Using the Semple bundle construction, we derive an intersection-theoretic
formula for the number of simultaneous contacts of specified orders between
members of a generic family of degree d plane curves and finitely many fixed
curves. The contacts counted by the formula occur at nonsingular points of both
the members of the family and the fixed curves.Comment: 32 pages, AmS-TeX v2.1 (Revised statement and proof of one lemma;
other minor changes.