Reconsidering Newton’s Intuition Related to the Fundamental Theorem of Calculus

Abstract

The purpose of this study is to refute an argument in Kang (2019) and offer alternative views concerning the analysis of the historical genesis of the fundamental theorem of calculus. Kang (2019) indicated that Newton might have gained insight into the fundamental theorem of calculus using the area increments intuition based on strict distinctions of dimensions. In response, this study seeks to show that Newton addressed his method by focusing on the mean and instantaneous rate of area change rather than the area increments as in the analytic geometry characteristic that breaks the principle of homogeneity. The results of this study also show that the area increments intuition remains pertinent to implicitly recognizing the existence of average height.