line. Now a straight line, or a plane, is by this definition a curve,
since every point in it is subject to one and the same law of position.
A plane may, indeed, be considered a part of any curved surface you
please, if you only take that surface on a sufficiently large scale.
Thus, the surface of water conforms to the surface of a sphere eight
thousand miles in diameter; but, as the arc of such a circle would arch
up from a chord ten feet long by only the ten-millionth part of an
inch, the surface of water in a cistern may be considered a plane. But
no figure or outline can be composed of a single plane or a single
straight line; nor can the position of more than two straight lines,
not parallel, be defined by a single simple law of position of the
points in them. We may, therefore, regard it as the first deduction
from our fundamental canon, that figures with curving outline are in
general more beautiful than those composed of straight lines. The laws
of their formation are simpler, and the eye, sweeping round the
outline, feels the ease and gracefulness of the motion, recognizes the
simplicity of the law by which it is guided, and is pleased with the
result.

Our second deduction relates principally to rectilinear figures; it is,
that symmetry is in general, and particularly in rectilinear figures,
more beautiful than irregularity. It requires, in general, simpler laws
to produce symmetry than to produce what is unsymmetrical; since the
corresponding parts in a symmetrical figure are instinctively
recognized as flowing from one and the same law. This preference for
symmetry is, however, frequently subordinated to higher demands of the
fundamental canon. If the outline be rectilineal, simplicity of law
produces symmetry, and variety of result can be attained only at the
expense of simplicity in the law. But in curved outlines it frequently
happens, that, with equally simple laws, we can obtain much greater