The Notebooks of Leonardo Da Vinci, Volume 2
Leonardo Da Vinci

Part 3 out of 10

and where they coalesce ...



Which is the part in man, which, as he grows fatter, never gains

Or what part which as a man grows lean never falls away with a too
perceptible diminution? And among the parts which grow fat which is
that which grows fattest?

Among those which grow lean which is that which grows leanest?

In very strong men which are the muscles which are thickest and most

In your anatomy you must represent all the stages of the limbs from
man's creation to his death, and then till the death of the bone;
and which part of him is first decayed and which is preserved the

And in the same way of extreme leanness and extreme fatness.

The divisions of the head (812. 813).



There are eleven elementary tissues:-- Cartilage, bones, nerves,
veins, arteries, fascia, ligament and sinews, skin, muscle and fat.


The divisions of the head are 10, viz. 5 external and 5 internal,
the external are the hair, skin, muscle, fascia and the skull; the
internal are the dura mater, the pia mater, [which enclose] the
brain. The pia mater and the dura mater come again underneath and
enclose the brain; then the rete mirabile, and the occipital bone,
which supports the brain from which the nerves spring.


_a_. hair

_n_. skin

_c_. muscle

_m_. fascia

_o_. skull _i.e._ bone

_b_. dura mater

_d_. pia mater

_f_. brain

_r_. pia mater, below

_t_. dura mater

_l_. rete mirablile

_s_. the occipitul bone.

[Footnote: See Pl. CVIII, No. 3.]

Physiological problems (814. 815).


Of the cause of breathing, of the cause of the motion of the heart,
of the cause of vomiting, of the cause of the descent of food from
the stomach, of the cause of emptying the intestines.

Of the cause of the movement of the superfluous matter through the

Of the cause of swallowing, of the cause of coughing, of the cause
of yawning, of the cause of sneezing, of the cause of limbs getting

Of the cause of losing sensibility in any limb.

Of the cause of tickling.

Of the cause of lust and other appetites of the body, of the cause
of urine and also of all the natural excretions of the body.

[Footnote: By the side of this text stands the pen and ink drawing
reproduced on Pl. CVIII, No. 4; a skull with indications of the
veins in the fleshy covering.]


The tears come from the heart and not from the brain.

Define all the parts, of which the body is composed, beginning with
the skin with its outer cuticle which is often chapped by the
influence of the sun.



The divisions of the animal kingdom (816. 817).


_Man_. The description of man, which includes that of such creatures
as are of almost the same species, as Apes, Monkeys and the like,
which are many,

_The Lion_ and its kindred, as Panthers. [Footnote 3: _Leonza_--wild
cat? "_Secondo alcuni, lo stesso che Leonessa; e secondo altri con
piu certezza, lo stesso che Pantera_" FANFANI, _Vocabolario_ page
858.] Wildcats (?) Tigers, Leopards, Wolfs, Lynxes, Spanish cats,
common cats and the like.

_The Horse_ and its kindred, as Mule, Ass and the like, with incisor
teeth above and below.

_The Bull_ and its allies with horns and without upper incisors as
the Buffalo, Stag Fallow Deer, Wild Goat, Swine, Goat, wild Goats
Muskdeers, Chamois, Giraffe.


Describe the various forms of the intestines of the human species,
of apes and such like. Then, in what way the leonine species differ,
and then the bovine, and finally birds; and arrange this description
after the manner of a disquisition.

Miscellaneous notes on the study of Zoology (818-821).


Procure the placenta of a calf when it is born and observe the form
of the cotyledons, if their cotyledons are male or female.


Describe the tongue of the woodpecker and the jaw of the crocodile.


Of the flight of the 4th kind of butterflies that consume winged
ants. Of the three principal positions of the wings of birds in
downward flight.

[Footnote: A passing allusion is all I can here permit myself to
Leonardo's elaborate researches into the flight of birds. Compare
the observations on this subject in the Introduction to section
XVIII and in the Bibliography of Manuscripts at the end of the


Of the way in which the tail of a fish acts in propelling the fish;
as in the eel, snake and leech.

[Footnote: A sketch of a fish, swimming upwards is in the original,
inserted above this text.--Compare No. 1114.]

Comparative study of the structure of bones and of the action of
muscles (822-826).



Then I will discourse of the hands of each animal to show in what
they vary; as in the bear, which has the ligatures of the sinews of
the toes joined above the instep.


A second demonstration inserted between anatomy and [the treatise
on] the living being.

You will represent here for a comparison, the legs of a frog, which
have a great resemblance to the legs of man, both in the bones and
in the muscles. Then, in continuation, the hind legs of the hare,
which are very muscular, with strong active muscles, because they
are not encumbered with fat.

[Footnote: This text is written by the side of a drawing in black
chalk of a nude male figure, but there is no connection between the
sketch and the text.]


Here I make a note to demonstrate the difference there is between
man and the horse and in the same way with other animals. And first
I will begin with the bones, and then will go on to all the muscles
which spring from the bones without tendons and end in them in the
same way, and then go on to those which start with a single tendon
at one end.

[Footnote: See Pl. CVIII, No. 2.]


Note on the bendings of joints and in what way the flesh grows upon
them in their flexions or extensions; and of this most important
study write a separate treatise: in the description of the movements
of animals with four feet; among which is man, who likewise in his
infancy crawls on all fours.



The walking of man is always after the universal manner of walking
in animals with 4 legs, inasmuch as just as they move their feet
crosswise after the manner of a horse in trotting, so man moves his
4 limbs crosswise; that is, if he puts forward his right foot in
walking he puts forward, with it, his left arm and vice versa,



Comparative study of the organs of sense in men and animals.


I have found that in the composition of the human body as compared
with the bodies of animals the organs of sense are duller and
coarser. Thus it is composed of less ingenious instruments, and of
spaces less capacious for receiving the faculties of sense. I have
seen in the Lion tribe that the sense of smell is connected with
part of the substance of the brain which comes down the nostrils,
which form a spacious receptacle for the sense of smell, which
enters by a great number of cartilaginous vesicles with several
passages leading up to where the brain, as before said, comes down.

The eyes in the Lion tribe have a large part of the head for their
sockets and the optic nerves communicate at once with the brain; but
the contrary is to be seen in man, for the sockets of the eyes are
but a small part of the head, and the optic nerves are very fine and
long and weak, and by the weakness of their action we see by day but
badly at night, while these animals can see as well at night as by
day. The proof that they can see is that they prowl for prey at
night and sleep by day, as nocturnal birds do also.

Advantages in the structure of the eye in certain animals (828-831).


Every object we see will appear larger at midnight than at midday,
and larger in the morning than at midday.

This happens because the pupil of the eye is much smaller at midday
than at any other time.

In proportion as the eye or the pupil of the owl is larger in
proportion to the animal than that of man, so much the more light
can it see at night than man can; hence at midday it can see nothing
if its pupil does not diminish; and, in the same way, at night
things look larger to it than by day.



The eyes of all animals have their pupils adapted to dilate and
diminish of their own accord in proportion to the greater or less
light of the sun or other luminary. But in birds the variation is
much greater; and particularly in nocturnal birds, such as horned
owls, and in the eyes of one species of owl; in these the pupil
dilates in such away as to occupy nearly the whole eye, or
diminishes to the size of a grain of millet, and always preserves
the circular form. But in the Lion tribe, as panthers, pards,
ounces, tigers, lynxes, Spanish cats and other similar animals the
pupil diminishes from the perfect circle to the figure of a pointed
oval such as is shown in the margin. But man having a weaker sight
than any other animal is less hurt by a very strong light and his
pupil increases but little in dark places; but in the eyes of these
nocturnal animals, the horned owl--a bird which is the largest of
all nocturnal birds--the power of vision increases so much that in
the faintest nocturnal light (which we call darkness) it sees with
much more distinctness than we do in the splendour of noon day, at
which time these birds remain hidden in dark holes; or if indeed
they are compelled to come out into the open air lighted up by the
sun, they contract their pupils so much that their power of sight
diminishes together with the quantity of light admitted.

Study the anatomy of various eyes and see which are the muscles
which open and close the said pupils of the eyes of animals.

[Footnote: Compare No. 24, lines 8 and fol.]


_a b n_ is the membrane which closes the eye from below, upwards,
with an opaque film, _c n b_ encloses the eye in front and behind
with a transparent membrane.

It closes from below, upwards, because it [the eye] comes downwards.

When the eye of a bird closes with its two lids, the first to close
is the nictitating membrane which closes from the lacrymal duct over
to the outer corner of the eye; and the outer lid closes from below
upwards, and these two intersecting motions begin first from the
lacrymatory duct, because we have already seen that in front and
below birds are protected and use only the upper portion of the eye
from fear of birds of prey which come down from above and behind;
and they uncover first the membrane from the outer corner, because
if the enemy comes from behind, they have the power of escaping to
the front; and again the muscle called the nictitating membrane is
transparent, because, if the eye had not such a screen, they could
not keep it open against the wind which strikes against the eye in
the rush of their rapid flight. And the pupil of the eye dilates and
contracts as it sees a less or greater light, that is to say intense


If at night your eye is placed between the light and the eye of a
cat, it will see the eye look like fire.

Remarks on the organs of speech

(832. 833).


_a e i o u
ba be bi bo bu
ca ce ci co cu
da de di do du
fa fe fi fo fu
ga ge gi go gu
la le li lo lu
ma me mi mo mu
na ne ni no nu
pa pe pi po pu
qa qe qi qo qu
ra re ri ro ru
sa se si so su
ta te ti to tu_

The tongue is found to have 24 muscles which correspond to the six
muscles which compose the portion of the tongue which moves in the

And when _a o u_ are spoken with a clear and rapid pronunciation, it
is necessary, in order to pronounce continuously, without any pause
between, that the opening of the lips should close by degrees; that
is, they are wide apart in saying _a_, closer in saying _o_, and
much closer still to pronounce _u_.

It may be shown how all the vowels are pronounced with the farthest
portion of the false palate which is above the epiglottis.


If you draw in breath by the nose and send it out by the mouth you
will hear the sound made by the division that is the membrane in
[Footnote 5: The text here breaks off.]...

On the conditions of sight (834. 835).



I say that sight is exercised by all animals, by the medium of
light; and if any one adduces, as against this, the sight of
nocturnal animals, I must say that this in the same way is subject
to the very same natural laws. For it will easily be understood that
the senses which receive the images of things do not project from
themselves any visual virtue [Footnote 4: Compare No. 68.]. On the
contrary the atmospheric medium which exists between the object and
the sense incorporates in itself the figure of things, and by its
contact with the sense transmits the object to it. If the
object--whether by sound or by odour--presents its spiritual force
to the ear or the nose, then light is not required and does not act.
The forms of objects do not send their images into the air if they
are not illuminated [8]; and the eye being thus constituted cannot
receive that from the air, which the air does not possess, although
it touches its surface. If you choose to say that there are many
animals that prey at night, I answer that when the little light
which suffices the nature of their eyes is wanting, they direct
themselves by their strong sense of hearing and of smell, which are
not impeded by the darkness, and in which they are very far superior
to man. If you make a cat leap, by daylight, among a quantity of
jars and crocks you will see them remain unbroken, but if you do the
same at night, many will be broken. Night birds do not fly about
unless the moon shines full or in part; rather do they feed between
sun-down and the total darkness of the night.

[Footnote 8: See No. 58-67.]

No body can be apprehended without light and shade, and light and
shade are caused by light.



Sight is better from a distance than near in those men who are
advancing in age, because the same object transmits a smaller
impression of itself to the eye when it is distant than when it is

The seat of the common sense.


The Common Sense, is that which judges of things offered to it by
the other senses. The ancient speculators have concluded that that
part of man which constitutes his judgment is caused by a central
organ to which the other five senses refer everything by means of
impressibility; and to this centre they have given the name Common
Sense. And they say that this Sense is situated in the centre of the
head between Sensation and Memory. And this name of Common Sense is
given to it solely because it is the common judge of all the other
five senses _i.e._ Seeing, Hearing, Touch, Taste and Smell. This
Common Sense is acted upon by means of Sensation which is placed as
a medium between it and the senses. Sensation is acted upon by means
of the images of things presented to it by the external instruments,
that is to say the senses which are the medium between external
things and Sensation. In the same way the senses are acted upon by
objects. Surrounding things transmit their images to the senses and
the senses transfer them to the Sensation. Sensation sends them to
the Common Sense, and by it they are stamped upon the memory and are
there more or less retained according to the importance or force of
the impression. That sense is most rapid in its function which is
nearest to the sensitive medium and the eye, being the highest is
the chief of the others. Of this then only we will speak, and the
others we will leave in order not to make our matter too long.
Experience tells us that the eye apprehends ten different natures of
things, that is: Light and Darkness, one being the cause of the
perception of the nine others, and the other its absence:-- Colour
and substance, form and place, distance and nearness, motion and
stillness [Footnote 15: Compare No. 23.].

On the origin of the soul.


Though human ingenuity may make various inventions which, by the
help of various machines answering the same end, it will never
devise any inventions more beautiful, nor more simple, nor more to
the purpose than Nature does; because in her inventions nothing is
wanting, and nothing is superfluous, and she needs no counterpoise
when she makes limbs proper for motion in the bodies of animals. But
she puts into them the soul of the body, which forms them that is
the soul of the mother which first constructs in the womb the form
of the man and in due time awakens the soul that is to inhabit it.
And this at first lies dormant and under the tutelage of the soul of
the mother, who nourishes and vivifies it by the umbilical vein,
with all its spiritual parts, and this happens because this
umbilicus is joined to the placenta and the cotyledons, by which the
child is attached to the mother. And these are the reason why a
wish, a strong craving or a fright or any other mental suffering in
the mother, has more influence on the child than on the mother; for
there are many cases when the child loses its life from them, &c.

This discourse is not in its place here, but will be wanted for the
one on the composition of animated bodies--and the rest of the
definition of the soul I leave to the imaginations of friars, those
fathers of the people who know all secrets by inspiration.

[Footnote 57: _lettere incoronate_. By this term Leonardo probably
understands not the Bible only, but the works of the early Fathers,
and all the books recognised as sacred by the Roman Church.] I leave
alone the sacred books; for they are supreme truth.

On the relations of the soul to the organs of sense.



The soul seems to reside in the judgment, and the judgment would
seem to be seated in that part where all the senses meet; and this
is called the Common Sense and is not all-pervading throughout the
body, as many have thought. Rather is it entirely in one part.
Because, if it were all-pervading and the same in every part, there
would have been no need to make the instruments of the senses meet
in one centre and in one single spot; on the contrary it would have
sufficed that the eye should fulfil the function of its sensation on
its surface only, and not transmit the image of the things seen, to
the sense, by means of the optic nerves, so that the soul--for the
reason given above-- may perceive it in the surface of the eye. In
the same way as to the sense of hearing, it would have sufficed if
the voice had merely sounded in the porous cavity of the indurated
portion of the temporal bone which lies within the ear, without
making any farther transit from this bone to the common sense, where
the voice confers with and discourses to the common judgment. The
sense of smell, again, is compelled by necessity to refer itself to
that same judgment. Feeling passes through the perforated cords and
is conveyed to this common sense. These cords diverge with infinite
ramifications into the skin which encloses the members of the body
and the viscera. The perforated cords convey volition and sensation
to the subordinate limbs. These cords and the nerves direct the
motions of the muscles and sinews, between which they are placed;
these obey, and this obedience takes effect by reducing their
thickness; for in swelling, their length is reduced, and the nerves
shrink which are interwoven among the particles of the limbs; being
extended to the tips of the fingers, they transmit to the sense the
object which they touch.

The nerves with their muscles obey the tendons as soldiers obey the
officers, and the tendons obey the Common [central] Sense as the
officers obey the general. [27] Thus the joint of the bones obeys
the nerve, and the nerve the muscle, and the muscle the tendon and
the tendon the Common Sense. And the Common Sense is the seat of the
soul [28], and memory is its ammunition, and the impressibility is
its referendary since the sense waits on the soul and not the soul
on the sense. And where the sense that ministers to the soul is not
at the service of the soul, all the functions of that sense are also
wanting in that man's life, as is seen in those born mute and blind.

[Footnote: The peculiar use of the words _nervo_, _muscolo_,
_corda_, _senso comune_, which are here literally rendered by nerve,
muscle cord or tendon and Common Sense may be understood from lines
27 and 28.]

On involuntary muscular action.



This is most plainly seen; for you will see palsied and shivering
persons move, and their trembling limbs, as their head and hands,
quake without leave from their soul and their soul with all its
power cannot prevent their members from trembling. The same thing
happens in falling sickness, or in parts that have been cut off, as
in the tails of lizards. The idea or imagination is the helm and
guiding-rein of the senses, because the thing conceived of moves the
sense. Pre-imagining, is imagining the things that are to be.
Post-imagining, is imagining the things that are past.

Miscellaneous physiological observations (840-842).


There are four Powers: memory and intellect, desire and
covetousness. The two first are mental and the others sensual. The
three senses: sight, hearing and smell cannot well be prevented;
touch and taste not at all. Smell is connected with taste in dogs
and other gluttonous animals.


I reveal to men the origin of the first, or perhaps second cause of
their existence.


Lust is the cause of generation.

Appetite is the support of life. Fear or timidity is the
prolongation of life and preservation of its instruments.

The laws of nutrition and the support of life (843-848).



The body of any thing whatever that takes nourishment constantly
dies and is constantly renewed; because nourishment can only enter
into places where the former nourishment has expired, and if it has
expired it no longer has life. And if you do not supply nourishment
equal to the nourishment which is gone, life will fail in vigour,
and if you take away this nourishment, the life is entirely
destroyed. But if you restore as much is destroyed day by day, then
as much of the life is renewed as is consumed, just as the flame of
the candle is fed by the nourishment afforded by the liquid of this
candle, which flame continually with a rapid supply restores to it
from below as much as is consumed in dying above: and from a
brilliant light is converted in dying into murky smoke; and this
death is continuous, as the smoke is continuous; and the continuance
of the smoke is equal to the continuance of the nourishment, and in
the same instant all the flame is dead and all regenerated,
simultaneously with the movement of its own nourishment.


King of the animals--as thou hast described him--I should rather say
king of the beasts, thou being the greatest--because thou hast
spared slaying them, in order that they may give thee their children
for the benefit of the gullet, of which thou hast attempted to make
a sepulchre for all animals; and I would say still more, if it were
allowed me to speak the entire truth [5]. But we do not go outside
human matters in telling of one supreme wickedness, which does not
happen among the animals of the earth, inasmuch as among them are
found none who eat their own kind, unless through want of sense (few
indeed among them, and those being mothers, as with men, albeit they
be not many in number); and this happens only among the rapacious
animals, as with the leonine species, and leopards, panthers lynxes,
cats and the like, who sometimes eat their children; but thou,
besides thy children devourest father, mother, brothers and friends;
nor is this enough for thee, but thou goest to the chase on the
islands of others, taking other men and these half-naked, the ...
and the ... thou fattenest, and chasest them down thy own
throat[18]; now does not nature produce enough simples, for thee to
satisfy thyself? and if thou art not content with simples, canst
thou not by the mixture of them make infinite compounds, as Platina
wrote[Footnote 21: _Come scrisse il Platina_ (Bartolomeo Sacchi, a
famous humanist). The Italian edition of his treatise _De arte
coquinaria_, was published under the title _De la honestra
voluptate, e valetudine, Venezia_ 1487.], and other authors on

[Footnote: We are led to believe that Leonardo himself was a
vegetarian from the following interesting passage in the first of
Andrea Corsali's letters to Giuliano de'Medici: _Alcuni gentili
chiamati Guzzarati non si cibano di cosa, alcuna che tenga sangue,
ne fra essi loro consentono che si noccia ad alcuna cosa animata,
come il nostro Leonardo da Vinci_.

5-18. Amerigo Vespucci, with whom Leonardo was personally
acquainted, writes in his second letter to Pietro Soderini, about
the inhabitants of the Canary Islands after having stayed there in
1503: "_Hanno una scelerata liberta di viuere; ... si cibano di
carne humana, di maniera che il padre magia il figliuolo, et
all'incontro il figliuolo il padre secondo che a caso e per sorte
auiene. Io viddi un certo huomo sceleratissimo che si vantaua, et si
teneua a non piccola gloria di hauer mangiato piu di trecento
huomini. Viddi anche vna certa citta, nella quale io dimorai forse
ventisette giorni, doue le carni humane, hauendole salate, eran
appicate alli traui, si come noi alli traui di cucina_ _appicchiamo
le carni di cinghali secche al sole o al fumo, et massimamente
salsiccie, et altre simil cose: anzi si marauigliauano gradem ete
che noi non magiaissimo della carne de nemici, le quali dicono
muouere appetito, et essere di marauiglioso sapore, et le lodano
come cibi soaui et delicati (Lettere due di Amerigo Vespucci
Fiorentino drizzate al magnifico Pietro Soderini, Gonfaloniere della
eccelsa Republica di Firenze_; various editions).]


Our life is made by the death of others.

In dead matter insensible life remains, which, reunited to the
stomachs of living beings, resumes life, both sensual and


Here nature appears with many animals to have been rather a cruel
stepmother than a mother, and with others not a stepmother, but a
most tender mother.


Man and animals are really the passage and the conduit of food, the
sepulchre of animals and resting place of the dead, one causing the
death of the other, making themselves the covering for the
corruption of other dead [bodies].

On the circulation of the blood (848-850).


Death in old men, when not from fever, is caused by the veins which
go from the spleen to the valve of the liver, and which thicken so
much in the walls that they become closed up and leave no passage
for the blood that nourishes it.

[6]The incessant current of the blood through the veins makes these
veins thicken and become callous, so that at last they close up and
prevent the passage of the blood.


The waters return with constant motion from the lowest depths of the
sea to the utmost height of the mountains, not obeying the nature of
heavier bodies; and in this they resemble the blood of animated
beings which always moves from the sea of the heart and flows
towards the top of the head; and here it may burst a vein, as may be
seen when a vein bursts in the nose; all the blood rises from below
to the level of the burst vein. When the water rushes out from the
burst vein in the earth, it obeys the law of other bodies that are
heavier than the air since it always seeks low places.

[Footnote: From this passage it is quite plain that Leonardo had not
merely a general suspicion of the circulation of the blood but a
very clear conception of it. Leonardo's studies on the muscles of
the heart are to be found in the MS. W. An. III. but no information
about them has hitherto been made public. The limits of my plan in
this work exclude all purely anatomical writings, therefore only a
very brief excerpt from this note book can be given here. WILLIAM
HARVEY (born 1578 and Professor of Anatomy at Cambridge from 1615)
is always considered to have been the discoverer of the circulation
of the blood. He studied medicine at Padua in 1598, and in 1628
brought out his memorable and important work: _De motu cordis et


That the blood which returns when the heart opens again is not the
same as that which closes the valves of the heart.

Some notes on medicine (851-855).


Make them give you the definition and remedies for the case ... and
you will see that men are selected to be doctors for diseases they
do not know.


A remedy for scratches taught me by the Herald to the King of
France. 4 ounces of virgin wax, 4 ounces of colophony, 2 ounces of
incense. Keep each thing separate; and melt the wax, and then put in
the incense and then the colophony, make a mixture of it and put it
on the sore place.


Medicine is the restoration of discordant elements; sickness is the
discord of the elements infused into the living body.


Those who are annoyed by sickness at sea should drink extract of


To keep in health, this rule is wise: Eat only when you want and
relish food. Chew thoroughly that it may do you good. Have it well
cooked, unspiced and undisguised. He who takes medicine is ill

[Footnote: This appears to be a sketch for a poem.]


I teach you to preserve your health; and in this you will succed
better in proportion as you shun physicians, because their medicines
are the work of alchemists.

[Footnote: This passage is written on the back of the drawing Pl.
CVIII. Compare also No. 1184.]



_Ever since the publication by Venturi in_ 1797 _and Libri in_ 1840
_of some few passages of Leonardo's astronomical notes, scientific
astronomers have frequently expressed the opinion, that they must
have been based on very important discoveries, and that the great
painter also deserved a conspicuous place in the history of this
science. In the passages here printed, a connected view is given of
his astronomical studies as they lie scattered through the
manuscripts, which have come down to us. Unlike his other purely
scientific labours, Leonardo devotes here a good deal of attention
to the opinions of the ancients, though he does not follow the
practice universal in his day of relying on them as authorities; he
only quotes them, as we shall see, in order to refute their
arguments. His researches throughout have the stamp of independent
thought. There is nothing in these writings to lead us to suppose
that they were merely an epitome of the general learning common to
the astronomers of the period. As early as in the XIVth century
there were chairs of astronomy in the universities of Padua and
Bologna, but so late as during the entire XVIth century Astronomy
and Astrology were still closely allied._

_It is impossible now to decide whether Leonardo, when living in
Florence, became acquainted in his youth with the doctrines of Paolo
Toscanelli the great astronomer and mathematician (died_ 1482_), of
whose influence and teaching but little is now known, beyond the
fact that he advised and encouraged Columbus to carry out his
project of sailing round the world. His name is nowhere mentioned by
Leonardo, and from the dates of the manuscripts from which the texts
on astronomy are taken, it seems highly probable that Leonardo
devoted his attention to astronomical studies less in his youth than
in his later years. It was evidently his purpose to treat of
Astronomy in a connected form and in a separate work (see the
beginning of Nos._ 866 _and_ 892_; compare also No._ 1167_). It is
quite in accordance with his general scientific thoroughness that he
should propose to write a special treatise on Optics as an
introduction to Astronomy (see Nos._ 867 _and_ 877_). Some of the
chapters belonging to this Section bear the title "Prospettiva"
_(see Nos._ 869 _and_ 870_), this being the term universally applied
at the time to Optics as well as Perspective (see Vol. I, p._ 10,
_note to No._ 13, _l._ 10_)_.

_At the beginning of the XVIth century the Ptolemaic theory of the
universe was still universally accepted as the true one, and
Leonardo conceives of the earth as fixed, with the moon and sun
revolving round it, as they are represented in the diagram to No._
897. _He does not go into any theory of the motions of the planets;
with regard to these and the fixed stars he only investigates the
phenomena of their luminosity. The spherical form of the earth he
takes for granted as an axiom from the first, and he anticipates
Newton by pointing out the universality of Gravitation not merely in
the earth, but even in the moon. Although his acute research into
the nature of the moon's light and the spots on the moon did not
bring to light many results of lasting importance beyond making it
evident that they were a refutation of the errors of his
contemporaries, they contain various explanations of facts which
modern science need not modify in any essential point, and
discoveries which history has hitherto assigned to a very much later

_The ingenious theory by which he tries to explain the nature of
what is known as earth shine, the reflection of the sun's rays by
the earth towards the moon, saying that it is a peculiar refraction,
originating in the innumerable curved surfaces of the waves of the
sea may be regarded as absurd; but it must not be forgotten that he
had no means of detecting the fundamental error on which he based
it, namely: the assumption that the moon was at a relatively short
distance from the earth. So long as the motion of the earth round
the sun remained unknown, it was of course impossible to form any
estimate of the moon's distance from the earth by a calculation of
its parallax_.

_Before the discovery of the telescope accurate astronomical
observations were only possible to a very limited extent. It would
appear however from certain passages in the notes here printed for
the first time, that Leonardo was in a position to study the spots
in the moon more closely than he could have done with the unaided
eye. So far as can be gathered from the mysterious language in which
the description of his instrument is wrapped, he made use of
magnifying glasses; these do not however seem to have been
constructed like a telescope--telescopes were first made about_
1600. _As LIBRI pointed out_ (Histoire des Sciences mathematiques
III, 101) _Fracastoro of Verona_ (1473-1553) _succeeded in
magnifying the moon's face by an arrangement of lenses (compare No._
910, _note), and this gives probability to Leonardo's invention at a
not much earlier date._



The earth's place in the universe (857. 858).


The equator, the line of the horizon, the ecliptic, the meridian:

These lines are those which in all their parts are equidistant from
the centre of the globe.


The earth is not in the centre of the Sun's orbit nor at the centre
of the universe, but in the centre of its companion elements, and
united with them. And any one standing on the moon, when it and the
sun are both beneath us, would see this our earth and the element of
water upon it just as we see the moon, and the earth would light it
as it lights us.

The fundamental laws of the solar system (859-864).


Force arises from dearth or abundance; it is the child of physical
motion, and the grand-child of spiritual motion, and the mother and
origin of gravity. Gravity is limited to the elements of water and
earth; but this force is unlimited, and by it infinite worlds might
be moved if instruments could be made by which the force could be

Force, with physical motion, and gravity, with resistance are the
four external powers on which all actions of mortals depend.

Force has its origin in spiritual motion; and this motion, flowing
through the limbs of sentient animals, enlarges their muscles. Being
enlarged by this current the muscles are shrunk in length and
contract the tendons which are connected with them, and this is the
cause of the force of the limbs in man.

The quality and quantity of the force of a man are able to give
birth to other forces, which will be proportionally greater as the
motions produced by them last longer.

[Footnote: Only part of this passage belongs, strictly speaking, to
this section. The principle laid down in the second paragraph is
more directly connected with the notes given in the preceding
section on Physiology.]


Why does not the weight _o_ remain in its place? It does not remain
because it has no resistance. Where will it move to? It will move
towards the centre [of gravity]. And why by no other line? Because a
weight which has no support falls by the shortest road to the lowest
point which is the centre of the world. And why does the weight know
how to find it by so short a line? Because it is not independant and
does not move about in various directions.

[Footnote: This text and the sketch belonging to it, are reproduced
on Pl. CXXI.]


Let the earth turn on which side it may the surface of the waters
will never move from its spherical form, but will always remain
equidistant from the centre of the globe.

Granting that the earth might be removed from the centre of the
globe, what would happen to the water?

It would remain in a sphere round that centre equally thick, but the
sphere would have a smaller diameter than when it enclosed the

[Footnote: Compare No. 896, lines 48-64; and No. 936.]


Supposing the earth at our antipodes which supports the ocean were
to rise and stand uncovered, far out of the sea, but remaining
almost level, by what means afterwards, in the course of time, would
mountains and vallies be formed?

And the rocks with their various strata?


Each man is always in the middle of the surface of the earth and
under the zenith of his own hemisphere, and over the centre of the


Mem.: That I must first show the distance of the sun from the earth;
and, by means of a ray passing through a small hole into a dark
chamber, detect its real size; and besides this, by means of the
aqueous sphere calculate the size of the globe ...

Here it will be shown, that when the sun is in the meridian of our
hemisphere [Footnote 10: _Antipodi orientali cogli occidentali_. The
word _Antipodes_ does not here bear its literal sense, but--as we
may infer from the simultaneous reference to inhabitants of the
North and South-- is used as meaning men living at a distance of 90
degrees from the zenith of the rational horizon of each observer.],
the antipodes to the East and to the West, alike, and at the same
time, see the sun mirrored in their waters; and the same is equally
true of the arctic and antarctic poles, if indeed they are

How to prove that the earth is a planet (865-867).


That the earth is a star.


In your discourse you must prove that the earth is a star much like
the moon, and the glory of our universe; and then you must treat of
the size of various stars, according to the authors.



First describe the eye; then show how the twinkling of a star is
really in the eye and why one star should twinkle more than another,
and how the rays from the stars originate in the eye; and add, that
if the twinkling of the stars were really in the stars --as it seems
to be--that this twinkling appears to be an extension as great as
the diameter of the body of the star; therefore, the star being
larger than the earth, this motion effected in an instant would be a
rapid doubling of the size of the star. Then prove that the surface
of the air where it lies contiguous to fire, and the surface of the
fire where it ends are those into which the solar rays penetrate,
and transmit the images of the heavenly bodies, large when they
rise, and small, when they are on the meridian. Let _a_ be the earth
and _n d m_ the surface of the air in contact with the sphere of
fire; _h f g_ is the orbit of the moon or, if you please, of the
sun; then I say that when the sun appears on the horizon _g_, its
rays are seen passing through the surface of the air at a slanting
angle, that is _o m_; this is not the case at _d k_. And so it
passes through a greater mass of air; all of _e m_ is a denser


Beyond the sun and us there is darkness and so the air appears blue.

[Footnote: Compare Vol. I, No. 301.]



It is possible to find means by which the eye shall not see remote
objects as much diminished as in natural perspective, which
diminishes them by reason of the convexity of the eye which
necessarily intersects, at its surface, the pyramid of every image
conveyed to the eye at a right angle on its spherical surface. But
by the method I here teach in the margin [9] these pyramids are
intersected at right angles close to the surface of the pupil. The
convex pupil of the eye can take in the whole of our hemisphere,
while this will show only a single star; but where many small stars
transmit their images to the surface of the pupil those stars are
extremely small; here only one star is seen but it will be large.
And so the moon will be seen larger and its spots of a more defined
form [Footnote 20 and fol.: Telescopes were not in use till a century
later. Compare No. 910 and page 136.]. You must place close to the
eye a glass filled with the water of which mention is made in number
4 of Book 113 "On natural substances" [Footnote 23: _libro_ 113.
This is perhaps the number of a book in some library catalogue. But
it may refer, on the other hand, to one of the 120 Books mentioned
in No. 796. l. 84.]; for this water makes objects which are enclosed
in balls of crystalline glass appear free from the glass.


Among the smaller objects presented to the pupil of the eye, that
which is closest to it, will be least appreciable to the eye. And at
the same time, the experiments here made with the power of sight,
show that it is not reduced to speck if the &c. [32][Footnote 32:
Compare with this the passage in Vol. I, No. 52, written about
twenty years earlier.].

Read in the margin.

[34]Those objects are seen largest which come to the eye at the
largest angles.

But the images of the objects conveyed to the pupil of the eye are
distributed to the pupil exactly as they are distributed in the air:
and the proof of this is in what follows; that when we look at the
starry sky, without gazing more fixedly at one star than another,
the sky appears all strewn with stars; and their proportions to the
eye are the same as in the sky and likewise the spaces between them

[Footnote: 9. 32. _in margine:_ lines 34-61 are, in the original,
written on the margin and above them is the diagram to which
Leonardo seems to refer here.]



Among objects moved from the eye at equal distance, that undergoes
least diminution which at first was most remote.

When various objects are removed at equal distances farther from
their original position, that which was at first the farthest from
the eye will diminish least. And the proportion of the diminution
will be in proportion to the relative distance of the objects from
the eye before they were removed.

That is to say in the object _t_ and the object _e_ the proportion
of their distances from the eye _a_ is quintuple. I remove each from
its place and set it farther from the eye by one of the 5 parts into
which the proposition is divided. Hence it happens that the nearest
to the eye has doubled the distance and according to the last
proposition but one of this, is diminished by the half of its whole
size; and the body _e_, by the same motion, is diminished 1/5 of its
whole size. Therefore, by that same last proposition but one, that
which is said in this last proposition is true; and this I say of
the motions of the celestial bodies which are more distant by 3500
miles when setting than when overhead, and yet do not increase or
diminish in any sensible degree.


_a b_ is the aperture through which the sun passes, and if you could
measure the size of the solar rays at _n m_, you could accurately
trace the real lines of the convergence of the solar rays, the
mirror being at _a b_, and then show the reflected rays at equal
angles to _n m_; but, as you want to have them at _n m_, take them
at the. inner side of the aperture at cd, where they maybe measured
at the spot where the solar rays fall. Then place your mirror at the
distance _a b_, making the rays _d b_, _c a_ fall and then be
reflected at equal angles towards _c d_; and this is the best
method, but you must use this mirror always in the same month, and
the same day, and hour and instant, and this will be better than at
no fixed time because when the sun is at a certain distance it
produces a certain pyramid of rays.


_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.]



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).


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.


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

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_.


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).]


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.].


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



The question of the true and of the apparent size 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

[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.]


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.

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.


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.]


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.


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.


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.



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).


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



[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.


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



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


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.



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



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



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

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



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

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.


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.]


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?



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

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

[Footnote 48-64: Compare No. 861.]

The innumerable images of the solar rays reflected from the
innumerable waves of the sea, as they fall upon those waves, are
what cause us to see the very broad and continuous radiance on the
surface of the sea.


That the sun could not be mirrored in the body of the moon, which is
a convex mirror, in such a way as that so much of its surface as is
illuminated by the sun, should reflect the sun unless the moon had a
surface adapted to reflect it--in waves and ridges, like the surface
of the sea when its surface is moved by the wind.

[Footnote: In the original diagrams _sole_ is written at the place
marked _A; luna_ at _C,_ and _terra_ at the two spots marked _B_.]

The waves in water multiply the image of the object reflected in it.

These waves reflect light, each by its own line, as the surface of
the fir cone does [Footnote 14: See the diagram p. 145.]

These are 2 figures one different from the other; one with
undulating water and the other with smooth water.

It is impossible that at any distance the image of the sun cast on
the surface of a spherical body should occupy the half of the

Here you must prove that the earth produces all the same effects
with regard to the moon, as the moon with regard to the earth.

The moon, with its reflected light, does not shine like the sun,
because the light of the moon is not a continuous reflection of that
of the sun on its whole surface, but only on the crests and hollows
of the waves of its waters; and thus the sun being confusedly
reflected, from the admixture of the shadows that lie between the
lustrous waves, its light is not pure and clear as the sun is.

[Footnote 38: This refers to the small diagram placed between _B_
and _B_.--]. The earth between the moon on the fifteenth day and the
sun. [Footnote 39: See the diagram below the one referred to in the
preceding note.] Here the sun is in the East and the moon on the
fifteenth day in the West. [Footnote 40.41: Refers to the diagram
below the others.] The moon on the fifteenth [day] between the earth
and the sun. [41]Here it is the moon which has the sun to the West
and the earth to the East.



The moon is not of itself luminous, but is highly fitted to
assimilate the character of light after the manner of a mirror, or
of water, or of any other reflecting body; and it grows larger in
the East and in the West, like the sun and the other planets. And
the reason is that every luminous body looks larger in proportion as
it is remote. It is easy to understand that every planet and star is
farther from us when in the West than when it is overhead, by about
3500 miles, as is proved on the margin [Footnote 7: refers to the
first diagram.--A = _sole_ (the sun), B = _terra_ (the earth), C =
_luna_ (the moon).], and if you see the sun or moon mirrored in the
water near to you, it looks to you of the same size in the water as
in the sky. But if you recede to the distance of a mile, it will
look 100 times larger; and if you see the sun reflected in the sea
at sunset, its image would look to you more than 10 miles long;
because that reflected image extends over more than 10 miles of sea.
And if you could stand where the moon is, the sun would look to you,
as if it were reflected from all the sea that it illuminates by day;
and the land amid the water would appear just like the dark spots
that are on the moon, which, when looked at from our earth, appears
to men the same as our earth would appear to any men who might dwell
in the moon.

[Footnote: This text has already been published by LIBRI: _Histoire
des Sciences,_ III, pp. 224, 225.]


When the moon is entirely lighted up to our sight, we see its full
daylight; and at that time, owing to the reflection of the solar
rays which fall on it and are thrown off towards us, its ocean casts
off less moisture towards us; and the less light it gives the more
injurious it is.



I say that as the moon has no light in itself and yet is luminous,
it is inevitable but that its light is caused by some other body.



All my opponent's arguments to say that there is no water in the
moon. [Footnote: The objections are very minutely noted down in the
manuscript, but they hardly seem to have a place here.]


Answer to Maestro Andrea da Imola, who said that the solar rays
reflected from a convex mirror are mingled and lost at a short
distance; whereby it is altogether denied that the luminous side of
the moon is of the nature of a mirror, and that consequently the
light is not produced by the innumerable multitude of the waves of
that sea, which I declared to be the portion of the moon which is
illuminated by the solar rays.

Let _o p_ be the body of the sun, _c n s_ the moon, and _b_ the eye
which, above the base _c n_ of the cathetus _c n m_, sees the body
of the sun reflected at equal angles _c n_; and the same again on
moving the eye from _b_ to _a_. [Footnote: The large diagram on the
margin of page 161 belongs to this chapter.]

Explanation of the lumen cinereum in the moon.



No solid body is less heavy than the atmosphere.

[Footnote: 1. On the margin are the words _tola romantina,
tola--ferro stagnato_ (tinned iron); _romantina_ is some special
kind of sheet-iron no longer known by that name.]

Having proved that the part of the moon that shines consists of
water, which mirrors the body of the sun and reflects the radiance
it receives from it; and that, if these waters were devoid of waves,
it would appear small, but of a radiance almost like the sun; --[5]
It must now be shown whether the moon is a heavy or a light body:
for, if it were a heavy body--admitting that at every grade of
distance from the earth greater levity must prevail, so that water
is lighter than the earth, and air than water, and fire than air and
so on successively--it would seem that if the moon had density as it
really has, it would have weight, and having weight, that it could
not be sustained in the space where it is, and consequently that it
would fall towards the centre of the universe and become united to
the earth; or if not the moon itself, at least its waters would fall
away and be lost from it, and descend towards the centre, leaving
the moon without any and so devoid of lustre. But as this does not
happen, as might in reason be expected, it is a manifest sign that
the moon is surrounded by its own elements: that is to say water,
air and fire; and thus is, of itself and by itself, suspended in
that part of space, as our earth with its element is in this part of
space; and that heavy bodies act in the midst of its elements just
as other heavy bodies do in ours [Footnote 15: This passage would
certainly seem to establish Leonardo's claim to be regarded as the
original discoverer of the cause of the ashy colour of the new moon
(_lumen cinereum_). His observations however, having hitherto
remained unknown to astronomers, Moestlin and Kepler have been
credited with the discoveries which they made independently a
century later.

Some disconnected notes treat of the same subject in MS. C. A. 239b;
718b and 719b; "_Perche la luna cinta della parte alluminata dal
sole in ponente, tra maggior splendore in mezzo a tal cerchio, che
quando essa eclissava il sole. Questo accade perche nell' eclissare
il sole ella ombrava il nostro oceano, il qual caso non accade
essendo in ponente, quando il sole alluma esso oceano_." The editors
of the "_Saggio_" who first published this passage (page 12) add
another short one about the seasons in the moon which I confess not
to have seen in the original manuscript: "_La luna ha ogni mese un
verno e una state, e ha maggiori freddi e maggiori caldi, e i suoi
equinozii son piu freddi de' nostri._"]

When the eye is in the East and sees the moon in the West near to
the setting sun, it sees it with its shaded portion surrounded by
luminous portions; and the lateral and upper portion of this light
is derived from the sun, and the lower portion from the ocean in the
West, which receives the solar rays and reflects them on the lower
waters of the moon, and indeed affords the part of the moon that is
in shadow as much radiance as the moon gives the earth at midnight.
Therefore it is not totally dark, and hence some have believed that
the moon must in parts have a light of its own besides that which is
given it by the sun; and this light is due, as has been said, to the
above- mentioned cause,--that our seas are illuminated by the sun.

Again, it might be said that the circle of radiance shown by the
moon when it and the sun are both in the West is wholly borrowed
from the sun, when it, and the sun, and the eye are situated as is
shown above.

[Footnote 23. 24: The larger of the two diagrams reproduced above
stands between these two lines, and the smaller one is sketched in
the margin. At the spot marked _A_ Leonardo wrote _corpo solare_
(solar body) in the larger diagram and _Sole_ (sun) in the smaller
one. At _C luna_ (moon) is written and at _B terra_ (the earth).]

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

Some have thought that the moon has a light of its own, but this
opinion is false, because they have founded it on that dim light
seen between the hornes of the new moon, which looks dark where it
is close to the bright part, while against the darkness of the
background it looks so light that many have taken it to be a ring of
new radiance completing the circle where the tips of the horns
illuminated by the sun cease to shine [Footnote 34: See Pl. CVIII,
No. 5.]. And this difference of background arises from the fact that
the portion of that background which is conterminous with the bright
part of the moon, by comparison with that brightness looks darker
than it is; while at the upper part, where a portion of the luminous
circle is to be seen of uniform width, the result is that the moon,
being brighter there than the medium or background on which it is
seen by comparison with that darkness it looks more luminous at that
edge than it is. And that brightness at such a time itself is
derived from our ocean and other inland-seas. These are, at that
time, illuminated by the sun which is already setting in such a way
as that the sea then fulfils the same function to the dark side of
the moon as the moon at its fifteenth day does to us when the sun is
set. And the small amount of light which the dark side of the moon
receives bears the same proportion to the light of that side which
is illuminated, as that... [Footnote 42: Here the text breaks off;
lines 43-52 are written on the margin.].

If you want to see how much brighter the shaded portion of the moon
is than the background on which it is seen, conceal the luminous
portion of the moon with your hand or with some other more distant

On the spots in the moon (903-907).



Some have said that vapours rise from the moon, after the manner of
clouds and are interposed between the moon and our eyes. But, if
this were the case, these spots would never be permanent, either as
to position or form; and, seeing the moon from various aspects, even
if these spots did not move they would change in form, as objects do
which are seen from different sides.



Others say that the moon is composed of more or less transparent
parts; as though one part were something like alabaster and others
like crystal or glass. It would follow from this that the sun
casting its rays on the less transparent portions, the light would
remain on the surface, and so the denser part would be illuminated,
and the transparent portions would display the shadow of their
darker depths; and this is their account of the structure and nature
of the moon. And this opinion has found favour with many
philosophers, and particularly with Aristotle, and yet it is a false
view--for, in the various phases and frequent changes of the moon
and sun to our eyes, we should see these spots vary, at one time
looking dark and at another light: they would be dark when the sun
is in the West and the moon in the middle of the sky; for then the
transparent hollows would be in shadow as far as the tops of the
edges of those transparent hollows, because the sun could not then
fling his rays into the mouth of the hollows, which however, at full
moon, would be seen in bright light, at which time the moon is in
the East and faces the sun in the West; then the sun would
illuminate even the lowest depths of these transparent places and
thus, as there would be no shadows cast, the moon at these times
would not show us the spots in question; and so it would be, now
more and now less, according to the changes in the position of the
sun to the moon, and of the moon to our eyes, as I have said above.



It has been asserted, that the spots on the moon result from the
moon being of varying thinness or density; but if this were so, when
there is an eclipse of the moon the solar rays would pierce through
the portions which were thin as is alleged [Footnote 3-5: _Eclissi_.
This word, as it seems to me, here means eclipses of the sun; and
the sense of the passage, as I understand it, is that by the
foregoing hypothesis the moon, when it comes between the sun and the
earth must appear as if pierced,--we may say like a sieve.]. But as
we do not see this effect the opinion must be false.

Others say that the surface of the moon is smooth and polished and
that, like a mirror, it reflects in itself the image of our earth.
This view is also false, inasmuch as the land, where it is not
covered with water, presents various aspects and forms. Hence when
the moon is in the East it would reflect different spots from those
it would show when it is above us or in the West; now the spots on
the moon, as they are seen at full moon, never vary in the course of
its motion over our hemisphere. A second reason is that an object
reflected in a convex body takes up but a small portion of that
body, as is proved in perspective [Footnote 18: _come e provato_.
This alludes to the accompanying diagram.]. The third reason is that
when the moon is full, it only faces half the hemisphere of the
illuminated earth, on which only the ocean and other waters reflect
bright light, while the land makes spots on that brightness; thus
half of our earth would be seen girt round with the brightness of
the sea lighted up by the sun, and in the moon this reflection would
be the smallest part of that moon. Fourthly, a radiant body cannot
be reflected from another equally radiant; therefore the sea, since
it borrows its brightness from the sun,--as the moon does--, could
not cause the earth to be reflected in it, nor indeed could the body
of the sun be seen reflected in it, nor indeed any star opposite to


If you keep the details of the spots of the moon under observation
you will often find great variation in them, and this I myself have
proved by drawing them. And this is caused by the clouds that rise
from the waters in the moon, which come between the sun and those
waters, and by their shadow deprive these waters of the sun's rays.
Thus those waters remain dark, not being able to reflect the solar


How the spots on the moon must have varied from what they formerly
were, by reason of the course of its waters.

On the moon's halo.



I have found, that the circles which at night seem to surround the
moon, of various sizes, and degrees of density are caused by various
gradations in the densities of the vapours which exist at different
altitudes between the moon and our eyes. And of these halos the
largest and least red is caused by the lowest of these vapours; the
second, smaller one, is higher up, and looks redder because it is
seen through two vapours. And so on, as they are higher they will
appear smaller and redder, because, between the eye and them, there
is thicker vapour. Whence it is proved that where they are seen to
be reddest, the vapours are most dense.

On instruments for observing the moon (909. 910).


If you want to prove why the moon appears larger than it is, when it
reaches the horizon; take a lens which is highly convex on one
surface and concave on the opposite, and place the concave side next
the eye, and look at the object beyond the convex surface; by this
means you will have produced an exact imitation of the atmosphere
included beneath the sphere of fire and outside that of water; for
this atmosphere is concave on the side next the earth, and convex
towards the fire.


Construct glasses to see the moon magnified.

[Footnote: See the Introduction, p. 136, Fracastoro says in his work
Homocentres: "_Per dua specilla ocularla si quis perspiciat, alteri
altero superposito, majora multo et propinquiora videbit
omnia.--Quin imo quaedam specilla ocularia fiunt tantae densitatis,
ut si per ea quis aut lunam, aut aliud siderum spectet, adeo
propinqua illa iudicet, ut ne turres ipsas excedant_" (sect. II c. 8
and sect. III, c. 23).]

******** 911 - 912 MISSING ***

when the sun is seen through the boughs of trees bare of their
leaves, at some distance the branches do not conceal any portion of
the sun from our eye. The same thing happens with the above
mentioned planets which, though they have no light of their own, do


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