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5
Relativity: The Special and General Theory
possible relative position of practically rigid bodies.¹
)
Geometry which has been supplemented i
this way is then to be treated as a branch of physics. We can now legitimately ask as to the "truth"
of geometrical propositions interpreted in this way, since we are justified in asking whether these
propositions are satisfied for those real things we have associated with the geometrical ideas. In
less exact terms we can express this by saying that by the "truth" of a geometrical proposition in
this sense we understand its validity for a construction with rule and compasses.
Of course the conviction of the "truth" of geometrical propositions in this sense is founded
exclusively on rather incomplete experience. For the present we shall assume the "truth" of the
geometrical propositions, then at a later stage (in the general theory of relativity) we shall see that
this "truth" is limited, and we shall consider the extent of its limitation.
Next: The System of Co?ordinates
Notes
1
)
It follows that a natural object is associated also with a straight line. Three points A, B and C on
a rigid body thus lie in a straight line when the points A and C being given, B is chosen such that
the sum of the distances AB and BC is as short as possible. This incomplete suggestion will suffice
for the present purpose.
Relativity: The Special and General Theory