Levi’s Lemma, pseudolinear drawings of, and empty triangles.

There are three main thrusts to this article: a new proof of Levi’s Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudolinear drawings of the complete graph; and proofs that pseudolinear and convex drawings of $K_n$ have $n^2+O(n\log n)$ and $O(n)$, respectively, empty triangles. All the arguments are elementary, algorithmic, and self-contained.