52

Experimental proof of the existence of the pyramid of sight.

Perspective is a rational demonstration, confirmed by experience, that all objects transmit their image to the eye by a pyramid of lines.

By a pyramid of lines I understand those lines which start from the edges of the surface of bodies, and converging from a distance, meet in a single point; and this point, in the present instance, I will show to be situated in the eye which is the universal judge of all objects. By a point I mean that which cannot be divided into parts; therefore this point, which is situated in the eye, being indivisible, no body is seen by the eye, that is not larger than this point. This being the case it is inevitable that the lines which come from the object to the point must form a pyramid. And if any man seeks to prove that the sense of sight does not reside in this point, but rather in the black spot which is visible in the middle of the pupil, I might reply to him that a small object could never diminish at any distance, as it might be a grain of millet or of oats or of some similar thing, and that object, if it were larger than the said [black] spot would never be seen as a whole; as may be seen in the diagram below. Let a. be the seat of sight, b e the lines which reach the eye. Let e d be the grains of millet within these lines. You plainly see that these will never diminish by distance, and that the body m n could not be entirely covered by it. Therefore you must confess that the eye contains within itself one single indivisible point a, to which all the points converge of the pyramid of lines starting from an object, as is shown below. Let a. b. be the eye; in the centre of it is the point above mentioned. If the line e f is to enter as an image into so small an opening in the eye, you must confess that the smaller object cannot enter into what is smaller than itself unless it is diminished, and by diminishing it must take the form of a pyramid.

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

51 * 53

I * III

Notebooks of Leonoardo da Vinci

II: Linear Perspective.

. . .

General remarks on perspective.

40,

The elements of perspective--Of the Point.

42,

43,

44,

45,

Of the line.

47,

48,

The nature of the outline.

Definition of Perspective.

Experimental proof of the existence of the pyramid of sight.

52,

53,

The relations of the distance points to the vanishing point.

55,

How to measure the pyramid of vision.

The Production of pyramid of Vision.

58,

59,

60,

61,

62,

63,

Proof by experiment.

65,

General conclusions.

That the contrary is impossible.

A parallel case.

The function of the eye as explained by the camera obscura.

70,

The practice of perspective.

. . .