B), whose ratio to each other varies with the direction of the
curve. Then, if the right lines which form the curve at _c_ (fig. A) be
increased, we have the figure _c d e_, that is, the apparent
interruption of the curve is an increased part of the curve itself. To
the mathematical reader we can explain our meaning more clearly, by
pointing out that, taking _c_ for our origin, we have _a c_, _a e_, for
the co-ordinates of _e_, and that, therefore, their ratio is the
equation to the curve. Whence it appears, that, when any curve is broken
in upon by a building composed of simple vertical and horizontal lines,
the eye is furnished, by the interruption, with the equation to that
part of the curve which is interrupted. If, instead of square forms, we
take obliquity, as _r s t_ (fig. C), we have one line, _s t_, an
absolute break, and the other _r s_, in false proportion. If we take
another curve, we have an infinite number of lines, only two of which
are where they ought to be. And this is the true reason for the constant
introduction of features which appear to be somewhat formal, into the
most perfect imaginations of the old masters, and the true cause of the
extreme beauty of the groups formed by Italian villages in general.
145. Thus much for the mere effect on the eye. Of correspondence with
national character, we have shown that we must not be disappointed, if
we find little in the villa.
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