  Due to the inconsistency in the results of the GEp/Gmp ratio of the proton,
as extracted from the Rosenbluth and recoil polarization techniques, high
precision measurements of the e-p elastic scattering cross sections were made
at Q^2 = 2.64, 3.20, and 4.10 GeV^2. Protons were detected, in contrast to
previous measurements where the scattered electrons were detected, which
dramatically decreased epsilon-dependent systematic uncertainties and
corrections. A single spectrometer measured the scattered protons of interest
while simultaneous measurements at Q^2 = 0.5 GeV^2 were carried out using
another spectrometer which served as a luminosity monitor in order to remove
any uncertainties due to beam charge and target density fluctuations. The
absolute uncertainty in the measured cross sections is \approx 3% for both
spectrometers and with relative uncertainties, random and slope, below 1% for
the higher Q^2 protons, and below 1% random and 6% slope for the monitor
spectrometer. The extracted electric and magnetic form factors were determined
to 4%-7% for GEp and 1.5% for GMp. The ratio GEp/Gmp was determined to 4%-7%
and showed mu_p GEp/GMp \approx 1.0. The results of this work are in agreement
with the previous Rosenbluth data and inconsistent with high-Q^2 recoil
polarization results, implying a systematic difference between the two
techniques.
