Textbooks revealing the development of a concept—the case of the number line in the analytic geometry (1708–1829)

Abstract

The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from Germany of that time, to understand when and how this notion was used. Additionally, pertinent entries from encyclopedias of that time are used to contrast with what was not sufficiently explained in the aforementioned textbooks, until, finally, we can identify this object as it is currently characterized. I analyze how the negative numbers were used to constitute the number line and survey several number line diagrams, which were sometimes similar, but most often quite different from each other. The intention is to understand the historical contexts that configure the emergence and development of the notion of the number line.