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In this case, corresponding points will be joined by lines which do not lie in a plane, but on some surface, which like every surface generated by lines is called a ruled surface.

A Ruled Surface, Regulus or Skew is a configuration of lines which satisfy three conditions, and therefore depend on only one parameter.

Now from the form of the above equation this is a ruled surface, and through every point of it two generators pass.

The degree of a ruled surface qua line geometry is the number of its generating lines contained in a linear complex.

The lines common to three complexes of degrees, n1n2n3, form a ruled surface of degree 2n1n2n3; but not every ruled surface is the complete intersection of three complexes.