Hyperplane-section divisor of a projective plane curve
= Hyperplane-section divisor of a projective plane curve
If a <projective line> $H$ does not contain the <projective plane curve> $X$, its hyperplane-section divisor is
$$
[X\cap H]=\sum_{p\in X\cap H}I_p(X,H)p,
$$
where $I_p(X,H)$ is the <intersection multiplicity>. The <Bézout theorem> gives $\deg[X\cap H]=(\deg X)(\deg H)=\deg X$.