  The points of a straight line stand in mutual relations of neighborhood and order. To see how the ideal point fits into these relations let H rotate continually about the straight line m where it intersects Γ. (See Figure 4.) When H is parallel to PQ—say, at time t—the projection of Q on H from P is the ideal point of the straight line through P and Q. Right before t the said projection is an ordinary point of H, very far from m.  Right after t the projection is again an ordinary point of H, very far from m, but at the opposite end of the plane. Studying the continuous displacement of the projection during a short time interval surrounding t, one concludes that if A and B are any two points of H that stand, respectively, on either side of m, the ideal point of the straight line through A and B must be placed between A and B.  Thus, in projective geometry, the points of a straight line are ordered cyclically, i.e., like the points of a circle. As a result of this, the neighborhood relations among points in projective space and on projective planes differ drastically from those familiar from standard geometry, and are highly counterintuitive. It is fair to say that projective geometry signified a much deeper and far-reaching revolution in human thought than did the mere denial of Euclid's Postulate.