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  1. From Magnitudes to Geometry and Back: De Zolt's Postulate.Eduardo N. Giovannini & Abel Lassalle-Casanave - forthcoming - Theoria.
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  • David Hilbert and the Foundations of the Theory of Plane Area.Eduardo N. Giovannini - 2021 - Archive for History of Exact Sciences 75 (6):649-698.
    This paper provides a detailed study of David Hilbert’s axiomatization of the theory of plane area, in the classical monograph Foundation of Geometry. On the one hand, we offer a precise contextualization of this theory by considering it against its nineteenth-century geometrical background. Specifically, we examine some crucial steps in the emergence of the modern theory of geometrical equivalence. On the other hand, we analyze from a more conceptual perspective the significance of Hilbert’s theory of area for the foundational program (...)
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  • Euclid’s Common Notions and the Theory of Equivalence.Vincenzo De Risi - 2021 - Foundations of Science 26 (2):301-324.
    The “common notions” prefacing the Elements of Euclid are a very peculiar set of axioms, and their authenticity, as well as their actual role in the demonstrations, have been object of debate. In the first part of this essay, I offer a survey of the evidence for the authenticity of the common notions, and conclude that only three of them are likely to have been in place at the times of Euclid, whereas others were added in Late Antiquity. In the (...)
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