[en] The proton-proton absolute elastic differential cross section, σ_pp(θ), has been measured at incident proton beam energies of 491.9, 575.5, 641.6, 728.2, and 793.0 MeV at laboratory scattering angles of ∼15 degree to ∼42 degree with a total uncertainty on the order of 1%. The measurements were made at the Clinton P. Anderson Los Alamos Meson Physics Facility (LAMPF) and employed a new beam counting technique which provided a better overall beam normalization compared to previous experiments of this type. The cross section was measured with CH₂ targets and a primary liquid, LH₂, target to determine the uncertainties in some systematic corrections. Extreme care was taken to reduce individual systematic errors to less than 0.5%