Talk:Cayley–Bacharach theorem

Intrinsic form

The intrinsic form states: "Every cubic curve C1 on an algebraically closed field that passes through a given set of eight points P1, ..., P8 also passes through a certain (fixed) ninth point P9, counting multiplicities." Take a cubic curve C1; it certainly passes through some ninth point, but definitely not through a ninth point of my choice. Madyno (talk) 23:07, 22 November 2021 (UTC)

The intent is supposed to be that P₉ depends only on P₁, ..., P₈, not on the curve. I've tried to clarify the article. Ozob (talk) 16:52, 25 November 2021 (UTC)