with which their achievements are accomplished. We seek in all things
simplicity and unity. In Nature we have faith that there is such unity,
even in the midst of the wildest diversity. We honor intellectual
conceptions in proportion to the greatness of their consequences and to
the simplicity of their assumptions. Laws of form are beautiful in
proportion to their simplicity and to the variety which they can
comprise in unity. The beauty of forms themselves is in proportion to
the simplicity of their law and to the variety of their outline.

This last sentence we regard as the fundamental canon concerning
beauty,--governing, with a slight change of terms, beauty in all its
departments.

Beginning with the fundamental division of figures into curvilinear and
rectilinear, this _dictum_ decides, that, in general, a curved outline
is more beautiful than a right-lined figure. For a straight-lined
figure necessarily requires at least half as many laws as it has sides,
while a curvilinear outline requires, in general, but a single law. In
a true curve, every point in the whole line (or surface) is subject to
one and the same law of position. Thus, in the circle, every point of
the circumference is subject to one and the same law,--that it must be
at a certain distance from the centre. Half a dozen other laws, equally
simple, might be named, which in like manner govern every point in the
circumference of a circle: for instance, the curve bends at every point
by a certain fixed but infinitesimal amount, just enough to make the
adjacent points to be equally near the centre. Or, to take another
example, every point of the elastic curve, that is, of the curve in
which a spring of uniform stiffness can be bent by a force applied at
the ends of the spring, is subject to this very simple law, that the
curve bends in exact proportion to its distance from a certain straight