to one another. The very word geometry, which, of course, means
earth-measuring, proves this. For earth-measuring has to do with
the possibilities of the disposition of certain natural objects
with respect to one another, namely, with parts of the earth,
measuring-lines, measuring-wands, etc. It is clear that the system
of concepts of axiomatic geometry alone cannot make any assertions
as to the relations of real objects of this kind, which we will
call practically-rigid bodies. To be able to make such assertions,
geometry must be stripped of its merely logical-formal character
by the co-ordination of real objects of experience with the empty
conceptual frame-work of axiomatic geometry. To accomplish this,
we need only add the proposition:--Solid bodies are related, with
respect to their possible dispositions, as are bodies in Euclidean
geometry of three dimensions. Then the propositions of Euclid contain
affirmations as to the relations of practically-rigid bodies.

Geometry thus completed is evidently a natural science; we may in
fact regard it as the most ancient branch of physics. Its affirmations
rest essentially on induction from experience, but not on logical
inferences only. We will call this completed geometry "practical
geometry," and shall distinguish it in what follows from "purely
axiomatic geometry." The question whether the practical geometry
of the universe is Euclidean or not has a clear meaning, and its
answer can only be furnished by experience. All linear measurement
in physics is practical geometry in this sense, so too is geodetic
and astronomical linear measurement, if we call to our help the
law of experience that light is propagated in a straight line, and
indeed in a straight line in the sense of practical geometry.

I attach special importance to the view of geometry which I