The Compressibility of a substance, dependent on My Chemistry book states that (talking about compressibility equation):


  "A sample with Volume V is subjected to a pressure increase, delta P,
  and the resulting change in volume, change in V, is measured.  The
  ratio is divided by V; thus, the tabulated value depends only on the
  substance being measured and not on the geometry of the sample."


I'm not sure exactly how they are drawing this conclusion.  How does dividing by (-) volume cause the compressibility factor to not be dependent on the "geometry" of the sample?

Thanks.
If you apply an external pressure on an object and analyze the deformational response of the object (say using Hooke's law in 3D), you find that the state of stress and strain within the object are completely uniform and independent of direction within the object (if the object has direction-independent properties to begin with), irrespective of the shape of the object.  This is sort of the same kind of thing that happens in thermal expansion, where the object strains uniformly in all directions, and the strains are independent of the object shape.