Data on antiproton-proton cross sections at the c.m. energies 200 and 900 GeV are presented. The data were obtained at the CERN antiproton-proton Collider operated in a new pulsed mode in which the same beams were accelerated and decelerated between beam energies of 450 and 100 GeV. The properties of the machine determine the ratio of the luminosities at the two energies to about 1% and thus an accurate measurement of the ratioR of the inelastic cross sections could be made. We findR (=σ900/σ200)=1.20±0.01±0.02, where the first error is statistical and the second systematic. Interpolating existing data to estimateσine1(200 GeV) this measurement ofR leads toσine1(900 GeV)=50.3+0.4+1.0 mb. Using an extrapolated value ofσe1/σtot we estimate the total cross section at 900 GeV to be 65.3±0.7±1.5 mb. Both the inelastic and total cross sections are compatible with a ln2s dependence. Comparisons are made with different fits to the total cross section energy dependence.