The Notebooks of Leonardo Da Vinci (64 page)

Footnote: From this and other remarks (see No. 902) it is clear
hat Leonardo was familiar with the phenomena of Irradiation.]

13.

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.

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
found in the Codex Atlanticus. Nor was it possible to include his
considerations on the regulation of rivers, the making of canals and
so forth (No.
920,
Books
10, 11
and
12_); but those passages in
which the structure of a canal is directly connected with notices of
particular places will be found duly inserted under section XVII
(Topographical notes). In Vol. I, No._ 5
the text refers to
canal-making in general.

On one point only can the collection of passages included under the
general heading of Physical Geography claim to be complete. When
comparing and sorting the materials for this work I took particular
care not to exclude or omit any text in which a geographical name
was mentioned even incidentally, since in all such researches the
chief interest, as it appeared to me, attached to the question
whether these acute observations on the various local
characteristics of mountains, rivers or seas, had been made by
Leonardo himself, and on the spot. It is self-evident that the few
general and somewhat superficial observations on the Rhine and the
Danube, on England and Flanders, must have been obtained from maps
or from some informants, and in the case of Flanders Leonardo
himself acknowledges this (see No.
1008_). But that most of the
other and more exact observations were made, on the spot, by
Leonardo himself, may be safely assumed from their method and the
style in which he writes of them; and we should bear it in mind that
in all investigations, of whatever kind, experience is always spoken
of as the only basis on which he relies. Incidentally, as in No._
984,
he thinks it necessary to allude to the total absence of all
recorded observations.

Schemes for the arrangement of the materials (919-928).

919.

These books contain in the beginning: Of the nature of water itself
in its motions; the others treat of the effects of its currents,
which change the world in its centre and its shape.

920.

921.

First you shall make a book treating of places occupied by fresh
waters, and the second by salt waters, and the third, how by the
disappearance of these, our parts of the world were made lighter and
in consequence more remote from the centre of the world.

922.

First write of all water, in each of its motions; then describe all
its bottoms and their various materials, always referring to the
propositions concerning the said waters; and let the order be good,
for otherwise the work will be confused.

Describe all the forms taken by water from its greatest to its
smallest wave, and their causes.

923.

924.

Place at the beginning what a river can effect.

925.

A book of driving back armies by the force of a flood made by
releasing waters.

A book showing how the waters safely bring down timber cut in the
mountains.

A book of boats driven against the impetus of rivers.

A book of raising large bridges higher. Simply by the swelling of
the waters.

A book of guarding against the impetus of rivers so that towns may
not be damaged by them.

926.

A book of the ordering of rivers so as to preserve their banks.

A book of the mountains, which would stand forth and become land, if
our hemisphere were to be uncovered by the water.

A book of the earth carried down by the waters to fill up the great
abyss of the seas.

A book of the ways in which a tempest may of itself clear out filled
up sea-ports.

A book of the shores of rivers and of their permanency.

A book of how to deal with rivers, so that they may keep their
bottom scoured by their own flow near the cities they pass.

A book of how to make or to repair the foundations for bridges over
the rivers.

A book of the repairs which ought to be made in walls and banks of
rivers where the water strikes them.

A book of the formation of hills of sand or gravel at great depths
in water.

927.

Water gives the first impetus to its motion.

A book of the levelling of waters by various means,

A book of diverting rivers from places where they do mischief.

A book of guiding rivers which occupy too much ground.

A book of parting rivers into several branches and making them
fordable.

A book of the waters which with various currents pass through seas.

A book of deepening the beds of rivers by means of currents of
water.

A book of controlling rivers so that the little beginnings of
mischief, caused by them, may not increase.

A book of the various movements of waters passing through channels
of different forms.

A book of preventing small rivers from diverting the larger one into
which their waters run.

A book of the lowest level which can be found in the current of the
surface of rivers.

A book of the origin of rivers which flow from the high tops of
mountains.

A book of the various motions of waters in their rivers.

928.

[1] Of inequality in the concavity of a ship. [Footnote 1: The first
line of this passage was added subsequently, evidently as a
correction of the following line.]

[1] A book of the inequality in the curve of the sides of ships.

[1] A book of the inequality in the position of the tiller.

[1] A book of the inequality in the keel of ships.

[2] A book of various forms of apertures by which water flows out.

[3] A book of water contained in vessels with air, and of its
movements.

[4] A book of the motion of water through a syphon. [Footnote 7:
cicognole
, see No. 966, 11, 17.]

[5] A book of the meetings and union of waters coming from different
directions.

[6] A book of the various forms of the banks through which rivers
pass.

[7] A book of the various forms of shoals formed under the sluices
of rivers.

[8] A book of the windings and meanderings of the currents of
rivers.

[9] A book of the various places whence the waters of rivers are
derived.

[10] A book of the configuration of the shores of rivers and of
their permanency.

[11] A book of the perpendicular fall of water on various objects.

[12] Abook of the course of water when it is impeded in various
places.

[12] A book of the various forms of the obstacles which impede the
course of waters.

[13] A book of the concavity and globosity formed round various
objects at the bottom.