The Notebooks of Leonardo Da Vinci — Complete
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.]
860.
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.]
861.
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
earth.
[Footnote: Compare No. 896, lines 48-64; and No. 936.]
862.
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?
863.
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
earth.
864.
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
inhabited.
How to prove that the earth is a planet (865-867).
865.
That the earth is a star.
866.
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.
867.
THE METHOD OF PROVING THAT THE EARTH IS A STAR.
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
atmosphere.
868.
Beyond the sun and us there is darkness and so the air appears blue.
[Footnote: Compare Vol. I, No. 301.]
869.
PERSPECTIVE.
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.
OF THE EYE.
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
[61].
[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.]
870.
PERSPECTIVE.
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.
871.
_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.
872.
_a_, the side of the body in light and shade _b_, faces the whole
portion of the hemisphere bed _e f_, and does not face any part of
the darkness of the earth. And the same occurs at the point _o_;
therefore the space a _o_ is throughout of one and the same
brightness, and s faces only four degrees of the hemisphere _d e f g
h_, and also the whole of the earth _s h_, which will render it
darker; and how much must be demonstrated by calculation. [Footnote:
This passage, which has perhaps a doubtful right to its place in
this connection, stands in the Manuscript between those given in
Vol. I as No. 117 and No. 427.]
873.
THE REASON OF THE INCREASED SIZE OF THE SUN IN THE WEST.
Some mathematicians explain that the sun looks larger as it sets,
because the eye always sees it through a denser atmosphere, alleging
that objects seen through mist or through water appear larger. To
these I reply: No; because objects seen through a mist are similar
in colour to those at a distance; but not being similarly diminished
they appear larger. Again, nothing increases in size in smooth
water; and the proof of this may be seen by throwing a light on a
board placed half under water. But the reason why the sun looks
larger is that every luminous body appears larger in proportion as
it is more remote. [Footnote: Lines 5 and 6 are thus rendered by M.
RAVAISSON in his edition of MS. A. "_De meme, aucune chose ne croit
dans l'eau plane, et tu en feras l'experience_ en calquant un ais
sous l'eau."--Compare the diagrams in Vol. I, p. 114.]
On the luminosity of the Earth in the universal space (874-878).
874.
In my book I propose to show, how the ocean and the other seas must,
by means of the sun, make our world shine with the appearance of a
moon, and to the remoter worlds it looks like a star; and this I
shall prove.
Show, first that every light at a distance from the eye throws out
rays which appear to increase the size of the luminous body; and
from this it follows that 2 ...[Footnote 10: Here the text breaks
off; lines 11 and fol. are written in the margin.].
[11]The moon is cold and moist. Water is cold and moist. Thus our
seas must appear to the moon as the moon does to us.
875.
The waves in water magnify the image of an object reflected in it.
Let _a_ be the sun, and _n m_ the ruffled water, _b_ the image of
the sun when the water is smooth. Let _f_ be the eye which sees the
image in all the waves included within the base of the triangle _c e
f_. Now the sun reflected in the unruffled surface occupied the
space _c d_, while in the ruffled surface it covers all the watery
space _c e_ (as is proved in the 4th of my "Perspective") [Footnote
9: _Nel quarto della mia prospettiva_. If this reference is to the
diagrams accompanying the text--as is usual with Leonardo--and not
to some particular work, the largest of the diagrams here given must
be meant. It is the lowest and actually the fifth, but he would have