AS TO WHETHER THE CENTRAL LINE OF THE IMAGE CAN BE INTERSECTED, OR NOT, WITHIN THE OPENING.

It is impossible that the line should intersect itself; that is,
that its right should cross over to its left side, and so, its left
side become its right side. Because such an intersection demands two
lines, one from each side; for there can be no motion from right to
left or from left to right in itself without such extension and
thickness as admit of such motion. And if there is extension it is
no longer a line but a surface, and we are investigating the
properties of a line, and not of a surface. And as the line, having
no centre of thickness cannot be divided, we must conclude that the
line can have no sides to intersect each other. This is proved by
the movement of the line *a f* to *a b* and of the line *e b* to *e
f*, which are the sides of the surface *a f e b*. But if you move
the line *a b* and the line *e f*, with the frontends *a e*, to the
spot *c*, you will have moved the opposite ends *f b* towards each
other at the point *d*. And from the two lines you will have drawn
the straight line *c d* which cuts the middle of the intersection of
these two lines at the point *n* without any intersection. For, you
imagine these two lines as having breadth, it is evident that by
this motion the first will entirely cover the other—being equal
with it—without any intersection, in the position *c d*. And this
is sufficient to prove our proposition.

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

. . .

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.

72,

Refraction of the rays falling upon the eye.

74,

The inversion of the images.

The intersection of the rays.

77,

78,

79,

80,

81,

Demomstration of perspective by means of a vertical glass plane.

83,

84,

The angle of sight varies with the distance.

86,

87,

Opposite pyramids in juxtaposition.

On simple and complex perspective.

The proper distance of objects from the eye.

91,

eye.

93,

94,

95,

96,

97,

The apparent size of objects defined by calculation.

99,

. . .