Geodesic
Metric axioms of Euclidean space
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 89-110

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A version of axioms of Euclidean space based on the sole intain notion, namely on the notion of distance, is considered. The notions of straight line and plane are introduced in the terms of distance. Thus, Euclidean space is considered here as a metric space with metric satisfying the corresponding axioms. 
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     author = {A. A. Ivanov},
     title = {Metric axioms of {Euclidean} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {89--110},
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     volume = {279},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a5/}
}
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A. A. Ivanov. Metric axioms of Euclidean space. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 89-110. http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a5/