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08815_Field_TCGG T580.txt
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1996-04-10
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petitio principii and could not serve as a mathematical
definition.
The alternative is to inscribe in the arc a sequence
of rectilinear contours of an increasing number of sides.
The sequence of these contours approaches a limit, and
the length of the arc is defined as the limit of this
sequence.
And what is true of the notion of length is true of
areas, volumes, masses, movements, pressures, forces,
stresses and strains, velocities, accelerations, etc., etc.
All these notions were born in a ‘linear’, ‘rational’ world
where nothing takes place but what is straight, flat, and
uniform. Either, then, we must abandon these elementary
rational notions—and this would mean a veritable
revolution, so deeply are these concepts rooted in our
minds; or we must adapt those rational notions to a