Exercise 15, § 9

In a projective plane over a field $K$ having at least three elements, let $s, a, b, c, a', b', c'$ be seven points such that $\{s, a, b, c\}$ and $\{s, a', b', c'\}$ are projective frames (II, p. 202, Exercise 10) and that the lines $D_{sa}, D_{sb}, D_{sc}$ pass respectively through $a', b', c'$. Prove that the intersection points $r$ of $D_{ab}$ and $D_{a'b'}$, $p$ of $D_{bc}$ and $D_{b'c'}$, $q$ of $D_{ca}$ and $D_{c'a'}$, are collinear ("Desargues theorem"; method analogous to that of Exercise 14).