The Notebooks of Leonardo Da Vinci — Complete
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