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 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.
81.
HOW THE INNUMERABLE RAYS FROM INNUMERABLE IMAGES CAN CONVERGE TO A
POINT.
Just as all lines can meet at a point without interfering with each
other--being without breadth or thickness--in the same way all the
images of surfaces can meet there; and as each given point faces the
object opposite to it and each object faces an opposite point, the
converging rays of the image can pass through the point and diverge
again beyond it to reproduce and re-magnify the real size of that
image. But their impressions will appear reversed--as is shown in
the first, above; where it is said that every image intersects as it
enters the narrow openings made in a very thin substance.
Read the marginal text on the other side.
In proportion as the opening is smaller than the shaded body, so
much less will the images transmitted through this opening intersect
each other. The sides of images which pass through openings into a
dark room intersect at a point which is nearer to the opening in
proportion as the opening is narrower. To prove this let _a b_ be an
object in light and shade which sends not its shadow but the image
of its darkened form through the opening _d e_ which is as wide as
this shaded body; and its sides _a b_, being straight lines (as has
been proved) must intersect between the shaded object and the
opening; but nearer to the opening in proportion as it is smaller
than the object in shade. As is shown, on your right hand and your
left hand, in the two diagrams _a_ _b_ _c_ _n_ _m_ _o_ where, the
right opening _d_ _e_, being equal in width to the shaded object _a_
_b_, the intersection of the sides of the said shaded object occurs
half way between the opening and the shaded object at the point _c_.
But this cannot happen in the left hand figure, the opening _o_
being much smaller than the shaded object _n_ _m_.
It is impossible that the images of objects should be seen between
the objects and the openings through which the images of these
bodies are admitted; and this is plain, because where the atmosphere
is illuminated these images are not formed visibly.
When the images are made double by mutually crossing each other they
are invariably doubly as dark in tone. To prove this let _d_ _e_ _h_
be such a doubling which although it is only seen within the space
between the bodies in _b_ and _i_ this will not hinder its being
seen from _f_ _g_ or from _f_ _m_; being composed of the images _a_
_b_ _i_ _k_ which run together in _d_ _e_ _h_.
[Footnote: 81. On the original diagram at the beginning of this
chapter Leonardo has written "_azurro_" (blue) where in the
facsimile I have marked _A_, and "_giallo_" (yellow) where _B_
stands.]
[Footnote: 15--23. These lines stand between the diagrams I and III.]
[Footnote: 24--53. These lines stand between the diagrams I and II.]
[Footnote: 54--97 are written along the left side of diagram I.]
82.
An experiment showing that though the pupil may not be moved from
its position the objects seen by it may appear to move from their
places.
If you look at an object at some distance from you and which is
below the eye, and fix both your eyes upon it and with one hand
firmly hold the upper lid open while with the other you push up the
under lid--still keeping your eyes fixed on the object gazed at--you
will see that object double; one [image] remaining steady, and the
other moving in a contrary direction to the pressure of your finger
on the lower eyelid. How false the opinion is of those who say that
this happens because the pupil of the eye is displaced from its
position.
How the above mentioned facts prove that the pupil acts upside down
in seeing.
[Footnote: 82. 14--17. The subject indicated by these two headings is
fully discussed in the two chapters that follow them in the
original; but it did not seem to me appropriate to include them
here.]
Demostration of perspective by means of a vertical glass plane
(83-85).
83.