Let $k$ be an [algebraically closed field](/page/Algebraically%20Closed%20Field), let $X\subset \mathbb P_k^n$ be a positive-dimensional nonsingular irreducible projective variety, and let $L_0,L_1\in k[x_0,\dots,x_n]_1$ be nonzero homogeneous linear forms. For $i\in\{0,1\}$, set $H_i:=V_+(L_i)\subset \mathbb P_k^n$, and suppose that neither $H_0$ nor $H_1$ contains $X$. Then the hyperplane section divisors on $X$ are linearly equivalent:

\begin{align*} H_0|_X \sim H_1|_X. \end{align*}