Projective tangent plane
= Projective tangent plane
{title2=$\sum_iF_{x_i}(P)x_i=0$}
For a <smooth algebraic surface> defined by a <homogeneous polynomial> $F$ in <projective space> of dimension three, its tangent plane at $P$ is the displayed plane. Every <projective line> on the surface through $P$ lies in this plane.