , and by forming the locus of event-particles on rects or point-tracks through and intersecting , including also the event-particles on the rect through and parallel to . A 'matrix' is a two-dimensional plane in the four-dimensional geometry of event-particles. Levels and matrices together make up the complete set of such two-dimensional planes, and have the usual properties of such planes which need not be detailed here. 44.3 Matrices are also obtained by taking an event-particle and a point-track , and by forming the locus of event-particles on rects or point-tracks through and intersecting , including also event-particles on the point-track through and parallel to . Any matrix can be generated in either of the two ways. Furthermore matrices can be generated by the use of parallels in the same way as levels are generated as explained in 44.1 and as assumed in 43.4.