54. It is to be observed that single inversions in any direction, for
example the relation of attitudes I and II, II and III, III and IV,
IV and I, in Fig. 53, shows an opposition and Balance of Attitudes
upon the axis of inversion. The relation of positions I and II and
III and IV, the relation of the two groups on the left to the two
groups on the right, illustrates the idea of Symmetry of Attitudes,
the axis of balance being vertical. By Symmetry I mean, in all cases,
right and left balance on a vertical axis. All double inversions,
the relation of positions I and III, and II and IV, in Fig. 53, are
Attitude-Balances, not on axes, but on centers. The balance of these
double inversions is not symmetrical in the sense in which I use the
word symmetry, nor is it axial. It is central.