The Notebooks of Leonardo Da Vinci (11 page)

131.

Although the points of luminous pyramids may extend into shaded
places and those of pyramids of shadow into illuminated places, and
though among the luminous pyramids one may start from a broader base
than another; nevertheless, if by reason of their various length
these luminous pyramids acquire angles of equal size their light
will be equal; and the case will be the same with the pyramids of
shadow; as may be seen in the intersected pyramids
a b c
and
d e
f
, which though their bases differ in size are equal as to breadth
and light.

[Footnote: 51—55: This supplementary paragraph is indicated as being
a continuation of line 45, by two small crosses.]

The difference between light and lustre (132—135).

132.

Of the difference between light and lustre; and that lustre is not
included among colours, but is saturation of whiteness, and derived
from the surface of wet bodies; light partakes of the colour of the
object which reflects it (to the eye) as gold or silver or the like.

133.

Suppose the body to be the round object figured here and let the
light be at the point
a
, and let the illuminated side of the
object be
b c
and the eye at the point
d
: I say that, as lustre
is every where and complete in each part, if you stand at the point
d
the lustre will appear at
c
, and in proportion as the eye
moves from
d
to
a
, the lustre will move from
c
to
n
.

134.

Heigh light or lustre on any object is not situated [necessarily] in
the middle of an illuminated object, but moves as and where the eye
moves in looking at it.

135.

What is the difference between light and the lustre which is seen on
the polished surface of opaque bodies?

The lights which are produced from the polished surface of opaque
bodies will be stationary on stationary objects even if the eye on
which they strike moves. But reflected lights will, on those same
objects, appear in as many different places on the surface as
different positions are taken by the eye.

Opaque bodies which have a hard and rough surface never display any
lustre in any portion of the side on which the light falls.

Those bodies which are opaque and hard with a hard surface reflect
light [lustre] from every spot on the illuminated side which is in a
position to receive light at the same angle of incidence as they
occupy with regard to the eye; but, as the surface mirrors all the
surrounding objects, the illuminated [body] is not recognisable in
these portions of the illuminated body.

136.

The relations of luminous to illuminated bodies.

The middle of the light and shade on an object in light and shade is
opposite to the middle of the primary light. All light and shadow
expresses itself in pyramidal lines. The middle of the shadow on any
object must necessarily be opposite the middle of its light, with a
direct line passing through the centre of the body. The middle of
the light will be at
a
, that of the shadow at
b
. [Again, in
bodies shown in light and shade the middle of each must coincide
with the centre of the body, and a straight line will pass through
both and through that centre.]

[Footnote: In the original MS., at the spot marked
a
of the first
diagram Leonardo wrote
primitiuo
, and at the spot marked
c
—
primitiva
(primary); at the spot marked
b
he wrote
dirivatiuo
and at
d deriuatiua
(derived).]

Experiments on the relation of light and shadow within a room
(137—140).

137.

Although the balls
a b c
are lighted from one window,
nevertheless, if you follow the lines of their shadows you will see
they intersect at a point forming the angle
n
.

[Footnote: The diagram belonging to this passage is slightly
sketched on Pl. XXXII; a square with three balls below it. The first
three lines of the text belonging to it are written above the sketch
and the six others below it.]

138.

Every shadow cast by a body has a central line directed to a single
point produced by the intersection of luminous lines in the middle
of the opening and thickness of the window. The proposition stated
above, is plainly seen by experiment. Thus if you draw a place with
a window looking northwards, and let this be
s f
, you will see a
line starting from the horizon to the east, which, touching the 2
angles of the window
o f
, reaches
d
; and from the horizon on the
west another line, touching the other 2 angles
r s
, and ending at
c
; and their intersection falls exactly in the middle of the
opening and thickness of the window. Again, you can still better
confirm this proof by placing two sticks, as shown at
g h
; and you
will see the line drawn from the centre of the shadow directed to
the centre
m
and prolonged to the horizon
n f
.

[Footnote:
B
here stands for
cerchio del' orizonte tramontano
on
the original diagram (the circle of the horizon towards the North);
A
for
levante
(East) and
C
for
ponete
(West).]

139.

Every shadow with all its variations, which becomes larger as its
distance from the object is greater, has its external lines
intersecting in the middle, between the light and the object. This
proposition is very evident and is confirmed by experience. For, if
a b
is a window without any object interposed, the luminous
atmosphere to the right hand at
a
is seen to the left at
d
. And
the atmosphere at the left illuminates on the right at
c
, and the
lines intersect at the point
m
.

[Footnote:
A
here stands for
levante
(East),
B
for
ponente
(West).]

140.

Every body in light and shade is situated between 2 pyramids one
dark and the other luminous, one is visible the other is not. But
this only happens when the light enters by a window. Supposing
a b
to be the window and
r
the body in light and shade, the light to
the right hand
z
will pass the object to the left and go on to
p
; the light to the left at
k
will pass to the right of the
object at
i
and go on to
m
and the two lines will intersect at
c
and form a pyramid. Then again
a
b
falls on the shaded body
at
i
g
and forms a pyramid
f
i
g
.
f
will be dark because
the light
a
b
can never fall there;
i
g
c
will be
illuminated because the light falls upon it.

Light and shadow with regard to the position of the eye (141—145).

141.

Every shaded body that is larger than the pupil and that interposes
between the luminous body and the eye will be seen dark.

When the eye is placed between the luminous body and the objects
illuminated by it, these objects will be seen without any shadow.

[Footnote: The diagram which in the original stands above line 1 is
given on Plate II, No 2. Then, after a blank space of about eight
lines, the diagram Plate II No 3 is placed in the original. There is
no explanation of it beyond the one line written under it.]

142.

Why the 2 lights one on each side of a body having two pyramidal
sides of an obtuse apex leave it devoid of shadow.

[Footnote: The sketch illustrating this is on Plate XLI No 1.]

143.

A body in shadow situated between the light and the eye can never
display its illuminated portion unless the eye can see the whole of
the primary light.

[Footnote:
A
stands for
corpo
(body),
B
for
lume
(light).]

144.

The eye which looks (at a spot) half way between the shadow and the
light which surrounds the body in shadow will see that the deepest
shadows on that body will meet the eye at equal angles, that is at
the same angle as that of sight.

[Footnote: In both these diagrams
A
stands for
lume
(light)
B
for
ombra
(shadow).]

145.

If the sun is in the East and you look towards the West you will see
every thing in full light and totally without shadow because you see
them from the same side as the sun: and if you look towards the
South or North you will see all objects in light and shade, because
you see both the side towards the sun and the side away from it; and
if you look towards the coming of the sun all objects will show you
their shaded side, because on that side the sun cannot fall upon
them.

The law of the incidence of light.

146.

The edges of a window which are illuminated by 2 lights of equal
degrees of brightness will not reflect light of equal brightness
into the chamber within.

If
b
is a candle and
a c
our hemisphere both will illuminate the
edges of the window
m
n
, but light
b
will only illuminate
f
g
and the hemisphere
a
will light all of
d e
.

147.

That part of a body which receives the luminous rays at equal angles
will be in a higher light than any other part of it.

And the part which the luminous rays strike between less equal
angles will be less strongly illuminated.

Gradations of strength in the shadows (148. 149).

148.

That part of the object which is marked
m
is in the highest light
because it faces the window
a d
by the line
a f
;
n
is in the
second grade because the light
b d
strikes it by the line
b e
;
o
is in the third grade, as the light falls on it from
c d
by
the line
c h
;
p
is the lowest light but one as
c d
falls on it
by the line
d v
;
q
is the deepest shadow for no light falls on
it from any part of the window.

In proportion as
c d
goes into
a d
so will
n r s
be darker
than
m
, and all the rest is space without shadow.

[Footnote: The diagram belonging to this chapter is No. 1 on Plate
III. The letters
a b e d
and
r
are not reproduced in facsimile
of the original, but have been replaced by ordinary type in the
margin. 5-12. The original text of these lines is reproduced within
the diagram.—Compare No 275.]

149.

The light which falls on a shaded body at the acutest angle receives
the highest light, and the darkest portion is that which receives it
at an obtuse angle and both the light and the shadow form pyramids.
The angle
c
receives the highest grade of light because it is
directly in front of the window
a b
and the whole horizon of the
sky
m x
. The angle
a
differs but little from
c
because the
angles which divide it are not so unequal as those below, and only
that portion of the horizon is intercepted which lies between
y
and
x
. Although it gains as much on the other side its line is
nevertheless not very strong because one angle is smaller than its
fellow. The angles
e i
will have less light because they do not
see much of the light
m s
and the light
v x
and their angles are
very unequal. Yhe angle
k
and the angle
f
are each placed
between very unequal angles and therefore have but little light,
because at
k
it has only the light
p t
, and at
f
only
t q
;
o g
is the lowest grade of light because this part has no light at
all from the sky; and thence come the lines which will reconstruct a
pyramid that is the counterpart of the pyramid
c
; and this pyramid
l
is in the first grade of shadow; for this too is placed between
equal angles directly opposite to each other on either side of a
straight line which passes through the centre of the body and goes
to the centre of the light. The several luminous images cast within
the frame of the window at the points
a
and
b
make a light which
surrounds the derived shadow cast by the solid body at the points 4
and 6. The shaded images increase from
o g
and end at 7 and 8.

[Footnote: The diagram belonging to this chapter is No. 2 on Plate
III. In the original it is placed between lines 3 and 4, and in the
reproduction these are shown in part. The semi circle above is
marked
orizonte
(horizon). The number 6 at the left hand side,
outside the facsimile, is in the place of a figure which has become
indistinct in the original.]