
831.01
Our steel dividers have sharp, straightedged legs,
each tapering into sharp
points. We can call these dividers "scissors." Scissors
are dividers of either linear or
angular, i.e. circular, differentiation. We can even
make our explorations with some
superficial accommodation of the Greeks' propensity
for using a plane. For instance, we
can take a finite piece of paper, remembering (operationally),
however, that it has
"thickness" and "edges," which are in fact small area
faces. If it is a rectilinear sheet of
typewriter paper, we recognize that it has four minor
faces and two major faces. The
major faces we call "this side" and "the other side,"
but we must go operationally further
in our consideration of what the "piece of paper" is.
Looking at its edges with a
magnifying glass, we find that those surfaces round
over rather brokenly, like the
shoulders of a hillside leading to a plateau. We find
the piece of paper to be fundamentally
the same kind of entity as that which we have watched
the baker make as he concocts,
stirs, and thickens his piecrust dough, which, after
powdering with flour, can be formed
into a spherical mass and set upon a flourpowdered
surface to be progressively rolled into
a thick sheet that may be cut into separate increments
of the same approximate dimensions
as the "sheet" of typewriter paper.
