Exercise 14, § 9

In a projective plane $\mathbf{P}(V)$ over a field K with at least three elements, let D, $D'$ be two distinct lines. In order that, for any distinct points $a, b, c$ of D, $a', b', c'$ of $D'$, the intersection points $r$ of $D_{ab'}$ and $D_{ba'}$, $q$ of $D_{ac'}$ and $D_{ca'}$, $p$ of $D_{bc'}$ and $D_{cb'}$, lie on a straight line, it is necessary and sufficient that K be commutative ("Pappus's theorem"; reduce it to the case where $q$ and $r$ are on the line at infinity of an affine plane). Apply this theorem to the projective space of lines of $\mathbf{P}(V)$ (Exercise 12).