We report new results for the cosmic-ray antiproton-to-proton ratio from 3 to 50 GeV at the top of the atmosphere. These results represent the first measurements, on an event-by-event basis, of mass-resolved antiprotons above 18 GeV. The results were obtained with the NMSU-WIZARD/CAPRICE98 balloon-borne magnet spectrometer equipped with a gas-RICH (Ring-Imaging Cerenkov) counter and a silicon-tungsten imaging calorimeter. The RICH detector was the first ever flown that is capable of identifying charge-one particles at energies above 5 GeV. The spectrometer was flown on 1998 May 28-29 from Fort Sumner, New Mexico. The measured p/p ratio is in agreement with a pure secondary interstellar production.