  The original canonical ensemble formalism for the nonextensive entropy
thermostatistics is reconsidered. It is shown that the unambiguous connection
of the statistical mechanics with the equilibrium thermodynamics is provided if
the entropic parameter $1/(q-1)$ is an extensive variable of the state. Based
on a particular example of the perfect gas, it is proved that the Tsallis
thermostatistics meets all the requirements of equilibrium thermodynamics in
the thermodynamic limit. In particular, the entropy of the system is extensive
and the temperature is intensive. However, for finite systems both the Tsallis
and Boltzmann-Gibbs entropies are nonextensive. The equivalence of the
canonical and microcanonical ensembles of Tsallis thermostatistics in the
thermodynamic limit is established. The issue associated with physical
interpretation of the entropic variable is discussed in detail.
