ABSTRACT
The foundations of Geometry have been subjected, in recent times, to a threefold scrutiny. Projective Geometry begins with the whole straight line, i.e. it asserts that any two points determine a certain class of points which is also determined by any two other members of the class. If this class be regarded as determined in virtue of a relation between the two points, then this relation is symmetrical. Projective Geometry assumes a class of entities, called points, to which it assigns certain properties. These points are to determine a certain class of points. There is a certain definite relation which holds between any couple of points and one and only one corresponding class of points. Without some such definite relation, there could be no question of two points determining a class.
