Intersection Properties

Abstract

We proved many of the theorems in previous chapters by computing intersection multiplicities in two different ways and setting the results equal. Among the theorems we proved in this way are Pascal’s Theorem 6.2 and its variant Theorem 6.3, Pappus’ Theorem 6.5, and Theorem 9.7 on the associativity of addition on a cubic. The intersection properties guarantee that different ways of computing an intersection multiplicity give the same result. In Sections 13 and 14, we determine the multi­plicity of every intersection, and we derive the intersection properties. This completes the proofs of the theorems in previous chapters.