I have been reading my lecture notes, and I am stuck on this part. It states
"Let $C \subset \mathbb{P}^2_K$. We define on $C$ an abelian structure.
Take points $P$ and $Q$ on $C$ and pass a line through P and Q. Denote by $P ∗ Q$ the 3rd point of intersection of the line with $C$ "
, why is it automatic assumed that it will pass through a third point of the cubic curve. Is there some type of lemma I have missed.