  In this paper, we apply the Carath\'eodory's method of geometrothermodynamics
to investigate the behavior of the main thermodynamic parameters associated
with a Schwarzschild black hole surrounded by quintessence. The corresponding
Pfaffian form is constructed by means of the Schwarzschild radius $r_s$, and
the quintessential radius $r_{\gamma}$ as independent variables. This form is
then used to characterize the thermodynamic manifold. The homogeneity of the
system allows for the recognition of the empirical temperature and entropy, and
thus, connects with the usual laws of thermodynamics. In particular, we show
that the Helmholtz and Gibbs free energies lead to the same value for the
Schwarzschild black hole, in the case of the vanishing cosmological term.
