This is a reference request.
I asked how to find the horizontal tangents to the curve $x^3+y^3=6xy$ and @Angelo answered easily by applying the following theorem.
Theorem. The set of tangents to an algebraic curve at the origin is given by the homogeneous part of lowest total degree in the equation (of the curve).
He pointed me out to this math-doctors blog which talks more about the theorem. But the blog also just presents the theorem saying that "[i]n general, the number of tangents at a singular point is at most equal to the degree of the affine cone." They don't prove it nor cite any reference.
Ideally, I'm looking for a book where I can be prepared to read the proof of the theorem. Alternatively, any paper that proves it will be useful too.