Negatives as fictions in 16th and 17th century mathematics

The use of “negative” entities is a fact attested in various mathematical practices across various contexts since antiquity. Although we now have a better knowledge of this history in its complexity and its richness, many phenomena occurring in it are still blurred and oversimplified by the retrospective look we tend to posit on it under the heading of the history of negative numbers. In the first section, I detail several historical studies relying on a specific kind of conceptualization in terms of “domain extension” and point to several of their shortcomings. In the second section, I propose to turn to the actor's categories and put particular emphasis on the fact that negative entities were conceived as “fictitious” entities. In the third section, I show how this context allows a different reading of the various discussions and reflections on negatives occurring in the second half of the 17^th century.