Ground-level events (GLEs) are large solar energetic-particle events with sufficiently hard spectra for GeV protons to be detected by neutron monitors at ground level. For each of 30 well-observed historic GLEs from four solar cycles, extending back to 1973, I have plotted onset times versus velocity^–1 for particles observed on the IMP-7 and 8, ISEE-3, Wind, and GOES spacecraft and by neutron monitors. A linear fit on such a plot for each GLE determines the initial solar particle release (SPR) time, as the intercept, and the magnetic path length traversed, as the slope, of the fitted line. Magnetic path lengths and SPR times are well determined by the fits and cannot be used as adjustable parameters to make particle and photon emission times coincide. SPR times follow the onsets of shock-induced type II radio bursts and the coronal height of the coronal mass ejection (CME)-driven shock at SPR time can be determined for GLEs spanning an interval of solar longitude of ~140 deg. For a given GLE, all particle species and energies diverge from a single SPR point at a given coronal height and footpoint longitude of the field line to the Earth. These heights tend to increase with longitudinal distance away from the source, a pattern expected for shock acceleration. Acceleration for magnetically well-connected large GLEs begins at ~2 solar radii, in contrast to non-GLEs that have been found to be strongly associated with shocks above ~3 solar radii. The higher densities and magnetic field strengths at lower altitudes may be responsible for the acceleration of higher-energy particles in GLEs, while those GLEs that begin above 3R _S may compensate by having higher shock speeds. These results support the joint dependence of maximum particle energy on magnetic field strength, injected particle density, and shock speed, all predicted theoretically.