2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147055Using 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.32 pages, AmS-TeX v2.1 (Revised statement and proof of one lemma; other minor changes.)Algebraic Geometrytext