A partial-wave analysis of all antiproton-proton scattering data below 925 MeV/c antiproton laboratory momentum is presented. The method used is adapted from the Nijmegen phase-shift analyses of pp and np scattering data. The Nijmegen 1993 antiproton-proton database, consisting of 3646 antiproton-proton scattering data, is presented and discussed. The best fit to this database results in chi^2_min/Ndata = 1.043. The pseudovector coupling constant of the charged pion to nucleons is determined to be (f_c)^2 = 0.0732(11) at the pion pole, where the error is statistical.