The proton elastic form factors [ital G][sub [ital E][ital p]]([ital Q][sup 2]) and [ital G][sub [ital M][ital p]]([ital Q][sup 2]) have been extracted for [ital Q][sup 2]=1.75 to 8.83 (GeV/[ital c])[sup 2] via a Rosenbluth separation to [ital ep] elastic cross section measurements in the angular range 13[degree][le][theta][le]90[degree]. The [ital Q][sup 2] range covered more than doubles that of the existing data. For [ital Q][sup 2][lt]4 (GeV/[ital c])[sup 2], where the data overlap with previous measurements, the total uncertainties have been reduced to [lt] 14% in [ital G][sub [ital E][ital p]] and [lt] 1.5% in [ital G][sub [ital M][ital p]]. Results for [ital G][sub [ital E][ital p]]([ital Q][sup 2]) are consistent with the dipole fit [ital G][sub [ital D]]([ital Q][sup 2])=(1+[ital Q][sup 2]/0.71)[sup [minus]2], while those for [ital G][sub [ital M][ital p]]([ital Q][sup 2])/[mu][sub [ital p]][ital G][sub [ital D]]([ital Q][sup 2]) decrease smoothly from 1.05 to 0.92. Deviations from form factor scaling are observed up to 20%. The ratio [ital Q][sup 2][ital F][sub 2]/[ital F][sub 1] is observed to approach a constant value for [ital Q][sup 2][gt]3 (GeV/[ital c])[sup 2]. Comparisons are made to vector meson dominance, dimensional scaling, QCD sum rule, diquark, and constituent quark models, none of whichmore » fully characterize all the new data.« less