  Using a `height-to-radical' identity, we define the archimedean contribution
to the radical, $r_\arch$, and we give a new proof of the abc theorem for the
field of meromorphic functions. The first step of the proof is completely
formal and yields that the height is bounded by the radical, $h\leq r$, where
$r=r_\na+r_\arch$ is the radical completed with the archimedean contribution.
The second step is analytic in nature and uses the lemma on the logarithmic
derivative to derive a bound for $r_\arch$.
