The Notebooks of Leonardo Da Vinci — Complete
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.
905.
OF THE SPOTS ON THE MOON.
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
it.
906.
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
body.
907.
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.
908.
OF HALOS ROUND THE MOON.
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).
909.
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.
910.
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
not--as has been said--conceal any part of the sun from our eye
[18].
SECOND ARGUMENT.
Some say that the stars appear most brilliant at night in proportion
as they are higher up; and that if they had no light of their own,
the shadow of the earth which comes between them and the sun, would
darken them, since they would not face nor be faced by the solar
body. But those persons have not considered that the conical shadow
of the earth cannot reach many of the stars; and even as to those it
does reach, the cone is so much diminished that it covers very
little of the star's mass, and all the rest is illuminated by the
sun.
913.
Why the planets appear larger in the East than they do overhead,
whereas the contrary should be the case, as they are 3500 miles
nearer to us when in mid sky than when on the horizon.
All the degrees of the elements, through which the images of the
celestial bodies pass to reach the eye, are equal curves and the
angles by which the central line of those images passes through
them, are unequal angles [Footnote 13: _inequali_, here and
elsewhere does not mean unequal in the sense of not being equal to
each other, but angles which are not right angles.]; and the
distance is greater, as is shown by the excess of _a b_ beyond _a
d_; and the enlargement of these celestial bodies on the horizon is
shown by the 9th of the 7th.
Observations on the stars.
914.
To see the real nature of the planets open the covering and note at
the base [Footnote 4: _basa_. This probably alludes to some
instrument, perhaps the Camera obscura.] one single planet, and the
reflected movement of this base will show the nature of the said
planet; but arrange that the base may face only one at the time.
On history of astronomy.
915.
Cicero says in [his book] De Divinatione that Astrology has been
practised five hundred seventy thousand years before the Trojan war.
57000.
[Footnote: The statement that CICERO, _De Divin._ ascribes the
discovery of astrology to a period 57000 years before the Trojan war
I believe to be quite erroneous. According to ERNESTI, _Clavis
Ciceroniana,_ CH. G. SCHULZ (_Lexic. Cicer._) and the edition of _De
Divin._ by GIESE the word Astrologia occurs only twice in CICERO:
_De Divin. II_, 42. _Ad Chaldaeorum monstra veniamus, de quibus
Eudoxus, Platonis auditor, in astrologia judicio doctissimorum
hominum facile princeps, sic opinatur (id quod scriptum reliquit):
Chaldaeis in praedictione et in notatione cujusque vitae ex natali
die minime esse credendum._" He then quotes the condemnatory verdict
of other philosophers as to the teaching of the Chaldaeans but says
nothing as to the antiquity and origin of astronomy. CICERO further
notes _De oratore_ I, 16 that Aratus was "_ignarus astrologiae_" but
that is all. So far as I know the word occurs nowhere else in
CICERO; and the word _Astronomia_ he does not seem to have used at
all. (H. MULLER-STRUBING.)]
Of time and its divisions (916-918).
916.
Although time is included in the class of Continuous Quantities,
being indivisible and immaterial, it does not come entirely under
the head of Geometry, which represents its divisions by means of
figures and bodies of infinite variety, such as are seen to be
continuous in their visible and material properties. But only with
its first principles does it agree, that is with the Point and the
Line; the point may be compared to an instant of time, and the line
may be likened to the length of a certain quantity of time, and just
as a line begins and terminates in a point, so such a space of time.
begins and terminates in an instant. And whereas a line is
infinitely divisible, the divisibility of a space of time is of the
same nature; and as the divisions of the line may bear a certain
proportion to each other, so may the divisions of time.
[Footnote: This passage is repeated word for word on page 190b of
the same manuscript and this is accounted for by the text in Vol. I,
No. 4. Compare also No. 1216.]
917.
Describe the nature of Time as distinguished from the Geometrical
definitions.
918.
Divide an hour into 3000 parts, and this you can do with a clock by
making the pendulum lighter or heavier.
_XVI.
Physical Geography.
Leonardo's researches as to the structure of the earth and sea were
made at a time, when the extended voyages of the Spaniards and
Portuguese had also excited a special interest in geographical
questions in Italy, and particularly in Tuscany. Still, it need
scarcely surprise us to find that in deeper questions, as to the
structure of the globe, the primitive state of the earth's surface,
and the like, he was far in advance of his time.
The number of passages which treat of such matters is relatively
considerable; like almost all Leonardo's scientific notes they deal
partly with theoretical and partly with practical questions. Some of
his theoretical views of the motion of water were collected in a
copied manuscript volume by an early transcriber, but without any
acknowledgment of the source whence they were derived. This copy is
now in the Library of the Barberini palace at Rome and was published
under the title: "De moto e misura dell'acqua," by FRANCESCO
CARDINALI, Bologna_ 1828. _In this work the texts are arranged under
the following titles:_ Libr. I. Della spera dell'acqua; Libr. II.
Del moto dell'acqua; Libr. III. Dell'onda dell'acqua; Libr. IV. Dei
retrosi d'acqua; Libr. V. Dell'acqua cadente; Libr. VI. Delle
rotture fatte dall'acqua; Libr. VII Delle cose portate dall'acqua;
Libr. VIII. Dell'oncia dell'acqua e delle canne; Libr. IX. De molini
e d'altri ordigni d'acqua.
_The large number of isolated observations scattered through the
manuscripts, accounts for our so frequently finding notes of new
schemes for the arrangement of those relating to water and its
motions, particularly in the Codex Atlanticus: I have printed
several of these plans as an introduction to the Physical Geography,
and I have actually arranged the texts in accordance with the clue
afforded by one of them which is undoubtedly one of the latest notes
referring to the subject (No._ 920_). The text given as No._ 930
_which is also taken from a late note-book of Leonardo's, served as
a basis for the arrangement of the first of the seven books--or
sections--, bearing the title: Of the Nature of Water_ (Dell'acque
in se).
_As I have not made it any part of this undertaking to print the
passages which refer to purely physical principles, it has also been
necessary to exclude those practical researches which, in accordance
with indications given in_ 920, _ought to come in as Books_ 13, 14
_and_ 15. _I can only incidentally mention here that Leonardo--as it
seems to me, especially in his youth--devoted a great deal of
attention to the construction of mills. This is proved by a number
of drawings of very careful and minute execution, which are to be