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Autonomy of Geometry

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Baldwin J. T., Mueller A.
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
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2019
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vol. 11
5-24
EN
In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from a geometric as opposed to an arithmetic viewpoint.
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