Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

摘要

Fermat, Leibniz, Euler, and Cauchy all used one or another form ofapproximate equality, or the idea of discarding "negligible" terms, so as toobtain a correct analytic answer. Their inferential moves find suitable proxiesin the context of modern theories of infinitesimals, and specifically theconcept of shadow. We give an application to decreasing rearrangements of realfunctions.