2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59328In the context of Synthetic Differential Geometry, we describe the square volume of a ``second-infinitesimal simplex'', in terms of square-distance between its vertices. The square-volume function thus described is symmetric in the vertices. The square-volume gives rise to a characterization of the volume form in the top dimension.10 pagesCategory TheoryDifferential Geometry18F99; 58A03text