It is in
Menger, K., Untersuchungen über allgemeine Metrik., Math. Ann. 100, 75-163 (1928). ZBL54.0622.02.
A modern exposition can be found in
Bowers, John C.; Bowers, Philip L., A Menger redux: embedding metric spaces isometrically in Euclidean space, Am. Math. Mon. 124, No. 7, 621-636 (2017).