Da Vinci Notes #67 - Whole and Parts

General conclusions.

All objects project their whole image and likeness, diffused and
mingled in the whole of the atmosphere, opposite to themselves. The
image of every point of the bodily surface, exists in every part of
the atmosphere.

All the images of the objects are in every part of the atmosphere.
The whole, and each part of the image of the atmosphere is
[reflected] in each point of the surface of the bodies presented to
it. Therefore both the part and the whole of the images of the
objects exist, both in the whole and in the parts of the surface of

these visible bodies.

Whence we may evidently say that the image of each object exists,
as a whole and in every part, in each part and in the whole
interchangeably in every existing body. As is seen in two mirrors
placed opposite to each other.

Keith's Ideas:

1. One projects his/her image in whole and in parts.

2. One can pick up the parts or the whole.

3. How could the parts be consistent with the whole?

Keith To

www.keithto.com

Da Vinci Notes #66 - Images are Everywhere

The images of objects are all diffused through the atmosphere which

receives them; and all on every side in it. To prove this, let _a c

e_ be objects of which the images are admitted to a dark chamber by

the small holes _n p_ and thrown upon the plane _f i_ opposite to

these holes. As many images will be produced in the chamber on the

Every point is the termination of an infinite number of lines, which

diverge to form a base, and immediately, from the base the same

lines converge to a pyramid [imaging] both the colour and form. No

sooner is a form created or compounded than suddenly infinite lines

and angles are produced from it; and these lines, distributing

themselves and intersecting each other in the air, give rise to an

infinite number of angles opposite to each other. Given a base, each

opposite angle, will form a triangle having a form and proportion

equal to the larger angle; and if the base goes twice into each of

All bodies together, and each by itself, give off to the surrounding

air an infinite number of images which are all-pervading and each

complete, each conveying the nature, colour and form of the body

which produces it.

It can clearly be shown that all bodies are, by their images,

all-pervading in the surrounding atmosphere, and each complete in

itself as to substance form and colour; this is seen by the images

of the various bodies which are reproduced in one single perforation

through which they transmit the objects by lines which intersect and

cause reversed pyramids, from the objects, so that they are upside

Da Vinci Notes #60 - Atmosphere Reflecting What's Inside It

That the atmosphere attracts to itself, like a loadstone, all the

images of the objects that exist in it, and not their forms merely

but their nature may be clearly seen by the sun, which is a hot and

luminous body. All the atmosphere, which is the all-pervading

matter, absorbs light and heat, and reflects in itself the image of

the source of that heat and splendour and, in each minutest portion,

does the same. The Northpole does the same as the loadstone shows;

and the moon and the other planets, without suffering any

diminution, do the same. Among terrestrial things musk does the same

Da Vinci Notes #55 - It is OK to Have No Idea!

ELEMENTS OF PERSPECTIVE.

All objects transmit their image to the eye in pyramids, and the

nearer to the eye these pyramids are intersected the smaller will

the image appear of the objects which cause them. Therefore, you may

Da Vinci Notes 53 - Eye Can Never Be a True Judge

PERSPECTIVE.

Perspective comes in where judgment fails [as to the distance] in

objects which diminish. The eye can never be a true judge for

determining with exactitude how near one object is to another which

is equal to it [in size], if the top of that other is on the level

of the eye which sees them on that side, excepting by means of the

vertical plane which is the standard and guide of perspective.

Let _n_ be the eye, _e f_ the vertical plane above mentioned. Let

_a b c d_ be the three divisions, one below the other; if the lines

_a n_ and _c n_ are of a given length and the eye _n_ is in the centre,

then _a b_ will look as large as _b c. c d_ is lower and farther off

from _n_, therefore it will look smaller. And the same effect will

appear in the three divisions of a face when the eye of the painter

who is drawing it is on a level with the eye of the person he is

Da Vinci Notes #52 - Focus

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

Da Vinci Notes #51 - Seeing One Thing at a Time

IN WHAT WAY THE EYE SEES OBJECTS PLACED IN FRONT
OF IT.

The perception of the object depends on the direction of the eye.

Supposing that the ball figured above is the ball of the eye and let

the small portion of the ball which is cut off by the line _s t_ be

the pupil and all the objects mirrored on the centre of the face of

the eye, by means of the pupil, pass on at once and enter the pupil,

passing through the crystalline humour, which does not interfere in

the pupil with the things seen by means of the light. And the pupil

having received the objects, by means of the light, immediately

refers them and transmits them to the intellect by the line _a b_.

And you must know that the pupil transmits nothing perfectly to the

intellect or common sense excepting when the objects presented to it

by means of light, reach it by the line _a b;_ as, for instance, by

the line _b c_. For although the lines _m n_ and _f g_ may be seen

by the pupil they are not perfectly taken in, because they do not

coincide with the line _a b_. And the proof is this: If the eye,

shown above, wants to count the letters placed in front, the eye

will be obliged to turn from letter to letter, because it cannot

discern them unless they lie in the line _a b;_ as, for instance, in

the line _a c_. All visible objects reach the eye by the lines of a

pyramid, and the point of the pyramid is the apex and centre of it,

Da Vinci Notes #49 - Don't Surround Yourself with Boundary

The nature of the outline.

The boundaries of bodies are the least of all things. The

proposition is proved to be true, because the boundary of a thing is

a surface, which is not part of the body contained within that

surface; nor is it part of the air surrounding that body, but is the

medium interposted between the air and the body, as is proved in its

place.

But the lateral boundaries of these bodies is the line forming

the boundary of the surface, which line is of invisible thickness.

Wherefore O painter! do not surround your bodies with lines,

and above all when representing objects smaller than nature;

for not only will their external outlines become indistinct, but

Da Vinci Notes #46 - Something Has No Form, Has No Limitation

The point, being indivisible, occupies no space. That which occupies

no space is nothing. The limiting surface of one thing is the

beginning of another. 2. That which is no part of any body is called

nothing. 1. That which has no limitations, has no form.

The limitations of two conterminous bodies are interchangeably the

surface of each. All the surfaces of a body are not parts of that

Da Vinci Notes #45 - Your Surface Limits You

1, The superficies is a limitation of the body. 2, and the

limitation of a body is no part of that body. 3, and the limitation

of one body is that which begins another. 4, that which is not part

of any body is nothing. Nothing is that which fills no space.

If one single point placed in a circle may be the starting point of

an infinite number of lines, and the termination of an infinite

number of lines, there must be an infinite number of points

separable from this point, and these when reunited become one again;

The elements of perspective--Of the Point (42-46)

Da Vinci Notes #42 - Analyzing Through Perspective

All the problems of perspective are made clear by the five terms of

mathematicians, which are:--the point, the line, the angle, the

superficies and the solid.

The point is unique of its kind. And the point has neither height,

breadth, length, nor depth, whence it is to be regarded as

indivisible and as having no dimensions in space.

The line is of three kinds, straight, curved and sinuous and it has

neither breadth, height, nor depth. Hence it is indivisible,

excepting in its length, and its ends are two points. The angle is

Da Vinci Notes #41 - Seeing Things Differently

The art of perspective is of such a nature as to make what is flat