y 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
modified rendering of the famous zodiacal ceiling of the Temple of
Denderah, in Egypt. A sun and its corona have been substituted for the
zodiacal signs and symbols which fill the centre of the original, for
except to an Egyptologist these are meaningless. In all essentials the
drawing faithfully follows the original--was traced, indeed, from a
measured drawing.

[Illustration: Figure 17. CEILING DECORATION FROM THE TEMPLE OF
DENDERAH]

Here is one of the most magnificent decorative schemes in the whole
world, arranged with a feeling for balance and rhythm exceeding the
power of the modern artist, and executed with a mastery beyond the
compass of a modern craftsman. The fact that first forces itself upon
the beholder is that the thing is so obviously mathematical in its
rhythms, that to reduce it to terms of geometry and number is a matter
of small difficulty. Compare the frozen music of these rhymed and
linked figures with the herded, confused, and cluttered compositions
of even our best decorative artists, and argument becomes
unnecessary--the fact stands forth that we have lost something
precious and vital out of art of which the ancients possessed the
secret.

It is for the restoration of these ancient verities and the discovery