Some aspects of the geometry of the surfaces with the system of plane coordinate lines

In the article, the geometry of the surfaces with the system of the plane coordinate lines is investigated. The common vector formula of these surfaces is received.
The formulas of the coefficients of the quadratic forms are presented too. The conditions, when of the plane coordinate lines are lines of the principle curvatures of the surface, are received.
The subclass of the surfaces with the system of the plane coordinate lines in the normal plane of the directrix curve is investigated. The formula of the Monge's ruled surfaces is received on the base of the common formula.
The drawings of the Monge's ruled surfaces made in MathСad system are shown.

surfaces with the system of plane coordinate lines, a vector equation, quadratic forms, lines of principle curvatures, normal surfaces, ruled Monge's surfaces