Abstract

KATZ, MIKHAIL G.; SHERRY, DAVID  and  UGAGLIA, MONICA. When Does a Hyperbola Meet Its Asymptote?: Bounded Infinities, Fictions, and Contradictions in Leibniz. Rev. latinoam. filos. [online]. 2023, vol.49, n.2, pp.3-3. ISSN 1852-7353.  http://dx.doi.org/10.36446/rlf2023359.

In his 1676 text De Quadratura Ari-thmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of the point of intersection at infinite distance for parallel lines. We examine con-trasting interpretations of these notions in the context of Leibniz’s analysis of asymptotes for logarithmic curves and hyperbolas. We point out difficulties that arise due to conflating these notions of infinity. As noted by Rodríguez Hurtado et al., a significant difference exists between the Cartesian model of magnitudes and Leibniz’s search for a qualitative model for studying perspective, including ideal points at infinity. We show how respecting the distinction between these notions enables a consistent interpretation thereof.

Keywords : infinitesimal calculus; useful fiction; infinity; infinites-imals; ideal perspective point.

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