[Footnote:  77. 2.  In the first of the three diagrams Leonardo had drawn only one of the two margins, et m.]

78.

Necessity has provided that all the images of objects in front of the eye shall intersect in two places.  One of these intersections is in the pupil, the other in the crystalline lens; and if this were not the case the eye could not see so great a number of objects as it does.  This can be proved, since all the lines which intersect do so in a point.  Because nothing is seen of objects excepting their surface; and their edges are lines, in contradistinction to the definition of a surface.  And each minute part of a line is equal to a point; for smallest is said of that than which nothing can be smaller, and this definition is equivalent to the definition of the point.  Hence it is possible for the whole circumference of a circle to transmit its image to the point of intersection, as is shown in the 4th of this which shows:  all the smallest parts of the images cross each other without interfering with each other.  These demonstrations are to illustrate the eye.  No image, even of the smallest object, enters the eye without being turned upside down; but as it penetrates into the crystalline lens it is once more reversed and thus the image is restored to the same position within the eye as that of the object outside the eye.

79.

OF THE CENTRAL LINE OF THE EYE.

Only one line of the image, of all those that reach the visual virtue, has no intersection; and this has no sensible dimensions because it is a mathematical line which originates from a mathematical point, which has no dimensions.

According to my adversary, necessity requires that the central line of every image that enters by small and narrow openings into a dark chamber shall be turned upside down, together with the images of the bodies that surround it.

80.

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