multiplying illustrations, he would only be going over ground already
covered in his book _Projective Ornament_ and in his second Scammon
lecture.

Of course this elaborate mechanism for producing quite obvious and
even ordinary decorative motifs may appear to some readers like
Goldberg's nightmare mechanics, wherein the most absurd and intricate
devices are made to accomplish the most simple ends. The author is
undisturbed by such criticisms. If the designs dealt with in this
chapter are "obvious and even ordinary" they are so for the reason
that they were chosen less with an eye to their interest and beauty
than as lending themselves to development and demonstration by an
orderly process which should not put too great a tax upon the patience
and intelligence of the reader. Four-dimensional geometry yields
numberless other patterns whose beauty and interest could not possibly
be impeached--patterns beyond the compass of the cleverest designer
unacquainted with projective geometry.

[Illustration: Figure 16.]

The great need of the ornamentalist is this or some other solid
foundation. Lacking it, he has been forced to build either on the
shifting sands of his own fancy, or on the wrecks and sediment of the
past. Geometry provides this sure foundation. We may have to work hard
and dig deep, but the results will be worth the effort, for only on
such a foundation can arise a temple which is beautiful and strong.

In confirmation of his general contention that the basis of all
effective decoration is geometry and number, the author, in closing,
desires to direct the reader's attention to Figure 17 a slightly