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We report the measurement of secondary charge and isotopic fragmentation cross sections in a liquid hydrogen target from 30 incident beams of relativistic nuclei ranging from 10 B to 55 Mn. These individual beams were obtained by initially accelerating 580 MeV/nucleon 40 Ar and 630 MeV/nucleon 56 Fe nuclei and letting these nuclei interact in a thin CH 2 target in the beam line. The fragments of these interactions were then focused according to their A/Z ratios onto a hydrogen target and the charge and isotopic composition of the fragmentation in this target was measured using our standard cosmic ray telescope. Several of these nuclei have had their cross sections measured previously and a comparison with earlier data confirms the estimated precision ϳ5% of the new cross section data. The 30 nuclei for which the cross sections were measured doubles the previously reported data for 15 nuclei from several experiments in the charge range from Li to Ni. The systematics of these new cross sections are discussed both with respect to the charge changing and isotopic cross sections. These systematics will lead to improvements in the productive capability of the formulas used to describe the unmeasured cross sections. It should be noted, however, that from the point of view of the propagation of galactic cosmic rays through the interstellar medium, which is one of the main goals of this experiment, the fragmentation cross sections have now been measured at at least one energy for over 98% of the arriving particles with Zϭ3 -28. ͓S0556-2813͑98͒07412-3͔ PACS number͑s͒: 25.70. Mn, 25.75.Ϫq, 98.70.Sa