On the basis of a nine-parameter expanding source model that includes special relativity, quantum statistics, resonance decays, and freeze-out on a realistic hypersurface in spacetime, we analyze in detail invariant {pi}{sup +}, {pi}{sup {minus}}, K{sup +}, and K{sup {minus}} one-particle multiplicity distributions and {pi}{sup +} and K{sup +} two-particle correlations in nearly central collisions of Si+Au at p{sub lab}/A=14.6thinspGeV/c. By considering separately the one-particle data and the correlation data, we find that the central baryon density, nuclear temperature, transverse collective velocity, longitudinal collective velocity, and source velocity are determined primarily by one-particle multiplicity distributions and that the transverse radius, longitudinal proper time, width in proper time, and pion incoherence fraction are determined primarily by two-particle correlations. By considering separately the pion data and the kaon data, we find that although the pion freeze-out occurs somewhat later than the kaon freeze-out, the 99{percent} confidence-level error bars associated with the two freeze-outs overlap. By constraining the transverse freeze-out to the same source time for all points with the same longitudinal position and by allowing a more flexible freeze-out in the longitudinal direction, we find that the precise shape of the freeze-out hypersurface is relatively unimportant. By regarding the pion and kaon one-particlemore » data to be unnormalized, we find that the nuclear temperature increases slightly, but that its uncertainty increases substantially. By including proton one-particle data (which are contaminated by spectator protons), we find that the nuclear temperature increases slightly. These detailed studies confirm our earlier conclusion based on the simultaneous consideration of the pion and kaon one-particle and correlation data that the freeze-out temperature is less than 100 MeV and that both the longitudinal and transverse collective velocities{emdash}which are anticorrelated with the temperature{emdash}are substantial. We also discuss the flaws in several previous analyses that yielded a much higher freeze-out temperature of approximately 140 MeV for both this reaction and other reactions involving heavier projectiles and/or higher bombarding energies. thinsp {copyright} {ital 1998} {ital The American Physical Society}« less