[en] A measurement of the inclusive cross section for the deep-inelastic scattering of positrons on protons at low four-momentum transfer squared Q² is presented. The measurement is used for the extraction of the longitudinal proton structure function F_L. The analysis is based on data collected by the H1 experiment during special, low energy runs in the year 2007. The direct technique of the F_L determination based on the extraction of the reduced DIS cross sections for three different centre-of-mass energies is used. For the purpose of the analysis a dedicated electron finder has been developed and integrated with the standard H1 reconstruction software H1REC. The algorithm employs information from two independent tracking detectors the Backward Silicon Tracker and the Central Jet Chamber. The performance of the finder is studied. The thesis presents the cross section and the F_L measurements in the range of 2.5 GeV²≤Q²≤25 GeV². (orig.)