Thesis (Ph.D.) - Indiana University, History and Philosophy of Science, 2015This dissertation charts the development of the quantitative rules of collision in the 17th century. These were central to the mathematization of nature, offering natural philosophy a framework to explain all the changes of nature in terms of the size and speed of bodies in motion. The mathematization of nature is a classic thesis in the history of early modern science. However, the significance of the dynamism within mathematics should not be neglected. One important change was the emergence of a new language of nature, an algebraic physico-mathematics, whose development was intertwined with the rules of collision. The symbolic equations provided a unified system to express previously diverse kinds of collision with a new representation of speed with direction, while at the same time collision provided a practical justification of the otherwise "impossible" negative numbers. In private manuscripts, Huygens criticized Descartes's rules of collision with heuristic use of Cartesian symbolic algebra. After he successfully predicted the outcomes of experiments using algebraic calculations at an early meeting of the Royal Society, Wallis and Wren extended the algebraic investigations in their published works. In addition to the impact of the changes in mathematics itself, the rules of collision were shaped by the inventive use of principles formulated by 'thinking with objects,' such as the balance and the pendulum. The former provided an initial framework to relate the speeds and sizes of bodies, and the latter was key both in the development of novel conservation principles and made possible experimental investigations of collision. This dissertation documents the formation of concepts central to modern physical science, and re-evaluates the mathematics of collision, with implications for our understanding of major figures in early modern science, such as Descartes and Huygens, and repercussions for the mathematization of nature.