Geodesic
On some Axioms in Foundations of Cartesian Spaces
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 831-836

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The present paper seeks to put into a clearer focus the roles of certain axioms in axiomatic studies of finite dimensional Cartesian spaces over various classes of ordered fields. Following Tarski [3], we define a Cartesian space as follows. 
Gupta, Haragauri N. On some Axioms in Foundations of Cartesian Spaces. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 831-836. doi: 10.4153/CMB-1969-108-8
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[1] 1. Gupta, H.N., An axiomatization of finite-dimensional Cartesian spaces over arbitrary ordered fields. Bull. Acad. Polon. Sci. 13 (1965) 550–551. Google Scholar

[2] 2. Scott, D., Dimension in elementary Euclidean geometry, in the axiomatic method. (Amsterdam, 1959) 53–67. Google Scholar

[3] 3. Tarski, A., What is elementary geometry? in the axiomatic method. (Amsterdam, 1959) 16–29. Google Scholar

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