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It is well known in euclidean geometry that the quadrilateral obtained from an arbitrary quadrilateral by joining its midpoints is a parallelogram. The purpose of this paper is to show that a complete metric space with a unique metric line joining any pair of its. distinct points is a Banach space if and only if it has the above mentioned property.doi:10.2140/pjm.1972.43.251 fatcat:tzoqmxa765e53d46v24toe2xe4