planes in space is an infinitude of the third order._




*18.* Consider now the planes perpendicular to these three lines. Every
set of three planes so drawn will determine a point in space, and,
conversely, through every point in space may be drawn one and only one set
of three planes at right angles to the three given lines. It follows,
therefore, that _the totality of points in space is an infinitude of the
third order._




*19. Space system.* Space of three dimensions, considered as made up of
all its planes and points, is then a fundamental form of the _third_
order, which we shall call a _space system._




*20. Lines in space.* If we join the twofold infinity of points in one
plane with the twofold infinity of points in another plane, we get a
totality of lines of space which is of the fourth order of infinity. _The
totality of lines in space gives, then, a fundamental form of the fourth
order._