Let $C$ be a plane curve given by the set $\{(x,y) \in \mathbb{R}^2: \, P(x,y) = 0 \}$ and define $\omega=\frac{\mathrm{d}x}{y}$. Then, it is
$$\int\limits_0^A \omega + \int\limits_0^B \omega = \int\limits_0^{A \oplus B} \omega$$
(with $\oplus$ being addition on a group on the curve) a theorem?
I'm quite sure this is what's happening when C is an elliptic curve, but I have failed to make this work out when C is defined by $P(x,y) = x^2 + y^2 - 1$ (unit circle) and the group law is defined by firing a ray through $(3/5,4/5)$ (chosen arbitrarily) parallel to $AB$ and taking it's intersection with the circle as $A \oplus B$.