Analytical geometry in Spain during the nineteenth century: a study of the negative solutions of an equation

Abstract

This article shows the study and interpretation of the negative solutions of a geometric problem found in the textbooks of Analytical Geometry used in Spain during the nineteenth century. Through the content analysis of eleven books, we have identified three interpretations of negative solutions: they indicate a change of position; they point out an error in the hypotheses of the problem or a possible modification of the formulation that implies a more general problem, or the existence of an inverse quantity.