The Notebooks of Leonardo Da Vinci (61 page)

[Footnote: In the original sketch, inside the circle in the first
diagram, is written
Sole
(sun), and to the right of it
luna
(moon). Thus either of these heavenly bodies may be supposed to fill
that space. Within the lower circle is written
simulacro
(image).
In the two next diagrams at the spot here marked
L
the word
Luna
is written, and in the last
sole
is written in the top circle at
a
.]

The image of the sun will be more brightly shown in small waves than
in large ones—and this is because the reflections or images of the
sun are more numerous in the small waves than in large ones, and the
more numerous reflections of its radiance give a larger light than
the fewer.

Waves which intersect like the scales of a fir cone reflect the
image of the sun with the greatest splendour; and this is the case
because the images are as many as the ridges of the waves on which
the sun shines, and the shadows between these waves are small and
not very dark; and the radiance of so many reflections together
becomes united in the image which is transmitted to the eye, so that
these shadows are imperceptible.

That reflection of the sun will cover most space on the surface of
the water which is most remote from the eye which sees it.

Let
a
be the sun,
p q
the reflection of the sun;
a b
is the
surface of the water, in which the sun is mirrored, and
r
the eye
which sees this reflection on the surface of the water occupying the
space
o m
.
c
is the eye at a greater distance from the surface
of the water and also from the reflection; hence this reflection
covers a larger space of water, by the distance between
n
and
o
.

876.

It is impossible that the side of a spherical mirror, illuminated by
the sun, should reflect its radiance unless this mirror were
undulating or filled with bubbles.

You see here the sun which lights up the moon, a spherical mirror,
and all of its surface, which faces the sun is rendered radiant.

Whence it may be concluded that what shines in the moon is water
like that of our seas, and in waves as that is; and that portion
which does not shine consists of islands and terra firma.

This diagram, of several spherical bodies interposed between the eye
and the sun, is given to show that, just as the reflection of the
sun is seen in each of these bodies, in the same way that image may
be seen in each curve of the waves of the sea; and as in these many
spheres many reflections of the sun are seen, so in many waves there
are many images, each of which at a great distance is much magnified
to the eye. And, as this happens with each wave, the spaces
interposed between the waves are concealed; and, for this reason, it
looks as though the many suns mirrored in the many waves were but
one continuous sun; and the shadows,, mixed up with the luminous
images, render this radiance less brilliant than that of the sun
mirrored in these waves.

[Footnote: In the original, at letter
A
in the diagram "
Sole
"
(the sun) is written, and at
o
"
occhio
" (the eye).]

877.

This will have before it the treatise on light and shade.

The edges in the moon will be most strongly lighted and reflect most
light, because, there, nothing will be visible but the tops of the
waves of the water [Footnote 5: I have thought it unnecessary to
reproduce the detailed explanation of the theory of reflection on
waves contained in the passage which follows this.].

878.

The sun will appear larger in moving water or on waves than in still
water; an example is the light reflected on the strings of a
monochord.

The question of the true and of the apparent size of the sun
(879-884).

879.

If you look at the stars, cutting off the rays (as may be done by
looking through a very small hole made with the extreme point of a
very fine needle, placed so as almost to touch the eye), you will
see those stars so minute that it would seem as though nothing could
be smaller; it is in fact their great distance which is the reason
of their diminution, for many of them are very many times larger
than the star which is the earth with water. Now reflect what this
our star must look like at such a distance, and then consider how
many stars might be added—both in longitude and latitude—between
those stars which are scattered over the darkened sky. But I cannot
forbear to condemn many of the ancients, who said that the sun was
no larger than it appears; among these was Epicurus, and I believe
that he founded his reason on the effects of a light placed in our
atmosphere equidistant from the centre of the earth. Any one looking
at it never sees it diminished in size at whatever distance; and the
rea-

[Footnote 879-882: What Leonardo says of Epicurus— who according to
LEWIS,
The Astronomy of the ancients
, and MADLER,
Geschichte der
Himmelskunde
, did not devote much attention to the study of
celestial phenomena—, he probably derived from Book X of Diogenes
Laertius, whose
Vitae Philosophorum
was not printed in Greek till
1533, but the Latin translation appeared in 1475.]

880.

sons of its size and power I shall reserve for Book 4. But I wonder
greatly that Socrates

[Footnote 2:
Socrates;
I have little light to throw on this
reference. Plato's Socrates himself declares on more than one
occasion that in his youth he had turned his mind to the study of
celestial phenomena (METEWPA) but not in his later years (see G. C.
LEWIS,
The Astronomy of the ancients
, page 109; MADLER,
Geschichte der Himmelskunde
, page 41). Here and there in Plato's
writings we find incidental notes on the sun and other heavenly
bodies. Leonardo may very well have known of these, since the Latin
version by Ficinus was printed as early as 1491; indeed an undated
edition exists which may very likely have appeared between 1480—90.

There is but one passage in Plato, Epinomis (p. 983) where he speaks
of the physical properties of the sun and says that it is larger
than the earth.

Aristotle who goes very fully into the subject says the same. A
complete edition of Aristotele's works was first printed in Venice
1495-98, but a Latin version of the Books
De Coelo et Mundo
and
De Physica
had been printed in Venice as early as in 1483 (H.
MULLER-STRUBING).]

should have depreciated that solar body, saying that it was of the
nature of incandescent stone, and the one who opposed him as to that
error was not far wrong. But I only wish I had words to serve me to
blame those who are fain to extol the worship of men more than that
of the sun; for in the whole universe there is nowhere to be seen a
body of greater magnitude and power than the sun. Its light gives
light to all the celestial bodies which are distributed throughout
the universe; and from it descends all vital force, for the heat
that is in living beings comes from the soul [vital spark]; and
there is no other centre of heat and light in the universe as will
be shown in Book 4; and certainly those who have chosen to worship
men as gods—as Jove, Saturn, Mars and the like—have fallen into
the gravest error, seeing that even if a man were as large as our
earth, he would look no bigger than a little star which appears but
as a speck in the universe; and seeing again that these men are
mortal, and putrid and corrupt in their sepulchres.

Marcellus [Footnote 23: I have no means of identifying
Marcello
who is named in the margin. It may be Nonius Marcellus, an obscure
Roman Grammarian of uncertain date (between the IInd and Vth
centuries A. C.) the author of the treatise
De compendiosa doctrina
per litteras ad filium
in which he treats
de rebus omnibus et
quibusdam aliis
. This was much read in the middle ages. The
editto
princeps
is dated 1470 (H. MULLER-STRUBING).] and many others
praise the sun.

881.

Epicurus perhaps saw the shadows cast by columns on the walls in
front of them equal in diameter to the columns from which the
shadows were cast; and the breadth of the shadows being parallel
from beginning to end, he thought he might infer that the sun also
was directly opposite to this parallel and that consequently its
breadth was not greater than that of the column; not perceiving that
the diminution in the shadow was insensibly slight by reason of the
remoteness of the sun. If the sun were smaller than the earth, the
stars on a great portion of our hemisphere would have no light,
which is evidence against Epicurus who says the sun is only as large
as it appears.

[Footnote: In the original the writing is across the diagram.]

882.

Epicurus says the sun is the size it looks. Hence as it looks about
a foot across we must consider that to be its size; it would follow
that when the moon eclipses the sun, the sun ought not to appear the
larger, as it does. Then, the moon being smaller than the sun, the
moon must be less than a foot, and consequently when our world
eclipses the moon, it must be less than a foot by a finger's
breadth; inasmuch as if the sun is a foot across, and our earth
casts a conical shadow on the moon, it is inevitable that the
luminous cause of the cone of shadow must be larger than the opaque
body which casts the cone of shadow.

883.

To measure how many times the diameter of the sun will go into its
course in 24 hours.

Make a circle and place it to face the south, after the manner of a
sundial, and place a rod in the middle in such a way as that its
length points to the centre of this circle, and mark the shadow cast
in the sunshine by this rod on the circumference of the circle, and
this shadow will be—let us say— as broad as from
a
to
n
. Now
measure how many times this shadow will go into this circumference
of a circle, and that will give you the number of times that the
solar body will go into its orbit in 24 hours. Thus you may see
whether Epicurus was [right in] saying that the sun was only as
large as it looked; for, as the apparent diameter of the sun is
about a foot, and as that sun would go a thousand times into the
length of its course in 24 hours, it would have gone a thousand
feet, that is 300 braccia, which is the sixth of a mile. Whence it
would follow that the course of the sun during the day would be the
sixth part of a mile and that this venerable snail, the sun will
have travelled 25 braccia an hour.

884.

Posidonius composed books on the size of the sun. [Footnote:
Poseidonius of Apamea, commonly called the Rhodian, because he
taught in Rhodes, was a Stoic philosopher, a contemporary and friend
of Cicero's, and the author of numerous works on natural science,
among them.

Strabo quotes no doubt from one of his works, when he says that
Poseidonius explained how it was that the sun looked larger when it
was rising or setting than during the rest of its course (III, p.
135). Kleomedes, a later Greek Naturalist also mentions this
observation of Poseidonius' without naming the title of his work;
however, as Kleomedes' Cyclia Theorica was not printed till 1535,
Leonardo must have derived his quotation from Strabo. He probably
wrote this note in 1508, and as the original Greek was first printed
in Venice in 1516, we must suppose him to quote here from the
translation by Guarinus Veronensis, which was printed as early as
1471, also at Venice (H. MULLER-STRUBING).]

Of the nature of Sunlight.

885.

Of the nature of Sunlight.

That the heat of the sun resides in its nature and not in its virtue
[or mode of action] is abundantly proved by the radiance of the
solar body on which the human eye cannot dwell and besides this no
less manifestly by the rays reflected from a concave mirror,
which—when they strike the eye with such splendour that the eye
cannot bear them—have a brilliancy equal to the sun in its own
place. And that this is true I prove by the fact that if the mirror
has its concavity formed exactly as is requisite for the collecting
and reflecting of these rays, no created being could endure the
heat that strikes from the reflected rays of such a mirror. And if
you argue that the mirror itself is cold and yet send forth hot
rays, I should reply that those rays come really from the sun and
that it is the ray of the concave mirror after having passed through
the window.

Considerations as to the size of the sun (886-891).

886.

The sun does not move. [Footnote: This sentence occurs incidentally
among mathematical notes, and is written in unusually large
letters.]

887.

[Footnote: Lines 4 and fol. Compare Vol. I, Nos. 130, 131.] If it is
from the centre that the sun employs its radiance to intensify the
power of its whole mass, it is evident that the farther its rays
extend, the more widely they will be divided; and this being so,
you, whose eye is near the water that mirrors the sun, see but a
small portion of the rays of the sun strike the surface of the
water, and reflecting the form of the sun. But if you were near to
the sun—as would be the case when the sun is on the meridian and
the sea to the westward—you would see the sun, mirrored in the sea,
of a very great size; because, as you are nearer to the sun, your
eye taking in the rays nearer to the point of radiation takes more
of them in, and a great splendour is the result. And in this way it
can be proved that the moon must have seas which reflect the sun,
and that the parts which do not shine are land.