The Notebooks of Leonardo Da Vinci, Complete by Leonardo Da Vinci

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872.

_a_, the side of the body in light and shade _b_, faces the whole
portion of the hemisphere bed _e f_, and does not face any part of
the darkness of the earth. And the same occurs at the point _o_;
therefore the space a _o_ is throughout of one and the same
brightness, and s faces only four degrees of the hemisphere _d e f g
h_, and also the whole of the earth _s h_, which will render it
darker; and how much must be demonstrated by calculation. [Footnote:
This passage, which has perhaps a doubtful right to its place in
this connection, stands in the Manuscript between those given in
Vol. I as No. 117 and No. 427.]

873.

THE REASON OF THE INCREASED SIZE OF THE SUN IN THE WEST.

Some mathematicians explain that the sun looks larger as it sets,
because the eye always sees it through a denser atmosphere, alleging
that objects seen through mist or through water appear larger. To
these I reply: No; because objects seen through a mist are similar
in colour to those at a distance; but not being similarly diminished
they appear larger. Again, nothing increases in size in smooth
water; and the proof of this may be seen by throwing a light on a
board placed half under water. But the reason why the sun looks
larger is that every luminous body appears larger in proportion as
it is more remote. [Footnote: Lines 5 and 6 are thus rendered by M.
RAVAISSON in his edition of MS. A. "_De meme, aucune chose ne croit
dans l'eau plane, et tu en feras l'experience_ en calquant un ais
sous l'eau."--Compare the diagrams in Vol. I, p. 114.]

On the luminosity of the Earth in the universal space (874-878).

874.

In my book I propose to show, how the ocean and the other seas must,
by means of the sun, make our world shine with the appearance of a
moon, and to the remoter worlds it looks like a star; and this I
shall prove.

Show, first that every light at a distance from the eye throws out
rays which appear to increase the size of the luminous body; and
from this it follows that 2 ...[Footnote 10: Here the text breaks
off; lines 11 and fol. are written in the margin.].

[11]The moon is cold and moist. Water is cold and moist. Thus our
seas must appear to the moon as the moon does to us.

875.

The waves in water magnify the image of an object reflected in it.

Let _a_ be the sun, and _n m_ the ruffled water, _b_ the image of
the sun when the water is smooth. Let _f_ be the eye which sees the
image in all the waves included within the base of the triangle _c e
f_. Now the sun reflected in the unruffled surface occupied the
space _c d_, while in the ruffled surface it covers all the watery
space _c e_ (as is proved in the 4th of my "Perspective") [Footnote
9: _Nel quarto della mia prospettiva_. If this reference is to the
diagrams accompanying the text--as is usual with Leonardo--and not
to some particular work, the largest of the diagrams here given must
be meant. It is the lowest and actually the fifth, but he would have
called it the fourth, for the text here given is preceded on the
same page of the manuscript by a passage on whirlpools, with the
diagram belonging to it also reproduced here. The words _della mia
prospettiva_ may therefore indicate that the diagram to the
preceding chapter treating on a heterogeneal subject is to be
excluded. It is a further difficulty that this diagram belongs
properly to lines 9-10 and not to the preceding sentence. The
reflection of the sun in water is also discussed in the Theoretical
part of the Book on Painting; see Vol. I, No. 206, 207.] and it will
cover more of the water in proportion as the reflected image is
remote from the eye [10].

[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.

II.

THE SUN.

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

879.

IN PRAISE OF THE SUN.

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 PROOF THAT THE SUN IS HOT BY NATURE AND NOT BY VIRTUE.

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.

PROOF THAT THE NEARER YOU ARE TO THE SOURCE OF THE SOLAR RAYS, THE
LARGER WILL THE REFLECTION OF THE SUN FROM THE SEA APPEAR TO YOU.

[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.

888.

Take the measure of the sun at the solstice in mid-June.

889.

WHY THE SUN APPEARS LARGER WHEN SETTING THAN AT NOON, WHEN IT IS
NEAR TO US.

Every object seen through a curved medium seems to be of larger size
than it is.

[Footnote: At A is written _sole_ (the sun), at B _terra_ (the
earth).]

890.

Because the eye is small it can only see the image of the sun as of
a small size. If the eye were as large as the sun it would see the
image of the sun in water of the same size as the real body of the
sun, so long as the water is smooth.

891.

A METHOD OF SEEING THE SUN ECLIPSED WITHOUT PAIN TO THE EYE.

Take a piece of paper and pierce holes in it with a needle, and look
at the sun through these holes.

III.

THE MOON.

On the luminousity of the moon (892-901).

892.

OF THE MOON.

As I propose to treat of the nature of the moon, it is necessary
that first I should describe the perspective of mirrors, whether
plane, concave or convex; and first what is meant by a luminous ray,
and how it is refracted by various kinds of media; then, when a
reflected ray is most powerful, whether when the angle of incidence
is acute, right, or obtuse, or from a convex, a plane, or a concave
surface; or from an opaque or a transparent body. Besides this, how
it is that the solar rays which fall on the waves of the sea, are
seen by the eye of the same width at the angle nearest to the eye,
as at the highest line of the waves on the horizon; but
notwithstanding this the solar rays reflected from the waves of the
sea assume the pyramidal form and consequently, at each degree of
distance increase proportionally in size, although to our sight,
they appear as parallel.

1st. Nothing that has very little weight is opaque.

2dly. Nothing that is excessively weighty can remain beneath that
which is heavier.

3dly. As to whether the moon is situated in the centre of its
elements or not.

And, if it has no proper place of its own, like the earth, in the
midst of its elements, why does it not fall to the centre of our
elements? [Footnote 26: The problem here propounded by Leonardo was
not satisfactorily answered till Newton in 1682 formulated the law
of universal attraction and gravitation. Compare No. 902, lines
5-15.]

And, if the moon is not in the centre of its own elements and yet
does not fall, it must then be lighter than any other element.

And, if the moon is lighter than the other elements why is it opaque
and not transparent?

When objects of various sizes, being placed at various distances,
look of equal size, there must be the same relative proportion in
the distances as in the magnitudes of the objects.

[Footnote: In the diagram Leonardo wrote _sole_ at the place marked
_A_.]

893.

OF THE MOON AND WHETHER IT IS POLISHED AND SPHERICAL.

The image of the sun in the moon is powerfully luminous, and is only
on a small portion of its surface. And the proof may be seen by
taking a ball of burnished gold and placing it in the dark with a
light at some distance from it; and then, although it will
illuminate about half of the ball, the eye will perceive its
reflection only in a small part of its surface, and all the rest of
the surface reflects the darkness which surrounds it; so that it is
only in that spot that the image of the light is seen, and all the
rest remains invisible, the eye being at a distance from the ball.
The same thing would happen on the surface of the moon if it were
polished, lustrous and opaque, like all bodies with a reflecting
surface.

Show how, if you were standing on the moon or on a star, our earth
would seem to reflect the sun as the moon does.

And show that the image of the sun in the sea cannot appear one and
undivided, as it appears in a perfectly plane mirror.

894.

How shadows are lost at great distances, as is shown by the shadow
side of the moon which is never seen. [Footnote: Compare also Vol.
I, Nos. 175-179.]

895.

Either the moon has intrinsic luminosity or not. If it has, why does
it not shine without the aid of the sun? But if it has not any light
in itself it must of necessity be a spherical mirror; and if it is a
mirror, is it not proved in Perspective that the image of a luminous
object will never be equal to the extent of surface of the
reflecting body that it illuminates? And if it be thus [Footnote 13:
At A, in the diagram, Leonardo wrote "_sole_" (the sun), and at B
"_luna o noi terra_" (the moon or our earth). Compare also the text
of No. 876.], as is here shown at _r s_ in the figure, whence comes
so great an extent of radiance as that of the full moon as we see
it, at the fifteenth day of the moon?

896.

OF THE MOON.

The moon has no light in itself; but so much of it as faces the sun
is illuminated, and of that illumined portion we see so much as
faces the earth. And the moon's night receives just as much light as
is lent it by our waters as they reflect the image of the sun, which
is mirrored in all those waters which are on the side towards the
sun. The outside or surface of the waters forming the seas of the
moon and of the seas of our globe is always ruffled little or much,
or more or less--and this roughness causes an extension of the
numberless images of the sun which are repeated in the ridges and
hollows, the sides and fronts of the innumerable waves; that is to
say in as many different spots on each wave as our eyes find
different positions to view them from. This could not happen, if the
aqueous sphere which covers a great part of the moon were uniformly
spherical, for then the images of the sun would be one to each
spectator, and its reflections would be separate and independent and
its radiance would always appear circular; as is plainly to be seen
in the gilt balls placed on the tops of high buildings. But if those
gilt balls were rugged or composed of several little balls, like
mulberries, which are a black fruit composed of minute round
globules, then each portion of these little balls, when seen in the
sun, would display to the eye the lustre resulting from the
reflection of the sun, and thus, in one and the same body many tiny
suns would be seen; and these often combine at a long distance and
appear as one. The lustre of the new moon is brighter and stronger,
than when the moon is full; and the reason of this is that the angle
of incidence is more obtuse in the new than in the full moon, in
which the angles [of incidence and reflection] are highly acute. The
waves of the moon therefore mirror the sun in the hollows of the
waves as well as on the ridges, and the sides remain in shadow. But
at the sides of the moon the hollows of the waves do not catch the
sunlight, but only their crests; and thus the images are fewer and
more mixed up with the shadows in the hollows; and this
intermingling of the shaded and illuminated spots comes to the eye
with a mitigated splendour, so that the edges will be darker,
because the curves of the sides of the waves are insufficient to
reflect to the eye the rays that fall upon them. Now the new moon
naturally reflects the solar rays more directly towards the eye from
the crests of the waves than from any other part, as is shown by the
form of the moon, whose rays a strike the waves _b_ and are
reflected in the line _b d_, the eye being situated at _d_. This
cannot happen at the full moon, when the solar rays, being in the
west, fall on the extreme waters of the moon to the East from _n_ to
_m_, and are not reflected to the eye in the West, but are thrown
back eastwards, with but slight deflection from the straight course
of the solar ray; and thus the angle of incidence is very wide
indeed.

The moon is an opaque and solid body and if, on the contrary, it
were transparent, it would not receive the light of the sun.

The yellow or yolk of an egg remains in the middle of the albumen,
without moving on either side; now it is either lighter or heavier
than this albumen, or equal to it; if it is lighter, it ought to
rise above all the albumen and stop in contact with the shell of the
egg; and if it is heavier, it ought to sink, and if it is equal, it
might just as well be at one of the ends, as in the middle or below
[54].