  In the historical literature there has been an extended discussion on the
question, whether the report of Sartorius von Waltershausen about C. F. Gauss
checking the largest triangle of the geodetical measurement campaign in the
kingdom of Hannover as a kind of ``test'' for the Euclididean nature of
physical space can be taken seriously or not. Among others, it was argued that
it even was logically impossible for Gauss to do so in the early 1820s (i.e. in
particular, before J. Bolyai's, N.I. Lobachevsy's, or even B. Riemann's works).
This article shows, in which sense Gauss's methodology of curvature of
surfaces, although logically developed in all clarity only for surfaces
embedded in Euclidean 3-space, could very well be used already in the early
1820 to investigate the above mentioned question in the sense of physical
geometry. Although we do not have a definitive proof of the respective
calculations by Gauss's own hand, the latter's account of the situation to
contemporaries (correspondents, friend and students) changed clearly between
the early and the late 1820s. That speaks very much in favour of a basic
correctness of Sartorius von Waltershausen's report on this topic.
