Titlebook: Lectures on Geometry; Lucian B?descu,Ettore Carletti Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclusive licens

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Affine Geometry and Projective Geometry,Throughout this chapter we focus on the standard projective space . of dimension . over a field ..

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Cayley--Klein Geometries,expressed by the cross-ratio (.), i.e. by means of a .. In the first half of 1800 J. V. Poncelet (1788–1867) discovered that some euclidean notions might be formulated in terms of projective geometry. In order to show these connections we have to consider the euclidean plane immersed into the complex projective plane.

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978-3-031-51413-5The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Lectures on Geometry978-3-031-51414-2Series ISSN 2038-5714 Series E-ISSN 2532-3318

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Lucian B?descu,Ettore CarlettiA comparative presentation of affine, euclidean and projective geometries.An elementary but complete proof of the strong Bézout’s theorem for curves of P2 (K).A detailed exposition of Cayley-Klein pla