Two ways of reasoning and two ways of arguing in geometry. Some remarks concerning the application of figures in Euclidean geometry (Q1408669)
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scientific article; zbMATH DE number 1985802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two ways of reasoning and two ways of arguing in geometry. Some remarks concerning the application of figures in Euclidean geometry |
scientific article; zbMATH DE number 1985802 |
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Two ways of reasoning and two ways of arguing in geometry. Some remarks concerning the application of figures in Euclidean geometry (English)
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25 September 2003
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The author analyses the logic problems that arise from the procedure of superposition used in Euclid's \textit{Elements} in proposition I-4, I-8, and III-24. Hilbert's elimination of these problems in \textit{Grundlagen der Geometrie} is discussed. The author gives a new axiomatic framework related to segments and arcs in order to prove Euclid's proposition III-24.
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Euclid
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Hilbert
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superposition
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