Abstract
The chapter is an introduction to the axiomatic method and the developments from Euclides to the refoundation of the geometry as conceived by Hilbert. The chapter considers the significant results of synthetic geometry necessary for a more agile construction of the analytic geometry in the plane and in the space. The concepts of convexity, symmetry, projection and proportionality are related.
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References
Beutelspacher, A., Rosenbaum, U.: Projective geometry: from foundations to applications. Cambridge University Press (1998)
Guedj, D.: Le Théorème du Perroquet. Éditions du Seuil, Paris (1998)
Hilbert, D.: Grundlagen der Geometrie. G.B. Teubner, Stuttgart (1968)
Bibliography
Hartshorne, R.: Geometry: Euclid and Beyond. Springer, New York (2000)
Lobačevskij, N.I.: Nuovi Principi Della Geometria. Boringhieri, Torino (1965)
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Ventre, A.G.S. (2023). Euclidean Geometry. In: Calculus and Linear Algebra. Springer, Cham. https://doi.org/10.1007/978-3-031-20549-1_4
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DOI: https://doi.org/10.1007/978-3-031-20549-1_4
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