Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

INVARIANCE 191
these are then projected from FV respectively into
Pi',, P, P3',..., so that we have finally P1, P2, P,..-,
corresponding respectively to Pi', P2', P3',..., as required by the given transformation.
The oo3 projective transformations of form (I) are
included in a yet larger class of projective transformations
of the plane, which latter are included in a still larger
L/
P.
\ \P,
FIG. 24.
class of projective transformations of (ordinary) space,
and so on for spaces of higher dimensionality. Imagine
two planes r and ir' in ordinary space; let F be some
figure in r; let O be a point in neither plane; the lines
through O and the points of F project (as we say) the
latter points into points of -r' constituting a figure F'.
F and F' have certain properties in common; that is, certain properties of a figure are invariant under projection.