Systematic study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi>p</mml:mi></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi>p</mml:mi></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>pp</mml:mi></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>p</mml:mi></mml:math>forward elastic scattering from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mi> </mml:mi><mml:mi mathvariant="normal">to</mml:mi><mml:mi> </mml:mi><mml:mn>6</mml:mn><mml:mi> </mml:mi><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">GeV</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:mfrac></mml:math>

Measurements of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$, ${K}^{\ifmmode\pm\else\textpm\fi{}}p$, $\mathrm{pp}$, and $\overline{p}p$ elastic scattering are presented for incident momenta of 3, 3.65, 5, and $6 \frac{\mathrm{GeV}}{c}$ and momentum transfers typically $0.03 \mathrm{to} 1.8 \mathrm{Ge}{\mathrm{V}}^{2}$. The angle and momentum of the scattered particle were measured with the Argonne Effective Mass Spectrometer for 300 000 events, yielding 930 cross-section values with an uncertainty in absolute normalization of \ifmmode\pm\else\textpm\fi{}4%. Only the ${K}^{+}$ and proton data show any significant change in slope of the forward diffraction peak with incident momentum. The particle-antiparticle crossover positions are consistent with no energy dependence, average values being 0.14 \ifmmode\pm\else\textpm\fi{} 0.03, 0.190 \ifmmode\pm\else\textpm\fi{} 0.006, and 0.162 \ifmmode\pm\else\textpm\fi{} 0.004 Ge${\mathrm{V}}^{2}$ for $\ensuremath{\pi}$' s, $K$' s, and protons, respectively; these errors reflect both statistics and the \ifmmode\pm\else\textpm\fi{}1.5% uncertainty in particle-antiparticle relative normalization. Differences between particle and antiparticle cross sections isolate interference terms between amplitudes of opposite $C$ parity in the $t$ channel; these differences indicate that the imaginary part of the odd-$C$ nonflip-helicity amplitude has a ${J}_{0}(r{(\ensuremath{-}t)}^{\frac{1}{2}})$ structure for $\ensuremath{-}t&lt;0.8$ Ge${\mathrm{V}}^{2}$, as predicted by strong absorption models. The cross-section differences for ${K}^{\ifmmode\pm\else\textpm\fi{}}$ and proton-antiproton are in qualitative agreement with the predictions of $\ensuremath{\omega}$ universality, the agreement improving with increasing energy. The corresponding quark-model predictions relating the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${K}^{\ifmmode\pm\else\textpm\fi{}}$ differences failed by more than a factor of 2. We have combined our ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ cross sections with other data to better determine the $\ensuremath{\pi}N$ amplitudes in a model-independent way; results of this analysis are presented.