ultimate principles beyond which nothing in nature can be found which
forms a part of that science: as in the continued quantity, that is to
say, the science of geometry, which, starting from the surfaces of
bodies, has its origin in the line, which is the end of the
superficies; and we are not satisfied by this, because we know that the
line terminates in the point, and the point is that which is the least
of things. Therefore the point is the first principle of geometry, and
nothing else can exist either {143} in nature or in the human mind from
which the point can issue. Because if you say that the contact between
a surface and the extreme point of an iron instrument is the creation
of the point, it is not true; but let us say that this point of contact
is a superficies which surrounds its centre, and in the centre the
point dwells. And such a point is not a part of the substance of the
superficies, neither it nor all the points of the universe can, even if
combined,--it being granted that they could be combined,--compose any
part of a superficies. And granted, as you imagined, a whole composed
of a thousand points, if we divide any part of this quantity of a
thousand, we can very well say that this part shall equal its whole;
and this we can prove by zero, or naught, that is, the tenth figure of
arithmetic, which is represented by a cipher as being nothing, and
placed after unity it will signify 10, and if two ciphers are placed
after unity it will signify 100, and thus the number will go on
increasing by ten to infinity whenever a cipher is added, and the
cipher in itself is worth nothing more than naught, and all the naughts
in the universe are equal to one naught alone, in regard to their
substance and value.
[Sidenote: True Science based on the Testimony of the Senses]
9.
Knowledge which is the issue of experience is termed mechanical; that
which is born and ends {144} in the mind is termed scientific; that
which issues from science and ends in manual work is termed
semi-mechanical. But I consider vain and full of error that science
which is not the offspring of experience, mother of all certitude, and
which does not result in established experience, that is to say, whose
origin, middle and end do not pass through any of the five senses. And
if we doubt of everything we perceive by the senses, should we not
doubt much more of what is contrary to the senses, such as the
existence of God and of the soul, and similar matters constantly under
dispute and contention?
And it is truly the case that where reason is lacking it is
supplemented by noise, which never happens in matters of certainty. On
account of this we will say that where there is noise there is no true
science, because truth has one end only, which, when it is made known,
eternally silences controversy, and should controversy come to life
again, it is lying and confused knowledge which is reborn, and not
certainty. But true science is that which has penetrated into the
senses through experience and silenced the tongue of the disputers, and
which does not feed those who investigate it with dreams, but proceeds
from the basis of primary truths and established principles
successively and by true sequence to the end; as, for instance, what
comes under the heading of elementary mathematics, {145} that is,
numeration and measurement, termed arithmetic and geometry, which treat
with the highest truth of the discontinued and continued quantity.
Here there will be no dispute as to whether twice three make more or
less than six, nor whether two angles of a triangle are less than two
right angles, but eternal silence shall ignore all controversy, and the
devotees of the true science will finish their studies in peace, which
the lying mental sciences cannot do. And if thou sayest that true and
established science of this kind is a species of mechanics, because
they can only be completed by the hand, I will say the same of all the
arts, such as that which passes through the hand of the sculptor, which
is a kind of drawing, a part of painting; and astrology and the other
sciences pass through manual operation, but they are mental in the
first place, as painting, which first of all exists in the mind of the
composer, and cannot attain to fulfilment without manual labour. With
regard to painting, its true and scientific principles must be
established: what constitutes a shaded body, what constitutes a primary
shade, a derivative shade, what constitutes light: that is, darkness,
light, colour, size, shape, position, distance, propinquity, motion,
rest, which are comprehended by the mind only, and without manual
labour. And this is the science of painting which remains in the mind
of those who meditate on it, from which {146} issues the work in due
time, and is infinitely superior to the aforesaid contemplation or
science.
[Sidenote: Mechanics]
10.
Mechanics are the paradise of scientific mathematics, because with them
we arrive at the fruits of mathematics.
[Sidenote: Mechanics and Experience]
11.
Experience is indispensable for the making of any instrument.
12.
Proportion is not only to be found in figures and measurements, but
also in sound, weight, time and position, and in whatever power which
exists.
[Sidenote: Reason and Experience]
13.
The power of the projecting force increases in proportion as the object
projected is smaller; the acceleration of the motion increases to
infinity proportionately to this diminution. It would follow that an
atom would be almost as rapid as the imagination or the eye, which in a
moment attains to the height of the stars, and consequently its voyage
would be infinite, because the thing which can be infinitely diminished
would have an infinite velocity and would travel on an infinite course
(because every continuous quantity is divisible to infinity). And this
opinion is {147} condemned by reason and consequently by experience.
Thus, you who observe rely not on authors who have merely by their
imagination wished to be interpreters between nature and man, but on
those alone who have applied their minds not to the hints of nature but
to the results of their experience. And you must realize the
deceptiveness of experiments; because those which often appear to be
one and the same are often different, as is shown here.
[Sidenote: Effects correspond to the Force of their Cause]
14.
A spherical body which possesses a dense and resisting superficies will
move as much in the rebound resulting from the resistance of a smooth
and solid plane as it would if you threw it freely through the air, if
the force applied be equal in both cases.
Oh, admirable justice of thine, thou first mover! thou hast not
permitted that any tone should fail to produce its necessary effects,
either as regards order or quantity. Seeing that a force impels an
object which it overcomes a distance of one hundred arms' length, and
if in obeying this law it meets with resistance, thou hast ordained
that the force of the shock will cause afresh a further movement, which
in its various bounds recuperates the whole sum of the distance it
should have travelled. And if you measure the distance {148}
accomplished by the aforesaid bounds you will find that they equal the
length of distance through which a similar object set in motion by an
equal force would travel freely through the air.
15.
Every action must be caused by motion.
16.
Motion is the cause of all life.
[Sidenote: Of Force]
17.
What is force? Force, I say, is a spiritual virtue, an invisible
power, which by accidental external violence is caused by motion, and
communicated and infused into bodies which are inert by nature, giving
them an active life of marvellous power.
18.
What is force? I say that force is a spiritual, incorporate and
invisible power, which for a brief duration is produced in bodies that
by accidental violence are displaced from their natural state of
inertia.
[Sidenote: Origin of Force]
19.
Force arises from dearth or abundance; it is the child of physical
motion and the grandchild of spiritual motion, and the mother and
origin of gravity. Gravity is confined to the elements of {149} water
and earth, and this force is infinite, because infinite worlds could be
moved by it if instruments could be made by which the force could be
generated. Force, with physical motion, and gravity, with resistance,
are the four accidental powers by which all mortal things live and die.
Force has its origin in spiritual motion, and this motion, flowing
through the limbs of sentient animals, enlarges their muscles, and thus
enlarged the muscles are shrunk in length and contract the tendons with
which they are connected, and this is the cause of the strength in
human limbs. The quality and quantity of the strength of a man can
generate a further force, which will increase in proportion to the
duration of the motions produced by them.
[Sidenote: Aspects of Force]
20.
Gravity, force and casual motion together with resistance are the four
external powers by which all the visible actions of man live and die.
[Sidenote: Of Inertia]
21.
A motion tends to be continuous; a body set in motion continues to move
as long as the impression of the motive power lasts in it.
[Sidenote: Can Man imitate a Bird's Flight?]
22.
The bird is an instrument which operates by mathematical laws, and man
can reproduce all {150} the movements of this instrument, but cannot
attain to the intensity of its power; and can only succeed in acquiring
balance. Thus we will say that such an instrument constructed by man
lacks only the soul of the bird, and the soul of man must counterfeit
the soul of the bird. The spirit in the frame of the bird doubtless
would respond to needs of that frame better than would the spirit of
man, whose frame is different, more especially in the almost insensible
motions of balance; and since we see the bird make provision for the
many sensible varieties of movement, we can conclude by such experience
that man can acquire knowledge of the more markedly sensible of these
movements, and that he will be able to make ample provision against the
destruction of that instrument of which he has made himself the spirit
and the guide.
[Sidenote: Of Inertia]
23.
A natural and continuous motion seeks to preserve its course along the
line of its starting-point, that is to say, let us call starting-point
whatever place in which it varies.
24.
Everything maintains itself by motion. And if it were possible to
describe a diameter of air on the sphere of the earth, like to a well,
which would extend from one superficies to the other, {151} and if a
weighty body were dropped into this well, the body would seek to remain
stationary at the centre, but so strong would be the impetus that for
many years it would prevent it from so doing.
[Sidenote: Transmission of Motion]
25.
Impetus is a virtue created by motion and communicated by the motive
force to the object moved, and this object acquires motion in
proportion to the energy of the impetus.
[Sidenote: Matter is Inert]
26.
No lifeless matter moves of itself, but its motion is caused from
without.
27.
All elements displaced from their natural place seek to return to it,
and more especially fire, water and earth.
28.
All matter universally seeks to maintain itself in its natural state;
hence, water in motion seeks to maintain its course according to the
force by which it is propelled, and if it meets with opposition it
finishes the length of the course it began in a circular and reflex
motion.
[Sidenote: Conception of Energy]
29.
Impetus is the impression of motion conveyed by the motive power to the
object moved. Every {152} impression tends to permanence or seeks to
attain permanence. That every impression seeks after permanence is
proved by the impression made by the sun on the eye which regards it,
and in the impression of sound made by the hammer which strikes a bell.
Every impression seeks after permanence, as is shown in the image of
impetus communicated to the object moved.
30.
A weight seeks to fall to the centre of the earth by the most direct
way.
[Sidenote: In Praise of the Sun]
31.
If you look at the stars, warding off the rays (as may be done by
looking through a small hole made by the extreme point of a fine needle
placed so as almost to touch the eye), they will appear so small as to
seem as though nothing could be smaller; it is owing to their great
distance that they appear so small, for many of them are very many
times larger than the star which is the earth with its water. Now
reflect what appearance this our star must have from so great a
distance, and then consider how many stars might be placed--both in
longitude and latitude--between those stars which are sown in the dark
space. I can never refrain from blaming many of the ancients who said
that the size of the sun was no greater than {153} it appears; among
whom was Epicurus. I believe he founded his reasoning on a light
placed in our atmosphere equidistant from the centre of the earth,
which, to any one looking at it, never appears to diminish in size from
whatever distance it is seen.
32.
I shall reserve the reasons of its size and power for later. But I
greatly marvel that Socrates should have depreciated such a body, and
that he should have said that it resembled an incandescent stone; and
he who opposed him as regards this error acted rightly. But I wish I
had words to blame those who seek to exalt the worship of men more than
that of the sun, since in the universe there is no body of greater
magnitude and power to be seen than the sun. And its light illumines
all the celestial bodies which are distributed throughout the universe;
and the vital spark descends from it, because the heat which is in
living beings comes from the soul, and there is no other centre of heat
and light in the universe, as will be shown later; and it is certain
that those who have elected to worship men as gods--as Jupiter, Saturn,
Mars, &c.--have fallen into a profound error, since even if a man were
as great as our earth, he would have the appearance of a little star,
which appears like a dot in the universe; and moreover these men are
mortal, and decay and corrupt in their sepulchres.
{154}
33.
Epicurus perhaps saw the shadows of columns on the walls in front of
them equal to the diameter of the column which cast the shadow; and
since the breadth of the shadows are parallel from beginning to end he
considered that he might infer that the sun also was directly opposite
to this parallel, and consequently no broader than the column; and he
did not perceive that the diminution of the shadow was insensibly small
owing to the great distance of the sun. If the sun were smaller than
the earth, the stars in a great portion of our hemisphere would be
without light--in contradiction to Epicurus, who says the sun is only
as large as it appears to be.
34.
Epicurus says the sun is the size it seems to be; hence, as it seems to
be a foot in breadth, we must consider that to be its size. It follows
that when the moon eclipses the sun, the sun ought not to appear the
larger, as it does; hence, the moon being smaller than the sun, the
moon must be less than a foot in breadth, and consequently when the
earth eclipses the moon it must be less than a foot by a finger's
breadth; inasmuch as if the sun is a foot in breadth, and the earth
casts a conical shadow on the moon, it is inevitable that the luminous
cause of the conical shadow {155} must be greater than the opaque body
which causes it.
35.
Measure how many times the diameter of the sun will go into its course
in twenty-four hours. And thus we can see whether Epicurus was correct
in saying the sun was only as large as it appeared to be; for as the
apparent diameter of the sun is about a foot, and as the sun would go a
thousand times into its course in twenty-four hours, it would have
travelled a thousand feet, that is, three hundred arms' length, which
is the sixth of a mile. Thus the course of the sun during twenty-four
hours would have been the sixth part of a mile, and this venerable
snail, the sun, would have travelled twenty-five arms' length in an
hour.
[Sidenote: The Sun's Heat]
36.
They say that the sun is not hot because it is not the colour of fire
but whiter and clearer. And the answer to this is that when molten
bronze is hottest it resembles the colour of the sun, and when it is
less hot it has the colour of fire.
37.
It is proved that the sun is by nature hot and not cold, as has already
been stated. If rays of fire play on a concave mirror when it is cold,
the rays refracted by the mirror will be hotter than {156} the fire.
The rays emitted from a sphere of glass filled with cold water, which
are reflected from a fire, will be warmer than the fire. It follows
from these two experiments that the heat of the rays reflected by the
mirror or the sphere of cold water are hot by virtue, and not because
the mirror or the sphere is hot; and in this case it occurs that the
sun, passing through these bodies, heats them by its virtue. And owing
to this they have inferred that the sun is not hot,--which by the
aforesaid experiments has been proved to be exceedingly hot, by the
experiment of the mirror and the sphere, which are cold in themselves,
and reflect the hot rays of the fire and render them hotter, because
the first cause is hot; and the same thing occurs as regards the sun,
which, being hot in itself, and passing through these cold mirrors,
refracts great heat. It is not the light of the sun which gives
warmth, but its natural heat.
[Sidenote: Rays of the Sun]
38.
The rays of the sun pass through the cold region of the air without any
change being effected in their nature, they pass through glasses full
of cold water without suffering change; through whatever transparent
spot they pass, it is as though they passed through so much air.
[Sidenote: Light of the Stars]
39.
Some writers allege that the stars shine of {157} themselves, saying
that if Venus and Mercury did not shine of themselves, when their light
comes between them and the sun they would darken as much of the sun as
they could hide from our eye; this is false, because it is proved that
a dark body placed against a luminous body is enveloped and altogether
covered by the lateral rays of the remaining part of that body, and
thus remains invisible; as may be proved when the sun is seen through
the boughs of a leafless tree at a long distance, the boughs do not
hide any portion of the sun from our eyes. The same thing occurs with
the above-mentioned planets, which, though they have no light in
themselves, do not, as has been said, hide any portion of the sun from
our eyes.
Second proof. They say that the stars shine most brightly at night in
proportion as they are high; and that, if they did not shine of
themselves, the shadow cast by the earth between them and the sun would
darken them, since they would not see nor be seen by the sun. But
these have not taken into consideration that the conical shadow of the
moon does not reach many of the stars, and even for those it does reach
the shadow is diminished to such an extent that it covers very little
of the star, and the remaining part is illumined by the sun.
{158}
[Sidenote: On the Nature of the Moon]
40.
The moon having density and gravity, how does it stand?
41.
i. No very light object is opaque.
ii. Nothing light can remain beneath that which is heavier.
iii. Whether the moon is the centre of its elements or not. And if it
has no fixed position like the earth in the centre of its elements, why
does it not fall to the centre of our elements? And if the moon is not
in the centre of its elements and 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?
42.
No body which has density is lighter than the air. Having proved that
the part of the moon which shines consists of water which mirrors the
body of the sun and reflects for us the splendour it receives from the
sun, and that if there were no waves in these waters, it would appear
small, but almost as bright as the sun--it must now be shown whether
the moon is a heavy or a light body; if it is a heavy body--admitting
that from the earth upwards with every grade of distance lightness must
increase, so that water is lighter than earth, air is lighter than
water, and {159} fire lighter than air, and so on in succession--it
would seem that if the moon had density, as it has, it must have
gravity, and if it has gravity the space in which it lies could not
contain it, and consequently it would fall towards the centre of the
universe and be joined to the earth, or if not the moon itself, its
waters would fall from the moon and strip it and fall towards the
centre, leaving the moon bare and lustreless; whence, as this could not
happen, as reason would tell us, it is manifest that the moon is
surrounded by its elements, that is to say, water, air and fire, and
thus it sustains itself by itself in that space as our earth is
suspended with its elements in this part of space; heavy bodies act in
their elements there just as other heavy bodies act in ours.
[Sidenote: On the Harmony of the Spheres]
43.
A sound is produced by the movement of the air in friction against a
dense body, and should it be produced by two weighty bodies it is owing
to the atmosphere which surrounds them, and this friction consumes the
bodies, so that it follows that the spheres in their friction, owing to
there being no atmosphere between them, do not generate sound. And if
this friction were a fact, during the many centuries the spheres have
revolved they would be consumed by the immense velocity expended daily;
and even if they produce sound, the sound could not travel, {160}
because the sound caused by percussion under water is scarcely
noticeable, and it would be less than noticeable in the case of dense
bodies. The friction of polished bodies produces no sound, and similar
result would be produced in the contact or friction of the spheres; and
if the spheres are not polished in their contact and friction, it
follows that they are rough.
Again, their contact is not continuous; this being the case a vacuum is
produced, which it has been proved does not exist in nature. Therefore
we conclude that friction would have consumed the ends of each sphere,
and in proportion as a sphere has a greater velocity in the centre than
at the poles, it would be consumed to a higher degree at the centre
than at the poles; and then the friction would cease, and the sound
would cease also, and the spheres would cease to revolve unless one
sphere revolved eastward and the other northward.
44.
Worlds gravitate in the midst of their own elements. The yellow or
yolk of an egg remains in the middle of the albumen without moving on
either side, and is lighter or heavier or equal to this albumen; and 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 {161}
to sink; and if it is equal to it, it can stand at one of the ends as
well as in the centre or below.
[Sidenote: The Earth appears a Star]
45.
The object of my book is to prove that the ocean, with the other seas,
by means of the sun causes our world to shine like the moon and to
appear as a star to other worlds; and this I will prove.
[Sidenote: The Earth a Star]
46.
In your discourse you must prove that the earth is a star like the
moon, and thus you will bear witness to the glory of our universe! And
thus you must discourse on the size of many stars.
47.
How the earth is a star. The earth, in the midst of the sphere of
water which clothes the greater part of it, taking its light from the
sun and shining in the universe like the other stars, shows itself to
be a star as well.
[Sidenote: To prove the Earth a Star]
48.
First of all define the eye; then show how the twinkling of a star
exists really in the eye, and why one star should twinkle more than
another, and how the rays of the stars are born in the eye. Say, that
if the twinkling of the stars were, as it appears to be, really in the
stars, that this {162} twinkling appears to extend in proportion to the
body of the star. The star, therefore, being larger than the earth,
this motion made in an instant of time would in its velocity double the
size of the star. Then prove that the surface of the atmosphere,
contiguous to fire and the surface of fire, where it ends, is the point
in which the rays of the sun penetrate and bear the image of the
celestial bodies which are large when they rise and set, and small when
they are on the meridian.
[Sidenote: Earth not the Center of Universe]
49.
The earth is not the centre of the orbit of the sun, nor the centre of
the universe, but in the centre of its companion elements and united
with them; and if any one were to stand on the moon when the moon and
the sun are beneath us, our earth, with its element of water, would
appear and shine for him just as the moon appears and shines for us.
50.
The earth, shining like the moon, has lost a great part of its ancient
splendour by the decrease of the waters.
51.