closing boundary and that of the design itself;
and, _vice versa_, as the design becomes more pictorial in its appeal
and more complex and varied in its elements, the more we may combine the
leading motive or principle of line with secondary ones, or with
variations, since every fresh element, every new direction of line,
every new form introduced, demands some kind of re-echo to bring it into
relation with the other elements of the design, or parts of the
composition, whatever may be its nature and purpose.

Now, if we seek further the meaning and origin of this necessity of the
control of geometric lines and spaces in design, I think we shall find
it in the constructive necessities of architecture: for it is certainly
from architecture that we derive those typical spaces and panels the
designer is so often called upon to fill.

[Illustration (f067): The Parthenon: Sketch to Show Spaces Used for
Decorative Sculpture in Greek Architecture.]

[Origin of Geometric Decorative Spaces]

Lintel architecture--the Egyptian and the Greek--gave us the frieze,
both continuous, as in that of the Cella of the Parthenon, or divided by
triglyphs, which represented the ends of the beams of the primitive
timber construction; and the interstices left between these determined
the shape of the sculptured panel or slab inserted, and influenced the
character of its masses and the lines of its design, which was under the
necessity of harmonizing with the whole building (see illustration, p.
114[f067]).

[Illustration (f068): Tower of the Winds Athens BC 50]

The same may be said of the pediments. The angle of the low-pitched roof
left another interstice for the sculptor at each end of the building;
and I have elsewhere* pointed out the influence of the inclosing space
and the angles of the pediment of the Parthenon upon the arrangement of
the groups within it, and even upon the lines taken by some of the
figures, especially the reclining figures near the acute angles.

[*] See "Bases of Design."

Certain lines become inseparably associated with constructive
expression, and are used to emphasize it, as the vertical flutings of
the Doric column, by repeating the lines of the column itself, emphasize
its constructive expression of supporting the weight of the horizontal
lintels, the lines of which, repeated in the mouldings of the frieze and
cornice, are associated with level restfulness and secure r