Several applications of mathematics to empirical domains are described, including a small portion of Newtonian mechanics. The simplest case is one where a nonmathematical empirical description of the domain of application is already in place. A far more (ontologically) complicated case is one where no such empirical description is in place; instead mathematical nomenclature is applied empirically by reinterpreting some of that nomenclature as empirically referring. A concern due to Mark Steiner, that the empirical success of the drafting of mathematical kind-terms for the role of projectable (empirical) predicates in empirical theories, involves an unexplained methodological miracle, is shown to be groundless.
Keywords: applying mathematics, methodological miracles, Newtonian mechanics, projectability, reinterpreting mathematical nomenclature, Mark Steiner,