56.

there are only bases without pyramids which constantly diminish up
to this point. And from the first base where the vertical plane is
placed towards the point in the eye there will be only pyramids
without bases; as shown in the example given above. Now, let _a b_
be the said vertical plane and _r_ the point of the pyramid
terminating in the eye, and _n_ the point of diminution which is
always in a straight line opposite the eye and always moves as the
eye moves--just as when a rod is moved its shadow moves, and moves
with it, precisely as the shadow moves with a body. And each point
is the apex of a pyramid, all having a common base with the
intervening vertical plane. But although their bases are equal their
angles are not equal, because the diminishing point is the
termination of a smaller angle than that of the eye. If you ask me:
"By what practical experience can you show me these points?" I
reply--so far as concerns the diminishing point which moves with you
--when you walk by a ploughed field look at the straight furrows
which come down with their ends to the path where you are walking,
and you will see that each pair of furrows will look as though they
tried to get nearer and meet at the [farther] end.

[Footnote: For the easier understanding of the diagram and of its
connection with the preceding I may here remark that the square
plane shown above in profile by the line _c s_ is here indicated by
_e d o p_. According to lines 1, 3 _a b_ must be imagined as a plane
of glass placed perpendicularly at _o p_.]

57.