A elliptic curve over $\mathbb{C}:y^2=4x^3+ax+b$ can be associated with a torus over $\mathbb{C}$ by Weierstrass $\wp$-function, and therefore obtains a group structure. My question is how to prove that if $P,Q,R$ is colinear, then $P+Q+R=0$? I know this can be proved by divisor theory, but hwo to get a direct proof by Weierstrass $\wp$-function?
Thank you!