  In 1941, L. Ahlfors gave another proof of a 1933 theorem of H. Cartan on
approximation to hyperplanes of holomorphic curves in P^n. Ahlfors' proof built
on earlier work of H. and J. Weyl (1938), and proved Cartan's theorem by
studying the associated curves of the holomorphic curve. This work has
subsequently been reworked by H.-H. Wu in 1970, using differential geometry, M.
Cowen and P. A. Griffiths in 1976, further emphasizing curvature, and by Y.-T.
Siu in 1987 and 1990, emphasizing meromorphic connections. This paper gives
another variation of the proof, motivated by successive minima as in the proof
of Schmidt's Subspace Theorem, and using McQuillan's "tautological inequality."
In this proof, essentially all of the analysis is encapsulated within a
modified McQuillan-like inequality, so that most of the proof primarily uses
methods of algebraic geometry, in particular flag varieties. A diophantine
conjecture based on McQuillan's inequality is also posed.
