  The conic sections, as well as the solids obtained by revolving these curves,
and many of their surprising properties, were already studied by Greek
mathematicians since at least the fourth century B.C. Some of these properties
come to the light, or are rediscovered, from time to time. In this paper we
characterize the conic sections as the plane curves whose tangent lines cut off
from a certain similar curve segments of constant area. We also characterize
some quadrics as the surfaces whose tangent planes cut off from a certain
similar surface compact sets of constant volume. Our work is developed in the
most general multidimensional case.
