87. Any line or linear progression may be turned upon a center, and so
made to take an indefinite number and variety of attitudes. It may be
inverted upon an axis, and the inversion may be turned upon a center
producing another series of attitudes which, except in the case of
axial symmetry in the line, will be different from those of the first
series.
[Illustration: Fig. 112]
In this case the line changes its attitude.
[Illustration: Fig. 113]
In this case I have inverted the line, and turning the inversion upon a
center I get a different set of attitudes.
[Illustration: Fig. 114]
In this case, which is a case of axial symmetry in the line, the
inversion gives us no additional attitudes.