Titlebook: Geometry: Euclid and Beyond; Robin Hartshorne Textbook 2000 Robin Hartshorne 2000 Area.Euclid.Euclid‘s Elements.Geometry.Non-Euclidean Geo

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978-1-4419-3145-0Robin Hartshorne 2000

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Geometry over Fields,d. The axioms of incidence are valid over any field (Section 14). For the notion of betweenness we need an ordered field (Section 15). For the axiom (C1) on transferring a line segment to a given ray, we need a property (*) on the existence of certain square roots in the field .. To carry out Euclid

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Area,ng that two figures have equal content if we can transform one figure into the other by adding and subtracting congruent triangles (Section 22). We can prove all the properties of area that Euclid uses, except that “the whole is greater than the part.” This is established only when we relate the geo

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