[Footnote: The two diagrams above the chapter are explained by the first five lines. They have, however, more letters than are referred to in the text, a circumstance we frequently find occasion to remark.]
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_.]
As regards the point in the eye; it is made more intelligible by this: If you look into the eye of another person you will see your own image. Now imagine 2 lines starting from your ears and going to the ears of that image which you see in the other man's eye; you will understand that these lines converge in such a way that they would meet in a point a little way beyond your own image mirrored in the eye. And if you want to measure the diminution of the pyramid in the air which occupies the space between the object seen and the eye, you must do it according to the diagram figured below. Let _m n_ be a tower, and _e f_ a, rod, which you must move backwards and forwards till its ends correspond with those of the tower [Footnote 9: _I sua stremi .. della storre_ (its ends ... of the tower) this is the case at _e f_.]; then bring it nearer to the eye, at _c d_ and you will see that the image of the tower seems smaller, as at _r o_. Then [again] bring it closer to the eye and you will see the rod project far beyond the image of the tower from _a_ to _b_ and from _t_ to _b_, and so you will discern that, a little farther within, the lines must converge in a point.