We present the measurement of two event samples induced by atmospheric v(mu) of average energy (E) over bar(v) similar to 4 GeV. In the first sample, a neutrino interacts inside the MACRO detector producing an upward-going muon leaving the apparatus. The ratio of the number of observed to expected events is 0.57 +/- 0.05(stat) +/- 0.06(syst) +/- 0.14(theor) with an angular distribution similar to that expected from the Bartol atmospheric neutrino flux. The second is a mixed sample of internally produced downward-going muons and externally produced upward-going muons stopping inside the detector. These two subsamples are selected by topological criteria; the lack of timing information makes it impossible to distinguish stopping from downgoing muons. The ratio of the number of observed to expected events is 0.71 +/- 0.05(stat) +/- 0.07(syst) +/- 0.18(theor). The observed deficits in each subsample is in agreement with neutrino oscillations, although the significance is reduced by the large theoretical errors. However, the ratio of the two samples causes a large cancellation of theoretical and of some systematic errors. With the ratio, we rule out the no-oscillation hypothesis at 95% c.l. Furthermore, the ratio tests the pathlength dependence of possible oscillations. The data of both samples and their ratio favor maximal mixing and Delta m(2) similar to 10(-3)-10(-2) eV(2). These parameters are in agreement with our results from upward throughgoing muons, induced by v(mu) of much higher energies. (C) 2000 Elsevier Science B.V. All rights reserved.