Abstract. In some sense reversing the historical traject, in § 1 it will be indicated how all scalar-valued intrinsic curvatures of Riemannian manifolds can be determined in terms of the curvatures of associated Euclidean curves. This involves the consideration of arbitrary-dimensional normal sections of submanifolds in Euclidean spaces and their projections on appropriate subspaces. In terms of such normal sections of Euclidean submanifolds and of such projections, in § 2 some comments will be made concerning general inequalities for Euclidean submanifolds between their scalar curvature and their mean- and normal scalar curvatures.