Abstract
The development of abstract algebra during the 19th century allows using structural algebraic arguments instead of calculations in terms of coordinates. It allows also developing geometry over an arbitrary field of coordinates, not just the reals or the complexes. Affine geometry is classically devoted to the study of all geometric properties valid over an arbitrary field; this contains in particular the theory of parallelism, translations, projections, symmetries, conics, quadrics, and so on.
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References and Further Reading
R.F. Ballieu, Algèbre Supérieure (Cabay, Louvain-la-Neuve, 1977)
F. Borceux, An Axiomatic Approach to Geometry, Geometric Trilogy I (Springer, Berlin, 2014)
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© 2014 Springer International Publishing Switzerland
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Borceux, F. (2014). Affine Geometry. In: An Algebraic Approach to Geometry. Springer, Cham. https://doi.org/10.1007/978-3-319-01733-4_2
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DOI: https://doi.org/10.1007/978-3-319-01733-4_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01732-7
Online ISBN: 978-3-319-01733-4
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