  Let $\Theta=(\alpha,\beta)$ be a point in $\bR^2$, with $1,\alpha,\beta$
linearly independent over $\bQ$. We attach to $\Theta$ a quadruple
$\Omega(\Theta)$ of exponents which measure the quality of approximation to
$\Theta$ both by rational points and by rational lines. The two ``uniform''
components of $\Omega(\Theta)$ are related by an equation, due to Jarn{\'\i}k,
and the four exponents satisfy two inequalities which refine Khintchine's
transference principle. Conversely, we show that for any quadruple $\Omega$
fulfilling these necessary conditions, there exists a point $\Theta\in \bR^2$
for which $\Omega(\Theta) =\Omega$.
