Lionardo da Vinci

Astronomy

Astronomy 

'The moon has every month a winter and a 
summer. And it has greater colds and greater 
heats and its equinoxes are colder than ours! 

Make glasses in order to see the moon large. c.a. 190 r. a 

If you know the distance of a body you will know the size of the 
visual pyramid if you take a section of it near the eye upon a wall and 
then remove the line so far from the eye as to double the size of the 
section. Then note the distance from the first to the second section and 
ask yourself: — if within such a space the diameter of the moon in- 
creases for me so much above the first section what will it do in the 
whole space that is between the eye and the moon? It will form the 
exact diameter of this moon. 
[Diagram] 

Measure of the size of the sun, knowing the distance, c.a. 243 r. b 

If the water of the moon had its centre of gravity at the centre of the 
earth, it would strip the moon and fall upon us . . . suspended from 
the centre of its sphere. 

If you should be moving towards the sun along that line of water 
which lies between this sun and its image, you will be sailing along a 
continuous image which will be of the length of your movement. 

Why the moon when surrounded by the luminous part of the sun in 
the west has greater radiance in the centre of this circle than when there 
is an eclipse of the sun. This comes about because as it eclipses the 
sun it casts a shadow upon our ocean, and this does not occur when 
it is in the west, for then the sun lights up this ocean. 

Why in the eclipse of the sun the body of the moon when it is op- 
posite to us shows itself in the middle of the sun with part of its ra- 
diance somewhat like that of molten iron. This proceeds from the 

273 

 

274 ASTRONOMY 

moon which derives its radiance from the stars, and not from the earth, 
because this is darkened. . . . c.a. 243 v. a 

The image of the sun is all in all the water which sees it, and all ir 
every minutest part of it. 

This is proved because there are as many images of the sun as there 
are positions of the eyes which see the water between themselves and 
the sun. 

Moreover as the eye moves when carried along the line of the ship 
it sees the image of the sun moving along the same line as that of the 
movement of the eye; but it will not be parallel for as the sun moves 
to the west the line of the images moves in a curve towards the sun, 
in such a way as to seem finally to unite with the image of the sun 
when it has reached the horizon. 

If the ship's movement be to the south and the sun is in the middle 
of the heaven the line of the image of the sun will be curved, and it 
will always go on extending itself, so that at the last it will unite with 
the sun on the horizon and the image will seem equal in size to this 
sun. c.a. 243 v. b 

How bodies send forth from themselves their form heat and potency: 
When the sun during an eclipse assumes the shape of a crescent, take 
a thin plate of iron and make a small hole in it, and turn the face of 
this plate towards the sun, holding a sheet of paper behind it at a dis- 
tance of half a braccio, and you will see the image of the sun appear 
on this sheet in the shape of a crescent, similar in form and colour to 
its cause. 

Quality of the sun: 

The sun has substance, shape, movement, radiance, heat and genera- 
tive power; and these qualities all emanate from itself without its 
diminution. c.a. 270 v. b 

The solar rays after penetrating the little holes which come between 
the various rounded particles of the clouds take a straight and con- 
tinuous course to the ground where they strike, illuminating with their 
radiance all the air through which they pass. c.a. 297 v. a 

 

ASTRONOMY 275 

It the moon is a mirror of our earth, when it is at the full the earth 
will be half dark and half illuminated, or perhaps more than half dark. 

And of dark things we cannot discern the shapes of the objects which 
are within their boundaries. 

The adversary says that the light of the moon illumines the portion 
of the earth seen by it, and for this reason, as the earth is surrounded 
by water, that only the water reflects the light of the moon, and the 
earth as it is not smooth or polished in its surface as is the water, does 
not transmit the image of itself to this water, and so it remains dark, 
and thus our water shines in the moon with the darkness of the islands 
which it surrounds. c.a. 300 r. b 

The moon has every month a winter and a summer. 
And it has greater colds and greater heats and its equinoxes are 
colder than ours. c.a. 303 v. b 

How it is possible for the quantity of the images of the sun to pass 
through the indivisible point of the primitive into the derivative 
pyramid: 

The sun is composed of a very great number of indivisible parts; and 
although this sun is possessed of bodily substance its powers are incor- 
poreal consisting of heat and radiance; and since an incorporeal power 
has no substance not having substance it does not occupy space, and 
not occupying space it does not close the aperture, and consequently the 
passage through this aperture to and fro is permitted to each spirit at 
the same time. 

It is possible that the solar rays reduced through a pyramid to a point 
by the concave mirror is redoubled in warmth and radiance; as these 
rays are in the derived pyramid they are thrown back by a similar mir- 
ror to an equal distance from the point. c.a. 347 v. a 

OF THE CIRCLES OF THE MOON 

I find that those circles which at night seem to surround the moon, 
varying in circumference and in their degree of redness, are caused by 
the different degrees of thickness of the vapours which are situated at 
different altitudes between the moon and our eyes. And the circle that 
is larger and less red is in the first part lower than the said vapours; the 

 

276 ASTRONOMY 

second, being less, is higher and appears redder, because it is seen 
through two sets of vapours; and so the higher they are the smaller and 
the redder will they appear, for between the eye and them there will be 
more layers of vapours, and this goes to prove that where there appears 
greater redness, there is a greater quantity of vapours. c.a. 349 v. e 

 

BURNING MIRROR [sketch] 

As many times as the point of the solar pyramid cut in any part what- 
ever is contained in its base so many times is it hotter than this base. 

a 54 r. 

WHAT THE MOON IS 

The moon is not luminous in itself, but it is well fitted to take the 
characteristics of light after the manner of the mirror or of water or 
any other shining body; and it grows larger in the east and in the west 
like the sun and the other planets, and the reason of this is that every 
luminous body grows larger as it becomes more remote. 

It may be readily understood that every planet and star is farther 
away from us when in the west than when it is overhead, by about 
three thousand Rvt hundred [miles] according to the proof given at 
the side [of the page]; 1 and if you see the sun and moon reflected in 
water which is near at hand it will seem to be the same size in the 
water as it does in the sky, while if you go away to the distance of a 
mile it will seem a hundred times as large. And if you see it reflected in 
the sea at the moment of its setting the image of the sun will seem to 
you to be more than ten miles long, because it will cover in the reflec- 
tion more than ten miles of sea. And if you were where the moon is, it 
would appear to you that the sun was reflected over as much of the sea 
as it illumines in its daily course, and the land would appear amid this 
water like the dark spots that are upon the moon, which when looked 
at from the earth presents to mankind the same appearance that our 
earth would present to men dwelling in the moon. 

1 Here the margin of the MS. contains a diagram representing the earth with the 
sun shown in two positions. 

 

ASTRONOMY 277 

OF THE NATURE OF THE MOON 

When all that we can see of the moon is illumined it gives us its 
maximum of light, and then from the reflection of the rays of the sun 
which strike upon it and rebound towards us its ocean throws off less 
moisture to us, and the less light it gives the more it is harmful. 

a 64 r. 

 

EXPLANATION OF WHY THE SUN SEEMS LARGER IN 

THE WEST 

Certain mathematicians contend that the sun grows larger when it is 
setting, because the eye sees it continually through atmosphere of 
greater density, alleging that objects seen through mist and in water 
seem larger. 

To this I reply that this is not the case, for the things seen through 
ihe mist are similar in colour to those which are at a distance, but as 
they do not undergo the same process of diminution, they appear 
greater in size. 

In the same way nothing seems larger in smooth water, and this you 
may prove by tracing upon a board which is placed under water. 

The real reason why the sun grows larger is that every luminous 
body appears larger, as it is farther away. a 64 v. 

PRAISE OF THE SUN 

If you look at the stars without their rays, — as may be done by look- 
ing at them through a small hole made with the extreme point of a 
fine needle and placed so as almost to touch the eye, — you will perceive 
these stars to be so small that nothing appears less; and in truth the 
great distance gives them a natural diminution, although there are 
many there which are a great many times larger than the star which is 
our earth together with the water. Think, then, what this star of ours 
would seem like at so great a distance, and then consider how many 
stars might be set longitudinally and latitudinally amid these stars 
which are scattered throughout this dark expanse. I can never do other 
than blame those many ancients who said that the sun was no larger 

 

278 ASTRONOMY 

than it appears, — among these being Epicurus; and I believe that such 
a theory is borrowed from the idea of a light set in our atmosphere 
equidistant from the centre [of the earth]; whoever sees it never sees 
it lessened in size at any distance, and the reasons of its size and 
potency I shall reserve for the Fourth Book. 

But I marvel greatly that Socrates should have spoken with dis- 
paragement of that body, and that he should have said that it resembled 
a burning stone, and it is certain that whoever opposes him in such an 
error can scarcely do wrong. I could wish that I had such power of 
language as should avail me to censure those who would fain extol the 
worship of men above that of the sun, for I do not perceive in the whole 
universe a body greater and more powerful than this, and its light 
illumines all the celestial bodies which are distributed throughout the 
universe. 

All vital principle descends from it, since the heat there is in living 
creatures proceeds from this vital principle; and there is no other heat 
or light in the universe as I shall show in the Fourth Book, and indeed 
those who have wished to worship men as gods, such as Jupiter, Saturn, 
Mars and the like, have made a very grave error seeing that even if a 
man were as large as our earth he would seem like one of the least of 
the stars, which appears but a speck in the universe; and seeing also 
that these men are mortal and subject to decay and corruption in 
their tombs. 

The Spera, and Marullo, and many others praise the Sun. 

f 5 r. and 4 v. 

The stars are visible by night and not by day owing to our being 
beneath the dense atmosphere which is full of an infinite number of 
particles of moisture. Each of these is lit up when it is struck by the rays 
of the sun and consequently the innumerable radiant particles veil these 
stars; and if it were not for this atmosphere the sky would always show 
the stars against the darkness. f 5 v - 

Epicurus perhaps perceived that the shadows of columns striking the 
opposite walls were equal in diameter to the column from which they 
proceeded. As therefore the mass of the shadow from beginning to end 
was a parallelogram he thought he might infer that the sun also was 
opposite to this parallelogram and as a consequence would not be larger 

 

ASTRONOMY 279 

than this column, not perceiving that such a diminution of the shadow 
would be imperceptible on account of the great distance of the sun. 

If the sun were smaller than the earth, the stars in a great part of our 
hemisphere would be without light: this is contrary to Epicurus who 
savs that the sun is only as large as it appears. f 6 r. 

Epicurus says that the sun is as large as it shows itself; as therefore it 
appears to be a foot we have to reckon it as such. 

It would follow that when the moon obscured the sun the sun would 
not surpass it in size as it does; therefore the moon being smaller than 
the sun the moon would be less than a foot, and consequently when 
our earth obscured the moon it would be less by a finger's breadth, see- 
ing that if the sun be a foot across and our earth casts a pyramidal 
shadow towards the moon it is inevitable that the luminous body which 
is the cause of the shaded pyramid must be greater than the opaque 
body which casts this pyramid. f 8 v. 

A calculation of how many times the sun will go into its course in 
twenty four hours: 

Make a circle and set it to face south after the manner of sundials; 
place a rod in the middle of it so that its length is pointing to the centre 
of the circle and note the shadow made by the sun from this rod upon 
the circumference of the circle, and let us say that the breadth of the 
shadow is all a n (diagram). Now measure how many times this 
shadow will go into this circumference of the circle, and this will be the 
number of times that the solar body will go into its course in twenty 
four hours. In this way one may see whether Epicurus was right in say- 
ing that the sun is as large as it seems to be, for as the apparent diame- 
ter of the sun is about a foot and as the sun would go a thousand times 
into its course in twenty four hours, the length of its course would be 
a thousand feet, that is five hundred braccia, which is the sixth of a 
mile; so then the course of the sun between day and night would be 
the sixth part of a mile, and this venerable snail the sun would have 
travelled twenty five braccia an hour. nor. 

 

280 ASTRONOMY 

THE ORDER OF PROVING THAT THE EARTH IS A STAR 

First explain the mechanism of the eye, then show how the scintilla- 
tion of each star originates in the eye, and why the scintillation of one 
star is greater than that of another. And how the rays of the stars origi- 
nate in the eye. I affirm that if the scintillation of the stars was as it 
appears, in the stars, this scintillation would show itself as widely ex- 
tended as the body of the star; and since it is larger than the earth this 
movement made instantaneously would swiftly be found to cause the 
star to seem double in size. See afterwards how the surface of the air 
on the confines of the fire, and the surface of the fire at its boundary, is 
that in which the solar rays penetrating carry the resemblance of the 
heavenly bodies, large in their rising and setting and small when they 
are in the centre of the sky. f 25 v. 

 

AN EXPERIMENT IN ORDER TO SHOW HOW RAYS 
PENETRATE LIQUID BODIES 

Make two vessels each of parallel sides, the one four fifths of the 
other and of equal height. Then Rx one within the other as you see in 
the drawing, and cover outside with colour and leave an opening of the 
size of a lentil, and allow a ray of the sun to enter there which makes 
its exit through another dark hole or by the window. Then observe 
whether the ray that passes within the water enclosed between the two 
vessels keeps the direction that it has outside or no; and from this de- 
duce your rule. 

In order to see how the solar rays penetrate this curve of the sphere 
of the air have two balls made of glass one twice as large as the other, 
and let them be as round as possible. Then cut them in half, place one 
inside the other, close them in front and fill them with water, then let 
the solar ray pass within as you have done above, and observe whether 
the ray is bent or curved and from this deduce your rule. And in this 
way you can make an infinite number of experiments. 

Observe as you place yourself with your eye in the centre of the ball 
whether the light of a candle keeps its size or no. f 33 v. 

 

ASTRONOMY 281 

OF THE SUN 

Some say that the sun is not hot because it is not the colour of fire 
hut is much paler and clearer. To these we may reply that when liqui- 
fied bronze is at its maximum of heat it most resembles the sun in 
colour, and when it is less hot it has more of the colour of fire. 

F34 v. 

The solar rays reflected by the surface of the undulating water cause 
the image of the sun to seem continuous over all that water which is 
between the universe and the sun. f 38 v. 

Why the image of the sun is all in all the sphere of the water which 
sees the sun and all in each part of the said water: 

All the sky which sees the part of the sphere of the water seen by the 
sun sees all this water covered by the image of the sun, and each part 
of the sky sees all. 

The surface of the water without waves lights equally the places 
struck by the reflected rays of the image of the sun in the water. 

The image of the sun is unique in the sphere of the water seen by 
the sun, which shows itself however to all the sky that finds itself 
before it, and every point of this sky itself sees an image, and that 
which sees one in one position is seen by the other in another position, 
in such a way that no part of the sky sees it all. 

That image of the sun will cover a greater space in the surface of the 
water which is seen from a place more distant from it. f 39 r. 

How the earth is not in the centre of the circle of the sun, nor in the 
centre of the universe, but is in fact in the centre of its elements which 
accompany it and are united to it. And if one were to be upon the 
moon, then to the extent to which it together with the sun is above us, 1 
so far below it would our earth appear with the element of water, per- 
forming the same office as the moon does for us. f 41 v. 

All your discourse points to the conclusion that the earth is a star 
almost like the moon, and thus you will prove the majesty of our uni- 
verse; and thus you will make a discourse concerning the size of many 
of the stars according to the authorities. f 56 r. 

MS. sotto. I have followed M. Ravaisson-Mollien's rendering. 

 

282 ASTRONOMY 

Whether the friction of the heavens makes a sound or no: 
Every sound is caused by the air striking a dense body, and if it i 
made by two heavy bodies one with another it is by means of the ai 
that surrounds them; and this friction wears away the bodies that ar 
rubbed. It would follow therefore that the heavens in their friction nc 
having air between them would not produce sound. Had however thi 
friction really existed, in the many centuries that these heavens hav 
revolved they would have been consumed by their own immense spee< 
of every day. And if they made a sound it would not be able to spreac 
because the sound of the percussion made underneath the water is bu 
little heard and it would be heard even less or not at all in the case c 
dense bodies. Further in the case of smooth bodies the friction does nc 
create sound, and it would happen in a similar manner that ther 
would be no sound in the contact or friction of the heavens. And i 
these heavens are not smooth at the contact of their friction it follow 
that they are full of lumps and rough, and therefore their contact is nc 
continuous, and if this is the case the vacuum is produced, which it ha 
been concluded does not exist in nature. We arrive therefore at th 
conclusion that the friction would have rubbed away the boundaries c 
each heaven, and in proportion as its movement is swifter towards th 
centre than towards the poles it would be more consumed in the centr 
than at the poles; and then there would not be friction any more, am 
the sound would cease, and the dancers would stop, except that th 
heavens were turning one to the east and the other to the north. 

f 56 v. 

Whether stars have light from the sun or in themselves : 
It is said that they have light in themselves, since if Venus and Mer 
cury had no light of their own, when they come between our eye an< 
the sun they would darken as much of the sun as they cover from ou 
eyes. This however is false, because it has been proved how a dark ob 
ject placed against a luminous body is surrounded and entirely covere< 
by the lateral rays of the remainder of this luminous body, and so i 
remains invisible. As is shown when the sun is seen through the rami 
fication of leafless trees in the far distance these branches do not con 
ceal any part of the sun from our eyes. The same thing happens witl 
the above mentioned planets, for though they are themselves withou 

 

ASTRONOMY 283 

li^ht they do not as has been said cover any part of the sun from our 
eyes. 

It is said that the stars at night appear most brilliant in proportion as 
they are higher up, and that if they have no light of their own the 
shadow cast by the earth when it comes between them and the sun 
would come to darken them, since these stars neither see nor are seen 
by the solar body. 

But those who say this have not considered that the pyramidal 
shadow of the earth does not reach many of the stars, and that in those 
which it does reach the pyramid is so diminished that it covers little of 
the body of the star, and all the rest is illuminated by the sun. 

F 57 r. 

Why the planets appear greater in the east than above us, though it 
ought to be the opposite seeing that they are three thousand five hun- 
dred miles nearer to us when they are in the middle of the sky than 
when they are on the horizon: 

All the degrees of the elements through which pass the images of 
the celestial bodies which come to the eye are curved, and the angles by 
which the central line of these images penetrates there are unequal, 
and the distance is greater as is shown by the excess of a b over a d; 
and by the Ninth of the Sixth the size of heavenly bodies on the hori- 
zon is proved. f 60 r. 

Explain the earth with its longer and shorter day in the north and 
in the south, and do the same for the moon and define them accurately. 

f 63 r. 

DARKNESS OF SUN MOON AND EARTH 

The moon has its days and nights as has the earth: the night in the 
part which does not shine and the day in that which does. 

Here the night of the moon sees the light of the earth, that is to say 
of its water, grow dim — and the darkened water sees the darkness of 
the sun, and to the night of the moon there is lacking the reverberation 
of the solar rays which are reflected there from this earth. 

In this other figure it is shown that the day of the moon is darkened 
and the night of the earth remains deprived of the solar rays reflected 
trom the moon. 

 

284 ASTRONOMY 

When the moon is in the east and the sun in the west, all the day that 
the moon enjoyed, such as it was with the sun in the west, is changed 
into night. 

Such day as has the moon which from the east looks at the sun in 
the west will all be night when this moon is with the sun in the west. 

f 64 v. 

OF THE RAINBOW 

Whether the rainbow is produced by the eye, that is its curve, or by 
the sun by means of the cloud: 

The mirror does not take any images except those of visible bodies, 
and the images are not produced without these bodies; therefore if this 
arch is seen in the mirror, and the images converge there which have 
their origin in this rainbow, it follows that this arch is produced by the 
sun and by the cloud. 

The rainbow is seen in the fine rains by those eyes which have the 
sun behind and the cloud in front, and a perpetually straight imaginary 
line which starts from the centre of the sun and passes through the 
centre of the eye will end in the centre of the arch. 

And this arch will never be seen by one eye in the same position 
as by the other eye; it will be seen in as many positions of the cloud 
where it is formed as there are eyes that see it. 

Therefore this arch is all in all the cloud where it is produced, and 
all in each of the positions in which it may find itself, and so it will 
appear larger or smaller, half, whole, double, triple. 

If two spheres of metal transmit the solar rays into a dark place, as 
the water is turned into vapour it will make the solar spectrum * long 
in shape. 

This occurs also with the water turned into vapour when the solar 
ray is passing into a dark place with the sun behind it, and also with 
the light of torches or of the moon. f 67 v. 

How the earth in performing the function of the moon has lost a 
considerable amount of the ancient light in our hemisphere by the low- 
ering of the waters, as is proved in Book Four 'Of the Earth and the 
Waters': 

1 Thus Rav.-Moll. — 'le spectre solaire'. MS. 'arco iris'. 

 

ASTRONOMY 285 

The earth is heavy in its sphere, but so much the more as it is in a 
lighter element. 

Fire is light in its sphere, and so much the more as it is in a heavier 
element. 

No simple element has gravity or levity in its own sphere, and if a 
bladder filled with air weighs more in the scales than an empty one, 
this is because this air is compressed; and fire might be so compressed 
that it would be heavier than the air or equal to the air, and perhaps 
heavier than the water, and making itself equal to the earth, f 69 v. 

This will follow the treatise on light and shade: 

The extremities of the moon will be more illuminated and will show 
themselves more luminous because nothing will appear in them except 
the summits of the waves of its waters; and the shadowy depths of the 
valleys of these waves will not change the images of those luminous 
parts which from the summits of these waves come to the eye. 

F77 v. 

Omne grave tendit deorsum nee perpetuo potest sic sursum sustineri, 
quare jam totalis terra esset facta spherica. 1 

THE SPOTS ON THE MOON 

Some have said that vapours are given ofi from the moon after the 
manner of clouds, and are interposed between the moon and our eyes. 
If this were the case these spots would never be fixed either as to posi- 
tion or shape; and when the moon was seen from different points, even 
although these spots did not alter their position, they would change 
their shape, as does a thing which is seen on different sides, f 84 r. 

OF THE SPOTS ON THE MOON 

Others have said that the moon is made up of parts, some more, some 
less transparent, as though one part were after the manner of alabaster, 
and another like crystal or glass. It would then follow that when the 
rays of the sun struck the less transparent part the light would stay on 

1 Every heavy substance presses downwards, and thus cannot be upheld perpetually; 
wherefore the whole earth has been made spherical. 

 

286 ASTRONOMY 

the surface, and consequently the denser part would be illuminated, 
and the transparent part would reveal the shadows of its obscure depths. 
Thus then they define the nature of the moon, and this view has found 
favour with many philosophers, and especially with Aristotle; but 
nevertheless it is false, since in the different phases which the moon and 
the sun frequently present to our eyes we should be seeing these spots 
vary, and at one time they would appear dark and at another light. 
They would be dark when the sun is in the west and the moon in the 
centre of the sky, because the transparent hollows would then be in 
shadow, as far as the tops of their edges, since the sun could not cast 
its rays into the mouths of these same hollows; and they would appear 
bright at full moon, when the moon in the east faces the sun in the 
west; for then the sun would illumine even the lowest depths of these 
transparent parts, and in consequence as no shadow was created, the 
moon would not at such times reveal to us the above-mentioned spots, 
and so it would be, sometimes more sometimes less, according to the 
change in the position of the sun to the moon, and of the moon to our 
eyes, as I have said above. f 84 v. 

It has also been said that the spots on the moon are created in the 
moon itself, by the fact of it being of varying thinness or density. If this 
were so, then in the eclipses of the moon the solar rays could pierce 
through some part where it is thin, as has been stated, but since we do 
not see this result the aforesaid theory is false. 

Others say that the surface of the moon is smooth and polished, and 
that, like a mirror, it receives within itself the reflection of the earth. 
This theory is false, since the earth, when not covered by the water, 
presents different shapes from different points of view; so when the 
moon is in the east it would reflect other spots than when it is overhead 
or in the west, whereas the spots upon the moon, as seen at full moon, 
never change during the course which it makes in our hemisphere. A 
second reason is that an object reflected in a convex surface fills only a 
small part of the mirror, as is proved in perspective. The third reason is 
that when the moon is full it only faces half the orb of the illuminated 
earth, in which the ocean and the other waters shine brightly, while the 
land forms spots amid this brightness; and consequently the half of our 
earth would be seen girded round about by the radiance of the sea, 

 

ASTRONOMY 287 

which takes its light from the sun, and in the moon this reflection 
would be the least part of that moon. The fourth reason is that one 
radiant body cannot be reflected in another, and consequently as tin sea 
derives its radiance from the sun, as does also the moon, it could not 
show the reflected image of the earth, unless one also saw reflected 
there separately the orb of the sun and of each of the stars which look 
down upon it. f 85 r. 

SOLAR RAYS 

The solar rays pass through the cold region of the air and do not 
change their nature. They pass through glasses filled with cold water 
and lose nothing of their nature thereby; and whatever may be the 
transparent place through which they pass it is as though they passed 
through so much air. 

And if you maintain that the cold rays of the sun are clothed with 
the heat of fire as they traverse its element, just as they assume the 
colour of the glass they penetrate, it would follow that in penetrating 
the cold region they put on this mantle of cold after they have already 
put on the said mantle of heat, and thus the cold would counteract the 
heat, and therefore the solar rays would come to us deprived of heat, 
and as this is not confirmed by experience such method of reasoning as 
to the sun being cold is vain. 

But if you were to say that the cold through which the fiery rays of 
the sun pass somewhat modifies the excessive heat of these rays it 
would follow from this that one would feel greater heat on the high 
peaks of the Caucasus the mountain of Scythia than in the valleys, 
because the mountain towers above the middle regions of the air, and 
no clouds are found there nor anything that grows. 

And if you say that these solar rays thrust towards us the element of 
fire from whence they pass by local movement, this cannot be admitted 
because the local movement of such [a volume of] air cannot occur 
without the passing of a period of time, and this is greater in propor- 
tion as the sun is more on the horizon, for when there it is 3,500 miles 
farther away from us than when it is in the centre of our heaven. If it 
acted thus it would cool the part of our horizon opposite to it, because 
it would carry away in its rays such part of the element of fire opposite 
to it as it penetrated. 

 

 


288 ASTRONOMY 

If the lesser fire is attracted to and deflected by the greater fire as one 
sees happen by experience, it must needs be that the sun draws the 
element of fire to itself rather than that it banishes it from itself and 
drives it towards us. 

And the heat of the fire does not descend unless it follows burning 
matter, and in acting thus it is material and in consequence it is visible. 

f 86 r. 

How if the moon is polished and spherical the image of the sun upon 
it is powerfully luminous, and is only on a small part of its surface: 

You will see the proof of this by taking a ball of burnished gold and 
placing it in the darkness and setting a light at some distance from it. 
Although this illuminates about half the ball, the eye only sees it re- 
flected on a small part of its surface, and all the rest of the surface 
reflects the darkness which surrounds it. For this reason it is only there 
that the image of the light is apparent, and all the rest remains invisi- 
ble because the eye is at a distance from the ball. The same thing 
would happen with the surface of the moon if it were polished, glitter- 
ing and solid, as are bodies which have a reflecting surface. 

Show how if you were upon the moon or upon a star our earth 
would appear to you to perform the same function for the sun as now 
the moon does. And show how the reflection of the sun in the sea 
cannot itself appear a sun as it does in a flat mirror. f 93 r. 

My book attempts to show how the ocean with the other seas makes 
our world by means of the sunshine after the manner of a moon, and 
to the more remote worlds it appears a star; and this I prove. 

Moon cold and moist. 

Water is cold and moist. 

Our sea has the same influence on the moon as the moon has on us. 

f 94 v. 

 

EXPLANATION OF THE MOON WITH THE IMAGE 

OF THE SUN 

If the sun / reflected in the surface of the water n m should seem to be 
at d (that is to say seems to be as far below the water as it is above), and 
to the eye b appears to be of the size a, and this image doubles itself 

 

ASTRONOMY 289 

as the eye is removed from b to c\ how much would this Image grow it 
the eye were removed Erom c to the moon? 

Work with the rule of three and you will see that the light which 
there is in the moon on its fifteenth day can never be the light that this 
moon receives from it being spherical; therefore it is necessary that this 
moon contains water. c 20 r. 

 

[Of the nature of the suns heat] 

OF THE PROOF THAT THE SUN IS HOT BY NATURE 
AND NOT BY POWER 

That the sun is hot in itself by nature and not by power is shown 
very distinctly by the radiance of the solar body on which the human 
eye cannot continue to look. And this moreover the rays reflected by 
concave mirrors show very clearly, for when their percussion is of such 
radiance that the eye cannot endure it, this percussion will have a radi- 
ance resembling that of the sun in its own position. And the truth of 
this is proved by the fact that if such a mirror has such a concave sur- 
face as is required in order to produce this ray, no created thing will 
be able to support the heat of such percussion of ray reflected from 
any mirror. And if you say that the mirror also is cold and yet throws 
warm rays, I say in reply that the ray comes from the sun and will 
have to pass through the mirror in order to resemble its cause and can 
pass through whatever medium it wishes. . . . 

The ray of the concave mirror having passed across the windows of 
the furnaces where are cast . . . has not great heat nor any longer has 
whiteness. g 34 r. 

THE SOLAR RAYS 

Where there is the finer and more rarefied medium the solar rays 
meet with a less resistance and where there is the less resistance it is 
less permeated by the nature of the agent. Consequently for this reason 
one may infer that where the air is more rarefied the percussion of the 
said solar rays transmits less radiance, and as a consequence it is darker , 
and so also conversely. k 118 [38] r. 

 

290 ASTRONOMY 

A proof how the nearer you are to the source of the sun's rays the 
greater will the sun appear when reflected upon the sea: 

If the sun produces its radiance from its centre fortified by power 
from the whole body it must needs be that the farther its rays proceed 
from it the more they go on separating. This being so when you have 
your eye near water that reflects the sun, you see a very small part of 
the sun's rays carrying upon the surface of the water the form of the 
sun reflected; and if you are nearer to the sun as would be the case 
when the sun is at the meridian and the sea is to the west, you will see 
the sun reflected in the sea of very great size, because as you are nearer 
to the sun your eye as it takes the rays near to the point takes in more 
of them and so greater radiance ensues. For this reason it might be 
proved that the moon is another world similar to ours, and that the 
part of it which shines is a sea that reflects the sun and the part which 
does not shine is earth. ms. 2038 Bib. Nat. 16 v. 

If you keep the details of the spots of the moon under observation 
you will often find great differences in them, and I have myself proved 
this by making drawings of them. And this comes about because the 
clouds rise from the waters of the moon and come between the sun and 
this water, and with their shadows cut off the rays of the sun from it, 
and consequently it remains dark because it cannot reflect the solar 
body. b.m. 19 r. 

OF THE MOON 

As wishing to treat of the nature of the moon it is necessary in the 
first place that I should describe the perspective of mirrors, whether 
flat concave or convex, and first of all what is meant by a luminous ray 
and how it is refracted by various kinds of media. Then whether the 
reflected ray is more powerful if the angle of incidence be acute or a 
right angle or obtuse, or if the surface be convex or flat or concave, 
or the substance opaque or transparent. Furthermore how it is that the 
solar rays which strike the waves of the sea show themselves of the 
same width in the angle close to the eye as in the farthest crest of the 
waves on the horizon, notwithstanding which the solar radiance re- 
flected by the waves of the sea is of the shape of a pyramid, and as a 

 

ASTRONOMY 291 

consequence at every stage of distance acquires an access of breadth, 
although to our sight it may appear parallel. 

Nothing extremely light is opaque. 

Nothing that is lighter remains below what is less light. 

Whether the moon has its station in the midst of its elements or no. 

If it has not a particular station as has the earth in its elements why 
it does not fall to the centre of our elements. 

And if the moon is not in the midst of its elements and does not 
descend it is therefore lighter than the other element. 

And if the moon is lighter than the other element why it is solid and 
not transparent. 

Of things of different size which when placed at different distances 
show themselves equal, there will be the same proportion between 
their distances as there is between their sizes. b.m. 94 r. 

OF THE MOON 

The moon has no light of itself but so much of it as the sun sees, it 
illuminates. Of this illuminated part we see as much as faces us. And 
its night receives as much brightness as our waters lend it as they reflect 
upon it the image of the sun, which is mirrored in all those waters 
that face the sun and the moon. 

The crust or surface of the water of which the sea of the moon and 
the sea of our earth are composed is always wrinkled whether little or 
much or more or less; and this ruggedness is the cause of the expansion 
of the innumerable images of the sun which are reflected in the hills 
and valleys and sides and crests of the innumerable furrows, that is in 
as many different spots in each furrow as there are different positions 
of the eyes that see them. This could not happen if the sphere of water 
which in great part covers the moon were of uniform roundness, be- 
cause then there would be an image of the sun for every eye, and its 
reflection would be distinct and the radiance of it would always be 
spherical in shape, as is clearly shown in the gilded balls placed on the 
summits of lofty buildings. But if these gilded balls were furrowed or 
made up of many small globules like mulberries, which are a black 
fruit composed of minute round balls, then each of the parts of this 
rounded mass visible to the sun and to the eye will reveal to the eye 

 

292 ASTRONOMY 

the radiance produced by the reflection of the sun. And thus in the 
same body there will be seen many minute suns and very often on 
account of their great distance they will blend one with another and 
seem continuous. 

The lustre of the new moon is brighter and more powerful than 
when it is full; and this is due to the fact that the angle of its incidence 
is much more obtuse in the new moon than in the full moon, where 
the angles are extremely acute, and the waves of the moon reflect the 
sun both on their hollows and on their crests, and the sides remain 
dark. But at the sides of the moon the troughs of the waves do not see 
the sun, for it only sees the crests of these waves, and in consequence 
the reflections are less frequent and more mingled with the shadows of 
the valleys. And this intermixture of shaded and luminous images all 
blending together comes to the eye with only a moderate amount of 
radiance, and at its edges it will be even darker, because the curve of 
the side of these waves will be insufficient to reflect the rays which it 
receives to the eye. 

For which reason the new moon by its nature reflects the solar rays 
more towards the eye through these last waves than through any other 
place, as is shown by the figure of the moon striking with the rays a on 
the wave b and reflected in b d where the eye d is situated. And this 
cannot happen at full moon, where the solar ray standing in the west, 
strikes the last rays of the moon in the east from n to m, and does not 
reflect towards the eye in the west; but leaps back to the east, slightly 
bending the direction of this solar ray; and so the angle of the incidence 
is very great. 

The countless images which are reflected by the innumerable waves 
of the sea from the solar rays that strike upon these waves, cause a 
continuous and far reaching splendour upon the surface of the sea. 

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. b.m. 94 v. 

You have to prove how the earth performs all those same functions 
towards the moon which the moon does towards the earth. 

The moon does not shine with its reflected light as does the sun, 
because the moon x does not receive the light of the sun on its surface 

1 MS. has 'il lume della luna'. 

 

ASTRONOMY 293 

Continuously, but in the crests and hollows ot the waves ot its waters, 

through the sun being indistinctly reflected in the moon through the 
mingling of the shadows which arc above the waves that shed the radi- 
ance. Its light therefore is not bright and clear as is that of the sun. 

b.m. 104 r. 

To observe the nature of the planets have an opening made in the 
roof and show at the base one planet singly: the reflected movement 
on this base will record the structure of the said planet, but arrange 
so that this base only reflects one at a time. b.m. 279 v. 

The circles of the celestial spheres together with the elements equally 
drive and thrust away from themselves everything that has weight, 
whence for this reason it must be confessed that it is necessary for the 
centres of these spheres to meet and become stationary. 

Whence through this it is necessary to confess that the things falling 
towards the centre are rather thrust from above than drawn by this 
centre downwards; because if it were possible that this earth should 
be withdrawn in part in such a manner that the space occupied by the 
position of the earth were filled with air, you would see a stone thrown 
off from our world into this air become stationary in the centre of the 
two elements and of the spheres. Forster 111 6 v. 

The centre of the world cannot be the centre of the universal circles 
made by the course of the glittering stars, because in a like position it 
cannot be taken for granted that the universal parts of the earth, the 
encompasser and enveloper of this centre, are not of equal weight when 
removed at an equal distance from this centre. 

Naturally every heavy thing is thrust towards the centre because the 
centre is farthest removed from these expelling and rotatory forces. 

I conclude: the centre of the weight of the earth with the water is 
the centre of the spheres and not the centre of the mass of this world. 

Forster m 7 r. 

These heavy parts which were thrust down from there above, have 
of themselves already created bodies which always stand in continual 
desire of returning there above. Forster in 8 r. 

The sun does not move. Quaderni v 25 r. 

 

294 ASTRONOMY 

Between the sun and us there is darkness, and therefore the air 
appears blue. Windsor mss. r 868 

If you wish to prove that the moon appears larger than it is when it 
reaches the horizon, you take a lens convex on the one side and concave 
on the other and place the concave side to your eye and look at the 
object beyond the convex surface; and by this means you will have 
made a true imitation of the atmosphere which is enclosed between the 
sphere of fire and that of water, for this atmosphere is concave towards 
the earth and convex towards the fire. Windsor: Drawings 12326 v. 

Memorandum that I have first to show the distance of the sun from 
the earth and by means of one of its rays passing through a small hole 
into a dark place to discover its exact dimensions, and in addition to 
this by means of the sphere of water to calculate the size of the earth. 

And the size of the moon I shall discover as I discover that of the 
sun, that is by means of its ray at midnight when it is at the full. 

Leic. 1 r. 

Reply to Maestro Andrea da Imola who said that the solar rays 
reflected by the surface of the convex mirror intermingled and became 
lost at a short distance, and that for this reason it is altogether denied 
that the luminous side of the moon is of the nature of a mirror, and 
that in consequence this light is not produced by the innumerable muL 
titude of the waves of that sea, which I have demonstrated to be that 
part of the moon which is illuminated by the solar rays. Leic. 1 v. 

OF THE MOON 

No solid body is lighter than air. 

As we have proved that the part of the moon which shines consists 
of water and it serves the body of the sun as a mirror which reflects the 
radiance it receives from it; and that if this water were without waves 
it would show itself as small but of a radiance almost equal to that of 
the sun, it is necessary now to show whether the moon is a heavy or 
light body. Thus if it were a heavy body — considering that in progres- 
sion upwards from the earth at every stage of altitude there is an 
accession of lightness, inasmuch as water is lighter than earth, air than 

 

ASTRONOMY 295 

water and fire than air and so continuing in succession — it would set m 
that if the moon had density, as it has, it would have weight, and that 
having weight the space in which it finds itself would not be able to 
support it, and as a consequence it would have to descend towards the 
centre of the universe and to join itself to the earth; or if not the moon 
itself its waters at any rate would fall away and become lost to it and 
would fall towards the centre leaving the moon stripped of them and 
devoid of radiance. The fact however that these events do not occur 
as might with reason have been anticipated is a clear sign that the 
moon is clothed with her own elements, namely water air and fire and 
so sustains itself by itself in that part of space as does our earth with 
its elements in this other part of space; and that the heavy bodies per- 
form the same function in its elements which the other heavy bodies 
do in ours. 
[Diagratn] sun, moon, earth. 

When the eye in the east sees the moon in the west near the setting 
sun it sees it with its shaded part surrounded by the luminous part; of 
which light the lateral and upper portions are derived from the sun 
and the lower portion from the western ocean, which still receives the 
solar rays and reflects them in the lower seas of the moon, and more- 
over it imparts as much radiance to the whole of the shaded part of 
the moon as the moon gives to the earth at midnight, and for this 
reason it does not become absolutely dark. And from this some have 
believed that the moon has in part a light of its own in addition to that 
which is given it by the sun, and that this light is due to the cause 
already mentioned, namely that our seas are illumined by the sun. 
[Diagram] moon, solar body, earth. 

Further it might be said that the circle of radiance which the moon 
shows when it is in the west together with the sun is derived entirely 
from the sun, when its position with regard to the sun and the eye is 
as is shown above. 

Some might say that the air which is an element of the moon as it 
catches the light of the sun as does our atmosphere was that which 
completes the luminous circle on the body of the moon. 

Some have believed that the moon has some light of its own, but this 
opinion is false, for they have based it upon that glimmer which is 
visible in the middle between the horns of the new moon, which ap- 

 

296 ASTRONOMY 

pears dark where it borders on the bright part, and where it borders 
on the darkness of the background seems so bright that many have 
assumed it to be a ring of new radiance which completes the circle 
where the radiance of the tips of the horns illuminated by the sun 
ceases. 

And this difference in the background arises from the fact that the 
part of it which borders on the illuminated portion of the moon, by 
comparison with that brightness shows itself darker than it is, and in 
the part above where appears a portion of a luminous circle of uniform 
breadth it comes about that there the moon being brighter than the 
medium or background upon which it finds itself, in comparison with 
this darkness shows itself on that extremity brighter than it is, this 
brightness at such a time being derived from our ocean and the other 
inland seas, for they are at that time illumined by the sun which is 
then on the point of setting, in such a way that the sea then performs 
the same office for the dark side of the moon as the moon when at the 
full does for us when the sun is set, and there is the same proportion 
between that small quantity of light on the dark side of the moon and 
the brightness of the illuminated part, as there is between . . . 

If you want to see how much brighter the shaded part of the moon is 
than its background, cover from your eye with your hand or with some 
other object farther away the luminous part of the moon, so that . . . 

Leic. 2 r. 

I say that as the moon has no light of its own, but is luminous, it 
must needs be that this light is caused by some other body: this being 
so it is of the nature of a spherical mirror; and if it is spherical it takes 
the light pyramid-wise; and of this pyramid the sun is the base, and its 
angle ends in the centre of the body of the moon, and it is cut by the 
surface of this body, and only takes as much as corresponds to the 
section of this pyramid on its surface. And to the human eye this moon 
would only seem the size of this section of the pyramid. Whence there 
would follow from the light of the moon the contrary effect to that 
which experience shows us; for this is that as the moon turns it has its 
whole orb luminous as is shown us by this; for this clearly shows us 
that this lunar body has more than half its orb illuminated. But this 
would not happen if it were a polished body like the mirrors; conse- 
quently for this reason we are constrained to admit, by my fifth [rule], 

 

ASTRONOMY 297 

that the surface of the moon is furrowed; and this muchness only 
exists in liquid bodies when they are stirred by the wind, as we have 
seen with the sea how the sun is reflected by tiny waves near to the 
eve, and stage bv stage over a distance of more than forty miles these 
illuminated waves grow larger. Wherefore we conclude that the lumi- 
nous part of the moon is water, which if it were not in movement 
would not be luminous to the same degree; but by the movement of 
this water which has been stirred up by the winds it becomes filled 
with waves; and every wave takes the light from the sun; and the 
great multitude of waves beyond number reflect the solar body an 
infinite number of times; and the sun thus reflected will be as bright 
as the sun, for as is seen when the water does not move it gives back 
the sun to the eye in the pristine splendour that it has by nature. 

But the shadows also are beyond number as well as the waves, and 
these are interspersed between the waves; and their shapes blend with 
the shapes of the images of the sun, which are upon the waves; and 
each shadow shape becomes blended with a luminous shape and so 
they come to obscure the luminous rays and make them weak, as is 
clearly shown us by the light of the moon. And when the sea of the 
moon is stirred to tempest by the winds the waves are larger and the 
lights less frequent and the enlarged shadows intermingle more with 
the sparse images of the sun upon the waves, and for this reason the 
moon becomes less luminous. But when the moon is in its circle and 
has a position at about the centre of our hemisphere, each wave shows 
the reflection of the sun both in the centre of the valleys interposed 
between the waves and in the summits of these waves; and for this 
reason the moon shows itself more luminous than ever, through hav- 
ing the number of the parts in light doubled. 

It shows itself also strongly luminous a short time after its turn, 
because the sun which stands beyond the moon, striking the waves 
upon their summits, when these summits are near together and seem 
almost to clash one against another when the eye is on this side, causes 
the shadows which come between the waves not to transmit to the eye 
their images mingled with the luminous images; and for this reason the 
light of the moon is more powerful. 

And what is proved of one luminous body holds true of all the rest. 

Leic. 30 r. 

 

298 ASTRONOMY 

Of the moon: all the objections of the adversary, to say that in the 
moon there is no water. 

Objection: Every body thicker than the air is heavier than this air 
and cannot be supported upon it without other cause; and the more it 
rises the less it is resisted by its medium: therefore, if there were water 
in the moon, it would despoil the moon of itself, and would come to 
cover our earth, because in this moon the water would be above its air. 
Here the answer is that if there is water in the moon there is also earth 
there upon which this water supports itself, and consequently the other 
elements: and water is supported up there among the three other ele- 
ments, as down here our water is among its accompanying elements; 
if however as the adversary holds the water had to fall from the moon, 
it would rather be that the moon would have to fall as being a body 
heavier than the water; therefore not falling it is a clear proof that the 
water up there and the earth are supported with their other elements 
just as the heavy and light elements down here are supported in space 
that is lighter than themselves. 

The adversary says that the light of the moon, if not the whole of 
it, is the same in itself; and that it shows itself more or less illuminated, 
according as the eye sees more or less of its shaded part, that is, if it is 
more in the east than the west. 

Here, at this point, one replies, that if the . . . Leic. 36 v.