Euclidean geometry, statics, and classical mechanics, being in some sense the simplest physical theories based on a full-fledged mathematical apparatus, are well suited to a historico-philosophical analysis of the way in which a physical theory differs from a purely mathematical theory. Through a series of examples including Newton’s Principia and later forms of mechanics, we will identify the interpretive substructure that connects the mathematical apparatus of the theory to the world of experience. This substructure includes models of experiments, models of measurement, and modular connections with partial theories. It evolves during the life of a theory as physicists learn how to apply it in various contexts. It should nevertheless be regarded as an integral part of a genuine physical theory since the theory would otherwise degenerate into pure mathematics.

欧几里得几何、静力学和经典力学，在某种意义上是基于成熟数学工具的最简单的物理理论，非常适合对物理理论与纯数学理论的区别进行历史哲学分析。通过包括牛顿原理在内的一系列例子以及后来的力学形式，我们将确定将理论的数学装置与经验世界联系起来的解释性子结构。该子结构包括实验模型、测量模型以及与部分理论的模块化连接。随着物理学家学习如何在各种情况下应用它，它在理论的生命周期中不断发展。尽管如此，它仍应被视为真正物理理论的组成部分，否则该理论将退化为纯数学。