Let $k$ be a field with $\operatorname{char}(k) \ne 2,3$, and let $E \subset \mathbb{P}^2_k$ be the nonsingular short Weierstrass cubic defined by $Y^2Z=X^3+aXZ^2+bZ^3$. For $E(k)$ with identity $O=[0:1:0]$, the algebraic addition checklist for short Weierstrass equations gives the same binary operation as the geometric chord-and-tangent law.