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