Exercise 14, § 9

Dans a projective plan $\mathbf{P}(V)$ over a field $K$ having at least three elements, let $D, D'$ be two distinct rights. In order that, whatever the distinct points $a, b, c$ of $D, a', b', c'$ of $D'$ may be, the intersection points $r$ of $D_{ab'}$ and $D_{ba'}$, $q$ of $D_{ac'}$ and $D_{ca'}$, $p$ of $D_{bc'}$ and $D_{cb'}$ be collinear, it is necessary and sufficient that $K$ be commutative (“Pappus theorem”; reduce to the case where $q$ and $r$ are on the right at infinity of an affine plan). Apply this theorem to the projective space of the rights of $\mathbf{P}(V)$ (exerc. 12).