Chord-and-tangent group law
= Chord-and-tangent group law
{wiki=Elliptic_curve#The_group_law}
On a smooth plane cubic with identity point $O$, a line through points $P$ and $Q$, interpreted as the tangent when $P=Q$, meets the cubic in a third point $R$. The chord-and-tangent group law defines $P+Q$ as the third intersection of the line through $R$ and $O$ with the cubic.