Physical Meaning of Geometrical Propositions
Section One
Euclidean Geometry as a Mathematical System, vs. Euclidean Geometry as a Physical Geometry.
... we now supplement the propositions of Euclidean geometry by the single proposition that two points on a practically rigid body always correspond to the same distance (line-interval), independently of any changes in position to which we may subject the body, the propositions of Euclidean geometry then resolve themselves into propositions on the possible relative position of practically rigid bodies. (p. 5)
The abstract notion of "distance" in Euclidean geometry is interpreted in terms of this physical assumption; in other words, a physical meaning is given by this assumption. And this changes the abstract geometry into a physical geometry, which may become true or false in the physical world.
See also Riemann and Helmholz.
Last modified, April 18, 2002. (c) Soshichi Uchii
suchii@bun.kyoto-u.ac.jp
