At the Tevatron Collider, the E-710 Collaboration has measured the slope of the elastic scattering cross section up to \t\ = 0.65 (GeV /c)2, at square root s = 1800 GeV. The data clearly show a transition from the region in which the shape of the scattering is dominated by the hadronic matter form factor of the nucleon to the region in which the nucleon develops a sharp edge, i.e., a disk-like behavior. This transition is interpreted as the onset of asymptopia.