Geodesic
Metric axioms of Euclidean space
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 89-110 
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/
@article{ZNSL_2001_279_a5,
     author = {A. A. Ivanov},
     title = {Metric axioms of {Euclidean} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {89--110},
     year = {2001},
     volume = {279},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.