It is in 

<cite authors="Menger, K.">_Menger, K._, [**Untersuchungen über allgemeine Metrik.**](https://doi.org/10.1007/BF01448840), Math. Ann. 100, 75-163 (1928). [ZBL54.0622.02](https://zbmath.org/?q=an:54.0622.02).</cite> 

A modern exposition can be found in 

<cite authors="Bowers, John C.; Bowers, Philip L.">_Bowers, John C.; Bowers, Philip L._, [**A Menger redux: embedding metric spaces isometrically in Euclidean space**](https://doi.org/10.4169/amer.math.monthly.124.7.621), Am. Math. Mon. 124, No. 7, 621-636 (2017).</cite>