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The Notebooks of Leonardo Da Vinci

Volume 1

Translated by Jean Paul Richter



A singular fatality has ruled the destiny of nearly all the most
famous of Leonardo da Vinci's works. Two of the three most important
were never completed, obstacles having arisen during his life-time,
which obliged him to leave them unfinished; namely the Sforza
Monument and the Wall-painting of the Battle of Anghiari, while the
third--the picture of the Last Supper at Milan--has suffered
irremediable injury from decay and the repeated restorations to
which it was recklessly subjected during the XVIIth and XVIIIth
centuries. Nevertheless, no other picture of the Renaissance has
become so wellknown and popular through copies of every description.

Vasari says, and rightly, in his Life of Leonardo, "that he laboured
much more by his word than in fact or by deed", and the biographer
evidently had in his mind the numerous works in Manuscript which
have been preserved to this day. To us, now, it seems almost
inexplicable that these valuable and interesting original texts
should have remained so long unpublished, and indeed forgotten. It
is certain that during the XVIth and XVIIth centuries their
exceptional value was highly appreciated. This is proved not merely
by the prices which they commanded, but also by the exceptional
interest which has been attached to the change of ownership of
merely a few pages of Manuscript.

That, notwithstanding this eagerness to possess the Manuscripts,
their contents remained a mystery, can only be accounted for by the
many and great difficulties attending the task of deciphering them.
The handwriting is so peculiar that it requires considerable
practice to read even a few detached phrases, much more to solve
with any certainty the numerous difficulties of alternative
readings, and to master the sense as a connected whole. Vasari
observes with reference to Leonardos writing: "he wrote backwards,
in rude characters, and with the left hand, so that any one who is
not practised in reading them, cannot understand them". The aid of a
mirror in reading reversed handwriting appears to me available only
for a first experimental reading. Speaking from my own experience,
the persistent use of it is too fatiguing and inconvenient to be
practically advisable, considering the enormous mass of Manuscripts
to be deciphered. And as, after all, Leonardo's handwriting runs
backwards just as all Oriental character runs backwards--that is
to say from right to left--the difficulty of reading direct from the
writing is not insuperable. This obvious peculiarity in the writing
is not, however, by any means the only obstacle in the way of
mastering the text. Leonardo made use of an orthography peculiar to
himself; he had a fashion of amalgamating several short words into
one long one, or, again, he would quite arbitrarily divide a long
word into two separate halves; added to this there is no punctuation
whatever to regulate the division and construction of the sentences,
nor are there any accents--and the reader may imagine that such
difficulties were almost sufficient to make the task seem a
desperate one to a beginner. It is therefore not surprising that the
good intentions of some of Leonardo s most reverent admirers should
have failed.

Leonardos literary labours in various departments both of Art and of
Science were those essentially of an enquirer, hence the analytical
method is that which he employs in arguing out his investigations
and dissertations. The vast structure of his scientific theories is
consequently built up of numerous separate researches, and it is
much to be lamented that he should never have collated and arranged
them. His love for detailed research--as it seems to me--was the
reason that in almost all the Manuscripts, the different paragraphs
appear to us to be in utter confusion; on one and the same page,
observations on the most dissimilar subjects follow each other
without any connection. A page, for instance, will begin with some
principles of astronomy, or the motion of the earth; then come the
laws of sound, and finally some precepts as to colour. Another page
will begin with his investigations on the structure of the
intestines, and end with philosophical remarks as to the relations
of poetry to painting; and so forth.

Leonardo himself lamented this confusion, and for that reason I do
not think that the publication of the texts in the order in which
they occur in the originals would at all fulfil his intentions. No
reader could find his way through such a labyrinth; Leonardo himself
could not have done it.

Added to this, more than half of the five thousand manuscript pages
which now remain to us, are written on loose leaves, and at present
arranged in a manner which has no justification beyond the fancy of
the collector who first brought them together to make volumes of
more or less extent. Nay, even in the volumes, the pages of which
were numbered by Leonardo himself, their order, so far as the
connection of the texts was concerned, was obviously a matter of
indifference to him. The only point he seems to have kept in view,
when first writing down his notes, was that each observation should
be complete to the end on the page on which it was begun. The
exceptions to this rule are extremely few, and it is certainly
noteworthy that we find in such cases, in bound volumes with his
numbered pages, the written observations: "turn over", "This is the
continuation of the previous page", and the like. Is not this
sufficient to prove that it was only in quite exceptional cases that
the writer intended the consecutive pages to remain connected, when
he should, at last, carry out the often planned arrangement of his

What this final arrangement was to be, Leonardo has in most cases
indicated with considerable completeness. In other cases this
authoritative clue is wanting, but the difficulties arising from
this are not insuperable; for, as the subject of the separate
paragraphs is always distinct and well defined in itself, it is
quite possible to construct a well-planned whole, out of the
scattered materials of his scientific system, and I may venture to
state that I have devoted especial care and thought to the due
execution of this responsible task.

The beginning of Leonardo's literary labours dates from about his
thirty-seventh year, and he seems to have carried them on without
any serious interruption till his death. Thus the Manuscripts that
remain represent a period of about thirty years. Within this space
of time his handwriting altered so little that it is impossible to
judge from it of the date of any particular text. The exact dates,
indeed, can only be assigned to certain note-books in which the year
is incidentally indicated, and in which the order of the leaves has
not been altered since Leonardo used them. The assistance these
afford for a chronological arrangement of the Manuscripts is
generally self evident. By this clue I have assigned to the original
Manuscripts now scattered through England, Italy and France, the
order of their production, as in many matters of detail it is highly
important to be able to verify the time and place at which certain
observations were made and registered. For this purpose the
Bibliography of the Manuscripts given at the end of Vol. II, may be
regarded as an Index, not far short of complete, of all Leonardo s
literary works now extant. The consecutive numbers (from 1 to 1566)
at the head of each passage in this work, indicate their logical
sequence with reference to the subjects; while the letters and
figures to the left of each paragraph refer to the original
Manuscript and number of the page, on which that particular passage
is to be found. Thus the reader, by referring to the List of
Manuscripts at the beginning of Volume I, and to the Bibliography at
the end of Volume II, can, in every instance, easily ascertain, not
merely the period to which the passage belongs, but also exactly
where it stood in the original document. Thus, too, by following the
sequence of the numbers in the Bibliographical index, the reader may
reconstruct the original order of the Manuscripts and recompose the
various texts to be found on the original sheets--so much of it,
that is to say, as by its subject-matter came within the scope of
this work. It may, however, be here observed that Leonardo s
Manuscripts contain, besides the passages here printed, a great
number of notes and dissertations on Mechanics, Physics, and some
other subjects, many of which could only be satisfactorily dealt
with by specialists. I have given as complete a review of these
writings as seemed necessary in the Bibliographical notes.

In 1651, Raphael Trichet Dufresne, of Paris, published a selection
from Leonardo's writings on painting, and this treatise became so
popular that it has since been reprinted about two-and-twenty times,
and in six different languages. But none of these editions were
derived from the original texts, which were supposed to have been
lost, but from early copies, in which Leonardo's text had been more
or less mutilated, and which were all fragmentary. The oldest and on
the whole the best copy of Leonardo's essays and precepts on
Painting is in the Vatican Library; this has been twice printed,
first by Manzi, in 1817, and secondly by Ludwig, in 1882. Still,
this ancient copy, and the published editions of it, contain much
for which it would be rash to hold Leonardo responsible, and some
portions--such as the very important rules for the proportions of
the human figure--are wholly wanting; on the other hand they contain
passages which, if they are genuine, cannot now be verified from any
original Manuscript extant. These copies, at any rate neither give
us the original order of the texts, as written by Leonardo, nor do
they afford any substitute, by connecting them on a rational scheme;
indeed, in their chaotic confusion they are anything rather than
satisfactory reading. The fault, no doubt, rests with the compiler
of the Vatican copy, which would seem to be the source whence all
the published and extensively known texts were derived; for, instead
of arranging the passages himself, he was satisfied with recording a
suggestion for a final arrangement of them into eight distinct
parts, without attempting to carry out his scheme. Under the
mistaken idea that this plan of distribution might be that, not of
the compiler, but of Leonardo himself, the various editors, down to
the present day, have very injudiciously continued to adopt this
order--or rather disorder.

I, like other enquirers, had given up the original Manuscript of the
Trattato della Pittura for lost, till, in the beginning of 1880, I
was enabled, by the liberality of Lord Ashburnham, to inspect his
Manuscripts, and was so happy as to discover among them the original
text of the best-known portion of the Trattato in his magnificent
library at Ashburnham Place. Though this discovery was of a fragment
only--but a considerable fragment--inciting me to further search,
it gave the key to the mystery which had so long enveloped the first
origin of all the known copies of the Trattato. The extensive
researches I was subsequently enabled to prosecute, and the results
of which are combined in this work, were only rendered possible by
the unrestricted permission granted me to investigate all the
Manuscripts by Leonardo dispersed throughout Europe, and to
reproduce the highly important original sketches they contain, by
the process of "photogravure". Her Majesty the Queen graciously
accorded me special permission to copy for publication the
Manuscripts at the Royal Library at Windsor. The Commission Centrale
Administrative de l'Institut de France, Paris, gave me, in the most
liberal manner, in answer to an application from Sir Frederic
Leighton, P. R. A., Corresponding member of the Institut, free
permission to work for several months in their private collection at
deciphering the Manuscripts preserved there. The same favour which
Lord Ashburnham had already granted me was extended to me by the
Earl of Leicester, the Marchese Trivulsi, and the Curators of the
Ambrosian Library at Milan, by the Conte Manzoni at Rome and by
other private owners of Manuscripts of Leonardo's; as also by the
Directors of the Louvre at Paris; the Accademia at Venice; the
Uffizi at Florence; the Royal Library at Turin; and the British
Museum, and the South Kensington Museum. I am also greatly indebted
to the Librarians of these various collections for much assistance
in my labours; and more particularly to Monsieur Louis Lalanne, of
the Institut de France, the Abbate Ceriani, of the Ambrosian
Library, Mr. Maude Thompson, Keeper of Manuscripts at the British
Museum, Mr. Holmes, the Queens Librarian at Windsor, the Revd Vere
Bayne, Librarian of Christ Church College at Oxford, and the Revd A.
Napier, Librarian to the Earl of Leicester at Holkham Hall.

In correcting the Italian text for the press, I have had the
advantage of valuable advice from the Commendatore Giov. Morelli,
Senatore del Regno, and from Signor Gustavo Frizzoni, of Milan. The
translation, under many difficulties, of the Italian text into
English, is mainly due to Mrs. R. C. Bell; while the rendering of
several of the most puzzling and important passages, particularly in
the second half of Vol. I, I owe to the indefatigable interest taken
in this work by Mr. E. J. Poynter R. A. Finally I must express my
thanks to Mr. Alfred Marks, of Long Ditton, who has most kindly
assisted me throughout in the revision of the proof sheets.

The notes and dissertations on the texts on Architecture in Vol. II
I owe to my friend Baron Henri de Geymuller, of Paris.

I may further mention with regard to the illustrations, that the
negatives for the production of the "photo-gravures" by Monsieur
Dujardin of Paris were all taken direct from the originals.

It is scarcely necessary to add that most of the drawings here
reproduced in facsimile have never been published before. As I am
now, on the termination of a work of several years' duration, in a
position to review the general tenour of Leonardos writings, I may
perhaps be permitted to add a word as to my own estimate of the
value of their contents. I have already shown that it is due to
nothing but a fortuitous succession of unfortunate circumstances,
that we should not, long since, have known Leonardo, not merely as a
Painter, but as an Author, a Philosopher, and a Naturalist. There
can be no doubt that in more than one department his principles and
discoveries were infinitely more in accord with the teachings of
modern science, than with the views of his contemporaries. For this
reason his extraordinary gifts and merits are far more likely to be
appreciated in our own time than they could have been during the
preceding centuries. He has been unjustly accused of having
squandered his powers, by beginning a variety of studies and then,
having hardly begun, throwing them aside. The truth is that the
labours of three centuries have hardly sufficed for the elucidation
of some of the problems which occupied his mighty mind.

Alexander von Humboldt has borne witness that "he was the first to
start on the road towards the point where all the impressions of our
senses converge in the idea of the Unity of Nature" Nay, yet more
may be said. The very words which are inscribed on the monument of
Alexander von Humboldt himself, at Berlin, are perhaps the most
appropriate in which we can sum up our estimate of Leonardo's

"Majestati naturae par ingenium."

LONDON, April 1883.

F. P. R.



Clavis Sigillorum and Index of Manuscripts.--The author's intention
to publish his MSS. (1).--The preparation of the MSS. for
publication (2).--Admonition to readers (3).--The disorder in the
MSS. (4).--Suggestions for the arrangement of MSS. treating of
particular subjects (5--8).--General introductions to the book on
painting (9--13).--The plan of the book on painting (14--17).--The
use of the book on painting (18).--Necessity of theoretical
knowledge (19, 20).--The function of the eye (21--23).--Variability
of the eye (24).--Focus of sight (25).--Differences of perception by
one eye and by both eyes (26--29).--The comparative size of the
image depends on the amount of light (30--39).



General remarks on perspective (40--41).--The elements of
perspective:--of the point (42--46).--Of the line (47--48).--The
nature of the outline (49).--Definition of perspective (50).--The
perception of the object depends on the direction of the eye
(51).--Experimental proof of the existence of the pyramid of sight
(52--55).--The relations of the distance point to the vanishing
point (55--56).--How to measure the pyramid of vision (57).--The
production of the pyramid of vision (58--64).--Proof by experiment
(65--66).--General conclusions (67).--That the contrary is
impossible (68).--A parallel case (69).--The function of the eye, as
explained by the camera obscura (70--71).--The practice of
perspective (72--73).--Refraction of the rays falling upon the eye
(74--75).--The inversion of the images (76).--The intersection of
the rays (77--82).--Demonstration of perspective by means of a
vertical glass plane (83--85.)--The angle of sight varies with the
distance (86--88).--Opposite pyramids in juxtaposition (89).--On
simple and complex perspective (90).--The proper distance of objects
from the eye (91--92).--The relative size of objects with regard to
their distance from the eye (93--98).--The apparent size of objects
denned by calculation (99--106).--On natural perspective (107--109).



GENERAL INTRODUCTION.--Prolegomena (110).--Scheme of the books on
light and shade (111).--Different principles and plans of treatment
(112--116).--Different sorts of light (117--118).--Definition of
the nature of shadows (119--122).--Of the various kinds of shadows
(123--125).--Of the various kinds of light (126--127).--General
remarks (128--129).--FIRST BOOK ON LIGHT AND SHADE.--On the nature
of light (130--131).--The difference between light and lustre
(132--135).--The relations of luminous to illuminated bodies (136).
--Experiments on the relation of light and shadow within a room
(137--140).--Light and shadow with regard to the position of the
eye (141--145).--The law of the incidence of light
(146--147).--SECOND BOOK ON LIGHT AND SHADE.--Gradations of strength
in the shadows (148--149).--On the intensity of shadows as dependent
on the distance from the light (150--152).--On the proportion of
light and shadow (153--157).--THIRD BOOK ON LIGHT AND
SHADE.--Definition of derived shadow (158--159).--Different sorts of
derived shadows (160--162).--On the relation of derived and primary
shadow (163--165).--On the shape of derived shadows (166--174).--On
the relative intensity of derived shadows (175--179).--Shadow as
produced by two lights of different size (180--181).--The effect of
light at different distances (182).--Further complications in the
derived shadows (183--187).--FOURTH BOOK ON LIGHT AND SHADE.--On the
shape of cast shadows (188--191).--On the outlines of cast shadows
(192--195).--On the relative size of cast shadows (196.
197).--Effects on cast shadows by the tone of the back ground
(198).--A disputed proposition (199).--On the relative depth of
cast shadows (200--202).--FIFTH BOOK ON LIGHT AND
SHADE.--Principles of reflection (203. 204).--On reverberation
(205).--Reflection on water (206. 207).--Experiments with the mirror
(208--210).--Appendix:--On shadows in movement (211--212).--SIXTH
BOOK ON LIGHT AND SHADE.--The effect of rays passing through holes
(213. 214).--On gradation of shadows (215. 216).--On relative
proportion of light and shadows (216--221).



Definition (222. 223).--An illustration by experiment (224).--A
guiding rule (225).---An experiment (226).--On indistinctness at
short distances (227--231).--On indistinctness at great distances
(232--234).--The importance of light and shade in the Prospettiva
de' perdimenti (235--239).--The effect of light or dark backgrounds
on the apparent size of objects (240--250).--Propositions on
Prospettiva de' perdimenti from MS. C. (250--262).



The reciprocal effects of colours on objects placed opposite each
other (263--271).--Combination of different colours in cast shadows
(272).--The effect of colours in the camera obscura (273. 274).--On
the colours of derived shadows (275. 276).--On the nature of colours
(277. 278).--On gradations in the depth of colours (279. 280).--On
the reflection of colours (281--283).--On the use of dark and light
colours in painting (284--286).--On the colours of the rainbow



General rules (289--291).--An exceptional case (292).--An experiment
(293).--The practice of the Prospettiva de' colori (294).--The rules
of aerial perspective (295--297).--On the relative density of the
atmosphere (298--299).--On the colour of the atmosphere (300--307).



Preliminary observations (308. 309).--Proportions of the head and
face (310--318).--Proportions of the head seen in front
(319--321).--Proportions of the foot (322--323).--Relative
proportions of the hand and foot (324).--Relative proportions of
the foot and of the face (325--327).--Proportions of the leg
(328--331).--On the central point of the whole body (332).--The
relative proportions of the torso and of the whole figure
(333).--The relative proportions of the head and of the torso
(334).--The relative proportions of the torso and of the leg (335.
336).--The relative proportions of the torso and of the foot
(337).--The proportions of the whole figure (338--341).--The torso
from the front and back (342).--Vitruvius' scheme of proportions
(343).--The arm and head (344).--Proportions of the arm
(345--349).--The movement of the arm (350--354).--The movement of
the torso (355--361).--The proportions vary at different ages
(362--367).--The movement of the human figure (368--375).--Of
walking up and down (375--379).--On the human body in action
(380--388).--On hair falling down in curls (389).--On draperies




Classification of trees (393).--The relative thickness of the
branches to the trunk (394--396).--The law of proportion in the
growth of the branches (397--402).--The direction of growth
(403--407).--The forms of trees (408--411).--The insertion of the
leaves (412--419).--Light on branches and leaves (420--422).--The
proportions of light and shade in a leaf (423--426).--Of the
transparency of leaves (427--429).--The gradations of shade and
colour in leaves (430--434).--A classification of trees according to
their colours (435).--The proportions of light and shade in trees
(436--440).--The distribution of light and shade with reference to
the position of the spectator (441--443).--The effects of morning
light (444--448).--The effects of midday light (449).--The
appearance of trees in the distance (450--451).--The cast shadow of
trees (452. 453).--Light and shade on groups of trees
(454--457).--On the treatment of light for landscapes
(458--464).--On the treatment of light for views of towns
(465--469).--The effect of wind on trees (470--473).--Light and
shade on clouds (474--477).--On images reflected in water (478).--Of
rainbows and rain (479. 480).--Of flower seeds (481).



dispositions for an artistic career (482).--The course of
instruction for an artist (483--485).--The study of the antique
(486. 487).--The necessity of anatomical knowledge (488. 489).--How
to acquire practice (490).--Industry and thoroughness the first
conditions (491--493.)--The artist's private life and choice of
company (493. 494).--The distribution of time for studying (495--
497).--On the productive power of minor artists (498--501).--A
caution against one-sided study (502).--How to acquire universality
(503--506).--Useful games and exercises (507. 508).--II. THE
PERSPECTIVE.--ON JUDGING OF A PICTURE.--On the size of the studio
(509).--On the construction of windows (510--512).--On the best
light for painting (513--520).--On various helps in preparing a
picture (521--530).--On the management of works (531. 532).--On the
limitations of painting (533--535).--On the choice of a position
(536. 537).--The apparent size of figures in a picture (538.
539).--The right position of the artist, when painting and of the
AND AERIAL PERSPECTIVE.--Gradations of light and shade (548).--On
the choice of light for a picture (549--554).--The distribution of
light and shade (555--559).--The juxtaposition of light and shade
(560. 561).--On the lighting of the background (562--565).--On the
lighting of white objects (566).--The methods of aerial perspective
(567--570).--IV. OF PORTRAIT AND FIGURE PAINTING.--Of sketching
figures and portraits (571. 572).--The position of the head
(573).--Of the light on the face (574--576).--General suggestions
for historical pictures (577--581).--How to represent the
differences of age and sex (582. 583).--Of representing the emotions
(584).--Of representing imaginary animals (585).--The selection of
forms (586--591).--How to pose figures (592).--Of appropriate
gestures (593--600).--V. SUGGESTIONS FOR COMPOSITIONS.--Of painting
battle-pieces (601--603).--Of depicting night-scenes (604).--Of
depicting a tempest (605. 606).--Of representing the deluge
(607--609).--Of depicting natural phenomena (610. 611).--VI. THE
ARTIST'S MATERIALS.--Of chalk and paper (612--617).--On the
preparation and use of colours (618--627).--Of preparing the panel
(628).--The preparation of oils (629--634).--On varnishes (635--
637).--On chemical _materials (638--650).--VII. PHILOSOPHY AND
HISTORY OF THE ART OF PAINTING.--The relation of art and nature
(651. 652).--Painting is superior to poetry (653. 654).--Painting is
superior to sculpture (655. 656).--Aphorisms (657--659).--On the
history of painting (660. 661).--The painter's scope (662).



On pictures of the Madonna (663).--Bernardo di Bandino's portrait
(664).--Notes on the Last Supper (665--668).--On the battle of
Anghiari (669).--Allegorical representations referring to the duke
of Milan (670--673).--Allegorical representations
(674--678).--Arrangement of a picture (679).--List of drawings
(680).--Mottoes and Emblems (681--702).

The author's intention to publish his MSS.


How by a certain machine many may stay some time under water. And
how and wherefore I do not describe my method of remaining under
water and how long I can remain without eating. And I do not publish
nor divulge these, by reason of the evil nature of men, who would
use them for assassinations at the bottom of the sea by destroying
ships, and sinking them, together with the men in them. Nevertheless
I will impart others, which are not dangerous because the mouth of
the tube through which you breathe is above the water, supported on
air sacks or cork.

[Footnote: The leaf on which this passage is written, is headed with
the words _Casi_ 39, and most of these cases begin with the word
'_Come_', like the two here given, which are the 26th and 27th. 7.
_Sughero_. In the Codex Antlanticus 377a; 1170a there is a sketch,
drawn with the pen, representing a man with a tube in his mouth, and
at the farther end of the tube a disk. By the tube the word
'_Channa_' is written, and by the disk the word '_sughero_'.]

The preparation of the MSS. for publication.


When you put together the science of the motions of water, remember
to include under each proposition its application and use, in order
that this science may not be useless.--

[Footnote: A comparatively small portion of Leonardo's notes on
water-power was published at Bologna in 1828, under the title: "_Del
moto e misura dell'Acqua, di L. da Vinci_".]

Admonition to readers.


Let no man who is not a Mathematician read the elements of my work.

The disorder in the MSS.


Begun at Florence, in the house of Piero di Braccio Martelli, on the
22nd day of March 1508. And this is to be a collection without
order, taken from many papers which I have copied here, hoping to
arrange them later each in its place, according to the subjects of
which they may treat. But I believe that before I am at the end of
this [task] I shall have to repeat the same things several times;
for which, O reader! do not blame me, for the subjects are many and
memory cannot retain them [all] and say: 'I will not write this
because I wrote it before.' And if I wished to avoid falling into
this fault, it would be necessary in every case when I wanted to
copy [a passage] that, not to repeat myself, I should read over all
that had gone before; and all the more since the intervals are long
between one time of writing and the next.

[Footnote: 1. In the history of Florence in the early part of the
XVIth century _Piero di Braccio Martelli_ is frequently mentioned as
_Commissario della Signoria_. He was famous for his learning and at
his death left four books on Mathematics ready for the press; comp.
LITTA, _Famiglie celebri Italiane_, _Famiglia Martelli di
Firenze_.--In the Official Catalogue of MSS. in the Brit. Mus., New
Series Vol. I., where this passage is printed, _Barto_ has been
wrongly given for Braccio.

2. _addi 22 di marzo 1508_. The Christian era was computed in
Florence at that time from the Incarnation (Lady day, March 25th).
Hence this should be 1509 by our reckoning.

3. _racolto tratto di molte carte le quali io ho qui copiate_. We
must suppose that Leonardo means that he has copied out his own MSS.
and not those of others. The first thirteen leaves of the MS. in the
Brit. Mus. are a fair copy of some notes on physics.]

Suggestions for the arrangement of MSS treating of particular


Of digging a canal. Put this in the Book of useful inventions and in
proving them bring forward the propositions already proved. And this
is the proper order; since if you wished to show the usefulness of
any plan you would be obliged again to devise new machines to prove
its utility and thus would confuse the order of the forty Books and
also the order of the diagrams; that is to say you would have to mix
up practice with theory, which would produce a confused and
incoherent work.


I am not to blame for putting forward, in the course of my work on
science, any general rule derived from a previous conclusion.


The Book of the science of Mechanics must precede the Book of useful
inventions.--Have your books on anatomy bound! [Footnote: 4. The
numerous notes on anatomy written on loose leaves and now in the
Royal collection at Windsor can best be classified in four Books,
corresponding to the different character and size of the paper. When
Leonardo speaks of '_li tua libri di notomia_', he probably means
the MSS. which still exist; if this hypothesis is correct the
present condition of these leaves might seem to prove that he only
carried out his purpose with one of the Books on anatomy. A borrowed
book on Anatomy is mentioned in F.O.]


The order of your book must proceed on this plan: first simple
beams, then (those) supported from below, then suspended in part,
then wholly [suspended]. Then beams as supporting other weights
[Footnote: 4. Leonardo's notes on Mechanics are extraordinarily
numerous; but, for the reasons assigned in my introduction, they
have not been included in the present work.].

General introductions to the book on Painting (9-13).



Seeing that I can find no subject specially useful or
pleasing--since the men who have come before me have taken for their
own every useful or necessary theme--I must do like one who, being
poor, comes last to the fair, and can find no other way of providing
himself than by taking all the things already seen by other buyers,
and not taken but refused by reason of their lesser value. I, then,
will load my humble pack with this despised and rejected
merchandise, the refuse of so many buyers; and will go about to
distribute it, not indeed in great cities, but in the poorer towns,
taking such a price as the wares I offer may be worth. [Footnote: It
need hardly be pointed out that there is in this 'Proemio' a covert
irony. In the second and third prefaces, Leonardo characterises his
rivals and opponents more closely. His protest is directed against
Neo-latinism as professed by most of the humanists of his time; its
futility is now no longer questioned.]



I know that many will call this useless work [Footnote: 3. questa
essere opera inutile. By opera we must here understand libro di
pittura and particularly the treatise on Perspective.]; and they
will be those of whom Demetrius [Footnote: 4. Demetrio. "With regard
to the passage attributed to Demetrius", Dr. H. MÜLLER STRÜBING
writes, "I know not what to make of it. It is certainly not
Demetrius Phalereus that is meant and it can hardly be Demetrius
Poliorcetes. Who then can it be--for the name is a very common one?
It may be a clerical error for Demades and the maxim is quite in the
spirit of his writings I have not however been able to find any
corresponding passage either in the 'Fragments' (C. MULLER, _Orat.
Att._, II. 441) nor in the Supplements collected by DIETZ (_Rhein.
Mus._, vol. 29, p. 108)."

The same passage occurs as a simple Memorandum in the MS. Tr. 57,
apparently as a note for this '_Proemio_' thus affording some data
as to the time where these introductions were written.] declared
that he took no more account of the wind that came out their mouth
in words, than of that they expelled from their lower parts: men who
desire nothing but material riches and are absolutely devoid of that
of wisdom, which is the food and the only true riches of the mind.
For so much more worthy as the soul is than the body, so much more
noble are the possessions of the soul than those of the body. And
often, when I see one of these men take this work in his hand, I
wonder that he does not put it to his nose, like a monkey, or ask me
if it is something good to eat.

[Footnote: In the original, the Proemio dì prospettiva cioè
dell'uffitio dell'occhio (see No. 21) stands between this and the
preceding one, No. 9.]


I am fully concious that, not being a literary man, certain
presumptuous persons will think that they may reasonably blame me;
alleging that I am not a man of letters. Foolish folks! do they not
know that I might retort as Marius did to the Roman Patricians
[Footnote 21: _Come Mario disse ai patriti Romani_. "I am unable to
find the words here attributed by Leonardo to Marius, either in
Plutarch's Life of Marius or in the Apophthegmata (_Moralia_,
p.202). Nor do they occur in the writings of Valerius Maximus (who
frequently mentions Marius) nor in Velleius Paterculus (II, 11 to
43), Dio Cassius, Aulus Gellius, or Macrobius. Professor E.
MENDELSON of Dorpat, the editor of Herodian, assures me that no such
passage is the found in that author" (communication from Dr. MULLER
STRUBING). Leonardo evidently meant to allude to some well known
incident in Roman history and the mention of Marius is the result
probably of some confusion. We may perhaps read, for Marius,
Menenius Agrippa, though in that case it is true we must alter
Patriti to Plebei. The change is a serious one. but it would render
the passage perfectly clear.] by saying: That they, who deck
themselves out in the labours of others will not allow me my own.
They will say that I, having no literary skill, cannot properly
express that which I desire to treat of [Footnote 26: _le mie cose
.... che d'altra parola_. This can hardly be reconciled with Mons.
RAVAISSON'S estimate of L. da Vinci's learning. "_Leonard de Vinci
etait un admirateur et un disciple des anciens, aussi bien dans
l'art que dans la science et il tenait a passer pour tel meme aux
yeux de la posterite._" _Gaz. des Beaux arts. Oct. 1877.]; but they
do not know that my subjects are to be dealt with by experience
rather than by words [Footnote 28: See Footnote 26]; and
[experience] has been the mistress of those who wrote well. And so,
as mistress, I will cite her in all cases.


Though I may not, like them, be able to quote other authors, I shall
rely on that which is much greater and more worthy:--on experience,
the mistress of their Masters. They go about puffed up and pompous,
dressed and decorated with [the fruits], not of their own labours,
but of those of others. And they will not allow me my own. They will
scorn me as an inventor; but how much more might they--who are not
inventors but vaunters and declaimers of the works of others--be


And those men who are inventors and interpreters between Nature and
Man, as compared with boasters and declaimers of the works of
others, must be regarded and not otherwise esteemed than as the
object in front of a mirror, when compared with its image seen in
the mirror. For the first is something in itself, and the other
nothingness.--Folks little indebted to Nature, since it is only by
chance that they wear the human form and without it I might class
them with the herds of beasts.


Many will think they may reasonably blame me by alleging that my
proofs are opposed to the authority of certain men held in the
highest reverence by their inexperienced judgments; not considering
that my works are the issue of pure and simple experience, who is
the one true mistress. These rules are sufficient to enable you to
know the true from the false--and this aids men to look only for
things that are possible and with due moderation--and not to wrap
yourself in ignorance, a thing which can have no good result, so
that in despair you would give yourself up to melancholy.


Among all the studies of natural causes and reasons Light chiefly
delights the beholder; and among the great features of Mathematics
the certainty of its demonstrations is what preeminently (tends to)
elevate the mind of the investigator. Perspective, therefore, must
be preferred to all the discourses and systems of human learning. In
this branch [of science] the beam of light is explained on those
methods of demonstration which form the glory not so much of
Mathematics as of Physics and are graced with the flowers of both
[Footnote: 5. Such of Leonardo's notes on Optics or on Perspective
as bear exclusively on Mathematics or Physics could not be included
in the arrangement of the _libro di pittura_ which is here presented
to the reader. They are however but few.]. But its axioms being laid
down at great length, I shall abridge them to a conclusive brevity,
arranging them on the method both of their natural order and of
mathematical demonstration; sometimes by deduction of the effects
from the causes, and sometimes arguing the causes from the effects;
adding also to my own conclusions some which, though not included in
them, may nevertheless be inferred from them. Thus, if the Lord--who
is the light of all things--vouchsafe to enlighten me, I will treat
of Light; wherefore I will divide the present work into 3 Parts
[Footnote: 10. In the middle ages--for instance, by ROGER BACON, by
VITELLONE, with whose works Leonardo was certainly familiar, and by
all the writers of the Renaissance Perspective and Optics were not
regarded as distinct sciences. Perspective, indeed, is in its widest
application the science of seeing. Although to Leonardo the two
sciences were clearly separate, it is not so as to their names; thus
we find axioms in Optics under the heading Perspective. According to
this arrangement of the materials for the theoretical portion of the
_libro di pittura_ propositions in Perspective and in Optics stand
side by side or occur alternately. Although this particular chapter
deals only with Optics, it is not improbable that the words _partirò
la presente opera in 3 parti_ may refer to the same division into
three sections which is spoken of in chapters 14 to 17.].

The plan of the book on Painting (14--17).



There are three branches of perspective; the first deals with the
reasons of the (apparent) diminution of objects as they recede from
the eye, and is known as Diminishing Perspective.--The second
contains the way in which colours vary as they recede from the eye.
The third and last is concerned with the explanation of how the
objects [in a picture] ought to be less finished in proportion as
they are remote (and the names are as follows):

Linear Perspective. The Perspective of Colour. The Perspective of

[Footnote: 13. From the character of the handwriting I infer that
this passage was written before the year 1490.].



The divisions of Perspective are 3, as used in drawing; of these,
the first includes the diminution in size of opaque objects; the
second treats of the diminution and loss of outline in such opaque
objects; the third, of the diminution and loss of colour at long

[Footnote: The division is here the same as in the previous chapter
No. 14, and this is worthy of note when we connect it with the fact
that a space of about 20 years must have intervened between the
writing of the two passages.]



Perspective, as bearing on drawing, is divided into three principal
sections; of which the first treats of the diminution in the size of
bodies at different distances. The second part is that which treats
of the diminution in colour in these objects. The third [deals with]
the diminished distinctness of the forms and outlines displayed by
the objects at various distances.



The first thing in painting is that the objects it represents should
appear in relief, and that the grounds surrounding them at different
distances shall appear within the vertical plane of the foreground
of the picture by means of the 3 branches of Perspective, which are:
the diminution in the distinctness of the forms of the objects, the
diminution in their magnitude; and the diminution in their colour.
And of these 3 classes of Perspective the first results from [the
structure of] the eye, while the other two are caused by the
atmosphere which intervenes between the eye and the objects seen by
it. The second essential in painting is appropriate action and a due
variety in the figures, so that the men may not all look like
brothers, &c.

[Footnote: This and the two foregoing chapters must have been
written in 1513 to 1516. They undoubtedly indicate the scheme which
Leonardo wished to carry out in arranging his researches on
Perspective as applied to Painting. This is important because it is
an evidence against the supposition of H. LUDWIG and others, that
Leonardo had collected his principles of Perspective in one book so
early as before 1500; a Book which, according to the hypothesis,
must have been lost at a very early period, or destroyed possibly,
by the French (!) in 1500 (see H. LUDWIG. L. da Vinci: _Das Buch van
der Malerei_. Vienna 1882 III, 7 and 8).]

The use of the book on Painting.


These rules are of use only in correcting the figures; since every
man makes some mistakes in his first compositions and he who knows
them not, cannot amend them. But you, knowing your errors, will
correct your works and where you find mistakes amend them, and
remember never to fall into them again. But if you try to apply
these rules in composition you will never make an end, and will
produce confusion in your works.

These rules will enable you to have a free and sound judgment; since
good judgment is born of clear understanding, and a clear
understanding comes of reasons derived from sound rules, and sound
rules are the issue of sound experience--the common mother of all
the sciences and arts. Hence, bearing in mind the precepts of my
rules, you will be able, merely by your amended judgment, to
criticise and recognise every thing that is out of proportion in a
work, whether in the perspective or in the figures or any thing

Necessity of theoretical knowledge (19. 20).



Those who are in love with practice without knowledge are like the
sailor who gets into a ship without rudder or compass and who never
can be certain whether he is going. Practice must always be founded
on sound theory, and to this Perspective is the guide and the
gateway; and without this nothing can be done well in the matter of


The painter who draws merely by practice and by eye, without any
reason, is like a mirror which copies every thing placed in front of
it without being conscious of their existence.

The function of the eye (21-23).



Behold here O reader! a thing concerning which we cannot trust our
forefathers, the ancients, who tried to define what the Soul and
Life are--which are beyond proof, whereas those things, which can at
any time be clearly known and proved by experience, remained for
many ages unknown or falsely understood. The eye, whose function we
so certainly know by experience, has, down to my own time, been
defined by an infinite number of authors as one thing; but I find,
by experience, that it is quite another. [Footnote 13: Compare the
note to No. 70.]

[Footnote: In section 13 we already find it indicated that the study
of Perspective and of Optics is to be based on that of the functions
of the eye. Leonardo also refers to the science of the eye, in his
astronomical researches, for instance in MS. F 25b '_Ordine del
provare la terra essere una stella: Imprima difinisce l'occhio'_,
&c. Compare also MS. E 15b and F 60b. The principles of astronomical


Here [in the eye] forms, here colours, here the character of every
part of the universe are concentrated to a point; and that point is
so marvellous a thing ... Oh! marvellous, O stupendous Necessity--by
thy laws thou dost compel every effect to be the direct result of
its cause, by the shortest path. These [indeed] are miracles;...

In so small a space it can be reproduced and rearranged in its whole
expanse. Describe in your anatomy what proportion there is between
the diameters of all the images in the eye and the distance from
them of the crystalline lens.



Painting is concerned with all the 10 attributes of sight; which
are:--Darkness, Light, Solidity and Colour, Form and Position,
Distance and Propinquity, Motion and Rest. This little work of mine
will be a tissue [of the studies] of these attributes, reminding the
painter of the rules and methods by which he should use his art to
imitate all the works of Nature which adorn the world.



Variability of the eye.

1st. The pupil of the eye contracts, in proportion to the increase
of light which is reflected in it. 2nd. The pupil of the eye expands
in proportion to the diminution in the day light, or any other
light, that is reflected in it. 3rd. [Footnote: 8. The subject of
this third proposition we find fully discussed in MS. G. 44a.]. The
eye perceives and recognises the objects of its vision with greater
intensity in proportion as the pupil is more widely dilated; and
this can be proved by the case of nocturnal animals, such as cats,
and certain birds--as the owl and others--in which the pupil varies
in a high degree from large to small, &c., when in the dark or in
the light. 4th. The eye [out of doors] in an illuminated atmosphere
sees darkness behind the windows of houses which [nevertheless] are
light. 5th. All colours when placed in the shade appear of an equal
degree of darkness, among themselves. 6th. But all colours when
placed in a full light, never vary from their true and essential



Focus of sight.

If the eye is required to look at an object placed too near to it,
it cannot judge of it well--as happens to a man who tries to see the
tip of his nose. Hence, as a general rule, Nature teaches us that an
object can never be seen perfectly unless the space between it and
the eye is equal, at least, to the length of the face.

Differences of perception by one eye and by both eyes (26-29).



When both eyes direct the pyramid of sight to an object, that object
becomes clearly seen and comprehended by the eyes.


Objects seen by one and the same eye appear sometimes large, and
sometimes small.


The motion of a spectator who sees an object at rest often makes it
seem as though the object at rest had acquired the motion of the
moving body, while the moving person appears to be at rest.


Objects in relief, when seen from a short distance with one eye,
look like a perfect picture. If you look with the eye _a_, _b_ at
the spot _c_, this point _c_ will appear to be at _d_, _f_, and if
you look at it with the eye _g_, _h_ will appear to be at _m_. A
picture can never contain in itself both aspects.


Let the object in relief _t_ be seen by both eyes; if you will look
at the object with the right eye _m_, keeping the left eye _n_ shut,
the object will appear, or fill up the space, at _a_; and if you
shut the right eye and open the left, the object (will occupy the)
space _b_; and if you open both eyes, the object will no longer
appear at _a_ or _b_, but at _e_, _r_, _f_. Why will not a picture
seen by both eyes produce the effect of relief, as [real] relief
does when seen by both eyes; and why should a picture seen with one
eye give the same effect of relief as real relief would under the
same conditions of light and shade?

[Footnote: In the sketch, _m_ is the left eye and _n_ the right,
while the text reverses this lettering. We must therefore suppose
that the face in which the eyes _m_ and _n_ are placed is opposite
to the spectator.]


The comparative size of the image depends on the amount of light

The eye will hold and retain in itself the image of a luminous body
better than that of a shaded object. The reason is that the eye is
in itself perfectly dark and since two things that are alike cannot
be distinguished, therefore the night, and other dark objects cannot
be seen or recognised by the eye. Light is totally contrary and
gives more distinctness, and counteracts and differs from the usual
darkness of the eye, hence it leaves the impression of its image.


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.


The pupil which is largest will see objects the largest. This is
evident when we look at luminous bodies, and particularly at those
in the sky. When the eye comes out of darkness and suddenly looks up
at these bodies, they at first appear larger and then diminish; and
if you were to look at those bodies through a small opening, you
would see them smaller still, because a smaller part of the pupil
would exercise its function.

[Footnote: 9. _buso_ in the Lomb. dialect is the same as _buco_.]


When the eye, coming out of darkness suddenly sees a luminous body,
it will appear much larger at first sight than after long looking at
it. The illuminated object will look larger and more brilliant, when
seen with two eyes than with only one. A luminous object will appear
smaller in size, when the eye sees it through a smaller opening. A
luminous body of an oval form will appear rounder in proportion as
it is farther from the eye.


Why when the eye has just seen the light, does the half light look
dark to it, and in the same way if it turns from the darkness the
half light look very bright?



If the eye, when [out of doors] in the luminous atmosphere, sees a
place in shadow, this will look very much darker than it really is.
This happens only because the eye when out in the air contracts the
pupil in proportion as the atmosphere reflected in it is more
luminous. And the more the pupil contracts, the less luminous do the
objects appear that it sees. But as soon as the eye enters into a
shady place the darkness of the shadow suddenly seems to diminish.
This occurs because the greater the darkness into which the pupil
goes the more its size increases, and this increase makes the
darkness seem less.

[Footnote 14: _La luce entrerà_. _Luce_ occurs here in the sense of
pupil of the eye as in no 51: C. A. 84b; 245a; I--5; and in many
other places.]



The eye which turns from a white object in the light of the sun and
goes into a less fully lighted place will see everything as dark.
And this happens either because the pupils of the eyes which have
rested on this brilliantly lighted white object have contracted so
much that, given at first a certain extent of surface, they will
have lost more than 3/4 of their size; and, lacking in size, they
are also deficient in [seeing] power. Though you might say to me: A
little bird (then) coming down would see comparatively little, and
from the smallness of his pupils the white might seem black! To this
I should reply that here we must have regard to the proportion of
the mass of that portion of the brain which is given up to the sense
of sight and to nothing else. Or--to return--this pupil in Man
dilates and contracts according to the brightness or darkness of
(surrounding) objects; and since it takes some time to dilate and
contract, it cannot see immediately on going out of the light and
into the shade, nor, in the same way, out of the shade into the
light, and this very thing has already deceived me in painting an
eye, and from that I learnt it.


Experiment [showing] the dilatation and contraction of the pupil,
from the motion of the sun and other luminaries. In proportion as
the sky is darker the stars appear of larger size, and if you were
to light up the medium these stars would look smaller; and this
difference arises solely from the pupil which dilates and contracts
with the amount of light in the medium which is interposed between
the eye and the luminous body. Let the experiment be made, by
placing a candle above your head at the same time that you look at a
star; then gradually lower the candle till it is on a level with the
ray that comes from the star to the eye, and then you will see the
star diminish so much that you will almost lose sight of it.

[Footnote: No reference is made in the text to the letters on the
accompanying diagram.]


The pupil of the eye, in the open air, changes in size with every
degree of motion from the sun; and at every degree of its changes
one and the same object seen by it will appear of a different size;
although most frequently the relative scale of surrounding objects
does not allow us to detect these variations in any single object we
may look at.


The eye--which sees all objects reversed--retains the images for
some time. This conclusion is proved by the results; because, the
eye having gazed at light retains some impression of it. After
looking (at it) there remain in the eye images of intense
brightness, that make any less brilliant spot seem dark until the
eye has lost the last trace of the impression of the stronger light.


Linear Perspective.

We see clearly from the concluding sentence of section 49, where the
author directly addresses the painter, that he must certainly have
intended to include the elements of mathematics in his Book on the
art of Painting. They are therefore here placed at the beginning. In
section 50 the theory of the "Pyramid of Sight" is distinctly and
expressly put forward as the fundamental principle of linear
perspective, and sections 52 to 57 treat of it fully. This theory of
sight can scarcely be traced to any author of antiquity. Such
passages as occur in Euclid for instance, may, it is true, have
proved suggestive to the painters of the Renaissance, but it would
be rash to say any thing decisive on this point.

Leon Battista Alberti treats of the "Pyramid of Sight" at some
length in his first Book of Painting; but his explanation differs
widely from Leonardo's in the details. Leonardo, like Alberti, may
have borrowed the broad lines of his theory from some views commonly
accepted among painters at the time; but he certainly worked out its
application in a perfectly original manner.

The axioms as to the perception of the pyramid of rays are followed
by explanations of its origin, and proofs of its universal
application (58--69). The author recurs to the subject with endless
variations; it is evidently of fundamental importance in his
artistic theory and practice. It is unnecessary to discuss how far
this theory has any scientific value at the present day; so much as
this, at any rate, seems certain: that from the artist's point of
view it may still claim to be of immense practical utility.

According to Leonardo, on one hand, the laws of perspective are an
inalienable condition of the existence of objects in space; on the
other hand, by a natural law, the eye, whatever it sees and wherever
it turns, is subjected to the perception of the pyramid of rays in
the form of a minute target. Thus it sees objects in perspective
independently of the will of the spectator, since the eye receives
the images by means of the pyramid of rays "just as a magnet
attracts iron".

In connection with this we have the function of the eye explained by
the Camera obscura, and this is all the more interesting and
important because no writer previous to Leonardo had treated of this
subject_ (70--73). _Subsequent passages, of no less special interest,
betray his knowledge of refraction and of the inversion of the image
in the camera and in the eye_ (74--82).

_From the principle of the transmission of the image to the eye and
to the camera obscura he deduces the means of producing an
artificial construction of the pyramid of rays or--which is the same
thing--of the image. The fundamental axioms as to the angle of sight
and the vanishing point are thus presented in a manner which is as
complete as it is simple and intelligible_ (86--89).

_Leonardo distinguishes between simple and complex perspective_ (90,
91). _The last sections treat of the apparent size of objects at
various distances and of the way to estimate it_ (92--109).

General remarks on perspective (40-41).



Perspective is the best guide to the art of Painting.

[Footnote: 40. Compare 53, 2.]


The art of perspective is of such a nature as to make what is flat
appear in relief and what is in relief flat.

The elements of perspective--Of the Point (42-46).


All the problems of perspective are made clear by the five terms of
mathematicians, which are:--the point, the line, the angle, the
superficies and the solid. The point is unique of its kind. And the
point has neither height, breadth, length, nor depth, whence it is
to be regarded as indivisible and as having no dimensions in space.
The line is of three kinds, straight, curved and sinuous and it has
neither breadth, height, nor depth. Hence it is indivisible,
excepting in its length, and its ends are two points. The angle is
the junction of two lines in a point.


A point is not part of a line.



The smallest natural point is larger than all mathematical points,
and this is proved because the natural point has continuity, and any
thing that is continuous is infinitely divisible; but the
mathematical point is indivisible because it has no size.

[Footnote: This definition was inserted by Leonardo on a MS. copy on
parchment of the well-known _"Trattato d'Architettura civile e
militare"_ &c. by FRANCESCO DI GIORGIO; opposite a passage where the
author says: _'In prima he da sapere che punto è quella parie della
quale he nulla--Linia he luncheza senza àpieza; &c.]


1, The superficies is a limitation of the body. 2, and the
limitation of a body is no part of that body. 4, and the limitation
of one body is that which begins another. 3, that which is not part
of any body is nothing. Nothing is that which fills no space.

If one single point placed in a circle may be the starting point of
an infinite number of lines, and the termination of an infinite
number of lines, there must be an infinite number of points
separable from this point, and these when reunited become one again;
whence it follows that the part may be equal to the whole.


The point, being indivisible, occupies no space. That which occupies
no space is nothing. The limiting surface of one thing is the
beginning of another. 2. That which is no part of any body is called
nothing. 1. That which has no limitations, has no form. The
limitations of two conterminous bodies are interchangeably the
surface of each. All the surfaces of a body are not parts of that

Of the line (47-48).



The line has in itself neither matter nor substance and may rather
be called an imaginary idea than a real object; and this being its
nature it occupies no space. Therefore an infinite number of lines
may be conceived of as intersecting each other at a point, which has
no dimensions and is only of the thickness (if thickness it may be
called) of one single line.


An angular surface is reduced to a point where it terminates in an
angle. Or, if the sides of that angle are produced in a straight
line, then--beyond that angle--another surface is generated,
smaller, or equal to, or larger than the first.



Consider with the greatest care the form of the outlines of every
object, and the character of their undulations. And these
undulations must be separately studied, as to whether the curves are
composed of arched convexities or angular concavities.


The nature of the outline.

The boundaries of bodies are the least of all things. The
proposition is proved to be true, because the boundary of a thing is
a surface, which is not part of the body contained within that
surface; nor is it part of the air surrounding that body, but is the
medium interposted between the air and the body, as is proved in its
place. But the lateral boundaries of these bodies is the line
forming the boundary of the surface, which line is of invisible
thickness. Wherefore O painter! do not surround your bodies with
lines, and above all when representing objects smaller than nature;
for not only will their external outlines become indistinct, but
their parts will be invisible from distance.


Definition of Perspective.

[Drawing is based upon perspective, which is nothing else than a
thorough knowledge of the function of the eye. And this function
simply consists in receiving in a pyramid the forms and colours of
all the objects placed before it. I say in a pyramid, because there
is no object so small that it will not be larger than the spot where
these pyramids are received into the eye. Therefore, if you extend
the lines from the edges of each body as they converge you will
bring them to a single point, and necessarily the said lines must
form a pyramid.]

[Perspective is nothing more than a rational demonstration applied
to the consideration of how objects in front of the eye transmit
their image to it, by means of a pyramid of lines. The _Pyramid_ is
the name I apply to the lines which, starting from the surface and
edges of each object, converge from a distance and meet in a single

[Perspective is a rational demonstration, by which we may
practically and clearly understand how objects transmit their own
image, by lines forming a Pyramid (centred) in the eye.]

Perspective is a rational demonstration by which experience confirms
that every object sends its image to the eye by a pyramid of lines;
and bodies of equal size will result in a pyramid of larger or
smaller size, according to the difference in their distance, one
from the other. By a pyramid of lines I mean those which start from
the surface and edges of bodies, and, converging from a distance
meet in a single point. A point is said to be that which [having no
dimensions] cannot be divided, and this point placed in the eye
receives all the points of the cone.

[Footnote: 50. 1-5. Compare with this the Proem. No. 21. The
paragraphs placed in brackets: lines 1-9, 10-14, and 17--20, are
evidently mere sketches and, as such, were cancelled by the writer;
but they serve as a commentary on the final paragraph, lines 22-29.]



The perception of the object depends on the direction of the eye.

Supposing that the ball figured above is the ball of the eye and let
the small portion of the ball which is cut off by the line _s t_ be
the pupil and all the objects mirrored on the centre of the face of
the eye, by means of the pupil, pass on at once and enter the pupil,
passing through the crystalline humour, which does not interfere in
the pupil with the things seen by means of the light. And the pupil
having received the objects, by means of the light, immediately
refers them and transmits them to the intellect by the line _a b_.
And you must know that the pupil transmits nothing perfectly to the
intellect or common sense excepting when the objects presented to it
by means of light, reach it by the line _a b;_ as, for instance, by
the line _b c_. For although the lines _m n_ and _f g_ may be seen
by the pupil they are not perfectly taken in, because they do not
coincide with the line _a b_. And the proof is this: If the eye,
shown above, wants to count the letters placed in front, the eye
will be obliged to turn from letter to letter, because it cannot
discern them unless they lie in the line _a b;_ as, for instance, in
the line _a c_. All visible objects reach the eye by the lines of a
pyramid, and the point of the pyramid is the apex and centre of it,
in the centre of the pupil, as figured above.

[Footnote: 51. In this problem the eye is conceived of as fixed and
immovable; this is plain from line 11.]

Experimental proof of the existence of the pyramid of sight (52-55).


Perspective is a rational demonstration, confirmed by experience,
that all objects transmit their image to the eye by a pyramid of

By a pyramid of lines I understand those lines which start from the
edges of the surface of bodies, and converging from a distance, meet
in a single point; and this point, in the present instance, I will
show to be situated in the eye which is the universal judge of all
objects. By a point I mean that which cannot be divided into parts;
therefore this point, which is situated in the eye, being
indivisible, no body is seen by the eye, that is not larger than
this point. This being the case it is inevitable that the lines
which come from the object to the point must form a pyramid. And if
any man seeks to prove that the sense of sight does not reside in
this point, but rather in the black spot which is visible in the
middle of the pupil, I might reply to him that a small object could
never diminish at any distance, as it might be a grain of millet or
of oats or of some similar thing, and that object, if it were larger
than the said [black] spot would never be seen as a whole; as may be
seen in the diagram below. Let _a_. be the seat of sight, _b e_ the
lines which reach the eye. Let _e d_ be the grains of millet within
these lines. You plainly see that these will never diminish by
distance, and that the body _m n_ could not be entirely covered by
it. Therefore you must confess that the eye contains within itself
one single indivisible point _a_, to which all the points converge
of the pyramid of lines starting from an object, as is shown below.
Let _a_. _b_. be the eye; in the centre of it is the point above
mentioned. If the line _e f_ is to enter as an image into so small
an opening in the eye, you must confess that the smaller object
cannot enter into what is smaller than itself unless it is
diminished, and by diminishing it must take the form of a pyramid.



Perspective comes in where judgment fails [as to the distance] in
objects which diminish. The eye can never be a true judge for
determining with exactitude how near one object is to another which
is equal to it [in size], if the top of that other is on the level
of the eye which sees them on that side, excepting by means of the
vertical plane which is the standard and guide of perspective. Let
_n_ be the eye, _e f_ the vertical plane above mentioned. Let _a b c
d_ be the three divisions, one below the other; if the lines _a n_
and _c n_ are of a given length and the eye _n_ is in the centre,
then _a b_ will look as large as _b c. c d_ is lower and farther off
from _n_, therefore it will look smaller. And the same effect will
appear in the three divisions of a face when the eye of the painter
who is drawing it is on a level with the eye of the person he is



If you look at the sun or some other luminous body and then shut
your eyes you will see it again inside your eye for a long time.
This is evidence that images enter into the eye.

The relations of the distance points to the vanishing point (55-56).



All objects transmit their image to the eye in pyramids, and the
nearer to the eye these pyramids are intersected the smaller will
the image appear of the objects which cause them. Therefore, you may
intersect the pyramid with a vertical plane [Footnote 4: _Pariete_.
Compare the definitions in 85, 2-5, 6-27. These lines refer
exclusively to the third diagram. For the better understanding of
this it should be observed that _c s_ must be regarded as
representing the section or profile of a square plane, placed
horizontally (comp. lines 11, 14, 17) for which the word _pianura_
is subsequently employed (20, 22). Lines 6-13 contain certain
preliminary observations to guide the reader in understanding the
diagram; the last three seem to have been added as a supplement.
Leonardo's mistake in writing _t denota_ (line 6) for _f denota_ has
been rectified.] which reaches the base of the pyramid as is shown
in the plane _a n_.

The eye _f_ and the eye _t_ are one and the same thing; but the eye
_f_ marks the distance, that is to say how far you are standing from
the object; and the eye _t_ shows you the direction of it; that is
whether you are opposite, or on one side, or at an angle to the
object you are looking at. And remember that the eye _f_ and the eye
_t_ must always be kept on the same level. For example if you raise
or lower the eye from the distance point _f_ you must do the same
with the direction point _t_. And if the point _f_ shows how far the
eye is distant from the square plane but does not show on which side
it is placed--and, if in the same way, the point _t_ show _s_ the
direction and not the distance, in order to ascertain both you must
use both points and they will be one and the same thing. If the eye
_f_ could see a perfect square of which all the sides were equal to
the distance between _s_ and _c_, and if at the nearest end of the
side towards the eye a pole were placed, or some other straight
object, set up by a perpendicular line as shown at _r s_--then, I
say, that if you were to look at the side of the square that is
nearest to you it will appear at the bottom of the vertical plane _r
s_, and then look at the farther side and it would appear to you at
the height of the point _n_ on the vertical plane. Thus, by this
example, you can understand that if the eye is above a number of
objects all placed on the same level, one beyond another, the more
remote they are the higher they will seem, up to the level of the
eye, but no higher; because objects placed upon the level on which
your feet stand, so long as it is flat--even if it be extended into
infinity--would never be seen above the eye; since the eye has in
itself the point towards which all the cones tend and converge which
convey the images of the objects to the eye. And this point always
coincides with the point of diminution which is the extreme of all
we can see. And from the base line of the first pyramid as far as
the diminishing point

[Footnote: The two diagrams above the chapter are explained by the
first five lines. They have, however, more letters than are referred
to in the text, a circumstance we frequently find occasion to


there are only bases without pyramids which constantly diminish up
to this point. And from the first base where the vertical plane is
placed towards the point in the eye there will be only pyramids
without bases; as shown in the example given above. Now, let _a b_
be the said vertical plane and _r_ the point of the pyramid
terminating in the eye, and _n_ the point of diminution which is
always in a straight line opposite the eye and always moves as the
eye moves--just as when a rod is moved its shadow moves, and moves
with it, precisely as the shadow moves with a body. And each point
is the apex of a pyramid, all having a common base with the
intervening vertical plane. But although their bases are equal their
angles are not equal, because the diminishing point is the
termination of a smaller angle than that of the eye. If you ask me:
"By what practical experience can you show me these points?" I
reply--so far as concerns the diminishing point which moves with you
--when you walk by a ploughed field look at the straight furrows
which come down with their ends to the path where you are walking,
and you will see that each pair of furrows will look as though they
tried to get nearer and meet at the [farther] end.

[Footnote: For the easier understanding of the diagram and of its
connection with the preceding I may here remark that the square
plane shown above in profile by the line _c s_ is here indicated by
_e d o p_. According to lines 1, 3 _a b_ must be imagined as a plane
of glass placed perpendicularly at _o p_.]


How to measure the pyramid of vision.

As regards the point in the eye; it is made more intelligible by
this: If you look into the eye of another person you will see your
own image. Now imagine 2 lines starting from your ears and going to
the ears of that image which you see in the other man's eye; you
will understand that these lines converge in such a way that they
would meet in a point a little way beyond your own image mirrored in
the eye. And if you want to measure the diminution of the pyramid in
the air which occupies the space between the object seen and the
eye, you must do it according to the diagram figured below. Let _m
n_ be a tower, and _e f_ a, rod, which you must move backwards and
forwards till its ends correspond with those of the tower [Footnote
9: _I sua stremi .. della storre_ (its ends ... of the tower) this
is the case at _e f_.]; then bring it nearer to the eye, at _c d_
and you will see that the image of the tower seems smaller, as at _r
o_. Then [again] bring it closer to the eye and you will see the rod
project far beyond the image of the tower from _a_ to _b_ and from
_t_ to _b_, and so you will discern that, a little farther within,
the lines must converge in a point.

The Production of pyramid of Vision (58-60).



The instant the atmosphere is illuminated it will be filled with an
infinite number of images which are produced by the various bodies
and colours assembled in it. And the eye is the target, a loadstone,
of these images.


The whole surface of opaque bodies displays its whole image in all
the illuminated atmosphere which surrounds them on all sides.


That the atmosphere attracts to itself, like a loadstone, all the
images of the objects that exist in it, and not their forms merely
but their nature may be clearly seen by the sun, which is a hot and
luminous body. All the atmosphere, which is the all-pervading
matter, absorbs light and heat, and reflects in itself the image of
the source of that heat and splendour and, in each minutest portion,
does the same. The Northpole does the same as the loadstone shows;
and the moon and the other planets, without suffering any
diminution, do the same. Among terrestrial things musk does the same
and other perfumes.


All bodies together, and each by itself, give off to the surrounding
air an infinite number of images which are all-pervading and each
complete, each conveying the nature, colour and form of the body
which produces it.

It can clearly be shown that all bodies are, by their images,
all-pervading in the surrounding atmosphere, and each complete in
itself as to substance form and colour; this is seen by the images
of the various bodies which are reproduced in one single perforation
through which they transmit the objects by lines which intersect and
cause reversed pyramids, from the objects, so that they are upside
down on the dark plane where they are first reflected. The reason of
this is--

[Footnote: The diagram intended to illustrate the statement (Pl. II
No. i) occurs in the original between lines 3 and 4. The three
circles must be understood to represent three luminous bodies which
transmit their images through perforations in a wall into a dark
chamber, according to a law which is more fully explained in 75?81.
So far as concerns the present passage the diagram is only intended
to explain that the images of the three bodies may be made to
coalesce at any given spot. In the circles are written,
giallo--yellow, biàcho--white, rosso--red.

The text breaks off at line 8. The paragraph No.40 follows here in
the original MS.]


Every point is the termination of an infinite number of lines, which
diverge to form a base, and immediately, from the base the same
lines converge to a pyramid [imaging] both the colour and form. No
sooner is a form created or compounded than suddenly infinite lines
and angles are produced from it; and these lines, distributing
themselves and intersecting each other in the air, give rise to an
infinite number of angles opposite to each other. Given a base, each
opposite angle, will form a triangle having a form and proportion
equal to the larger angle; and if the base goes twice into each of
the 2 lines of the pyramid the smaller triangle will do the same.


Every body in light and shade fills the surrounding air with
infinite images of itself; and these, by infinite pyramids diffused
in the air, represent this body throughout space and on every side.
Each pyramid that is composed of a long assemblage of rays includes
within itself an infinite number of pyramids and each has the same
power as all, and all as each. A circle of equidistant pyramids of
vision will give to their object angles of equal size; and an eye at
each point will see the object of the same size. The body of the
atmosphere is full of infinite pyramids composed of radiating
straight lines, which are produced from the surface of the bodies in
light and shade, existing in the air; and the farther they are from
the object which produces them the more acute they become and
although in their distribution they intersect and cross they never
mingle together, but pass through all the surrounding air,
independently converging, spreading, and diffused. And they are all
of equal power [and value]; all equal to each, and each equal to
all. By these the images of objects are transmitted through all
space and in every direction, and each pyramid, in itself, includes,
in each minutest part, the whole form of the body causing it.


The body of the atmosphere is full of infinite radiating pyramids
produced by the objects existing in it. These intersect and cross
each other with independent convergence without interfering with
each other and pass through all the surrounding atmosphere; and are
of equal force and value--all being equal to each, each to all. And
by means of these, images of the body are transmitted everywhere and
on all sides, and each receives in itself every minutest portion of
the object that produces it.

Proof by experiment (65-66).



The air is filled with endless images of the objects distributed in
it; and all are represented in all, and all in one, and all in each,
whence it happens that if two mirrors are placed in such a manner as
to face each other exactly, the first will be reflected in the
second and the second in the first. The first being reflected in the
second takes to it the image of itself with all the images
represented in it, among which is the image of the second mirror,
and so, image within image, they go on to infinity in such a manner
as that each mirror has within it a mirror, each smaller than the
last and one inside the other. Thus, by this example, it is clearly
proved that every object sends its image to every spot whence the
object itself can be seen; and the converse: That the same object
may receive in itself all the images of the objects that are in
front of it. Hence the eye transmits through the atmosphere its own
image to all the objects that are in front of it and receives them
into itself, that is to say on its surface, whence they are taken in
by the common sense, which considers them and if they are pleasing
commits them to the memory. Whence I am of opinion: That the
invisible images in the eyes are produced towards the object, as the
image of the object to the eye. That the images of the objects must
be disseminated through the air. An instance may be seen in several
mirrors placed in a circle, which will reflect each other endlessly.
When one has reached the other it is returned to the object that
produced it, and thence--being diminished--it is returned again to
the object and then comes back once more, and this happens
endlessly. If you put a light between two flat mirrors with a
distance of 1 braccio between them you will see in each of them an
infinite number of lights, one smaller than another, to the last. If
at night you put a light between the walls of a room, all the parts
of that wall will be tinted with the image of that light. And they
will receive the light and the light will fall on them, mutually,
that is to say, when there is no obstacle to interrupt the
transmission of the images. This same example is seen in a greater
degree in the distribution of the solar rays which all together, and
each by itself, convey to the object the image of the body which
causes it. That each body by itself alone fills with its images the
atmosphere around it, and that the same air is able, at the same
time, to receive the images of the endless other objects which are
in it, this is clearly proved by these examples. And every object is
everywhere visible in the whole of the atmosphere, and the whole in
every smallest part of it; and all the objects in the whole, and all
in each smallest part; each in all and all in every part.


The images of objects are all diffused through the atmosphere which
receives them; and all on every side in it. To prove this, let _a c
e_ be objects of which the images are admitted to a dark chamber by
the small holes _n p_ and thrown upon the plane _f i_ opposite to
these holes. As many images will be produced in the chamber on the
plane as the number of the said holes.


General conclusions.

All objects project their whole image and likeness, diffused and
mingled in the whole of the atmosphere, opposite to themselves. The
image of every point of the bodily surface, exists in every part of
the atmosphere. All the images of the objects are in every part of
the atmosphere. The whole, and each part of the image of the
atmosphere is [reflected] in each point of the surface of the bodies
presented to it. Therefore both the part and the whole of the images
of the objects exist, both in the whole and in the parts of the
surface of these visible bodies. Whence we may evidently say that
the image of each object exists, as a whole and in every part, in
each part and in the whole interchangeably in every existing body.
As is seen in two mirrors placed opposite to each other.


That the contrary is impossible.

It is impossible that the eye should project from itself, by visual
rays, the visual virtue, since, as soon as it opens, that front
portion [of the eye] which would give rise to this emanation would
have to go forth to the object and this it could not do without
time. And this being so, it could not travel so high as the sun in a
month's time when the eye wanted to see it. And if it could reach
the sun it would necessarily follow that it should perpetually
remain in a continuous line from the eye to the sun and should
always diverge in such a way as to form between the sun and the eye
the base and the apex of a pyramid. This being the case, if the eye
consisted of a million worlds, it would not prevent its being
consumed in the projection of its virtue; and if this virtue would
have to travel through the air as perfumes do, the winds would bent
it and carry it into another place. But we do [in fact] see the mass
of the sun with the same rapidity as [an object] at the distance of
a braccio, and the power of sight is not disturbed by the blowing of
the winds nor by any other accident.

[Footnote: The view here refuted by Leonardo was maintained among
others by Bramantino, Leonardo's Milanese contemporary. LOMAZZO
writes as follows in his Trattato dell' Arte della pittura &c.
(Milano 1584. Libr. V cp. XXI): Sovviemmi di aver già letto in certi
scritti alcune cose di Bramantino milanese, celebratissimo pittore,
attenente alla prospettiva, le quali ho voluto riferire, e quasi
intessere in questo luogo, affinchè sappiamo qual fosse l'opinione
di cosi chiaro e famoso pittore intorno alla prospettiva . . Scrive
Bramantino che la prospettiva è una cosa che contrafà il naturale, e
che ciò si fa in tre modi

Circa il primo modo che si fa con ragione, per essere la cosa in
poche parole conclusa da Bramantino in maniera che giudico non
potersi dir meglio, contenendovi si tutta Parte del principio al
fine, io riferirò per appunto le proprie parole sue (cp. XXII, Prima
prospettiva di Bramantino). La prima prospettiva fa le cose di
punto, e l'altra non mai, e la terza più appresso. Adunque la prima
si dimanda prospettiva, cioè ragione, la quale fa l'effetto dell'
occhio, facendo crescere e calare secondo gli effetti degli occhi.
Questo crescere e calare non procede della cosa propria, che in se
per esser lontana, ovvero vicina, per quello effetto non può
crescere e sminuire, ma procede dagli effetti degli occhi, i quali
sono piccioli, e perciò volendo vedere tanto gran cosa_, bisogna che
mandino fuora la virtù visiva, _la quale si dilata in tanta
larghezza, che piglia tutto quello che vuoi vedere, ed_ arrivando a
quella cosa la vede dove è: _e da lei agli occhi per quello circuito
fino all' occhio, e tutto quello termine è pieno di quella cosa_.

It is worthy of note that Leonardo had made his memorandum refuting
this view, at Milan in 1492]


A parallel case.

Just as a stone flung into the water becomes the centre and cause of
many circles, and as sound diffuses itself in circles in the air: so
any object, placed in the luminous atmosphere, diffuses itself in
circles, and fills the surrounding air with infinite images of
itself. And is repeated, the whole every-where, and the whole in
every smallest part. This can be proved by experiment, since if you
shut a window that faces west and make a hole [Footnote: 6. Here the
text breaks off.] . .

[Footnote: Compare LIBRI, _Histoire des sciences mathématiques en
Italie_. Tome III, p. 43.]

The function of the eye as explained by the camera obscura (70. 71).


If the object in front of the eye sends its image to the eye, the
eye, on the other hand, sends its image to the object, and no
portion whatever of the object is lost in the images it throws off,
for any reason either in the eye or the object. Therefore we may
rather believe it to be the nature and potency of our luminous
atmosphere which absorbs the images of the objects existing in it,
than the nature of the objects, to send their images through the
air. If the object opposite to the eye were to send its image to the
eye, the eye would have to do the same to the object, whence it
might seem that these images were an emanation. But, if so, it would
be necessary [to admit] that every object became rapidly smaller;
because each object appears by its images in the surrounding
atmosphere. That is: the whole object in the whole atmosphere, and
in each part; and all the objects in the whole atmosphere and all of
them in each part; speaking of that atmosphere which is able to
contain in itself the straight and radiating lines of the images
projected by the objects. From this it seems necessary to admit that
it is in the nature of the atmosphere, which subsists between the
objects, and which attracts the images of things to itself like a
loadstone, being placed between them.


I say that if the front of a building--or any open piazza or
field--which is illuminated by the sun has a dwelling opposite to
it, and if, in the front which does not face the sun, you make a
small round hole, all the illuminated objects will project their
images through that hole and be visible inside the dwelling on the
opposite wall which may be made white; and there, in fact, they will
be upside down, and if you make similar openings in several places
in the same wall you will have the same result from each. Hence the
images of the illuminated objects are all everywhere on this wall
and all in each minutest part of it. The reason, as we clearly know,
is that this hole must admit some light to the said dwelling, and
the light admitted by it is derived from one or many luminous
bodies. If these bodies are of various colours and shapes the rays
forming the images are of various colours and shapes, and so will
the representations be on the wall.

[Footnote: 70. 15--23. This section has already been published in the
"_Saggio delle Opere di Leonardo da Vinci_" Milan 1872, pp. 13, 14.
G. Govi observes upon it, that Leonardo is not to be regarded as the
inventor of the Camera obscura, but that he was the first to explain
by it the structure of the eye. An account of the Camera obscura
first occurs in CESARE CESARINI's Italian version of Vitruvius, pub.
1523, four years after Leonardo's death. Cesarini expressly names
Benedettino Don Papnutio as the inventor of the Camera obscura. In
his explanation of the function of the eye by a comparison with the
Camera obscura Leonardo was the precursor of G. CARDANO, Professor
of Medicine at Bologna (died 1576) and it appears highly probable
that this is, in fact, the very discovery which Leonardo ascribes to
himself in section 21 without giving any further details.]



An experiment, showing how objects transmit their images or
pictures, intersecting within the eye in the crystalline humour, is
seen when by some small round hole penetrate the images of
illuminated objects into a very dark chamber. Then, receive these
images on a white paper placed within this dark room and rather near
to the hole and you will see all the objects on the paper in their
proper forms and colours, but much smaller; and they will be upside
down by reason of that very intersection. These images being
transmitted from a place illuminated by the sun will seem actually
painted on this paper which must be extremely thin and looked at
from behind. And let the little perforation be made in a very thin
plate of iron. Let _a b e d e_ be the object illuminated by the sun
and _o r_ the front of the dark chamber in which is the said hole at
_n m_. Let _s t_ be the sheet of paper intercepting the rays of the
images of these objects upside down, because the rays being
straight, _a_ on the right hand becomes _k_ on the left, and _e_ on
the left becomes _f_ on the right; and the same takes place inside
the pupil.

[Footnote: This chapter is already known through a translation into
French by VENTURI. Compare his '_Essai sur les ouvrages
physico-mathématiques de L. da Vinci avec des fragments tirés de ses
Manuscrits, apportés de l'Italie. Lu a la premiere classe de
l'Institut national des Sciences et Arts.' Paris, An V_ (1797).]

The practice of perspective (72. 73).


In the practice of perspective the same rules apply to light and to
the eye.


The object which is opposite to the pupil of the eye is seen by that
pupil and that which is opposite to the eye is seen by the pupil.

Refraction of the rays falling upon the eye (74. 75)


The lines sent forth by the image of an object to the eye do not
reach the point within the eye in straight lines.


If the judgment of the eye is situated within it, the straight lines
of the images are refracted on its surface because they pass through
the rarer to the denser medium. If, when you are under water, you
look at objects in the air you will see them out of their true
place; and the same with objects under water seen from the air.

The intersection of the rays (76-82).


The inversion of the images.

All the images of objects which pass through a window [glass pane]
from the free outer air to the air confined within walls, are seen
on the opposite side; and an object which moves in the outer air
from east to west will seem in its shadow, on the wall which is
lighted by this confined air, to have an opposite motion.



What difference is there in the way in which images pass through
narrow openings and through large openings, or in those which pass
by the sides of shaded bodies? By moving the edges of the opening
through which the images are admitted, the images of immovable
objects are made to move. And this happens, as is shown in the 9th
which demonstrates: [Footnote 11: _per la 9a che dicie_. When
Leonardo refers thus to a number it serves to indicate marginal
diagrams; this can in some instances be distinctly proved. The ninth
sketch on the page W. L. 145 b corresponds to the middle sketch of
the three reproduced.] the images of any object are all everywhere,
and all in each part of the surrounding air. It follows that if one
of the edges of the hole by which the images are admitted to a dark
chamber is moved it cuts off those rays of the image that were in
contact with it and gets nearer to other rays which previously were
remote from it &c.


If you move the right side of the opening the image on the left will
move [being that] of the object which entered on the right side of
the opening; and the same result will happen with all the other
sides of the opening. This can be proved by the 2nd of this which
shows: all the rays which convey the images of objects through the
air are straight lines. Hence, if the images of very large bodies
have to pass through very small holes, and beyond these holes
recover their large size, the lines must necessarily intersect.

[Footnote: 77. 2. In the first of the three diagrams Leonardo had

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