In relation to the tetrahedron depicted, the book I'm reading says that this relation between its surfaces holds:
$d\sigma_i = d\sigma_n \cos(\mathbf{n}, x_i) = n_i d\sigma_m$
I don't understand how to derive it. If n is the unit exterior normal to the surface, (as the book defines it) then $n_i$ should be equal to 1, leading to $d\sigma_i = 1\cdot d\sigma_m$