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A mathematical approach to linguistics provides an array of insights for quantitative description on the ways language works. This area of investigation is still underexplored, but it is actually significant for the development of mathematical models to enhance linguists- understanding on linguistic structure. This study aims to present a mathematical analysis of how the English preposition on works under the framework of Trajector (TR) and Landmark (LM) relations (Tyler & Evans, 2003). Data were corpora taken from 10 dissertations written by American student writers. To sort the data, Ant Conc 3.4.1.0 was used to parse clauses or sentences based on the TR-LM configurations. Based on the TR-LM configurations, a mathematical model was developed to discover how these variables are quantitatively related to the number of senses produced by using a geometric representation of TR and LM. This study indicates that the relation between TRs and LMs, on the one hand, and the potential sum of senses, on the other, follows the integral function of ∑ C = ∫ TR d(LM), which means that the total number of senses of C equals the integral of TR with respect to LM. This mathematical modeling confirms the TR-LM hypothesis that every physical object has a unique sense established by their TR-LM configuration as spawned by Lakoff (1987).