The equal distances AB and AC balance in the directions AB and AC which diverge equally from the axis AD, making the equal angles CAD and DAB. Both directions and distances balance on the vertical axis AD.
31. The positions B and C in [Fig. 23], depending on balancing directions and distances, balance on the same axis. We should feel this balance of the positions A and B on the vertical axis even without any indication of the axis. We have so definite an image of the vertical axis that when it is not drawn we imagine it.
Fig. 24
In this case the two positions C and B cannot be said to balance, because there is no suggestion, no indication, and no visual image of any axis. It is only the vertical axis which will be imagined when not drawn.
32. Perfect verticality in relations of position suggests stability and balance. The relation of positions C-B in [Fig. 24] is one of instability.
Fig. 25
These two positions are felt to balance because they lie in a perfectly vertical relation, which is a relation of stability. Horizontality in relations, of position is also a relation of stability. [See Fig. 28, p. 21].
33. All these considerations lead us to the definition of Symmetry. By Symmetry I mean opposite directions or inclinations, opposite and equal distances, opposite positions, and in those positions equal, corresponding, and opposed attractions on a vertical axis. Briefly, Symmetry is right and left balance on a vertical axis. This axis will be imagined when not drawn. In Symmetry we have a balance which is perfectly obvious and instinctively felt by everybody. All other forms of Balance are comparatively obscure. Some of them may be described as occult.