In his Complete Guide to Perspective Drawing (page 27), Craig Attebery proposes a method for determining depth in a line going towards its vanishing point (VP):
VP = Vanishing Point HL = Horizon Line MP = Measuring Point
To put it in words, the author assumes the measuring line will intersect the vanishing point line and the picture plane at the same distance: 2 units. Still, this does not seem to make sense. Here's an apparent proof: the measuring line intersects many lines with different vanishing points. As such lines have different angles, the distance of the interception cannot be all the same:
Is Attebery (or my interpretation of his work) wrong? If so, how should depth be measured in perspective drawing?
If I understand what distance is being measured, the distance to the vanishing point from any other point in the figure is infinite.
But the lines through MP are all parallel in the scene, so lines that cut the viewing plane at uniformly spaced points will also cut the line from $0$ to VP at uniformly spaced points.
Any claim that the segment marked "$2$" is the same length as the segment between the marks $0$ and $2$, however, is a claim that those two segments are legs of an isosceles triangle, which is equivalent to a claim about a relationship between the direction to the vanishing point and the direction to the measuring point. This implies that the choice of measuring point depends on the choice of vanishing point.
Whether this particular technique gives the claimed result or not depends on how the directions to points in the scene map to points on the horizon and on how the technique tells us to decide on the position of the measuring point given the position of the vanishing point.