*12.* If the infinitude of points on a line is taken as the infinitude of
the first order, then the infinitude of lines in a pencil of rays and the
infinitude of planes in an axial pencil are also of the first order, while
the infinitude of lines cutting across two "skew" lines, as well as the
infinitude of points in a plane, are of the second order.




*13.* If we join each of the points of a plane to a point not in that
plane, we set up a one-to-one correspondence between the points in a plane
and the lines through a point in space. _Thus the infinitude of lines
through a point in space is of the second order._




*14.* If to each line through a point in space we make correspond that
plane at right angles to it and passing through the same point, we see
that _the infinitude of planes through a point in space is of the second
order._




*15.* If to each plane through a point in space we make correspond the