Attitudes
Relations of Position in Different Attitudes
50. Given any relation of positions (directions, distances, intervals), it may be turned upon a center and so made to take an indefinite number and variety of attitudes. It may be inverted and the inversion may be turned upon a center, producing another series of attitudes. Except in cases of axial balance, the attitudes of the second series will be different from those of the first.
In this case the relation of positions being turned upon a center changes its attitude, while the positions within the group remain relatively unchanged. There is no change of shape.
In this case the same group has been inverted, and a second series of attitudes is shown, differing from the first series.
In this case, however, which is a case of axial balance, the inversion of the group and the turning of the inversion on a center gives no additional attitudes.
51. Among all possible attitudes there are four which are principal or fundamental, which we may distinguish as follows:—
These principal attitudes are: First, I, the original attitude, whatever it is; second, II, the single inversion of that attitude, to the right on a vertical axis; third, III, the double inversion of the original attitude, first to the right then down; and, fourth, IV, the single inversion of the original position, down across the horizontal axis.