/ · The Notebooks of Leonardo da Vinci

56

The relations of the distance points to the vanishing point.

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.]

Taken from The Notebooks of Leonardo da Vinci edited by Jean Paul Richter, 1880.