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We propose an extension of the semi-analytical solutions derived by Lin et al. (1965) describing the two-dimensional homologous collapse of a self-gravitating rotating cloud having uniform density and spheroidal shape, which includes magnetic field (with important restrictions) and thermal pressure. The evolution of the cloud is reduced to three time dependent ordinary equations allowing to conduct a quick and preliminary investigation of the cloud dynamics during the precollapse phase, for adoi:10.1051/0004-6361:20031183 fatcat:b6qgjbeygbcvhhdvtruidk3qdm