We summarize the results of two experimental programs at the Alternating Gradient Synchrotron of BNL to measure the nuclear transparency of nuclei measured in the A(p, 2p) quasielastic scattering process near 90° in the pp center of mass. The incident momenta varied from 5.9 to 14.4 GeV/c. corresponding to 4.8<Q2<12.7 (GeV/c)2. Taking into account the motion of the target proton in the nucleus, the effective incident momenta extended from 5.0 to 15.8 GeV/c. First, we describe the measurements with the newer experiment, E850, which had more complete kinematic definition of quasielastic events. E850 covered a larger range of incident momenta, and thus provided more information regarding the nature of the energy dependence of the nuclear transparency. In E850 the angular dependence of the nuclear transparency near 90° and the nuclear transparency deuterons were studied. Second, we review the techniques used in an earlier experiment, E834, and show that the two experiments are consistent for the carbon data. E834 also determines the nuclear transparencies for lithium, aluminum, copper, and lead nuclei as well as for carbon. A determination of the (π+, π+p) transparencies is also reported. We find for both E850 and E834 that the A(p, 2p) nuclear transparency, unlike that for A(e,e' p) nuclear transparency, is incompatible with a constant value versus energy as predicted by Glauber calculations. The A(p, 2p) nuclear transparency for carbon and aluminum increases by a factor of two between 5.9 and 9.5 GeV/c incident proton momentum. At its peak the A(p, 2p) nuclear transparency is ∼80% of the constant A(e,e' p) nuclear transparency. Then the nuclear transparency falls back to a value at least as small as that at 5.9 GeV/c, and is compatible with the Glauber level again. This oscillating behavior is generally interpreted as an interplay between two components of the pN scattering amplitude; one short ranged and perturbative, and the other long ranged and strongly absorbed in the nuclear medium. A study of the A dependent nuclear transparency indicates that the effective cross section varies with incident momentum and is considerably smaller than the free pN cross section. We suggest a number of experiments for further studies of nuclear transparency effects.