1999 | OriginalPaper | Buchkapitel
The Origin of Mathematics 5: Problems and Theories
verfasst von : Benno Artmann
Erschienen in: Euclid—The Creation of Mathematics
Verlag: Springer New York
Enthalten in: Professional Book Archive
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In section C of Book III Euclid presents the prototype of a mathematical theory. He has a clear sense of its architecture. Let us recapitulate the main steps: III.20 is the preparing lemma with specific information about the size of angles.III.21 is the main theorem about an invariant.III.23-29 are technical expansions of the main theorem.III.31/32 deal with two remaining extreme cases.III.33/34 modifies the extreme case 32 to get a tool for applications.