ABSTRACT
The distinction between projective and descriptive Geometry is very recent, and is of an essentially ordinal nature. If we adopt the view-which, as we saw, is the simpler of two legitimate views-that the straight line is defined by a certain relation between any two of its points, then in projective Geometry this relation is symmetrical, while in descriptive Geometry it is asymmetrical. Beyond this we have the difference that, in projective Geometry, a line and a plane, two planes, or two lines in a plane, always intersect, while in descriptive Geometry the question whether this is the case or not is left open. But these differences are not very important for our present purpose, and it will therefore be convenient to speak of projective and descriptive Geometry together as non-quantitative Geometry.
