Let $V \subset \mathbb P^n$ is a smooth hypersurface of degree $d$. Then, a note I'm following says : $[V]$ is a point of $\mathbb P^{N_d-1}$ where $N_d = {n+d\choose d}$.
I'm looking for an explanation of what this means?
I'm familiar with the concept of dual projective space, but there the construction is just the Proj of the dual vector space and isn't dependent on any $d$.