Let $\xi$ be a real number and let $n$ be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents $w_n(\xi)$ and $w_n^*(\xi)$ defined by Mahler and Koksma. We calculate their six values when $n=2$ and $\xi$ is a real number whose continued fraction expansion coincides with some Sturmian sequence of positive integers, up to the initial terms. In particular, we obtain the exact exponent of approximation to such a continued fraction $\xi$ by quadratic surds.
