Click to place points. Every non-collinear point set must have an ordinary line — one passing through exactly two points.
Theorem (Sylvester 1893, Gallai 1944): Given any finite set of points in the plane, not all collinear, there exists a line passing through exactly two of them. Ordinary lines are highlighted in gold. Kelly's elegant proof (1948) fits in two lines. The theorem generalises to complex projective spaces only with extra conditions.