R. Musil, "Der mathematische Mensch." In: Der lose Vogel, Leipzig: K. Wolff 1913, pp. 310-314.
Der lose Vogel was intended to be published in monthly installments as a "Monatsschrift", but it appears the project lost impetus towards the end, and resorted to combining multiple issues into one. Musil's brief essay appeared in combined issues 10, 11, and 12. The quoted text from the question appears on page 312.
It should be noted that for each of the poems and essays in this publication the author is not stated. There is merely a list of all authors in the foreword on page VI which includes R. Musil among the essay writers:
[...] die Gedichte sind von M. Brod, F. Werfel, R. Walser. Die Aufsätze sind von:
Alain, H. Beloc, F. Blei, S. Butler, E. v. Gebsattel, G. Hecht, A. Kolb,
W. Krug, R. Musil, P. Scheffer, M. Scheler, H. Schott, R. Stadler, A. Suares,
Vogelstein, O. Vrieslander.
The identification of Robert Musil as the author of "Der mathematische Mensch" must have been based on a different source. Maybe his writing style was easily recognized by contemporaries. The earliest reference to Musil's authorship that I can find is in Musil's "Gesammelte Werke" (collected works) edited by Adolf Frisé, published in 1952, where the essay appears at page 592.