why hypersurface is called hypersurface and not Hyposurface from wikipedia: "Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface" Now, hyper- is the prefix of "over" hypo- is the prefix of "under" If we move form n to n-1 soundn't it be called Hyposurface?

The "hyper" prefix is used since hypersurfaces are the higher-dimensional analogs of regular two-dimensional surfaces.

It is used in the same way in expressions such as "hyperplane" and "hypercube".