We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with 90×10^{6} helium, 8.4×10^{6} carbon, and 7.0×10^{6} oxygen nuclei collected by the Alpha Magnetic Spectrometer (AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way.