this says that each point on the surface has its own pair of orthogonal lines through it, with their slope ratio depending only on that point. whereas (6) is a relation between specific slopes and variable values, (7) is a relation between slope functions and function variables. it holds true for any point on the surface, i.e. for any and all combinations of "p" and "v" values. to solve this equation for the function "kv"("v"), first separate the variables, "v" on the left and "p" on the right.