totality of points on a line a _point-row_, and the totality of lines
through a point a _pencil of rays_, we say that the point-row and the
pencil related as above are in _perspective position_, or that they are
_perspectively related_.




*7. Axial pencil; fundamental forms.* A similar correspondence may be set
up between the points on a line and the planes through another line which
does not meet the first. Such a system of planes is called an _axial
pencil_, and the three assemblages—the point-row, the pencil of rays, and
the axial pencil—are called _fundamental forms_. The fact that they may
all be set into one-to-one correspondence with each other is expressed by
saying that they are of the same order. It is usual also to speak of them
as of the first order. We shall see presently that there are other
assemblages which cannot be put into this sort of one-to-one
correspondence with the points on a line, and that they will very
reasonably be said to be of a higher order.




*8. Perspective position.* We have said that a point-row and a pencil of
rays are in perspective position if each ray of the pencil goes through
the point of the point-row which corresponds to it. Two pencils of rays
are also said to be in perspective position if corresponding rays meet on
a straight line which is called the axis of perspectivity. Also, two
point-rows are said to be in perspective position if corresponding points
lie on straight lines through a point which is called the center of