The Notebooks of Leonardo Da Vinci _ Complete da Vinci Leonardo 36033 downloads.pdf

The Project Gutenberg eBook of The Notebooks of Leonardo
Da Vinci — Complete

This eBook is for the use of anyone anywhere in the United States and most
other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms of
the Project Gutenberg License included with this eBook or online at
www.gutenberg.org. If you are not located in the United States, you will
have to check the laws of the country where you are located before using
this eBook.

Title: The Notebooks of Leonardo Da Vinci — Complete

Author: da Vinci Leonardo

Translator: Jean Paul Richter

Release date: January 1, 2004 [eBook #5000]
Most recently updated: June 3, 2026

Language: English

Original publication: , 1888

Other information and formats: www.gutenberg.org/ebooks/5000

Credits: This eBook was produced by Charles Aldarondo and the
Distributed Proofreaders team

*** START OF THE PROJECT GUTENBERG EBOOK THE
NOTEBOOKS OF LEONARDO DA VINCI — COMPLETE ***

The Notebooks of Leonardo Da Vinci

Volume 1
Translated by Jean Paul Richter

1888

PREFACE.

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interesting original texts should have remained so long unpublished, and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 writings?

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 genius:

"Majestati naturae par ingenium."

LONDON, April 1883.

F. P. R.

CONTENTS OF VOLUME I.

PROLEGOMENA AND
GENERAL INTRODUCTION TO
THE BOOK ON PAINTING
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).

II.

LINEAR PERSPECTIVE

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).

III.

SIX BOOKS ON LIGHT AND SHADE

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).

IV.

PERSPECTIVE OF DISAPPEARANCE

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).

V.

THEORY OF COLOURS

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 (287—288).

VI.

PERSPECTIVE OF COLOUR AND AERIAL PERSPECTIVE

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).

VII.

ON THE PROPORTIONS AND ON THE MOVEMENTS OF THE HUMAN FIGURE

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

(390—392).

VIII.

BOTANY FOR PAINTERS, AND ELEMENTS OF LANDSCAPE PAINTING

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).

IX.

THE PRACTICE OF PAINTING

I. MORAL PRECEPTS FOR THE STUDENT OF PAINTING.—How to
ascertain the 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 ARTIST'S STUDIO.—INSTRUMENTS AND HELPS
FOR THE APPLICATION OF 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
spectator (540—547).—III. THE PRACTICAL METHODS OF LIGHT
AND SHADE 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).

X.

STUDIES AND SKETCHES FOR PICTURES AND DECORATIONS

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.

1.

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.

2.

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.

3.

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

The disorder in the MSS.

4.

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 subjects.
(5-8).

5.

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.

6.

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

7.

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.]

8.

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).

9.

INTRODUCTION.

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.]

10.

INTRODUCTION.

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.]

INTRODUCTION.

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.

11.

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 blamed.

INTRODUCTION.

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.

12.

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.

13.

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).

14.

ON THE THREE BRANCHES OF PERSPECTIVE.

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
Disappearance.

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

15.

ON PAINTING AND PERSPECTIVE.

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 distances.

[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.]

16.

THE DISCOURSE ON PAINTING.

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.

17.

ON THE SECTIONS OF [THE BOOK ON] PAINTING.

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.

18.

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 else.

Necessity of theoretical knowledge (19. 20).

19.

OF THE MISTAKES MADE BY THOSE WHO PRACTISE WITHOUT KNOWLEDGE.

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 drawing.

20.

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).

21.

INTRODUCTION TO PERSPECTIVE:—THAT IS OF THE FUNCTION OF THE EYE.

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 perspective.]

22.

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.

23.

OF THE 10 ATTRIBUTES OF THE EYE, ALL CONCERNED IN PAINTING.

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.

24.

ON PAINTING.

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 hue.

25.

OF THE EYE.

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).

26.

OF THE EYE.

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

27.

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

28.

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.

ON PAINTING.

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.

29.

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.]

30.

The comparative size of the image depends on the amount of light (30-
39).

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.

31.

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.

32.

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.]

33.

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.

34.

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?

35.

ON PAINTING.

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.]

36.

ON PERSPECTIVE.

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.

37.

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.]

38.

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.

39.

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.

_II.

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).

40.

ON PAINTING.

Perspective is the best guide to the art of Painting.

[Footnote: 40. Compare 53, 2.]

41.

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).

42.

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.

43.

A point is not part of a line.

44.

OF THE NATURAL POINT.

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.]

45.

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.

46.

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 body.

Of the line (47-48).

47.

DEFINITION OF THE NATURE OF THE LINE.

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.

HOW WE MAY CONCLUDE THAT A SUPERFICIES TERMINATES IN A POINT?

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.

48.

OF DRAWING OUTLINE.

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.

49.

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.

50.

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 point.]

[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.]

51.

IN WHAT WAY THE EYE SEES OBJECTS PLACED IN FRONT OF IT.

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).

52.

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

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.

53.

PERSPECTIVE.

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
painting.

54.

TO PROVE HOW OBJECTS REACH THE EYE.

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).

55.

ELEMENTS OF PERSPECTIVE.

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 remark.]

56.

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.]

57.

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).

58.

PERSPECTIVE.

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.

59.

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

60.

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.

61.

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.]

62.

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.

63.

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.

64.

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).

65.

PERSPECTIVE.

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.

66.

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.

67.

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.

68.

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]

69.

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).

70.

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.

PROVE HOW ALL OBJECTS, PLACED IN ONE POSITION, ARE ALL EVERYWHERE
AND ALL IN EACH PART.

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.]

71.

HOW THE IMAGES OF OBJECTS RECEIVED BY THE EYE INTERSECT WITHIN THE
CRYSTALLINE HUMOUR OF THE EYE.

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).

72.

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

73.

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)

74.

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

75.

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).

76.

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.

77.

THE PRINCIPLE ON WHICH THE IMAGES OF BODIES PASS IN BETWEEN THE
MARGINS OF THE OPENINGS BY WHICH THEY ENTER.

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.

OF THE MOVEMENT OF THE EDGE AT THE RIGHT OR LEFT, OR THE UPPER, OR
LOWER EDGE.

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 drawn
only one of the two margins, et m.]

78.

Necessity has provided that all the images of objects in front of the eye
shall intersect in two places. One of these intersections is in the pupil, the
other in the crystalline lens; and if this were not the case the eye could not
see so great a number of objects as it does. This can be proved, since all the
lines which intersect do so in a point. Because nothing is seen of objects
excepting their surface; and their edges are lines, in contradistinction to the
definition of a surface. And each minute part of a line is equal to a point; for
smallest is said of that than which nothing can be smaller, and this
definition is equivalent to the definition of the point. Hence it is possible for
the whole circumference of a circle to transmit its image to the point of
intersection, as is shown in the 4th of this which shows: all the smallest
parts of the images cross each other without interfering with each other.
These demonstrations are to illustrate the eye. No image, even of the
smallest object, enters the eye without being turned upside down; but as it
penetrates into the crystalline lens it is once more reversed and thus the
image is restored to the same position within the eye as that of the object
outside the eye.

79.

OF THE CENTRAL LINE OF THE EYE.

Only one line of the image, of all those that reach the visual virtue, has
no intersection; and this has no sensible dimensions because it is a
mathematical line which originates from a mathematical point, which has
no dimensions.

According to my adversary, necessity requires that the central line of
every image that enters by small and narrow openings into a dark chamber
shall be turned upside down, together with the images of the bodies that
surround it.

80.

AS TO WHETHER THE CENTRAL LINE OF THE IMAGE CAN BE INTERSECTED, OR
NOT, WITHIN THE OPENING.

It is impossible that the line should intersect itself; that is, that its right
should cross over to its left side, and so, its left side become its right side.
Because such an intersection demands two lines, one from each side; for
there can be no motion from right to left or from left to right in itself
without such extension and thickness as admit of such motion. And if there
is extension it is no longer a line but a surface, and we are investigating the
properties of a line, and not of a surface. And as the line, having no centre
of thickness cannot be divided, we must conclude that the line can have no
sides to intersect each other. This is proved by the movement of the line a f
to a b and of the line e b to e f, which are the sides of the surface a f e b. But
if you move the line a b and the line e f, with the frontends a e, to the spot c,
you will have moved the opposite ends f b towards each other at the point d.
And from the two lines you will have drawn the straight line c d which cuts
the middle of the intersection of these two lines at the point n without any
intersection. For, you imagine these two lines as having breadth, it is

evident that by this motion the first will entirely cover the other—being
equal with it—without any intersection, in the position c d. And this is
sufficient to prove our proposition.

81.

HOW THE INNUMERABLE RAYS FROM INNUMERABLE IMAGES CAN CONVERGE
TO A POINT.

Just as all lines can meet at a point without interfering with each other—
being without breadth or thickness—in the same way all the images of
surfaces can meet there; and as each given point faces the object opposite to
it and each object faces an opposite point, the converging rays of the image
can pass through the point and diverge again beyond it to reproduce and re-
magnify the real size of that image. But their impressions will appear
reversed—as is shown in the first, above; where it is said that every image
intersects as it enters the narrow openings made in a very thin substance.

Read the marginal text on the other side.

In proportion as the opening is smaller than the shaded body, so much
less will the images transmitted through this opening intersect each other.
The sides of images which pass through openings into a dark room intersect
at a point which is nearer to the opening in proportion as the opening is
narrower. To prove this let a b be an object in light and shade which sends
not its shadow but the image of its darkened form through the opening d e
which is as wide as this shaded body; and its sides a b, being straight lines
(as has been proved) must intersect between the shaded object and the
opening; but nearer to the opening in proportion as it is smaller than the
object in shade. As is shown, on your right hand and your left hand, in the
two diagrams a b c n m o where, the right opening d e, being equal in width
to the shaded object a b, the intersection of the sides of the said shaded

object occurs half way between the opening and the shaded object at the
point c. But this cannot happen in the left hand figure, the opening o being
much smaller than the shaded object n m.

It is impossible that the images of objects should be seen between the
objects and the openings through which the images of these bodies are
admitted; and this is plain, because where the atmosphere is illuminated
these images are not formed visibly.

When the images are made double by mutually crossing each other they
are invariably doubly as dark in tone. To prove this let d e h be such a
doubling which although it is only seen within the space between the bodies
in b and i this will not hinder its being seen from f g or from f m; being
composed of the images a b i k which run together in d e h.

[Footnote: 81. On the original diagram at the beginning of this chapter
Leonardo has written "azurro" (blue) where in the facsimile I have marked
A, and "giallo" (yellow) where B stands.]

[Footnote: 15—23. These lines stand between the diagrams I and III.]

[Footnote: 24—53. These lines stand between the diagrams I and II.]

[Footnote: 54—97 are written along the left side of diagram I.]

82.

An experiment showing that though the pupil may not be moved from its
position the objects seen by it may appear to move from their places.

If you look at an object at some distance from you and which is below
the eye, and fix both your eyes upon it and with one hand firmly hold the
upper lid open while with the other you push up the under lid—still keeping

your eyes fixed on the object gazed at—you will see that object double; one
[image] remaining steady, and the other moving in a contrary direction to
the pressure of your finger on the lower eyelid. How false the opinion is of
those who say that this happens because the pupil of the eye is displaced
from its position.

How the above mentioned facts prove that the pupil acts upside down in
seeing.

[Footnote: 82. 14—17. The subject indicated by these two headings is
fully discussed in the two chapters that follow them in the original; but it
did not seem to me appropriate to include them here.]

Demostration of perspective by means of a vertical glass plane (83-85).

83.

OF THE PLANE OF GLASS.

Perspective is nothing else than seeing place [or objects] behind a plane
of glass, quite transparent, on the surface of which the objects behind that
glass are to be drawn. These can be traced in pyramids to the point in the
eye, and these pyramids are intersected on the glass plane.

84.

Pictorial perspective can never make an object at the same distance, look
of the same size as it appears to the eye. You see that the apex of the
pyramid f c d is as far from the object c d as the same point f is from the
object a b; and yet c d, which is the base made by the painter's point, is
smaller than a b which is the base of the lines from the objects converging
in the eye and refracted at s t, the surface of the eye. This may be proved by
experiment, by the lines of vision and then by the lines of the painter's

plumbline by cutting the real lines of vision on one and the same plane and
measuring on it one and the same object.

85.

PERSPECTIVE.

The vertical plane is a perpendicular line, imagined as in front of the
central point where the apex of the pyramids converge. And this plane bears
the same relation to this point as a plane of glass would, through which you
might see the various objects and draw them on it. And the objects thus
drawn would be smaller than the originals, in proportion as the distance
between the glass and the eye was smaller than that between the glass and
the objects.

PERSPECTIVE.

The different converging pyramids produced by the objects, will show,
on the plane, the various sizes and remoteness of the objects causing them.

PERSPECTIVE.

All those horizontal planes of which the extremes are met by
perpendicular lines forming right angles, if they are of equal width the more
they rise to the level of eye the less this is seen, and the more the eye is
above them the more will their real width be seen.

PERSPECTIVE.

The farther a spherical body is from the eye the more you will see of it.

The angle of sight varies with the distance (86-88)

86.

A simple and natural method; showing how objects appear to the eye
without any other medium.

The object that is nearest to the eye always seems larger than another of
the same size at greater distance. The eye m, seeing the spaces o v x, hardly
detects the difference between them, and the. reason of this is that it is close
to them [Footnote 6: It is quite inconceivable to me why M. RAVAISSON,
in a note to his French translation of this simple passage should have
remarked: Il est clair que c'est par erreur que Leonard a ècrit per esser
visino au lieu de per non esser visino. (See his printed ed. of MS. A. p.
38.)]; but if these spaces are marked on the vertical plane n o the space o v
will be seen at o r, and in the same way the space v x will appear at r q. And
if you carry this out in any place where you can walk round, it will look out
of proportion by reason of the great difference in the spaces o r and r q. And
this proceeds from the eye being so much below [near] the plane that the
plane is foreshortened. Hence, if you wanted to carry it out, you would have
[to arrange] to see the perspective through a single hole which must be at
the point m, or else you must go to a distance of at least 3 times the height
of the object you see. The plane o p being always equally remote from the
eye will reproduce the objects in a satisfactory way, so that they may be
seen from place to place.

87.

How every large mass sends forth its images, which may diminish
through infinity.

The images of any large mass being infinitely divisible may be infinitely
diminished.

88.

Objects of equal size, situated in various places, will be seen by different
pyramids which will each be smaller in proportion as the object is farther
off.

89.

Perspective, in dealing with distances, makes use of two opposite
pyramids, one of which has its apex in the eye and the base as distant as the
horizon. The other has the base towards the eye and the apex on the
horizon. Now, the first includes the [visible] universe, embracing all the
mass of the objects that lie in front of the eye; as it might be a vast
landscape seen through a very small opening; for the more remote the
objects are from the eye, the greater number can be seen through the
opening, and thus the pyramid is constructed with the base on the horizon
and the apex in the eye, as has been said. The second pyramid is extended
to a spot which is smaller in proportion as it is farther from the eye; and this
second perspective [= pyramid] results from the first.

90.

SIMPLE PERSPECTIVE.

Simple perspective is that which is constructed by art on a vertical plane
which is equally distant from the eye in every part. Complex perspective is
that which is constructed on a ground-plan in which none of the parts are
equally distant from the eye.

91.

PERSPECTIVE.

No surface can be seen exactly as it is, if the eye that sees it is not equally
remote from all its edges.

92.

WHY WHEN AN OBJECT IS PLACED CLOSE TO THE EYE ITS EDGES ARE
INDISTINCT.

When an object opposite the eye is brought too close to it, its edges must
become too confused to be distinguished; as it happens with objects close to
a light, which cast a large and indistinct shadow, so is it with an eye which
estimates objects opposite to it; in all cases of linear perspective, the eye
acts in the same way as the light. And the reason is that the eye has one
leading line (of vision) which dilates with distance and embraces with true
discernment large objects at a distance as well as small ones that are close.
But since the eye sends out a multitude of lines which surround this chief
central one and since these which are farthest from the centre in this cone of
lines are less able to discern with accuracy, it follows that an object brought
close to the eye is not at a due distance, but is too near for the central line to
be able to discern the outlines of the object. So the edges fall within the
lines of weaker discerning power, and these are to the function of the eye
like dogs in the chase which can put up the game but cannot take it. Thus
these cannot take in the objects, but induce the central line of sight to turn
upon them, when they have put them up. Hence the objects which are seen
with these lines of sight have confused outlines.

The relative size of objects with regard to their distance from the eye (93-
98).

93.

PERSPECTIVE.

Small objects close at hand and large ones at a distance, being seen
within equal angles, will appear of the same size.

94.

PERSPECTIVE.

There is no object so large but that at a great distance from the eye it does
not appear smaller than a smaller object near.

95.

Among objects of equal size that which is most remote from the eye will
look the smallest. [Footnote: This axiom, sufficiently clear in itself, is in the
original illustrated by a very large diagram, constructed like that here
reproduced under No. 108.

The same idea is repeated in C. A. I a; I a, stated as follows: Infra le cose
d'equal grandeza quella si dimostra di minor figura che sara più distante
dall' ochio.—]

96.

Why an object is less distinct when brought near to the eye, and why with
spectacles, or without the naked eye sees badly either close or far off [as the
case may be].

97.

PERSPECTIVE.

Among objects of equal size, that which is most remote from the eye will
look the smallest.

98.

PERSPECTIVE.

No second object can be so much lower than the first as that the eye will
not see it higher than the first, if the eye is above the second.

PERSPECTIVE.

And this second object will never be so much higher than the first as that
the eye, being below them, will not see the second as lower than the first.

PERSPECTIVE.

If the eye sees a second square through the centre of a smaller one, that is
nearer, the second, larger square will appear to be surrounded by the smaller
one.

PERSPECTIVE—PROPOSITION.

Objects that are farther off can never be so large but that those in front,
though smaller, will conceal or surround them.

DEFINITION.

This proposition can be proved by experiment. For if you look through a
small hole there is nothing so large that it cannot be seen through it and the
object so seen appears surrounded and enclosed by the outline of the sides
of the hole. And if you stop it up, this small stopping will conceal the view
of the largest object.

The apparent size of objects defined by calculation (99-105)

99.

OF LINEAR PERSPECTIVE.

Linear Perspective deals with the action of the lines of sight, in proving
by measurement how much smaller is a second object than the first, and
how much the third is smaller than the second; and so on by degrees to the
end of things visible. I find by experience that if a second object is as far
beyond the first as the first is from the eye, although they are of the same
size, the second will seem half the size of the first and if the third object is
of the same size as the 2nd, and the 3rd is as far beyond the second as the
2nd from the first, it will appear of half the size of the second; and so on by
degrees, at equal distances, the next farthest will be half the size of the
former object. So long as the space does not exceed the length of 20
braccia. But, beyond 20 braccia figures of equal size will lose 2/4 and at 40
braccia they will lose 9/10, and 19/20 at 60 braccia, and so on diminishing
by degrees. This is if the picture plane is distant from you twice your own
height. If it is only as far off as your own height, there will be a great
difference between the first braccia and the second.

[Footnote: This chapter is included in DUFRESNE'S and MANZI'S
editions of the Treatise on Painting. H. LUDWIG, in his commentary, calls
this chapter "eines der wichtigsten im ganzen Tractat", but at the same time
he asserts that its substance has been so completely disfigured in the best
MS. copies that we ought not to regard Leonardo as responsible for it.
However, in the case of this chapter, the old MS. copies agree with the
original as it is reproduced above. From the chapters given later in this
edition, which were written at a subsequent date, it would appear that
Leonardo corrected himself on these points.]

100.

OF THE DIMINUTION OF OBJECTS AT VARIOUS DISTANCES.

A second object as far distant from the first as the first is from the eye
will appear half the size of the first, though they be of the same size really.

OF THE DEGREES OF DIMINUTION.

If you place the vertical plane at one braccio from the eye, the first
object, being at a distance of 4 braccia from your eye will diminish to 3/4 of
its height at that plane; and if it is 8 braccia from the eye, to 7/8; and if it is
16 braccia off, it will diminish to 15/16 of its height and so on by degrees,
as the space doubles the diminution will double.

101.

Begin from the line m f with the eye below; then go up and do the same
with the line n f, then with the eye above and close to the 2 gauges on the
ground look at m n; then as c m is to m n so will n m be to n s.

If a n goes 3 times into f b, m p will do the same into p g. Then go
backwards so far as that c d goes twice into a n and p g will be equal to g h.
And m p will go into h p as often as d c into o p.

[Footnote: The first three lines are unfortunately very obscure.]

102.

I GIVE THE DEGREES OF THE OBJECTS SEEN BY THE EYE AS THE MUSICIAN DOES
THE NOTES HEARD BY THE EAR.

Although the objects seen by the eye do, in fact, touch each other as they
recede, I will nevertheless found my rule on spaces of 20 braccia each; as a
musician does with notes, which, though they can be carried on one into the
next, he divides into degrees from note to note calling them 1st, 2nd, 3rd,
4th, 5th; and has affixed a name to each degree in raising or lowering the
voice.

103.

PERSPECTIVE.

Let f be the level and distance of the eye; and a the vertical plane, as high
as a man; let e be a man, then I say that on the plane this will be the
distance from the plane to the 2nd man.

104.

The differences in the diminution of objects of equal size in consequence
of their various remoteness from the eye will bear among themselves the
same proportions as those of the spaces between the eye and the different
objects.

Find out how much a man diminishes at a certain distance and what its
length is; and then at twice that distance and at 3 times, and so make your
general rule.

105.

The eye cannot judge where an object high up ought to descend.

106.

PERSPECTIVE.

If two similar and equal objects are placed one beyond the other at a
given distance the difference in their size will appear greater in proportion
as they are nearer to the eye that sees them. And conversely there will seem
to be less difference in their size in proportion as they are remote from the
eve.

This is proved by the proportions of their distances among themselves;
for, if the first of these two objects were as far from the eye, as the 2nd from

the first this would be called the second proportion: since, if the first is at 1
braccia from the eye and the 2nd at two braccia, two being twice as much as
one, the first object will look twice as large as the second. But if you place
the first at a hundred braccia from you and the second at a hundred and one,
you will find that the first is only so much larger than the second as 100 is
less than 101; and the converse is equally true. And again, the same thing is
proved by the 4th of this book which shows that among objects that are
equal, there is the same proportion in the diminution of the size as in the
increase in the distance from the eye of the spectator.

On natural perspective (107—109).

107.

OF EQUAL OBJECTS THE MOST REMOTE LOOK THE SMALLEST.

The practice of perspective may be divided into … parts [Footnote 4: in
… parte. The space for the number is left blank in the original.], of which
the first treats of objects seen by the eye at any distance; and it shows all
these objects just as the eye sees them diminished, without obliging a man
to stand in one place rather than another so long as the plane does not
produce a second foreshortening.

But the second practice is a combination of perspective derived partly
from art and partly from nature and the work done by its rules is in every
portion of it, influenced by natural perspective and artificial perspective. By
natural perspective I mean that the plane on which this perspective is
represented is a flat surface, and this plane, although it is parallel both in
length and height, is forced to diminish in its remoter parts more than in its
nearer ones. And this is proved by the first of what has been said above, and
its diminution is natural. But artificial perspective, that is that which is
devised by art, does the contrary; for objects equal in size increase on the

plane where it is foreshortened in proportion as the eye is more natural and
nearer to the plane, and as the part of the plane on which it is figured is
farther from the eye.

And let this plane be d e on which are seen 3 equal circles which are
beyond this plane d e, that is the circles a b c. Now you see that the eye h
sees on the vertical plane the sections of the images, largest of those that are
farthest and smallest of the nearest.

108.

Here follows what is wanting in the margin at the foot on the other side
of this page.

Natural perspective acts in a contrary way; for, at greater distances the
object seen appears smaller, and at a smaller distance the object appears
larger. But this said invention requires the spectator to stand with his eye at
a small hole and then, at that small hole, it will be very plain. But since
many (men's) eyes endeavour at the same time to see one and the same
picture produced by this artifice only one can see clearly the effect of this
perspective and all the others will see confusion. It is well therefore to
avoid such complex perspective and hold to simple perspective which does
not regard planes as foreshortened, but as much as possible in their proper
form. This simple perspective, in which the plane intersects the pyramids by
which the images are conveyed to the eye at an equal distance from the eye
is our constant experience, from the curved form of the pupil of the eye on
which the pyramids are intersected at an equal distance from the visual
virtue.

[Footnote 24: la prima di sopra i. e. the first of the three diagrams which,
in the original MS., are placed in the margin at the beginning of this
chapter.]

109.

OF A MIXTURE OF NATURAL AND ARTIFICIAL PERSPECTIVE.

This diagram distinguishes natural from artificial perspective. But before
proceeding any farther I will define what is natural and what is artificial
perspective. Natural perspective says that the more remote of a series of
objects of equal size will look the smaller, and conversely, the nearer will
look the larger and the apparent size will diminish in proportion to the
distance. But in artificial perspective when objects of unequal size are
placed at various distances, the smallest is nearer to the eye than the largest
and the greatest distance looks as though it were the least of all; and the
cause of this is the plane on which the objects are represented; and which is
at unequal distances from the eye throughout its length. And this diminution
of the plane is natural, but the perspective shown upon it is artificial since it
nowhere agrees with the true diminution of the said plane. Whence it
follows, that when the eye is somewhat removed from the [station point of
the] perspective that it has been gazing at, all the objects represented look
monstrous, and this does not occur in natural perspective, which has been
defined above. Let us say then, that the square a b c d figured above is
foreshortened being seen by the eye situated in the centre of the side which
is in front. But a mixture of artificial and natural perspective will be seen in
this tetragon called el main [Footnote 20: el main is quite legibly written in
the original; the meaning and derivation of the word are equally doubtful.],
that is to say e f g h which must appear to the eye of the spectator to be
equal to a b c d so long as the eye remains in its first position between c and
d. And this will be seen to have a good effect, because the natural
perspective of the plane will conceal the defects which would [otherwise]
seem monstrous.

III.

Six books on Light and Shade.

Linear Perspective cannot be immediately followed by either the
"prospettiva de' perdimenti" or the "prospettiva de' colori" or the aerial
perspective; since these branches of the subject presuppose a knowledge of
the principles of Light and Shade. No apology, therefore, is here needed for
placing these immediately after Linear Perspective.

We have various plans suggested by Leonardo for the arrangement of the
mass of materials treating of this subject. Among these I have given the
preference to a scheme propounded in No. III, because, in all probability,
we have here a final and definite purpose expressed. Several authors have
expressed it as their opinion that the Paris Manuscript C is a complete and
finished treatise on Light and Shade. Certainly, the Principles of Light and
Shade form by far the larger portion of this MS. which consists of two
separate parts; still, the materials are far from being finally arranged. It is
also evident that he here investigates the subject from the point of view of
the Physicist rather than from that of the Painter.

The plan of a scheme of arrangement suggested in No. III and adopted by
me has been strictly adhered to for the first four Books. For the three last,
however, few materials have come down to us; and it must be admitted that
these three Books would find a far more appropriate place in a work on
Physics than in a treatise on Painting. For this reason I have collected in
Book V all the chapters on Reflections, and in Book VI I have put together
and arranged all the sections of MS. C that belong to the book on Painting,
so far as they relate to Light and Shade, while the sections of the same MS.
which treat of the "Prospettiva de' perdimenti" have, of course, been
excluded from the series on Light and Shade.

[Footnote III: This text has already been published with some slight
variations in Dozio's pamphlet Degli scritti e disegni di Leonardo da Vinci,

Milan 1871, pp. 30—31. Dozio did not transcribe it from the original MS.
which seems to have remained unknown to him, but from an old copy (MS.
H. 227 in the Ambrosian Library).]

GENERAL INTRODUCTION.

Prolegomena.

110.

You must first explain the theory and then the practice. First you must
describe the shadows and lights on opaque objects, and then on transparent
bodies.

Scheme of the books on Light and shade.

111.

INTRODUCTION.

[Having already treated of the nature of shadows and the way in which
they are cast [Footnote 2: Avendo io tractato.—We may suppose that he
here refers to some particular MS., possibly Paris C.], I will now consider
the places on which they fall; and their curvature, obliquity, flatness or, in
short, any character I may be able to detect in them.]

Shadow is the obstruction of light. Shadows appear to me to be of
supreme importance in perspective, because, without them opaque and solid
bodies will be ill defined; that which is contained within their outlines and
their boundaries themselves will be ill-understood unless they are shown
against a background of a different tone from themselves. And therefore in
my first proposition concerning shadow I state that every opaque body is
surrounded and its whole surface enveloped in shadow and light. And on

this proposition I build up the first Book. Besides this, shadows have in
themselves various degrees of darkness, because they are caused by the
absence of a variable amount of the luminous rays; and these I call Primary
shadows because they are the first, and inseparable from the object to which
they belong. And on this I will found my second Book. From these primary
shadows there result certain shaded rays which are diffused through the
atmosphere and these vary in character according to that of the primary
shadows whence they are derived. I shall therefore call these shadows
Derived shadows because they are produced by other shadows; and the
third Book will treat of these. Again these derived shadows, where they are
intercepted by various objects, produce effects as various as the places
where they are cast and of this I will treat in the fourth Book. And since all
round the derived shadows, where the derived shadows are intercepted,
there is always a space where the light falls and by reflected dispersion is
thrown back towards its cause, it meets the original shadow and mingles
with it and modifies it somewhat in its nature; and on this I will compose
my fifth Book. Besides this, in the sixth Book I will investigate the many
and various diversities of reflections resulting from these rays which will
modify the original [shadow] by [imparting] some of the various colours
from the different objects whence these reflected rays are derived. Again,
the seventh Book will treat of the various distances that may exist between
the spot where the reflected rays fall and that where they originate, and the
various shades of colour which they will acquire in falling on opaque
bodies.

Different principles and plans of treatment (112—116).

112.

First I will treat of light falling through windows which I will call
Restricted [Light] and then I will treat of light in the open country, to which

I will give the name of diffused Light. Then I will treat of the light of
luminous bodies.

113.

OF PAINTING.

The conditions of shadow and light [as seen] by the eye are 3. Of these
the first is when the eye and the light are on the same side of the object
seen; the 2nd is when the eye is in front of the object and the light is behind
it. The 3rd is when the eye is in front of the object and the light is on one
side, in such a way as that a line drawn from the object to the eye and one
from the object to the light should form a right angle where they meet.

114.

OF PAINTING.

This is another section: that is, of the nature of a reflection (from) an
object placed between the eye and the light under various aspects.

115.

OF PAINTING.

As regards all visible objects 3 things must be considered. These are the
position of the eye which sees: that of the object seen [with regard] to the
light, and the position of the light which illuminates the object, b is the eye,
a the object seen, c the light, a is the eye, b the illuminating body, c is the
illuminated object.

116.

Let a be the light, b the eye, c the object seen by the eye and in the light.
These show, first, the eye between the light and the body; the 2nd, the light
between the eye and the body; the 3rd the body between the eye and the
light, a is the eye, b the illuminated object, c the light.

117.

OF PAINTING.

OF THE THREE KINDS OF LIGHT THAT ILLUMINATE OPAQUE BODIES.

The first kind of Light which may illuminate opaque bodies is called
Direct light—as that of the sun or any other light from a window or flame.
The second is Diffused [universal] light, such as we see in cloudy weather
or in mist and the like. The 3rd is Subdued light, that is when the sun is
entirely below the horizon, either in the evening or morning.

118.

OF LIGHT.

The lights which may illuminate opaque bodies are of 4 kinds. These are:
diffused light as that of the atmosphere, within our horizon. And Direct, as
that of the sun, or of a window or door or other opening. The third is
Reflected light; and there is a 4th which is that which passes through [semi]
transparent bodies, as linen or paper or the like, but not transparent like
glass, or crystal, or other diaphanous bodies, which produce the same effect
as though nothing intervened between the shaded object and the light that
falls upon it; and this we will discuss fully in our discourse.

Definition of the nature of shadows (119—122).

119.

WHAT LIGHT AND SHADOW ARE.

Shadow is the absence of light, merely the obstruction of the luminous
rays by an opaque body. Shadow is of the nature of darkness. Light [on an
object] is of the nature of a luminous body; one conceals and the other
reveals. They are always associated and inseparable from all objects. But
shadow is a more powerful agent than light, for it can impede and entirely
deprive bodies of their light, while light can never entirely expel shadow
from a body, that is from an opaque body.

120.

Shadow is the diminution of light by the intervention of an opaque body.
Shadow is the counterpart of the luminous rays which are cut off by an
opaque body.

This is proved because the shadow cast is the same in shape and size as
the luminous rays were which are transformed into a shadow.

121.

Shadow is the diminution alike of light and of darkness, and stands
between darkness and light.

A shadow may be infinitely dark, and also of infinite degrees of absence
of darkness.

The beginnings and ends of shadow lie between the light and darkness
and may be infinitely diminished and infinitely increased. Shadow is the
means by which bodies display their form.

The forms of bodies could not be understood in detail but for shadow.

122.

OF THE NATURE OF SHADOW.

Shadow partakes of the nature of universal matter. All such matters are
more powerful in their beginning and grow weaker towards the end, I say at
the beginning, whatever their form or condition may be and whether visible
or invisible. And it is not from small beginnings that they grow to a great
size in time; as it might be a great oak which has a feeble beginning from a
small acorn. Yet I may say that the oak is most powerful at its beginning,
that is where it springs from the earth, which is where it is largest (To
return:) Darkness, then, is the strongest degree of shadow and light is its
least. Therefore, O Painter, make your shadow darkest close to the object
that casts it, and make the end of it fading into light, seeming to have no
end.

Of the various kinds of shadows. (123-125).

123.

Darkness is absence of light. Shadow is diminution of light. Primitive
shadow is that which is inseparable from a body not in the light. Derived
shadow is that which is disengaged from a body in shadow and pervades the
air. A cast transparent shadow is that which is surrounded by an illuminated
surface. A simple shadow is one which receives no light from the luminous
body which causes it. A simple shadow begins within the line which starts
from the edge of the luminous body a b.

124.

A simple shadow is one where no light at all interferes with it.

A compound shadow is one which is somewhat illuminated by one or
more lights.

125.

WHAT IS THE DIFFERENCE BETWEEN A SHADOW THAT IS INSEPARABLE FROM A
BODY AND A CAST SHADOW?

An inseparable shadow is that which is never absent from the illuminated
body. As, for instance a ball, which so long as it is in the light always has
one side in shadow which never leaves it for any movement or change of
position in the ball. A separate shadow may be and may not be produced by
the body itself. Suppose the ball to be one braccia distant from a wall with a
light on the opposite side of it; this light will throw upon the wall exactly as
broad a shadow as is to be seen on the side of the ball that is turned towards
the wall. That portion of the cast shadow will not be visible when the light
is below the ball and the shadow is thrown up towards the sky and finding
no obstruction on its way is lost.

126.

HOW THERE ARE 2 KINDS OF LIGHT, ONE SEPARABLE FROM, AND THE OTHER
INSEPARABLE FROM BODIES.

Of the various kinds of light (126, 127).

Separate light is that which falls upon the body. Inseparable light is the
side of the body that is illuminated by that light. One is called primary, the
other derived. And, in the same way there are two kinds of shadow:—One
primary and the other derived. The primary is that which is inseparable
from the body, the derived is that which proceeds from the body conveying
to the surface of the wall the form of the body causing it.

127.

How there are 2 different kinds of light; one being called diffused, the
other restricted. The diffused is that which freely illuminates objects. The
restricted is that which being admitted through an opening or window
illuminates them on that side only.

[Footnote: At the spot marked A in the first diagram Leonardo wrote
lume costretto (restricted light). At the spot B on the second diagram he
wrote lume libero (diffused light).]

General remarks (128. 129).

128.

Light is the chaser away of darkness. Shade is the obstruction of light.
Primary light is that which falls on objects and causes light and shade. And
derived lights are those portions of a body which are illuminated by the
primary light. A primary shadow is that side of a body on which the light
cannot fall.

The general distribution of shadow and light is that sum total of the rays
thrown off by a shaded or illuminated body passing through the air without
any interference and the spot which intercepts and cuts off the distribution
of the dark and light rays.

And the eye can best distinguish the forms of objects when it is placed
between the shaded and the illuminated parts.

129.

MEMORANDUM OF THINGS I REQUIRE TO HAVE GRANTED [AS AXIOMS] IN MY
EXPLANATION OF PERSPECTIVE.

I ask to have this much granted me—to assert that every ray passing
through air of equal density throughout, travels in a straight line from its
cause to the object or place it falls upon.

FIRST BOOK ON LIGHT AND SHADE.

On the nature of light (130. 131).

130.

The reason by which we know that a light radiates from a single centre is
this: We plainly see that a large light is often much broader than some small
object which nevertheless—and although the rays [of the large light] are
much more than twice the extent [of the small body]—always has its
shadow cast on the nearest surface very visibly. Let c f be a broad light and
n be the object in front of it, casting a shadow on the plane, and let a b be
the plane. It is clear that it is not the broad light that will cast the shadow n
on the plane, but that the light has within it a centre is shown by this
experiment. The shadow falls on the plane as is shown at m o t r.

[Footnote 13: In the original MS. no explanatory text is placed after this
title-line; but a space is left for it and the text beginning at line 15 comes
next.] Why, to two [eyes] or in front of two eyes do 3 objects appear as
two?

Why, when you estimate the direction of an object with two sights the
nearer appears confused. I say that the eye projects an infinite number of
lines which mingle or join those reaching it which come to it from the
object looked at. And it is only the central and sensible line that can discern
and discriminate colours and objects; all the others are false and illusory.
And if you place 2 objects at half an arm's length apart if the nearer of the
two is close to the eye its form will remain far more confused than that of

the second; the reason is that the first is overcome by a greater number of
false lines than the second and so is rendered vague.

Light acts in the same manner, for in the effects of its lines (=rays), and
particularly in perspective, it much resembles the eye; and its central rays
are what cast the true shadow. When the object in front of it is too quickly
overcome with dim rays it will cast a broad and disproportionate shadow, ill
defined; but when the object which is to cast the shadow and cuts off the
rays near to the place where the shadow falls, then the shadow is distinct;
and the more so in proportion as the light is far off, because at a long
distance the central ray is less overcome by false rays; because the lines
from the eye and the solar and other luminous rays passing through the
atmosphere are obliged to travel in straight lines. Unless they are deflected
by a denser or rarer air, when they will be bent at some point, but so long as
the air is free from grossness or moisture they will preserve their direct
course, always carrying the image of the object that intercepts them back to
their point of origin. And if this is the eye, the intercepting object will be
seen by its colour, as well as by form and size. But if the intercepting plane
has in it some small perforation opening into a darker chamber—not darker
in colour, but by absence of light—you will see the rays enter through this
hole and transmitting to the plane beyond all the details of the object they
proceed from both as to colour and form; only every thing will be upside
down. But the size [of the image] where the lines are reconstructed will be
in proportion to the relative distance of the aperture from the plane on
which the lines fall [on one hand] and from their origin [on the other].
There they intersect and form 2 pyramids with their point meeting [a
common apex] and their bases opposite. Let a b be the point of origin of the
lines, d e the first plane, and c the aperture with the intersection of the lines;
f g is the inner plane. You will find that a falls upon the inner plane below at
g, and b which is below will go up to the spot f; it will be quite evident to
experimenters that every luminous body has in itself a core or centre, from

which and to which all the lines radiate which are sent forth by the surface
of the luminous body and reflected back to it; or which, having been thrown
out and not intercepted, are dispersed in the air.

131.

THE RAYS WHETHER SHADED OR LUMINOUS HAVE GREATER STRENGTH AND
EFFECT AT THEIR POINTS THAN AT THEIR SIDES.

Although the points of luminous pyramids may extend into shaded places
and those of pyramids of shadow into illuminated places, and though
among the luminous pyramids one may start from a broader base than
another; nevertheless, if by reason of their various length these luminous
pyramids acquire angles of equal size their light will be equal; and the case
will be the same with the pyramids of shadow; as may be seen in the
intersected pyramids a b c and d e f, which though their bases differ in size
are equal as to breadth and light.

[Footnote: 51—55: This supplementary paragraph is indicated as being a
continuation of line 45, by two small crosses.]

The difference between light and lustre (132—135).

132.

Of the difference between light and lustre; and that lustre is not included
among colours, but is saturation of whiteness, and derived from the surface
of wet bodies; light partakes of the colour of the object which reflects it (to
the eye) as gold or silver or the like.

133.

OF THE HIGHEST LIGHTS WHICH TURN AND MOVE AS THE EYE MOVES WHICH
SEES THE OBJECT.

Suppose the body to be the round object figured here and let the light be
at the point a, and let the illuminated side of the object be b c and the eye at
the point d: I say that, as lustre is every where and complete in each part, if
you stand at the point d the lustre will appear at c, and in proportion as the
eye moves from d to a, the lustre will move from c to n.

134.

OF PAINTING.

Heigh light or lustre on any object is not situated [necessarily] in the
middle of an illuminated object, but moves as and where the eye moves in
looking at it.

135.

OF LIGHT AND LUSTRE.

What is the difference between light and the lustre which is seen on the
polished surface of opaque bodies?

The lights which are produced from the polished surface of opaque
bodies will be stationary on stationary objects even if the eye on which they
strike moves. But reflected lights will, on those same objects, appear in as
many different places on the surface as different positions are taken by the
eye.

WHAT BODIES HAVE LIGHT UPON THEM WITHOUT LUSTRE?

Opaque bodies which have a hard and rough surface never display any
lustre in any portion of the side on which the light falls.

WHAT BODIES WILL DISPLAY LUSTRE BUT NOT LOOK ILLUMINATED?

Those bodies which are opaque and hard with a hard surface reflect light
[lustre] from every spot on the illuminated side which is in a position to
receive light at the same angle of incidence as they occupy with regard to
the eye; but, as the surface mirrors all the surrounding objects, the
illuminated [body] is not recognisable in these portions of the illuminated
body.

136.

The relations of luminous to illuminated bodies.

The middle of the light and shade on an object in light and shade is
opposite to the middle of the primary light. All light and shadow expresses
itself in pyramidal lines. The middle of the shadow on any object must
necessarily be opposite the middle of its light, with a direct line passing
through the centre of the body. The middle of the light will be at a, that of
the shadow at b. [Again, in bodies shown in light and shade the middle of
each must coincide with the centre of the body, and a straight line will pass
through both and through that centre.]

[Footnote: In the original MS., at the spot marked a of the first diagram
Leonardo wrote primitiuo, and at the spot marked c—primitiva (primary);
at the spot marked b he wrote dirivatiuo and at d deriuatiua (derived).]

Experiments on the relation of light and shadow within a room (137—
140).

137.

SHOWS HOW LIGHT FROM ANY SIDE CONVERGES TO ONE POINT.

Although the balls a b c are lighted from one window, nevertheless, if
you follow the lines of their shadows you will see they intersect at a point

forming the angle n.

[Footnote: The diagram belonging to this passage is slightly sketched on
Pl. XXXII; a square with three balls below it. The first three lines of the text
belonging to it are written above the sketch and the six others below it.]

138.

Every shadow cast by a body has a central line directed to a single point
produced by the intersection of luminous lines in the middle of the opening
and thickness of the window. The proposition stated above, is plainly seen
by experiment. Thus if you draw a place with a window looking
northwards, and let this be s f, you will see a line starting from the horizon
to the east, which, touching the 2 angles of the window o f, reaches d; and
from the horizon on the west another line, touching the other 2 angles r s,
and ending at c; and their intersection falls exactly in the middle of the
opening and thickness of the window. Again, you can still better confirm
this proof by placing two sticks, as shown at g h; and you will see the line
drawn from the centre of the shadow directed to the centre m and prolonged
to the horizon n f.

[Footnote: B here stands for cerchio del' orizonte tramontano on the
original diagram (the circle of the horizon towards the North); A for levante
(East) and C for ponete (West).]

139.

Every shadow with all its variations, which becomes larger as its distance
from the object is greater, has its external lines intersecting in the middle,
between the light and the object. This proposition is very evident and is
confirmed by experience. For, if a b is a window without any object
interposed, the luminous atmosphere to the right hand at a is seen to the left

at d. And the atmosphere at the left illuminates on the right at c, and the
lines intersect at the point m.

[Footnote: A here stands for levante (East), B for ponente
(West).]

140.

Every body in light and shade is situated between 2 pyramids one dark
and the other luminous, one is visible the other is not. But this only happens
when the light enters by a window. Supposing a b to be the window and r
the body in light and shade, the light to the right hand z will pass the object
to the left and go on to p; the light to the left at k will pass to the right of the
object at i and go on to m and the two lines will intersect at c and form a
pyramid. Then again a b falls on the shaded body at i g and forms a
pyramid f i g. f will be dark because the light a b can never fall there; i g c
will be illuminated because the light falls upon it.

Light and shadow with regard to the position of the eye (141—145).

141.

Every shaded body that is larger than the pupil and that interposes
between the luminous body and the eye will be seen dark.

When the eye is placed between the luminous body and the objects
illuminated by it, these objects will be seen without any shadow.

[Footnote: The diagram which in the original stands above line 1 is given
on Plate II, No 2. Then, after a blank space of about eight lines, the diagram
Plate II No 3 is placed in the original. There is no explanation of it beyond
the one line written under it.]

142.

Why the 2 lights one on each side of a body having two pyramidal sides
of an obtuse apex leave it devoid of shadow.

[Footnote: The sketch illustrating this is on Plate XLI No 1.]

143.

A body in shadow situated between the light and the eye can never
display its illuminated portion unless the eye can see the whole of the
primary light.

[Footnote: A stands for corpo (body), B for lume (light).]

144.

The eye which looks (at a spot) half way between the shadow and the
light which surrounds the body in shadow will see that the deepest shadows
on that body will meet the eye at equal angles, that is at the same angle as
that of sight.

[Footnote: In both these diagrams A stands for lume (light) B for ombra
(shadow).]

145.

OF THE DIFFERENT LIGHT AND SHADE IN VARIOUS ASPECTS AND OF OBJECTS
PLACED IN THEM.

If the sun is in the East and you look towards the West you will see every
thing in full light and totally without shadow because you see them from the
same side as the sun: and if you look towards the South or North you will
see all objects in light and shade, because you see both the side towards the

sun and the side away from it; and if you look towards the coming of the
sun all objects will show you their shaded side, because on that side the sun
cannot fall upon them.

The law of the incidence of light.

146.

The edges of a window which are illuminated by 2 lights of equal
degrees of brightness will not reflect light of equal brightness into the
chamber within.

If b is a candle and a c our hemisphere both will illuminate the edges of
the window m n, but light b will only illuminate f g and the hemisphere a
will light all of d e.

147.

OF PAINTING.

That part of a body which receives the luminous rays at equal angles will
be in a higher light than any other part of it.

And the part which the luminous rays strike between less equal angles
will be less strongly illuminated.

SECOND BOOK ON LIGHT AND SHADE.

Gradations of strength in the shadows (148. 149).

148.

THAT PORTION OF A BODY IN LIGHT AND SHADE WILL BE LEAST LUMINOUS
WHICH IS SEEN UNDER THE LEAST AMOUNT OF LIGHT.

That part of the object which is marked m is in the highest light because
it faces the window a d by the line a f; n is in the second grade because the
light b d strikes it by the line b e; o is in the third grade, as the light falls on
it from c d by the line c h; p is the lowest light but one as c d falls on it by
the line d v; q is the deepest shadow for no light falls on it from any part of
the window.

In proportion as c d goes into a d so will n r s be darker than m, and all
the rest is space without shadow.

[Footnote: The diagram belonging to this chapter is No. 1 on Plate III.
The letters a b e d and r are not reproduced in facsimile of the original, but
have been replaced by ordinary type in the margin. 5-12. The original text
of these lines is reproduced within the diagram.—Compare No 275.]

149.

The light which falls on a shaded body at the acutest angle receives the
highest light, and the darkest portion is that which receives it at an obtuse
angle and both the light and the shadow form pyramids. The angle c
receives the highest grade of light because it is directly in front of the
window a b and the whole horizon of the sky m x. The angle a differs but
little from c because the angles which divide it are not so unequal as those
below, and only that portion of the horizon is intercepted which lies
between y and x. Although it gains as much on the other side its line is
nevertheless not very strong because one angle is smaller than its fellow.
The angles e i will have less light because they do not see much of the light
m s and the light v x and their angles are very unequal. Yhe angle k and the
angle f are each placed between very unequal angles and therefore have but
little light, because at k it has only the light p t, and at f only t q; o g is the
lowest grade of light because this part has no light at all from the sky; and
thence come the lines which will reconstruct a pyramid that is the

counterpart of the pyramid c; and this pyramid l is in the first grade of
shadow; for this too is placed between equal angles directly opposite to
each other on either side of a straight line which passes through the centre
of the body and goes to the centre of the light. The several luminous images
cast within the frame of the window at the points a and b make a light
which surrounds the derived shadow cast by the solid body at the points 4
and 6. The shaded images increase from o g and end at 7 and 8.

[Footnote: The diagram belonging to this chapter is No. 2 on Plate III. In
the original it is placed between lines 3 and 4, and in the reproduction these
are shown in part. The semi circle above is marked orizonte (horizon). The
number 6 at the left hand side, outside the facsimile, is in the place of a
figure which has become indistinct in the original.]

On the intensity of shadows as dependent on the distance from the light
(150-152).

150.

The smaller the light that falls upon an object the more shadow it will
display. And the light will illuminate a smaller portion of the object in
proportion as it is nearer to it; and conversely, a larger extent of it in
proportion as it is farther off.

A light which is smaller than the object on which it falls will light up a
smaller extent of it in proportion as it is nearer to it, and the converse, as it
is farther from it. But when the light is larger than the object illuminated it
will light a larger extent of the object in proportion as it is nearer and the
converse when they are farther apart.

151.

That portion of an illuminated object which is nearest to the source of
light will be the most strongly illuminated.

152.

That portion of the primary shadow will be least dark which is farthest
from the edges.

The derived shadow will be darker than the primary shadow where it is
contiguous with it.

On the proportion of light and shade (153-157).

153.

That portion of an opaque body will be more in shade or more in light,
which is nearer to the dark body, by which it is shaded, or to the light that
illuminates it.

Objects seen in light and shade show in greater relief than those which
are wholly in light or in shadow.

154.

OF PERSPECTIVE.

The shaded and illuminated sides of opaque objects will display the same
proportion of light and darkness as their objects [Footnote 6: The meaning
of obbietti (objects) is explained in no 153, lines 1-4.—Between the title-
line and the next there is, in the original, a small diagram representing a
circle described round a square.].

155.

OF PAINTING.

The outlines and form of any part of a body in light and shade are
indistinct in the shadows and in the high lights; but in the portions between
the light and the shadows they are highly conspicuous.

156.

OF PAINTING.

Among objects in various degrees of shade, when the light proceeds from
a single source, there will be the same proportion in their shadows as in the
natural diminution of the light and the same must be understood of the
degrees of light.

157.

A single and distinct luminous body causes stronger relief in the object
than a diffused light; as may be seen by comparing one side of a landscape
illuminated by the sun, and one overshadowed by clouds, and so
illuminated only by the diffused light of the atmosphere.

THIRD BOOK ON LIGHT AND SHADE.

Definition of derived shadow (158. 159).

158.

Derived shadow cannot exist without primary shadow. This is proved by
the first of this which says: Darkness is the total absence of light, and
shadow is an alleviation of darkness and of light, and it is more or less dark
or light in proportion as the darkness is modified by the light.

159.

Shadow is diminution of light.

Darkness is absence of light.

Shadow is divided into two kinds, of which the first is called primary
shadow, the second is derived shadow. The primary shadow is always the
basis of the derived shadow.

The edges of the derived shadow are straight lines.

[Footnote: The theory of the ombra dirivativa_—a technical expression
for which there is no precise English equivalent is elaborately treated by
Leonardo. But both text and diagrams (as Pl. IV, 1-3 and Pl. V) must at
once convince the student that the distinction he makes between ombra
primitiva and ombra dirivativa is not merely justifiable but scientific.
Ombra dirivativa is by no means a mere abstract idea. This is easily proved
by repeating the experiment made by Leonardo, and by filling with smoke
the room in which the existence of the ombra dirivativa is investigated,
when the shadow becomes visible. Nor is it difficult to perceive how much
of Leonardo's teaching depended on this theory. The recognised, but
extremely complicated science of cast shadows—percussione dell' ombre
dirivative as Leonardo calls them—is thus rendered more intelligible if not
actually simpler, and we must assume this theory as our chief guide through
the investigations which follow.]

The darkness of the derived shadow diminishes in proportion as it is
remote from the primary shadow.

Different sorts of derived shadows (160-162).

160.

SHADOW AND LIGHT.

The forms of shadows are three: inasmuch as if the solid body which
casts the shadow is equal (in size) to the light, the shadow resembles a
column without any termination (in length). If the body is larger than the
light the shadow resembles a truncated and inverted pyramid, and its length
has also no defined termination. But if the body is smaller than the light, the
shadow will resemble a pyramid and come to an end, as is seen in eclipses
of the moon.

161.

OF SIMPLE DERIVED SHADOWS.

The simple derived shadow is of two kinds: one kind which has its length
defined, and two kinds which are undefined; and the defined shadow is
pyramidal. Of the two undefined, one is a column and the other spreads out;
and all three have rectilinear outlines. But the converging, that is the
pyramidal, shadow proceeds from a body that is smaller than the light, and
the columnar from a body equal in size to the light, and the spreading
shadow from a body larger than the light; &c.

OF COMPOUND DERIVED SHADOWS.

Compound derived shadows are of two kinds; that is columnar and
spreading.

162.

OF SHADOW.

Derived shadows are of three kinds of which one is spreading, the second
columnar, the third converging to the point where the two sides meet and
intersect, and beyond this intersection the sides are infinitely prolonged or
straight lines. And if you say, this shadow must terminate at the angle where

the sides meet and extend no farther, I deny this, because above in the first
on shadow I have proved: that a thing is completely terminated when no
portion of it goes beyond its terminating lines. Now here, in this shadow,
we see the converse of this, in as much as where this derived shadow
originates we obviously have the figures of two pyramids of shadow which
meet at their angles. Hence, if, as [my] opponent says, the first pyramid of
shadow terminates the derivative shadow at the angle whence it starts, then
the second pyramid of shadow—so says the adversary—must be caused by
the angle and not from the body in shadow; and this is disproved with the
help of the 2nd of this which says: Shadow is a condition produced by a
body casting a shadow, and interposed between this shadow and the
luminous body. By this it is made clear that the shadow is not produced by
the angle of the derived shadow but only by the body casting the shadow;
&c. If a spherical solid body is illuminated by a light of elongated form the
shadow produced by the longest portion of this light will have less defined
outlines than that which is produced by the breadth of the same light. And
this is proved by what was said before, which is: That a shadow will have
less defined outlines in proportion as the light which causes it is larger, and
conversely, the outlines are clearer in proportion as it is smaller.

[Footnote: The two diagrams to this chapter are on Plate IV, No. 1.]

On the relation of derived and primary shadow (163-165).

163.

The derived shadow can never resemble the body from which it proceeds
unless the light is of the same form and size as the body causing the
shadow.

The derived shadow cannot be of the same form as the primary shadow
unless it is intercepted by a plane parallel to it.

164.

HOW A CAST SHADOW CAN NEVER BE OF THE SAME SIZE AS THE BODY THAT
CASTS IT.

If the rays of light proceed, as experience shows, from a single point and
are diffused in a sphere round this point, radiating and dispersed through the
air, the farther they spread the wider they must spread; and an object placed
between the light and a wall is always imaged larger in its shadow, because
the rays that strike it [Footnote: 7. The following lines are wanting to
complete the logical connection.] would, by the time they have reached the
wall, have become larger.

165.

Any shadow cast by a body in light and shade is of the same nature and
character as that which is inseparable from the body. The centre of the
length of a shadow always corresponds to that of the luminous body
[Footnote 6: This second statement of the same idea as in the former
sentence, but in different words, does not, in the original, come next to the
foregoing; sections 172 and 127 are placed between them.]. It is inevitable
that every shadow must have its centre in a line with the centre of the light.

On the shape of derived shadows (166-174).

166.

OF THE PYRAMIDAL SHADOW.

The pyramidal shadow produced by a columnar body will be narrower
than the body itself in proportion as the simple derived shadow is
intersected farther from the body which casts it.

[Footnote 166: Compare the first diagram to No. 161. If we here
conceive of the outlines of the pyramid of shadow on the ground as
prolonged beyond its apex this gives rise to a second pyramid; this is what
is spoken of at the beginning of No. 166.]

167.

The cast shadow will be longest when the light is lowest.

The cast shadow will be shortest when the light is highest.

168.

Both the primary and derived shadow will be larger when caused by the
light of a candle than by diffused light. The difference between the larger
and smaller shadows will be in inverse proportion to the larger and smaller
lights causing them.

[Footnote: In the diagrams A stands for celo (sky), B for cadela (candle).]

169.

ALL BODIES, IN PROPORTION AS THEY ARE NEARER TO, OR FARTHER FROM THE
SOURCE OF LIGHT, WILL PRODUCE LONGER OR SHORTER DERIVED SHADOWS.

Among bodies of equal size, that one which is illuminated by the largest
light will have the shortest shadow. Experiment confirms this proposition.
Thus the body m n is surrounded by a larger amount of light than the body p
q, as is shown above. Let us say that v c a b d x is the sky, the source of
light, and that s t is a window by which the luminous rays enter, and so m n
and p q are bodies in light and shade as exposed to this light; m n will have
a small derived shadow, because its original shadow will be small; and the
derivative light will be large, again, because the original light c d will be

large and p q will have more derived shadow because its original shadow
will be larger, and its derived light will be smaller than that of the body m n
because that portion of the hemisphere a b which illuminates it is smaller
than the hemisphere c d which illuminates the body m n.

[Footnote: The diagram, given on Pl. IV, No. 2, stands in the original
between lines 2 and 7, while the text of lines 3 to 6 is written on its left side.
In the reproduction of this diagram the letter v at the outer right-hand end
has been omitted.]

170.

The shadow m bears the same proportion to the shadow n as the line b c
to the line f c.

171.

OF PAINTING.

Of different shadows of equal strength that which is nearest the eye will
seem the least strong.

Why is the shadow e a b in the first grade of strength, b c in the second; c
d in the third? The reason is that as from e a b the sky is nowhere visible, it
gets no light whatever from the sky, and so has no direct [primary] light. b c
faces the portion of the sky f g and is illuminated by it. c d faces the sky at h
k. c d, being exposed to a larger extent of sky than b c, it is reasonable that
it should be more lighted. And thus, up to a certain distance, the wall a d
will grow lighter for the reasons here given, until the darkness of the room
overpowers the light from the window.

172.

When the light of the atmosphere is restricted [by an opening] and
illuminates bodies which cast shadows, these bodies being equally distant
from the centre of the window, that which is most obliquely placed will cast
the largest shadow beyond it.

173.

These bodies standing apart in a room lighted by a single window will
have derivative shadows more or less short according as they are more or
less opposite to the window. Among the shadows cast by bodies of equal
mass but at unequal distances from the opening by which they are
illuminated, that shadow will be the longest of the body which is least in the
light. And in proportion as one body is better illuminated than another its
shadow will be shorter than another. The proportion n m and e v k bear to r t
and v x corresponds with that of the shadow x to 4 and y.

The reason why those bodies which are placed most in front of the
middle of the window throw shorter shadows than those obliquely situated
is:—That the window appears in its proper form and to the obliquely placed
ones it appears foreshortened; to those in the middle, the window shows its
full size, to the oblique ones it appears smaller; the one in the middle faces
the whole hemisphere that is e f and those on the side have only a strip; that
is q r faces a b; and m n faces c d; the body in the middle having a larger
quantity of light than those at the sides is lighted from a point much below
its centre, and thus the shadow is shorter. And the pyramid g 4 goes into l y
exactly as often as a b goes into e f. The axis of every derivative shadow
passes through 6 1/2 [Footnote 31: passa per 6 1/2 (passes through 6 1/2).
The meaning of these words is probably this: Each of the three axes of the
derived shadow intersects the centre (mezzo) of the primary shadow (ombra
originale) and, by prolongation upwards crosses six lines.

This is self evident only in the middle diagram; but it is equally true of
the side figures if we conceive of the lines 4 f, x n v m, y l k v, and 4 e, as
prolonged beyond the semicircle of the horizon.] and is in a straight line
with the centre of the primary shadow, with the centre of the body casting it
and of the derivative light and with the centre of the window and, finally,
with the centre of that portion of the source of light which is the celestial
hemisphere, y h is the centre of the derived shade, l h of the primary
shadow, l of the body throwing it, l k of the derived light, v is the centre of
the window, e is the final centre of the original light afforded by that portion
of the hemisphere of the sky which illuminates the solid body.

[Footnote: Compare the diagram on Pl. IV, No. 3. In the original this
drawing is placed between lines 3 and 22; the rest, from line 4 to line 21, is
written on the left hand margin.]

174.

THE FARTHER THE DERIVED SHADOW IS PROLONGED THE LIGHTER IT
BECOMES.

You will find that the proportion of the diameter of the derived shadow to
that of the primary shadow will be the same as that between the darkness of
the primary shadow and that of the derived shadow.

[Footnote 6: Compare No. 177.] Let a b be the diameter of the primary
shadow and c d that of the derived shadow, I say that a b going, as you see,
three times into d c, the shadow d c will be three times as light as the
shadow a b. [Footnote 8: Compare No. 177.]

If the size of the illuminating body is larger than that of the illuminated
body an intersection of shadow will occur, beyond which the shadows will

run off in two opposite directions as if they were caused by two separate
lights.

On the relative intensity of derived shadows (175-179).

175.

ON PAINTING.

The derived shadow is stronger in proportion as it is nearer to its place of
origin.

176.

HOW SHADOWS FADE AWAY AT LONG DISTANCES.

Shadows fade and are lost at long distances because the larger quantity of
illuminated air which lies between the eye and the object seen tints the
shadow with its own colour.

177.

a b will be darker than c d in proportion as c d is broader than a b.

[Footnote: In the original MS. the word lume (light) is written at the apex
of the pyramid.]

178.

It can be proved why the shadow o p c h is darker in proportion as it is
nearer to the line p h and is lighter in proportion as it is nearer to the line o
c. Let the light a b, be a window, and let the dark wall in which this window
is, be b s, that is, one of the sides of the wall.

Then we may say that the line p h is darker than any other part of the
space o p c h, because this line faces the whole surface in shadow of
[Footnote: In the original the diagram is placed between lines 27 and 28.]
the wall b s. The line o c is lighter than the other part of this space o p c h,
because this line faces the luminous space a b.

Where the shadow is larger, or smaller, or equal the body which casts it.

[First of the character of divided lights. [Footnote 14: lumi divisi. The
text here breaks off abruptly.]

OF THE COMPOUND SHADOW F, R, C, H CAUSED BY A SINGLE LIGHT.

The shadow f r c h is under such conditions as that where it is farthest
from its inner side it loses depth in proportion. To prove this:

Let d a, be the light and f n the solid body, and let a e be one of the side
walls of the window that is d a. Then I say—according to the 2nd
[proposition]: that the surface of any body is affected by the tone of the
objects surrounding it,—that the side r c, which faces the dark wall a e must
participate of its darkness and, in the same way that the outer surface which
faces the light d a participates of the light; thus we get the outlines of the
extremes on each side of the centre included between them.]

This is divided into four parts. The first the extremes, which include the
compound shadow, secondly the compound shadow between these
extremes.

179.

THE ACTION OF THE LIGHT AS FROM ITS CENTRE.

If it were the whole of the light that caused the shadows beyond the
bodies placed in front of it, it would follow that any body much smaller
than the light would cast a pyramidal shadow; but experience not showing
this, it must be the centre of the light that produces this effect.

[Footnote: The diagram belonging to this passage is between lines 4 and
5 in the original. Comp. the reproduction Pl. IV, No. 4. The text and
drawing of this chapter have already been published with tolerable
accuracy. See M. JORDAN: "Das Malerbuch des Leonardo da Vinci".
Leipzig 1873, P. 90.]

PROOF.

Let a b be the width of the light from a window, which falls on a stick set
up at one foot from a c [Footnote 6: bastone (stick). The diagram has a
sphere in place of a stick.]. And let a d be the space where all the light from
the window is visible. At c e that part of the window which is between l b
cannot be seen. In the same way a m cannot be seen from d f and therefore
in these two portions the light begins to fail.

Shadow as produced by two lights of different size (180. 181).

180.

A body in light and shade placed between two equal lights side by side
will cast shadows in proportion to the [amount of] light. And the shadows
will be one darker than the other in proportion as one light is nearer to the
said body than the other on the opposite side.

A body placed at an equal distance between two lights will cast two
shadows, one deeper than the other in proportion, as the light which causes
it is brighter than the other.

[Footnote: In the MS. the larger diagram is placed above the first line; the
smaller one between l. 4 & 5.]

181.

A light which is smaller than the body it illuminates produces shadows of
which the outlines end within [the surface of] the body, and not much
compound shadow; and falls on less than half of it. A light which is larger
than the body it illuminates, falls on more than half of it, and produces
much compound shadow.

The effect of light at different distances.

182.

OF THE SHADOW CAST BY A BODY PLACED BETWEEN 2 EQUAL LIGHTS.

A body placed between 2 equal lights will cast 2 shadows of itself in the
direction of the lines of the 2 lights; and if you move this body placing it
nearer to one of the lights the shadow cast towards the nearer light will be
less deep than that which falls towards the more distant one.

Further complications in the derived shadows (183-187).

183.

The greatest depth of shadow is in the simple derived shadow because it
is not lighted by either of the two lights a b, c d.

The next less deep shadow is the derived shadow e f n; and in this the
shadow is less by half, because it is illuminated by a single light, that is c d.

This is uniform in natural tone because it is lighted throughout by one
only of the two luminous bodies [10]. But it varies with the conditions of

shadow, inasmuch as the farther it is away from the light the less it is
illuminated by it [13].

The third degree of depth is the middle shadow [Footnote 15: We gather
from what follows that q g r here means ombra media (the middle
shadow).]. But this is not uniform in natural tone; because the nearer it gets
to the simple derived shadow the deeper it is [Footnote 18: Compare lines
10-13], and it is the uniformly gradual diminution by increase of distance
which is what modifies it [Footnote 20: See Footnote 18]: that is to say the
depth of a shadow increases in proportion to the distance from the two
lights.

The fourth is the shadow k r s and this is all the darker in natural tone in
proportion as it is nearer to k s, because it gets less of the light a o, but by
the accident [of distance] it is rendered less deep, because it is nearer to the
light c d, and thus is always exposed to both lights.

The fifth is less deep in shadow than either of the others because it is
always entirely exposed to one of the lights and to the whole or part of the
other; and it is less deep in proportion as it is nearer to the two lights, and in
proportion as it is turned towards the outer side x t; because it is more
exposed to the second light a b.

[Footnote: The diagram to this section is given on Pl. V. To the left is the
facsimile of the beginning of the text belonging to it.]

184.

OF SIMPLE SHADOWS.

Why, at the intersections a, b of the two compound shadows e f and m e,
is a simple shadow pfoduced as at e h and m g, while no such simple

shadow is produced at the other two intersections c d made by the very
same compound shadows?

ANSWER.

Compound shadow are a mixture of light and shade and simple shadows
are simply darkness. Hence, of the two lights n and o, one falls on the
compound shadow from one side, and the other on the compound shadow
from the other side, but where they intersect no light falls, as at a b;
therefore it is a simple shadow. Where there is a compound shadow one
light or the other falls; and here a difficulty arises for my adversary since he
says that, where the compound shadows intersect, both the lights which
produce the shadows must of necessity fall and therefore these shadows
ought to be neutralised; inasmuch as the two lights do not fall there, we say
that the shadow is a simple one and where only one of the two lights falls,
we say the shadow is compound, and where both the lights fall the shadow
is neutralised; for where both lights fall, no shadow of any kind is produced,
but only a light background limiting the shadow. Here I shall say that what
my adversary said was true: but he only mentions such truths as are in his
favour; and if we go on to the rest he must conclude that my proposition is
true. And that is: That if both lights fell on the point of intersection, the
shadows would be neutralised. This I confess to be true if [neither of] the
two shadows fell in the same spot; because, where a shadow and a light fall,
a compound shadow is produced, and wherever two shadows or two equal
lights fall, the shadow cannot vary in any part of it, the shadows and the
lights both being equal. And this is proved in the eighth [proposition] on
proportion where it is said that if a given quantity has a single unit of force
and resistance, a double quantity will have double force and double
resistance.

DEFINITION.

The intersection n is produced by the shadows caused by the light b,
because this light b produces the shadow x b, and the shadow s b, but the
intersection m is produced by the light a which causes the shadow s a, and
the shadow x a.

But if you uncover both the lights a b, then you get the two shadows n m
both at once, and besides these, two other, simple shadows are produced at r
o where neither of the two lights falls at all. The grades of depth in
compound shadows are fewer in proportion as the lights falling on, and
crossing them are less numerous.

186.

Why the intersections at n being composed of two compound derived
shadows, forms a compound shadow and not a simple one, as happens with
other intersections of compound shadows. This occurs, according to the 2nd
[diagram] of this [prop.] which says:—The intersection of derived shadows
when produced by the intersection of columnar shadows caused by a single
light does not produce a simple shadow. And this is the corollary of the 1st
[prop.] which says:—The intersection of simple derived shadows never
results in a deeper shadow, because the deepest shadows all added together
cannot be darker than one by itself. Since, if many deepest shadows
increased in depth by their duplication, they could not be called the deepest
shadows, but only part-shadows. But if such intersections are illuminated
by a second light placed between the eye and the intersecting bodies, then
those shadows would become compound shadows and be uniformly dark
just as much at the intersection as throughout the rest. In the 1st and 2nd
above, the intersections i k will not be doubled in depth as it is doubled in
quantity. But in this 3rd, at the intersections g n they will be double in depth
and in quantity.

187.

HOW AND WHEN THE SURROUNDINGS IN SHADOW MINGLE THEIR DERIVED
SHADOW WITH THE LIGHT DERIVED FROM THE LUMINOUS BODY.

The derived shadow of the dark walls on each side of the bright light of
the window are what mingle their various degrees of shade with the light
derived from the window; and these various depths of shade modify every
portion of the light, except where it is strongest, at c. To prove this let d a be
the primary shadow which is turned towards the point e, and darkens it by
its derived shadow; as may be seen by the triangle a e d, in which the angle
e faces the darkened base d a e; the point v faces the dark shadow a s which
is part of a d, and as the whole is greater than a part, e which faces the
whole base [of the triangle], will be in deeper shadow than v which only
faces part of it. In consequence of the conclusion [shown] in the above
diagram, t will be less darkened than v, because the base of the t is part of
the base of the v; and in the same way it follows that p is less in shadow
than t, because the base of the p is part of the base of the t. And c is the
terminal point of the derived shadow and the chief beginning of the highest
light.

[Footnote: The diagram on Pl. IV, No. 5 belongs to this passage; but it
must be noted that the text explains only the figure on the right-hand side.]

FOURTH BOOK ON LIGHT AND SHADE.

On the shape of the cast shadows (188-191).

188.

The form of the shadow cast by any body of uniform density can never
be the same as that of the body producing it. [Footnote: Comp. the drawing
on PI. XXVIII, No. 5.]

189.

No cast shadow can produce the true image of the body which casts it on
a vertical plane unless the centre of the light is equally distant from all the
edges of that body.

190.

If a window a b admits the sunlight into a room, the sunlight will
magnify the size of the window and diminish the shadow of a man in such a
way as that when the man makes that dim shadow of himself, approach to
that which defines the real size of the window, he will see the shadows
where they come into contact, dim and confused from the strength of the
light, shutting off and not allowing the solar rays to pass; the effect of the
shadow of the man cast by this contact will be exactly that figured above.

[Footnote: It is scarcely possible to render the meaning of this sentence
with strict accuracy; mainly because the grammatical construction is
defective in the most important part—line 4. In the very slight original
sketch the shadow touches the upper arch of the window and the correction,
here given is perhaps not justified.]

191.

A shadow is never seen as of uniform depth on the surface which
intercepts it unless every portion of that surface is equidistant from the
luminous body. This is proved by the 7th which says:—The shadow will
appear lighter or stronger as it is surrounded by a darker or a lighter
background. And by the 8th of this:—The background will be in parts
darker or lighter, in proportion as it is farther from or nearer to the luminous
body. And:—Of various spots equally distant from the luminous body those
will always be in the highest light on which the rays fall at the smallest
angles: The outline of the shadow as it falls on inequalities in the surface

will be seen with all the contours similar to those of the body that casts it, if
the eye is placed just where the centre of the light was.

The shadow will look darkest where it is farthest from the body that casts
it. The shadow c d, cast by the body in shadow a b which is equally distant
in all parts, is not of equal depth because it is seen on a back ground of
varying brightness. [Footnote: Compare the three diagrams on Pl. VI, no 1
which, in the original accompany this section.]

On the outlines of cast shadows (192-195).

192.

The edges of a derived shadow will be most distinct where it is cast
nearest to the primary shadow.

193.

As the derived shadow gets more distant from the primary shadow, the
more the cast shadow differs from the primary shadow.

194.

OF SHADOWS WHICH NEVER COME TO AN END.

The greater the difference between a light and the body lighted by it, the
light being the larger, the more vague will be the outlines of the shadow of
that object.

The derived shadow will be most confused towards the edges of its
interception by a plane, where it is remotest from the body casting it.

195.

What is the cause which makes the outlines of the shadow vague and
confused?

Whether it is possible to give clear and definite outlines to the edges of
shadows.

On the relative size of shadows (196. 197).

196.

THE BODY WHICH IS NEAREST TO THE LIGHT CASTS THE LARGEST SHADOW,
AND WHY?

If an object placed in front of a single light is very close to it you will see
that it casts a very large shadow on the opposite wall, and the farther you
remove the object from the light the smaller will the image of the shadow
become.

WHY A SHADOW LARGER THAN THE BODY THAT PRODUCES IT BECOMES OUT OF
PROPORTION.

The disproportion of a shadow which is larger than the body producing it,
results from the light being smaller than the body, so that it cannot be at an
equal distance from the edges of the body [Footnote 11: H. LUDWIG in his
edition of the old copies, in the Vatican library—in which this chapter is
included under Nos. 612, 613 and 614 alters this passage as follows: quella
parte ch'e piu propinqua piu cresce che le distanti, although the Vatican
copy agrees with the original MS. in having distante in the former and
propinque in the latter place. This supposed amendment seems to me to
invert the facts. Supposing for instance, that on Pl. XXXI No. 3. f is the spot
where the light is that illuminates the figure there represented, and that the
line behind the figure represents a wall on which the shadow of the figure is
thrown. It is evident, that in that case the nearest portion, in this case the

under part of the thigh, is very little magnified in the shadow, and the
remoter parts, for instance the head, are more magnified.]; and the portions
which are most remote are made larger than the nearer portions for this
reason [Footnote 12: See Footnote 11].

WHY A SHADOW WHICH IS LARGER THAN THE BODY CAUSING IT HAS ILL-
DEFINED OUTLINES.

The atmosphere which surrounds a light is almost like light itself for
brightness and colour; but the farther off it is the more it loses this
resemblance. An object which casts a large shadow and is near to the light,
is illuminated both by that light by the luminous atmosphere; hence this
diffused light gives the shadow ill-defined edges.

197.

A luminous body which is long and narrow in shape gives more confused
outlines to the derived shadow than a spherical light, and this contradicts
the proposition next following: A shadow will have its outlines more clearly
defined in proportion as it is nearer to the primary shadow or, I should say,
the body casting the shadow; [Footnote 14: The lettering refers to the lower
diagram, Pl. XLI, No. 5.] the cause of this is the elongated form of the
luminous body a c, &c. [Footnote 16: See Footnote 14].

Effects on cast shadows by the tone of the back ground.

198.

OF MODIFIED SHADOWS.

Modified shadows are those which are cast on light walls or other
illuminated objects.

A shadow looks darkest against a light background. The outlines of a
derived shadow will be clearer as they are nearer to the primary shadow. A
derived shadow will be most defined in shape where it is intercepted, where
the plane intercepts it at the most equal angle.

Those parts of a shadow will appear darkest which have darker objects
opposite to them. And they will appear less dark when they face lighter
objects. And the larger the light object opposite, the more the shadow will
be lightened.

And the larger the surface of the dark object the more it will darken the
derived shadow where it is intercepted.

A disputed proposition.

199.

OF THE OPINION OF SOME THAT A TRIANGLE CASTS NO SHADOW ON A PLANE
SURFACE.

Certain mathematicians have maintained that a triangle, of which the
base is turned to the light, casts no shadow on a plane; and this they prove
by saying [5] that no spherical body smaller than the light can reach the
middle with the shadow. The lines of radiant light are straight lines [6];
therefore, suppose the light to be g h and the triangle l m n, and let the plane
be i k; they say the light g falls on the side of the triangle l n, and the
portion of the plane i q. Thus again h like g falls on the side l m, and then on
m n and the plane p k; and if the whole plane thus faces the lights g h, it is
evident that the triangle has no shadow; and that which has no shadow can
cast none. This, in this case appears credible. But if the triangle n p g were
not illuminated by the two lights g and h, but by i p and g and k neither side
is lighted by more than one single light: that is i p is invisible to h g and k

will never be lighted by g; hence p q will be twice as light as the two visible
portions that are in shadow.

[Footnote: 5—6. This passage is so obscure that it would be rash to offer
an explanation. Several words seem to have been omitted.]

On the relative depth of cast shadows (200-202).

200.

A spot is most in the shade when a large number of darkened rays fall
upon it. The spot which receives the rays at the widest angle and by
darkened rays will be most in the dark; a will be twice as dark as b, because
it originates from twice as large a base at an equal distance. A spot is most
illuminated when a large number of luminous rays fall upon it. d is the
beginning of the shadow d f, and tinges c but a little; d e is half of the
shadow d f and gives a deeper tone where it is cast at b than at f. And the
whole shaded space e gives its tone to the spot a. [Footnote: The diagram
here referred to is on Pl. XLI, No. 2.]

201.

A n will be darker than c r in proportion to the number of times that a b
goes into c d.

202.

The shadow cast by an object on a plane will be smaller in proportion as
that object is lighted by feebler rays. Let d e be the object and d c the plane
surface; the number of times that d e will go into f g gives the proportion of
light at f h to d c. The ray of light will be weaker in proportion to its
distance from the hole through which it falls.

FIFTH BOOK ON LIGHT AND SHADE.

Principles of reflection (203. 204).

203.

OF THE WAY IN WHICH THE SHADOWS CAST BY OBJECTS OUGHT TO BE DEFINED.

If the object is the mountain here figured, and the light is at the point a, I
say that from b d and also from c f there will be no light but from reflected
rays. And this results from the fact that rays of light can only act in straight
lines; and the same is the case with the secondary or reflected rays.

204.

The edges of the derived shadow are defined by the hues of the
illuminated objects surrounding the luminous body which produces the
shadow.

On reverberation.

205.

OF REVERBERATION.

Reverberation is caused by bodies of a bright nature with a flat and semi
opaque surface which, when the light strikes upon them, throw it back
again, like the rebound of a ball, to the former object.

WHERE THERE CAN BE NO REFLECTED LIGHTS.

All dense bodies have their surfaces occupied by various degrees of light
and shade. The lights are of two kinds, one called original, the other
borrowed. Original light is that which is inherent in the flame of fire or the

light of the sun or of the atmosphere. Borrowed light will be reflected light;
but to return to the promised definition: I say that this luminous
reverberation is not produced by those portions of a body which are turned
towards darkened objects, such as shaded spots, fields with grass of various
height, woods whether green or bare; in which, though that side of each
branch which is turned towards the original light has a share of that light,
nevertheless the shadows cast by each branch separately are so numerous,
as well as those cast by one branch on the others, that finally so much
shadow is the result that the light counts for nothing. Hence objects of this
kind cannot throw any reflected light on opposite objects.

Reflection on water (206. 207).

206.

PERSPECTIVE.

The shadow or object mirrored in water in motion, that is to say in small
wavelets, will always be larger than the external object producing it.

207.

It is impossible that an object mirrored on water should correspond in
form to the object mirrored, since the centre of the eye is above the surface
of the water.

This is made plain in the figure here given, which demonstrates that the
eye sees the surface a b, and cannot see it at l f, and at r t; it sees the surface
of the image at r t, and does not see it in the real object c d. Hence it is
impossible to see it, as has been said above unless the eye itself is situated
on the surface of the water as is shown below [13].

[Footnote: A stands for ochio [eye], B for aria [air], C for acqua [water],
D for cateto [cathetus].—In the original MS. the second diagram is placed
below line 13.]

Experiments with the mirror (208-210).

208.

THE MIRROR.

If the illuminated object is of the same size as the luminous body and as
that in which the light is reflected, the amount of the reflected light will
bear the same proportion to the intermediate light as this second light will
bear to the first, if both bodies are smooth and white.

209.

Describe how it is that no object has its limitation in the mirror but in the
eye which sees it in the mirror. For if you look at your face in the mirror, the
part resembles the whole in as much as the part is everywhere in the mirror,
and the whole is in every part of the same mirror; and the same is true of the
whole image of any object placed opposite to this mirror, &c.

210.

No man can see the image of another man in a mirror in its proper place
with regard to the objects; because every object falls on [the surface of] the
mirror at equal angles. And if the one man, who sees the other in the mirror,
is not in a direct line with the image he will not see it in the place where it
really falls; and if he gets into the line, he covers the other man and puts
himself in the place occupied by his image. Let n o be the mirror, b the eye
of your friend and d your own eye. Your friend's eye will appear to you at a,
and to him it will seem that yours is at c, and the intersection of the visual

rays will occur at m, so that either of you touching m will touch the eye of
the other man which shall be open. And if you touch the eye of the other
man in the mirror it will seem to him that you are touching your own.

Appendix:—On shadows in movement (211. 212).

211.

OF THE SHADOW AND ITS MOTION.

When two bodies casting shadows, and one in front of the other, are
between a window and the wall with some space between them, the shadow
of the body which is nearest to the plane of the wall will move if the body
nearest to the window is put in transverse motion across the window. To
prove this let a and b be two bodies placed between the window n m and the
plane surface o p with sufficient space between them as shown by the space
a b. I say that if the body a is moved towards s the shadow of the body b
which is at c will move towards d.

212.

OF THE MOTION OF SHADOWS.

The motion of a shadow is always more rapid than that of the body which
produces it if the light is stationary. To prove this let a be the luminous
body, and b the body casting the shadow, and d the shadow. Then I say that
in the time while the solid body moves from b to c, the shadow d will move
to e; and this proportion in the rapidity of the movements made in the same
space of time, is equal to that in the length of the space moved over. Thus,
given the proportion of the space moved over by the body b to c, to that
moved over by the shadow d to e, the proportion in the rapidity of their
movements will be the same.

But if the luminous body is also in movement with a velocity equal to
that of the solid body, then the shadow and the body that casts it will move
with equal speed. And if the luminous body moves more rapidly than the

solid body, the motion of the shadow will be slower than that of the body
casting it.

But if the luminous body moves more slowly than the solid body, then
the shadow will move more rapidly than that body.

SIXTH BOOK ON LIGHT AND SHADE.

The effect of rays passing through holes (213. 214).

213.

PERSPECTIVE.

If you transmit the rays of the sun through a hole in the shape of a star
you will see a beautiful effect of perspective in the spot where the sun's rays
fall.

[Footnote: In this and the following chapters of MS. C the order of the
original paging has been adhered to, and is shown in parenthesis. Leonardo
himself has but rarely worked out the subject of these propositions. The
space left for the purpose has occasionally been made use of for quite
different matter. Even the numerous diagrams, most of them very delicately
sketched, lettered and numbered, which occur on these pages, are hardly
ever explained, with the exception of those few which are here given.]

214.

No small hole can so modify the convergence of rays of light as to
prevent, at a long distance, the transmission of the true form of the
luminous body causing them. It is impossible that rays of light passing
through a parallel [slit], should not display the form of the body causing
them, since all the effects produced by a luminous body are [in fact] the

reflection of that body: The moon, shaped like a boat, if transmitted through
a hole is figured in the surface [it falls on] as a boatshaped object. [Footnote
8: In the MS. a blank space is left after this question.] Why the eye sees
bodies at a distance, larger than they measure on the vertical plane?.

[Footnote: This chapter, taken from another MS. may, as an exception, be
placed here, as it refers to the same subject as the preceding section.]

On gradation of shadows (215. 216).

215.

Although the breadth and length of lights and shadow will be narrower
and shorter in foreshortening, the quality and quantity of the light and shade
is not increased nor diminished.

[3]The function of shade and light when diminished by foreshortening,
will be to give shadow and to illuminate an object opposite, according to
the quality and quantity in which they fall on the body.

[5]In proportion as a derived shadow is nearer to its penultimate
extremities the deeper it will appear, g z beyond the intersection faces only
the part of the shadow [marked] y z; this by intersection takes the shadow
from m n but by direct line it takes the shadow a m hence it is twice as deep
as g z. Y x, by intersection takes the shadow n o, but by direct line the
shadow n m a, therefore x y is three times as dark as z g; x f, by intersection
faces o b and by direct line o n m a, therefore we must say that the shadow
between f x will be four times as dark as the shadow z g, because it faces
four times as much shadow.

Let a b be the side where the primary shadow is, and b c the primary
light, d will be the spot where it is intercepted,f g the derived shadow and f

e the derived light.

And this must be at the beginning of the explanation.

[Footnote: In the original MS. the text of No. 252 precedes the one given
here. In the text of No. 215 there is a blank space of about four lines
between the lines 2 and 3. The diagram given on Pl. VI, No. 2 is placed
between lines 4 and 5. Between lines 5 and 6 there is another space of about
three lines and one line left blank between lines 8 and 9. The reader will
find the meaning of the whole passage much clearer if he first reads the
final lines 11—13. Compare also line 4 of No. 270.]

On relative proportion of light and shadows (216—221).

216.

That part of the surface of a body on which the images [reflection] from
other bodies placed opposite fall at the largest angle will assume their hue
most strongly. In the diagram below, 8 is a larger angle than 4, since its base
a n is larger than e n the base of 4. This diagram below should end at a n 4
8. [4]That portion of the illuminated surface on which a shadow is cast will
be brightest which lies contiguous to the cast shadow. Just as an object
which is lighted up by a greater quantity of luminous rays becomes brighter,
so one on which a greater quantity of shadow falls, will be darker.

Let 4 be the side of an illuminated surface 4 8, surrounding the cast
shadow g e 4. And this spot 4 will be lighter than 8, because less shadow
falls on it than on 8. Since 4 faces only the shadow i n; and 8 faces and
receives the shadow a e as well as i n which makes it twice as dark. And the
same thing happens when you put the atmosphere and the sun in the place
of shade and light.

[12] The distribution of shadow, originating in, and limited by, plane
surfaces placed near to each other, equal in tone and directly opposite, will
be darker at the ends than at the beginning, which will be determined by the
incidence of the luminous rays. You will find the same proportion in the
depth of the derived shadows a n as in the nearness of the luminous bodies
m b, which cause them; and if the luminous bodies were of equal size you
would still farther find the same proportion in the light cast by the luminous
circles and their shadows as in the distance of the said luminous bodies.

[Footnote: The diagram originally placed between lines 3 and 4 is on Pl.
VI, No. 3. In the diagram given above line 14 of the original, and here
printed in the text, the words corpo luminoso [luminous body] are written in
the circle m, luminoso in the circle b and ombroso [body in shadow] in the
circle o.]

217.

THAT PART OF THE REFLECTION WILL BE BRIGHTEST WHERE THE REFLECTED
RAYS ARE SHORTEST.

[2] The darkness occasioned by the casting of combined shadows will be
in conformity with its cause, which will originate and terminate between
two plane surfaces near together, alike in tone and directly opposite each
other.

[4] In proportion as the source of light is larger, the luminous and shadow
rays will be more mixed together. This result is produced because wherever
there is a larger quantity of luminous rays, there is most light, but where
there are fewer there is least light, consequently the shadow rays come in
and mingle with them.

[Footnote: Diagrams are inserted before lines 2 and 4.]

218.

In all the proportions I lay down it must be understood that the medium
between the bodies is always the same. [2] The smaller the luminous body
the more distinct will the transmission of the shadows be.

[3] When of two opposite shadows, produced by the same body, one is
twice as dark as the other though similar in form, one of the two lights
causing them must have twice the diameter that the other has and be at
twice the distance from the opaque body. If the object is lowly moved
across the luminous body, and the shadow is intercepted at some distance
from the object, there will be the same relative proportion between the
motion of the derived shadow and the motion of the primary shadow, as
between the distance from the object to the light, and that from the object to
the spot where the shadow is intercepted; so that though the object is moved
slowly the shadow moves fast.

[Footnote: There are diagrams inserted before lines 2 and 3 but they are
not reproduced here. The diagram above line 6 is written upon as follows: at
A lume (light), at B obbietto (body), at C ombra d'obbietto (shadow of the
object).]

219.

A luminous body will appear less brilliant when surrounded by a bright
background.

[2] I have found that the stars which are nearest to the horizon look larger
than the others because light falls upon them from a larger proportion of the
solar body than when they are above us; and having more light from the sun
they give more light, and the bodies which are most luminous appear the
largest. As may be seen by the sun through a mist, and overhead; it appears

larger where there is no mist and diminished through mist. No portion of the
luminous body is ever visible from any spot within the pyramid of pure
derived shadow.

[Footnote: Between lines 1 and 2 there is in the original a large diagram
which does not refer to this text. ]

220.

A body on which the solar rays fall between the thin branches of trees far
apart will cast but a single shadow.

[2] If an opaque body and a luminous one are (both) spherical the base of
the pyramid of rays will bear the same proportion to the luminous body as
the base of the pyramid of shade to the opaque body.

[4] When the transmitted shadow is intercepted by a plane surface placed
opposite to it and farther away from the luminous body than from the object
[which casts it] it will appear proportionately darker and the edges more
distinct.

[Footnote: The diagram which, in the original, is placed above line 2, is
similar to the one, here given on page 73 (section 120).—The diagram here
given in the margin stands, in the original, between lines 3 and 4.]

221.

A body illuminated by the solar rays passing between the thick branches
of trees will produce as many shadows as there are branches between the
sun and itself.

Where the shadow-rays from an opaque pyramidal body are intercepted
they will cast a shadow of bifurcate outline and various depth at the points.

A light which is broader than the apex but narrower than the base of an
opaque pyramidal body placed in front of it, will cause that pyramid to cast
a shadow of bifurcate form and various degrees of depth.

If an opaque body, smaller than the light, casts two shadows and if it is
the same size or larger, casts but one, it follows that a pyramidal body, of
which part is smaller, part equal to, and part larger than, the luminous body,
will cast a bifurcate shadow.

[Footnote: Between lines 2 and 3 there are in the original two large
diagrams.]

IV.

Perspective of Disappearance.

The theory of the "Prospettiva de' perdimenti" would, in many important
details, be quite unintelligible if it had not been led up by the principles of
light and shade on which it is based. The word "Prospettiva" in the
language of the time included the principles of optics; what Leonardo
understood by "Perdimenti" will be clearly seen in the early chapters, Nos.
222—224. It is in the very nature of the case that the farther explanations
given in the subsequent chapters must be limited to general rules. The
sections given as 227—231 "On indistinctness at short distances" have, it is
true, only an indirect bearing on the subject; but on the other hand, the
following chapters, 232—234, "On indistinctness at great distances," go
fully into the matter, and in chapters 235—239, which treat "Of the
importance of light and shade in the Perspective of Disappearance", the
practical issues are distinctly insisted on in their relation to the theory. This
is naturally followed by the statements as to "the effect of light or dark
backgrounds on the apparent size of bodies" (Nos. 240—250). At the end I
have placed, in the order of the original, those sections from the MS. C

which treat of the "Perspective of Disappearance" and serve to some extent
to complete the treatment of the subject (251—262).

Definition (222. 223).

222.

OF THE DIMINISHED DISTINCTNESS OF THE OUTLINES OF OPAQUE BODIES.

If the real outlines of opaque bodies are indistinguishable at even a very
short distance, they will be more so at long distances; and, since it is by its
outlines that we are able to know the real form of any opaque body, when
by its remoteness we fail to discern it as a whole, much more must we fail
to discern its parts and outlines.

223.

OF THE DIMINUTION IN PERSPECTIVE OF OPAQUE OBJECTS.

Among opaque objects of equal size the apparent diminution of size will
be in proportion to their distance from the eye of the spectator; but it is an
inverse proportion, since, where the distance is greater, the opaque body
will appear smaller, and the less the distance the larger will the object
appear. And this is the fundamental principle of linear perspective and it
follows:—[11]every object as it becomes more remote loses first those parts
which are smallest. Thus of a horse, we should lose the legs before the
head, because the legs are thinner than the head; and the neck before the
body for the same reason. Hence it follows that the last part of the horse
which would be discernible by the eye would be the mass of the body in an
oval form, or rather in a cylindrical form and this would lose its apparent
thickness before its length—according to the 2nd rule given above, &c.
[Footnote 23: Compare line 11.].

If the eye remains stationary the perspective terminates in the distance in
a point. But if the eye moves in a straight [horizontal] line the perspective
terminates in a line and the reason is that this line is generated by the
motion of the point and our sight; therefore it follows that as we move our
sight [eye], the point moves, and as we move the point, the line is
generated, &c.

An illustration by experiment.

224.

Every visible body, in so far as it affects the eye, includes three attributes;
that is to say: mass, form and colour; and the mass is recognisable at a
greater distance from the place of its actual existence than either colour or
form. Again, colour is discernible at a greater distance than form, but this
law does not apply to luminous bodies.

The above proposition is plainly shown and proved by experiment;
because: if you see a man close to you, you discern the exact appearance of
the mass and of the form and also of the colouring; if he goes to some
distance you will not recognise who he is, because the character of the
details will disappear, if he goes still farther you will not be able to
distinguish his colouring, but he will appear as a dark object, and still
farther he will appear as a very small dark rounded object. It appears
rounded because distance so greatly diminishes the various details that
nothing remains visible but the larger mass. And the reason is this: We
know very well that all the images of objects reach the senses by a small
aperture in the eye; hence, if the whole horizon a d is admitted through such
an aperture, the object b c being but a very small fraction of this horizon
what space can it fill in that minute image of so vast a hemisphere? And
because luminous bodies have more power in darkness than any others, it is
evident that, as the chamber of the eye is very dark, as is the nature of all

colored cavities, the images of distant objects are confused and lost in the
great light of the sky; and if they are visible at all, appear dark and black, as
every small body must when seen in the diffused light of the atmosphere.

[Footnote: The diagram belonging to this passage is placed between lines
5 and 6; it is No. 4 on Pl. VI. ]

A guiding rule.

225.

OF THE ATMOSPHERE THAT INTERPOSES BETWEEN THE EYE AND VISIBLE
OBJECTS.

An object will appear more or less distinct at the same distance, in
proportion as the atmosphere existing between the eye and that object is
more or less clear. Hence, as I know that the greater or less quantity of the
air that lies between the eye and the object makes the outlines of that object
more or less indistinct, you must diminish the definiteness of outline of
those objects in proportion to their increasing distance from the eye of the
spectator.

An experiment.

226.

When I was once in a place on the sea, at an equal distance from the
shore and the mountains, the distance from the shore looked much greater
than that from the mountains.

On indistinctness at short distances (227-231).

227.

If you place an opaque object in front of your eye at a distance of four
fingers' breadth, if it is smaller than the space between the two eyes it will
not interfere with your seeing any thing that may be beyond it. No object
situated beyond another object seen by the eye can be concealed by this
[nearer] object if it is smaller than the space from eye to eye.

228.

The eye cannot take in a luminous angle which is too close to it.

229.

That part of a surface will be better lighted on which the light falls at the
greater angle. And that part, on which the shadow falls at the greatest angle,
will receive from those rays least of the benefit of the light.

230.

OF THE EYE.

The edges of an object placed in front of the pupil of the eye will be less
distinct in proportion as they are closer to the eye. This is shown by the
edge of the object n placed in front of the pupil d; in looking at this edge the
pupil also sees all the space a c which is beyond the edge; and the images
the eye receives from that space are mingled with the images of the edge, so
that one image confuses the other, and this confusion hinders the pupil from
distinguishing the edge.

231.

The outlines of objects will be least clear when they are nearest to the
eye, and therefore remoter outlines will be clearer. Among objects which

are smaller than the pupil of the eye those will be less distinct which are
nearer to the eye.

On indistinctness at great distances (232-234).

232.

Objects near to the eye will appear larger than those at a distance.

Objects seen with two eyes will appear rounder than if they are seen with
only one.

Objects seen between light and shadow will show the most relief.

233.

OF PAINTING.

Our true perception of an object diminishes in proportion as its size is
diminished by distance.

234.

PERSPECTIVE.

Why objects seen at a distance appear large to the eye and in the image
on the vertical plane they appear small.

PERSPECTIVE.

I ask how far away the eye can discern a non-luminous body, as, for
instance, a mountain. It will be very plainly visible if the sun is behind it;
and could be seen at a greater or less distance according to the sun's place in
the sky.

[Footnote: The clue to the solution of this problem (lines 1-3) is given in
lines 4-6, No. 232. Objects seen with both eyes appear solid since they are
seen from two distinct points of sight separated by the distance between the
eyes, but this solidity cannot be represented in a flat drawing. Compare No.
535.]

The importance of light and shade in the perspective of disappearance
(235-239).

235.

An opaque body seen in a line in which the light falls will reveal no
prominences to the eye. For instance, let a be the solid body and c the light;
c m and c n will be the lines of incidence of the light, that is to say the lines
which transmit the light to the object a. The eye being at the point b, I say
that since the light c falls on the whole part m n the portions in relief on that
side will all be illuminated. Hence the eye placed at c cannot see any light
and shade and, not seeing it, every portion will appear of the same tone,
therefore the relief in the prominent or rounded parts will not be visible.

236.

OF PAINTING.

When you represent in your work shadows which you can only discern
with difficulty, and of which you cannot distinguish the edges so that you
apprehend them confusedly, you must not make them sharp or definite lest
your work should have a wooden effect.

237.

OF PAINTING.

You will observe in drawing that among the shadows some are of
undistinguishable gradation and form, as is shown in the 3rd [proposition]
which says: Rounded surfaces display as many degrees of light and shade
as there are varieties of brightness and darkness reflected from the
surrounding objects.

238.

OF LIGHT AND SHADE.

You who draw from nature, look (carefully) at the extent, the degree, and
the form of the lights and shadows on each muscle; and in their position
lengthwise observe towards which muscle the axis of the central line is
directed.

239.

An object which is [so brilliantly illuminated as to be] almost as bright as
light will be visible at a greater distance, and of larger apparent size than is
natural to objects so remote.

The effect of light or dark backgrounds on the apparent size of objects
(240-250).

240.

A shadow will appear dark in proportion to the brilliancy of the light
surrounding it and conversely it will be less conspicuous where it is seen
against a darker background.

241.

OF ORDINARY PERSPECTIVE.

An object of equal breadth and colour throughout, seen against a
background of various colours will appear unequal in breadth.

And if an object of equal breadth throughout, but of various colours, is
seen against a background of uniform colour, that object will appear of
various breadth. And the more the colours of the background or of the
object seen against the ground vary, the greater will the apparent variations
in the breadth be though the objects seen against the ground be of equal
breadth [throughout].

242.

A dark object seen against a bright background will appear smaller than it
is.

A light object will look larger when it is seen against a background
darker than itself.

243.

OF LIGHT.

A luminous body when obscured by a dense atmosphere will appear
smaller; as may be seen by the moon or sun veiled by mists.

OF LIGHT.

Of several luminous bodies of equal size and brilliancy and at an equal
distance, that will look the largest which is surrounded by the darkest
background.

OF LIGHT.

I find that any luminous body when seen through a dense and thick mist
diminishes in proportion to its distance from the eye. Thus it is with the sun
by day, as well as the moon and the other eternal lights by night. And when
the air is clear, these luminaries appear larger in proportion as they are
farther from the eye.

244.

That portion of a body of uniform breadth which is against a lighter
background will look narrower [than the rest].

[4] e is a given object, itself dark and of uniform breadth; a b and c d are
two backgrounds one darker than the other; b c is a bright background, as it
might be a spot lighted by the sun through an aperture in a dark room. Then
I say that the object e g will appear larger at e f than at g h; because e f has a
darker background than g h; and again at f g it will look narrower from
being seen by the eye o, on the light background b c. [Footnote 12: The
diagram to which the text, lines 1-11, refers, is placed in the original
between lines 3 and 4, and is given on Pl. XLI, No. 3. Lines 12 to 14 are
explained by the lower of the two diagrams on Pl. XLI, No. 4. In the
original these are placed after line 14.] That part of a luminous body, of
equal breadth and brilliancy throughout, will look largest which is seen
against the darkest background; and the luminous body will seem on fire.

245.

WHY BODIES IN LIGHT AND SHADE HAVE THEIR OUTLINES ALTERED BY THE
COLOUR AND BRIGHTNESS OF THE OBJECTS SERVING AS A BACKGROUND TO
THEM.

If you look at a body of which the illuminated portion lies and ends
against a dark background, that part of the light which will look brightest
will be that which lies against the dark [background] at d. But if this

brighter part lies against a light background, the edge of the object, which is
itself light, will be less distinct than before, and the highest light will appear
to be between the limit of the background m f and the shadow. The same
thing is seen with regard to the dark [side], inasmuch as that edge of the
shaded portion of the object which lies against a light background, as at l, it
looks much darker than the rest. But if this shadow lies against a dark
background, the edge of the shaded part will appear lighter than before, and
the deepest shade will appear between the edge and the light at the point o.

[Footnote: In the original diagram o is inside the shaded surface at the
level of d.]

246.

An opaque body will appear smaller when it is surrounded by a highly
luminous background, and a light body will appear larger when it is seen
against a darker background. This may be seen in the height of buildings at
night, when lightning flashes behind them; it suddenly seems, when it
lightens, as though the height of the building were diminished. For the same
reason such buildings look larger in a mist, or by night than when the
atmosphere is clear and light.

247.

ON LIGHT BETWEEN SHADOWS

When you are drawing any object, remember, in comparing the grades of
light in the illuminated portions, that the eye is often deceived by seeing
things lighter than they are. And the reason lies in our comparing those
parts with the contiguous parts. Since if two [separate] parts are in different
grades of light and if the less bright is conterminous with a dark portion and
the brighter is conterminous with a light background—as the sky or

something equally bright—, then that which is less light, or I should say
less radiant, will look the brighter and the brighter will seem the darker.

248.

Of objects equally dark in themselves and situated at a considerable and
equal distance, that will look the darkest which is farthest above the earth.

249.

TO PROVE HOW IT IS THAT LUMINOUS BODIES APPEAR LARGER, AT A DISTANCE,
THAN THEY ARE.

If you place two lighted candles side by side half a braccio apart, and go
from them to a distance 200 braccia you will see that by the increased size
of each they will appear as a single luminous body with the light of the two
flames, one braccio wide.

TO PROVE HOW YOU MAY SEE THE REAL SIZE OF LUMINOUS BODIES.

If you wish to see the real size of these luminous bodies, take a very thin
board and make in it a hole no bigger than the tag of a lace and place it as
close to your eye as possible, so that when you look through this hole, at the
said light, you can see a large space of air round it. Then by rapidly moving
this board backwards and forwards before your eye you will see the light
increase [and diminish].

Propositions on perspective of disappearance from MS. C. (250-262).

250.

Of several bodies of equal size and equally distant from the eye, those
will look the smallest which are against the lightest background.

Every visible object must be surrounded by light and shade. A perfectly
spherical body surrounded by light and shade will appear to have one side
larger than the other in proportion as one is more highly lighted than the
other.

251.

PERSPECTIVE.

No visible object can be well understood and comprehended by the
human eye excepting from the difference of the background against which
the edges of the object terminate and by which they are bounded, and no
object will appear [to stand out] separate from that background so far as the
outlines of its borders are concerned. The moon, though it is at a great
distance from the sun, when, in an eclipse, it comes between our eyes and
the sun, appears to the eyes of men to be close to the sun and affixed to it,
because the sun is then the background to the moon.

252.

A luminous body will appear more brilliant in proportion as it is
surrounded by deeper shadow. [Footnote: The diagram which, in the
original, is placed after this text, has no connection with it.]

253.

The straight edges of a body will appear broken when they are
conterminous with a dark space streaked with rays of light. [Footnote: Here
again the diagrams in the original have no connection with the text.]

254.

Of several bodies, all equally large and equally distant, that which is most
brightly illuminated will appear to the eye nearest and largest. [Footnote:
Here again the diagrams in the original have no connection with the text.]

255.

If several luminous bodies are seen from a great distance although they
are really separate they will appear united as one body.

256.

If several objects in shadow, standing very close together, are seen
against a bright background they will appear separated by wide intervals.

257.

Of several bodies of equal size and tone, that which is farthest will
appear the lightest and smallest.

258.

Of several objects equal in size, brightness of background and length that
which has the flattest surface will look the largest. A bar of iron equally
thick throughout and of which half is red hot, affords an example, for the
red hot part looks thicker than the rest.

259.

Of several bodies of equal size and length, and alike in form and in depth
of shade, that will appear smallest which is surrounded by the most
luminous background.

260.

DIFFERENT PORTIONS OF A WALL SURFACE WILL BE DARKER OR BRIGHTER IN
PROPORTION AS THE LIGHT OR SHADOW FALLS ON THEM AT A LARGER ANGLE.

The foregoing proposition can be clearly proved in this way. Let us say
that m q is the luminous body, then f g will be the opaque body; and let a e
be the above-mentioned plane on which the said angles fall, showing
[plainly] the nature and character of their bases. Then: a will be more
luminous than b; the base of the angle a is larger than that of b and it
therefore makes a greater angle which will be a m q; and the pyramid b p m
will be narrower and m o c will be still finer, and so on by degrees, in
proportion as they are nearer to e, the pyramids will become narrower and
darker. That portion of the wall will be the darkest where the breadth of the
pyramid of shadow is greater than the breadth of the pyramid of light.

At the point a the pyramid of light is equal in strength to the pyramid of
shadow, because the base f g is equal to the base r f. At the point d the
pyramid of light is narrower than the pyramid of shadow by so much as the
base s f is less than the base f g.

Divide the foregoing proposition into two diagrams, one with the
pyramids of light and shadow, the other with the pyramids of light [only].

261.

Among shadows of equal depth those which are nearest to the eye will
look least deep.

262.

The more brilliant the light given by a luminous body, the deeper will the
shadows be cast by the objects it illuminates.

V.

Theory of colours.

Leonardo's theory of colours is even more intimately connected with his
principles of light and shade than his Perspective of Disappearance and is
in fact merely an appendix or supplement to those principles, as we gather
from the titles to sections 264, 267_, and 276, while others again_ (Nos.
281, 282_) are headed_ Prospettiva.

A very few of these chapters are to be found in the oldest copies and
editions of the Treatise on Painting, and although the material they afford is
but meager and the connection between them but slight, we must still
attribute to them a special theoretical value as well as practical utility—all
the more so because our knowledge of the theory and use of colours at the
time of the Renaissance is still extremely limited.

The reciprocal effects of colours on objects placed opposite each other
(263-272).

263.

OF PAINTING.

The hue of an illuminated object is affected by that of the luminous body.

264.

OF SHADOW.

The surface of any opaque body is affected by the colour of surrounding
objects.

265.

A shadow is always affected by the colour of the surface on which it is
cast.

266.

An image produced in a mirror is affected by the colour of the mirror.

267.

OF LIGHT AND SHADE.

Every portion of the surface of a body is varied [in hue] by the [reflected]
colour of the object that may be opposite to it.

EXAMPLE.

If you place a spherical body between various objects that is to say with
[direct] sunlight on one side of it, and on the other a wall illuminated by the
sun, which wall may be green or of any other colour, while the surface on
which it is placed may be red, and the two lateral sides are in shadow, you
will see that the natural colour of that body will assume something of the
hue reflected from those objects. The strongest will be [given by] the
luminous body; the second by the illuminated wall, the third by the
shadows. There will still be a portion which will take a tint from the colour
of the edges.

268.

The surface of every opaque body is affected by the colour of the objects
surrounding it. But this effect will be strong or weak in proportion as those
objects are more or less remote and more or less strongly [coloured].

269.

OF PAINTING.

The surface of every opaque body assumes the hues reflected from
surrounding objects.

The surface of an opaque body assumes the hues of surrounding objects
more strongly in proportion as the rays that form the images of those
objects strike the surface at more equal angles.

And the surface of an opaque body assumes a stronger hue from the
surrounding objects in proportion as that surface is whiter and the colour of
the object brighter or more highly illuminated.

270.

OF THE RAYS WHICH CONVEY THROUGH THE AIR THE IMAGES OF OBJECTS.

All the minutest parts of the image intersect each other without
interfering with each other. To prove this let r be one of the sides of the
hole, opposite to which let s be the eye which sees the lower end o of the
line n o. The other extremity cannot transmit its image to the eye s as it has
to strike the end r and it is the same with regard to m at the middle of the
line. The case is the same with the upper extremity n and the eye u. And if
the end n is red the eye u on that side of the holes will not see the green
colour of o, but only the red of n according to the 7th of this where it is
said: Every form projects images from itself by the shortest line, which
necessarily is a straight line, &c.

[Footnote: 13. This probably refers to the diagram given under No. 66.]

271.

OF PAINTING.

The surface of a body assumes in some degree the hue of those around it.
The colours of illuminated objects are reflected from the surfaces of one to
the other in various spots, according to the various positions of those
objects. Let o be a blue object in full light, facing all by itself the space b c
on the white sphere a b e d e f, and it will give it a blue tinge, m is a yellow
body reflected onto the space a b at the same time as o the blue body, and
they give it a green colour (by the 2nd [proposition] of this which shows
that blue and yellow make a beautiful green &c.) And the rest will be set
forth in the Book on Painting. In that Book it will be shown, that, by
transmitting the images of objects and the colours of bodies illuminated by
sunlight through a small round perforation and into a dark chamber onto a
plane surface, which itself is quite white, &c.

But every thing will be upside down.

Combination of different colours in cast shadows.

272.

That which casts the shadow does not face it, because the shadows are
produced by the light which causes and surrounds the shadows. The shadow
caused by the light e, which is yellow, has a blue tinge, because the shadow
of the body a is cast upon the pavement at b, where the blue light falls; and
the shadow produced by the light d, which is blue, will be yellow at c,
because the yellow light falls there and the surrounding background to these
shadows b c will, besides its natural colour, assume a hue compounded of
yellow and blue, because it is lighted by the yellow light and by the blue
light both at once.

Shadows of various colours, as affected by the lights falling on them.
That light which causes the shadow does not face it.

[Footnote: In the original diagram we find in the circle e "giallo"
(yellow) and the cirle d "azurro" (blue) and also under the circle of shadow
to the left "giallo" is written and under that to the right "azurro".

In the second diagram where four circles are placed in a row we find
written, beginning at the left hand, "giallo" (yellow), "azurro" (blue),
"verde" (green), "rosso" (red).]

The effect of colours in the camera obscura (273-274).

273.

The edges of a colour(ed object) transmitted through a small hole are
more conspicuous than the central portions.

The edges of the images, of whatever colour, which are transmitted
through a small aperture into a dark chamber will always be stronger than
the middle portions.

274.

OF THE INTERSECTIONS OF THE IMAGES IN THE PUPIL OF THE EYE.

The intersections of the images as they enter the pupil do not mingle in
confusion in the space where that intersection unites them; as is evident,
since, if the rays of the sun pass through two panes of glass in close contact,
of which one is blue and the other yellow, the rays, in penetrating them, do
not become blue or yellow but a beautiful green. And the same thing would
happen in the eye, if the images which were yellow or green should mingle
where they [meet and] intersect as they enter the pupil. As this does not
happen such a mingling does not exist.

OF THE NATURE OF THE RAYS COMPOSED OF THE IMAGES OF OBJECTS, AND OF
THEIR INTERSECTIONS.

The directness of the rays which transmit the forms and colours of the
bodies whence they proceed does not tinge the air nor can they affect each
other by contact where they intersect. They affect only the spot where they
vanish and cease to exist, because that spot faces and is faced by the
original source of these rays, and no other object, which surrounds that
original source can be seen by the eye where these rays are cut off and
destroyed, leaving there the spoil they have conveyed to it. And this is
proved by the 4th [proposition], on the colour of bodies, which says: The
surface of every opaque body is affected by the colour of surrounding
objects; hence we may conclude that the spot which, by means of the rays
which convey the image, faces—and is faced by the cause of the image,
assumes the colour of that object.

On the colours of derived shadows (275. 276).

275.

ANY SHADOW CAST BY AN OPAQUE BODY SMALLER THAN THE LIGHT CAUSING
THE SHADOW WILL THROW A DERIVED SHADOW WHICH IS TINGED BY THE
COLOUR OF THE LIGHT.

Let n be the source of the shadow e f; it will assume its hue. Let o be the
source of h e which will in the same way be tinged by its hue and so also
the colour of v h will be affected by p which causes it; and the shadow of
the triangle z k y will be affected by the colour of q, because it is produced
by it. [7] In proportion as c d goes into a d, will n r s be darker than m; and
the rest of the space will be shadowless [11]. f g is the highest light, because
here the whole light of the window a d falls; and thus on the opaque body m
e is in equally high light; z k y is a triangle which includes the deepest
shadow, because the light a d cannot reach any part of it. x h is the 2nd
grade of shadow, because it receives only 1/3 of the light from the window,
that is c d. The third grade of shadow is h e, where two thirds of the light

from the window is visible. The last grade of shadow is b d e f, because the
highest grade of light from the window falls at f.

[Footnote: The diagram Pl. III, No. 1 belongs to this chapter as well as
the text given in No. 148. Lines 7-11 (compare lines 8-12 of No. 148)
which are written within the diagram, evidently apply to both sections and
have therefore been inserted in both.]

276.

OF THE COLOURS OF SIMPLE DERIVED SHADOWS.

The colour of derived shadows is always affected by that of the body
towards which they are cast. To prove this: let an opaque body be placed
between the plane s c t d and the blue light d e and the red light a b, then I
say that d e, the blue light, will fall on the whole surface s c t d excepting at
o p which is covered by the shadow of the body q r, as is shown by the
straight lines d q o e r p. And the same occurs with the light a b which falls
on the whole surface s c t d excepting at the spot obscured by the shadow q
r; as is shown by the lines d q o, and e r p. Hence we may conclude that the
shadow n m is exposed to the blue light d e; but, as the red light a b cannot
fall there, n m will appear as a blue shadow on a red background tinted with
blue, because on the surface s c t d both lights can fall. But in the shadows
only one single light falls; for this reason these shadows are of medium
depth, since, if no light whatever mingled with the shadow, it would be of
the first degree of darkness &c. But in the shadow at o p the blue light does
not fall, because the body q r interposes and intercepts it there. Only the red
light a b falls there and tinges the shadow of a red hue and so a ruddy
shadow appears on the background of mingled red and blue.

The shadow of q r at o p is red, being caused by the blue light d e; and
the shadow of q r at o' p' is blue being caused by the red light a b. Hence we

say that the blue light in this instance causes a red derived shadow from the
opaque body q' r', while the red light causes the same body to cast a blue
derived shadow; but the primary shadow [on the dark side of the body
itself] is not of either of those hues, but a mixture of red and blue.

The derived shadows will be equal in depth if they are produced by lights
of equal strength and at an equal distance; this is proved. [Footnote 53: The
text is unfinished in the original.]

[Footnote: In the original diagram Leonardo has written within the circle
q r corpo obroso (body in shadow); at the spot marked A, luminoso azzurro
(blue luminous body); at B, luminoso rosso (red luminous body). At E we
read ombra azzurra (blue tinted shadow) and at D ombra rossa (red tinted
shadow).]

On the nature of colours (277. 278).

277.

No white or black is transparent.

278.

OF PAINTING.

[Footnote 2: See Footnote 3] Since white is not a colour but the neutral
recipient of every colour [Footnote 3: il bianco non e colore ma e inpotentia
ricettiva d'ogni colore (white is not a colour, but the neutral recipient of
every colour). LEON BATT. ALBERTI "Della pittura" libro I, asserts on
the contrary: "Il bianco e'l nero non sono veri colori, ma sono alteratione
delli altri colori" (ed. JANITSCHEK, p. 67; Vienna 1877).], when it is seen
in the open air and high up, all its shadows are bluish; and this is caused,
according to the 4th [prop.], which says: the surface of every opaque body

assumes the hue of the surrounding objects. Now this white [body] being
deprived of the light of the sun by the interposition of some body between
the sun and itself, all that portion of it which is exposed to the sun and
atmosphere assumes the colour of the sun and atmosphere; the side on
which the sun does not fall remains in shadow and assumes the hue of the
atmosphere. And if this white object did not reflect the green of the fields
all the way to the horizon nor get the brightness of the horizon itself, it
would certainly appear simply of the same hue as the atmosphere.

On gradations in the depth of colours (279. 280).

279.

Since black, when painted next to white, looks no blacker than when next
to black; and white when next to black looks no whiter than white, as is
seen by the images transmitted through a small hole or by the edges of any
opaque screen …

280.

OF COLOURS.

Of several colours, all equally white, that will look whitest which is
against the darkest background. And black will look intensest against the
whitest background.

And red will look most vivid against the yellowest background; and the
same is the case with all colours when surrounded by their strongest
contrasts.

On the reflection of colours (281-283).

281.

PERSPECTIVE.

Every object devoid of colour in itself is more or less tinged by the
colour [of the object] placed opposite. This may be seen by experience,
inasmuch as any object which mirrors another assumes the colour of the
object mirrored in it. And if the surface thus partially coloured is white the
portion which has a red reflection will appear red, or any other colour,
whether bright or dark.

PERSPECTIVE.

Every opaque and colourless body assumes the hue of the colour
reflected on it; as happens with a white wall.

282.

PERSPECTIVE.

That side of an object in light and shade which is towards the light
transmits the images of its details more distinctly and immediately to the
eye than the side which is in shadow.

PERSPECTIVE.

The solar rays reflected on a square mirror will be thrown back to distant
objects in a circular form.

PERSPECTIVE.

Any white and opaque surface will be partially coloured by reflections
from surrounding objects.

[Footnote 281. 282: The title line of these chapters is in the original
simply "pro", which may be an abbreviation for either Propositione or

Prospettiva—taking Prospettiva of course in its widest sense, as we often
find it used in Leonardo's writings. The title "pro" has here been understood
to mean Prospettiva, in accordance with the suggestion afforded by page
10b of this same MS., where the first section is headed Prospettiva in full
(see No. 94), while the four following sections are headed merely "pro" (see
No. 85).]

283.

WHAT PORTION OF A COLOURED SURFACE OUGHT IN REASON TO BE THE MOST
INTENSE.

If a is the light, and b illuminated by it in a direct line, c, on which the
light cannot fall, is lighted only by reflection from b which, let us say, is
red. Hence the light reflected from it, will be affected by the hue of the
surface causing it and will tinge the surface c with red. And if c is also red
you will see it much more intense than b; and if it were yellow you would
see there a colour between yellow and red.

On the use of dark and light colours in painting (284—286).

284.

WHY BEAUTIFUL COLOURS MUST BE IN THE [HIGHEST] LIGHT.

Since we see that the quality of colour is known [only] by means of light,
it is to be supposed that where there is most light the true character of a
colour in light will be best seen; and where there is most shadow the colour
will be affected by the tone of that. Hence, O Painter! remember to show
the true quality of colours in bright lights.

285.

An object represented in white and black will display stronger relief than
in any other way; hence I would remind you O Painter! to dress your
figures in the lightest colours you can, since, if you put them in dark
colours, they will be in too slight relief and inconspicuous from a distance.
And the reason is that the shadows of all objects are dark. And if you make
a dress dark there is little variety in the lights and shadows, while in light
colours there are many grades.

286.

OF PAINTING.

Colours seen in shadow will display more or less of their natural
brilliancy in proportion as they are in fainter or deeper shadow.

But if these same colours are situated in a well-lighted place, they will
appear brighter in proportion as the light is more brilliant.

THE ADVERSARY.

The variety of colours in shadow must be as great as that of the colours in
the objects in that shadow.

THE ANSWER.

Colours seen in shadow will display less variety in proportion as the
shadows in which they lie are deeper. And evidence of this is to be had by
looking from an open space into the doorways of dark and shadowy
churches, where the pictures which are painted in various colours all look of
uniform darkness.

Hence at a considerable distance all the shadows of different colours will
appear of the same darkness.

It is the light side of an object in light and shade which shows the true
colour.

On the colours of the rainbow (287. 288).

287.

Treat of the rainbow in the last book on Painting, but first write the book
on colours produced by the mixture of other colours, so as to be able to
prove by those painters' colours how the colours of the rainbow are
produced.

288.

WHETHER THE COLOURS OF THE RAINBOW ARE PRODUCED
BY THE SUN.

The colours of the rainbow are not produced by the sun, for they occur in
many ways without the sunshine; as may be seen by holding a glass of
water up to the eye; when, in the glass—where there are those minute
bubbles always seen in coarse glass—each bubble, even though the sun
does not fall on it, will produce on one side all the colours of the rainbow;
as you may see by placing the glass between the day light and your eye in
such a way as that it is close to the eye, while on one side the glass admits
the [diffused] light of the atmosphere, and on the other side the shadow of
the wall on one side of the window; either left or right, it matters not which.
Then, by turning the glass round you will see these colours all round the
bubbles in the glass &c. And the rest shall be said in its place.

THAT THE EYE HAS NO PART IN PRODUCING THE COLOURS OF THE RAINBOW.

In the experiment just described, the eye would seem to have some share
in the colours of the rainbow, since these bubbles in the glass do not display

the colours except through the medium of the eye. But, if you place the
glass full of water on the window sill, in such a position as that the outer
side is exposed to the sun's rays, you will see the same colours produced in
the spot of light thrown through the glass and upon the floor, in a dark
place, below the window; and as the eye is not here concerned in it, we may
evidently, and with certainty pronounce that the eye has no share in
producing them.

OF THE COLOURS IN THE FEATHERS OF CERTAIN BIRDS.

There are many birds in various regions of the world on whose feathers
we see the most splendid colours produced as they move, as we see in our
own country in the feathers of peacocks or on the necks of ducks or
pigeons, &c.

Again, on the surface of antique glass found underground and on the
roots of turnips kept for some time at the bottom of wells or other stagnant
waters [we see] that each root displays colours similar to those of the real
rainbow. They may also be seen when oil has been placed on the top of
water and in the solar rays reflected from the surface of a diamond or beryl;
again, through the angular facet of a beryl every dark object against a
background of the atmosphere or any thing else equally pale-coloured is
surrounded by these rainbow colours between the atmosphere and the dark
body; and in many other circumstances which I will not mention, as these
suffice for my purpose.

VI.

'Prospettiva de' colri' (Perspective of Colour)

and

'Prospettiva aerea' (Aerial Perspective).

Leonardo distinctly separates these branches of his subject, as may be
seen in the beginning of No. 295. Attempts have been made to cast doubts
on the results which Leonardo arrived at by experiment on the perspective
of colour, but not with justice, as may be seen from the original text of
section 294.

The question as to the composition of the atmosphere, which is
inseparable from a discussion on Aerial Perspective, forms a separate
theory which is treated at considerable length. Indeed the author enters into
it so fully that we cannot escape the conviction that he must have dwelt with
particular pleasure on this part of his subject, and that he attached great
importance to giving it a character of general applicability.

General rules (289—291).

289.

The variety of colour in objects cannot be discerned at a great distance,
excepting in those parts which are directly lighted up by the solar rays.

290.

As to the colours of objects: at long distances no difference is perceptible
in the parts in shadow.

291.

OF THE VISIBILITY OF COLOURS.

Which colour strikes most? An object at a distance is most conspicuous,
when it is lightest, and the darkest is least visible.

An exceptional case.

292.

Of the edges [outlines] of shadows. Some have misty and ill defined
edges, others distinct ones.

No opaque body can be devoid of light and shade, except it is in a mist,
on ground covered with snow, or when snow is falling on the open country
which has no light on it and is surrounded with darkness.

And this occurs [only] in spherical bodies, because in other bodies which
have limbs and parts, those sides of limbs which face each other reflect on
each other the accidental [hue and tone] of their surface.

An experiment.

293.

ALL COLOURS ARE AT A DISTANCE UNDISTINGUISHABLE AND UNDISCERNIBLE.

All colours at a distance are undistinguishable in shadow, because an
object which is not in the highest light is incapable of transmitting its image
to the eye through an atmosphere more luminous than itself; since the lesser
brightness must be absorbed by the greater. For instance: We, in a house,
can see that all the colours on the surface of the walls are clearly and
instantly visible when the windows of the house are open; but if we were to
go out of the house and look in at the windows from a little distance to see
the paintings on those walls, instead of the paintings we should see an
uniform deep and colourless shadow.

The practice of the prospettiva de colori.

294.

HOW A PAINTER SHOULD CARRY OUT THE PERSPECTIVE OF COLOUR IN
PRACTICE.

In order to put into practice this perspective of the variation and loss or
diminution of the essential character of colours, observe at every hundred
braccia some objects standing in the landscape, such as trees, houses, men
and particular places. Then in front of the first tree have a very steady plate
of glass and keep your eye very steady, and then, on this plate of glass,
draw a tree, tracing it over the form of that tree. Then move it on one side
so far as that the real tree is close by the side of the tree you have drawn;
then colour your drawing in such a way as that in colour and form the two
may be alike, and that both, if you close one eye, seem to be painted on the
glass and at the same distance. Then, by the same method, represent a
second tree, and a third, with a distance of a hundred braccia between each.
And these will serve as a standard and guide whenever you work on your
own pictures, wherever they may apply, and will enable you to give due
distance in those works. [14] But I have found that as a rule the second is
4/5 of the first when it is 20 braccia beyond it.

[Footnote: This chapter is one of those copied in the Manuscript of the
Vatican library Urbinas 1270, and the original text is rendered here with no
other alterations, but in the orthography. H. LUDWIG, in his edition of this
copy translates lines 14 and 15 thus: "Ich finde aber als Regel, dass der
zweite um vier Funftel des ersten abnimmt, wenn er namlich zwanzig Ellen
vom ersten entfernt ist (?)". He adds in his commentary: "Das Ende der
Nummer ist wohl jedenfalls verstummelt". However the translation given
above shows that it admits of a different rendering.]

The rules of aerial perspective (295—297).

295.

OF AERIAL PERSPECTIVE.

There is another kind of perspective which I call Aerial Perspective,
because by the atmosphere we are able to distinguish the variations in
distance of different buildings, which appear placed on a single line; as, for
instance, when we see several buildings beyond a wall, all of which, as they
appear above the top of the wall, look of the same size, while you wish to
represent them in a picture as more remote one than another and to give the
effect of a somewhat dense atmosphere. You know that in an atmosphere of
equal density the remotest objects seen through it, as mountains, in
consequence of the great quantity of atmosphere between your eye and
them—appear blue and almost of the same hue as the atmosphere itself
[Footnote 10: quado il sole e per leuante (when the sun is in the East).
Apparently the author refers here to morning light in general. H. LUDWIG
however translates this passage from the Vatican copy "wenn namlich die
Sonne (dahinter) im Osten steht".] when the sun is in the East [Footnote 11:
See Footnote 10]. Hence you must make the nearest building above the wall
of its real colour, but the more distant ones make less defined and bluer.
Those you wish should look farthest away you must make proportionately
bluer; thus, if one is to be five times as distant, make it five times bluer. And
by this rule the buildings which above a [given] line appear of the same
size, will plainly be distinguished as to which are the more remote and
which larger than the others.

296.

The medium lying between the eye and the object seen, tinges that object
with its colour, as the blueness of the atmosphere makes the distant
mountains appear blue and red glass makes objects seen beyond it, look red.

The light shed round them by the stars is obscured by the darkness of the
night which lies between the eye and the radiant light of the stars.

297.

Take care that the perspective of colour does not disagree with the size of
your objects, hat is to say: that the colours diminish from their natural
[vividness] in proportion as the objects at various distances dimmish from
their natural size.

On the relative density of the atmosphere (298—290).

298.

WHY THE ATMOSPHERE MUST BE REPRESENTED AS PALER TOWARDS THE
LOWER PORTION.

Because the atmosphere is dense near the earth, and the higher it is the
rarer it becomes. When the sun is in the East if you look towards the West
and a little way to the South and North, you will see that this dense
atmosphere receives more light from the sun than the rarer; because the rays
meet with greater resistance. And if the sky, as you see it, ends on a low
plain, that lowest portion of the sky will be seen through a denser and
whiter atmosphere, which will weaken its true colour as seen through that
medium, and there the sky will look whiter than it is above you, where the
line of sight travels through a smaller space of air charged with heavy
vapour. And if you turn to the East, the atmosphere will appear darker as
you look lower down because the luminous rays pass less freely through the
lower atmosphere.

299.

OF THE MODE OF TREATING REMOTE OBJECTS IN PAINTING.

It is easy to perceive that the atmosphere which lies closest to the level
ground is denser than the rest, and that where it is higher up, it is rarer and
more transparent. The lower portions of large and lofty objects which are at
a distance are not much seen, because you see them along a line which
passes through a denser and thicker section of the atmosphere. The summits
of such heights are seen along a line which, though it starts from your eye
in a dense atmosphere, still, as it ends at the top of those lofty objects,
ceases in a much rarer atmosphere than exists at their base; for this reason
the farther this line extends from your eye, from point to point the
atmosphere becomes more and more rare. Hence, O Painter! when you
represent mountains, see that from hill to hill the bases are paler than the
summits, and in proportion as they recede beyond each other make the
bases paler than the summits; while, the higher they are the more you must
show of their true form and colour.

On the colour of the atmosphere (300-307).

300.

OF THE COLOUR OF THE ATMOSPHERE.

I say that the blueness we see in the atmosphere is not intrinsic colour,
but is caused by warm vapour evaporated in minute and insensible atoms on
which the solar rays fall, rendering them luminous against the infinite
darkness of the fiery sphere which lies beyond and includes it. And this may
be seen, as I saw it by any one going up [Footnote 5: With regard to the
place spoken of as M'oboso (compare No. 301 line 20) its identity will be
discussed under Leonardo's Topographical notes in Vol. II.] Monboso, a
peak of the Alps which divide France from Italy. The base of this mountain
gives birth to the four rivers which flow in four different directions through
the whole of Europe. And no mountain has its base at so great a height as
this, which lifts itself almost above the clouds; and snow seldom falls there,

but only hail in the summer, when the clouds are highest. And this hail lies
[unmelted] there, so that if it were not for the absorption of the rising and
falling clouds, which does not happen twice in an age, an enormous mass of
ice would be piled up there by the hail, and in the middle of July I found it
very considerable. There I saw above me the dark sky, and the sun as it fell
on the mountain was far brighter here than in the plains below, because a
smaller extent of atmosphere lay between the summit of the mountain and
the sun. Again as an illustration of the colour of the atmosphere I will
mention the smoke of old and dry wood, which, as it comes out of a
chimney, appears to turn very blue, when seen between the eye and the dark
distance. But as it rises, and comes between the eye and the bright
atmosphere, it at once shows of an ashy grey colour; and this happens
because it no longer has darkness beyond it, but this bright and luminous
space. If the smoke is from young, green wood, it will not appear blue,
because, not being transparent and being full of superabundant moisture, it
has the effect of condensed clouds which take distinct lights and shadows
like a solid body. The same occurs with the atmosphere, which, when
overcharged with moisture appears white, and the small amount of heated
moisture makes it dark, of a dark blue colour; and this will suffice us so far
as concerns the colour of the atmosphere; though it might be added that, if
this transparent blue were the natural colour of the atmosphere, it would
follow that wherever a larger mass air intervened between the eye and the
element of fire, the azure colour would be more intense; as we see in blue
glass and in sapphires, which are darker in proportion as they are larger. But
the atmosphere in such circumstances behaves in an opposite manner,
inasmuch as where a greater quantity of it lies between the eye and the
sphere of fire, it is seen much whiter. This occurs towards the horizon. And
the less the extent of atmosphere between the eye and the sphere of fire, the
deeper is the blue colour, as may be seen even on low plains. Hence it
follows, as I say, that the atmosphere assumes this azure hue by reason of

the particles of moisture which catch the rays of the sun. Again, we may
note the difference in particles of dust, or particles of smoke, in the sun
beams admitted through holes into a dark chamber, when the former will
look ash grey and the thin smoke will appear of a most beautiful blue; and it
may be seen again in in the dark shadows of distant mountains when the air
between the eye and those shadows will look very blue, though the brightest
parts of those mountains will not differ much from their true colour. But if
any one wishes for a final proof let him paint a board with various colours,
among them an intense black; and over all let him lay a very thin and
transparent [coating of] white. He will then see that this transparent white
will nowhere show a more beautiful blue than over the black—but it must
be very thin and finely ground.

[Footnote 7: reta here has the sense of malanno.]

301.

Experience shows us that the air must have darkness beyond it and yet it
appears blue. If you produce a small quantity of smoke from dry wood and
the rays of the sun fall on this smoke, and if you then place behind the
smoke a piece of black velvet on which the sun does not shine, you will see
that all the smoke which is between the eye and the black stuff will appear
of a beautiful blue colour. And if instead of the velvet you place a white
cloth smoke, that is too thick smoke, hinders, and too thin smoke does not
produce, the perfection of this blue colour. Hence a moderate amount of
smoke produces the finest blue. Water violently ejected in a fine spray and
in a dark chamber where the sun beams are admitted produces these blue
rays and the more vividly if it is distilled water, and thin smoke looks blue.
This I mention in order to show that the blueness of the atmosphere is
caused by the darkness beyond it, and these instances are given for those
who cannot confirm my experience on Monboso.

302.

When the smoke from dry wood is seen between the eye of the spectator
and some dark space [or object], it will look blue. Thus the sky looks blue
by reason of the darkness beyond it. And if you look towards the horizon of
the sky, you will see the atmosphere is not blue, and this is caused by its
density. And thus at each degree, as you raise your eyes above the horizon
up to the sky over your head, you will see the atmosphere look darker [blue]
and this is because a smaller density of air lies between your eye and the
[outer] darkness. And if you go to the top of a high mountain the sky will
look proportionately darker above you as the atmosphere becomes rarer
between you and the [outer] darkness; and this will be more visible at each
degree of increasing height till at last we should find darkness.

That smoke will look bluest which rises from the driest wood and which
is nearest to the fire and is seen against the darkest background, and with
the sunlight upon it.

303.

A dark object will appear bluest in proportion as it has a greater mass of
luminous atmosphere between it and the eye. As may be seen in the colour
of the sky.

304.

The atmosphere is blue by reason of the darkness above it because black
and white make blue.

305.

In the morning the mist is denser above than below, because the sun
draws it upwards; hence tall buildings, even if the summit is at the same

distance as the base have the summit invisible. Therefore, also, the sky
looks darkest [in colour] overhead, and towards the horizon it is not blue
but rather between smoke and dust colour.

The atmosphere, when full of mist, is quite devoid of blueness, and only
appears of the colour of clouds, which shine white when the weather is fine.
And the more you turn to the west the darker it will be, and the brighter as
you look to the east. And the verdure of the fields is bluish in a thin mist,
but grows grey in a dense one.

The buildings in the west will only show their illuminated side, where the
sun shines, and the mist hides the rest. When the sun rises and chases away
the haze, the hills on the side where it lifts begin to grow clearer, and look
blue, and seem to smoke with the vanishing mists; and the buildings reveal
their lights and shadows; through the thinner vapour they show only their
lights and through the thicker air nothing at all. This is when the movement
of the mist makes it part horizontally, and then the edges of the mist will be
indistinct against the blue of the sky, and towards the earth it will look
almost like dust blown up. In proportion as the atmosphere is dense the
buildings of a city and the trees in a landscape will look fewer, because only
the tallest and largest will be seen.

Darkness affects every thing with its hue, and the more an object differs
from darkness, the more we see its real and natural colour. The mountains
will look few, because only those will be seen which are farthest apart;
since, at such a distance, the density increases to such a degree that it causes
a brightness by which the darkness of the hills becomes divided and
vanishes indeed towards the top. There is less [mist] between lower and
nearer hills and yet little is to be distinguished, and least towards the
bottom.

306.

The surface of an object partakes of the colour of the light which
illuminates it; and of the colour of the atmosphere which lies between the
eye and that object, that is of the colour of the transparent medium lying
between the object and the eye; and among colours of a similar character
the second will be of the same tone as the first, and this is caused by the
increased thickness of the colour of the medium lying between the object
and the eye.

307. OF PAINTING.

Of various colours which are none of them blue that which at a great
distance will look bluest is the nearest to black; and so, conversely, the
colour which is least like black will at a great distance best preserve its own
colour.

Hence the green of fields will assume a bluer hue than yellow or white
will, and conversely yellow or white will change less than green, and red
still less.

VII.

On the Proportions and on the Movements of the Human Figure.

Leonardo's researches on the proportions and movements of the human
figure must have been for the most part completed and written before the
year 1498; for LUCA PACIOLO writes, in the dedication to Ludovico il
Moro, of his book Divina Proportione, which was published in that year:
"Leonardo da venci … hauedo gia co tutta diligetia al degno libro de pictura
e movimenti humani posto fine".

The selection of Leonardo's axioms contained in the Vatican copy
attributes these words to the author: "e il resto si dira nella universale

misura del huomo". (MANZI, p. 147; LUDWIG, No. 264). LOMAZZO,
again, in his Idea del Tempio della Pittura Milano 1590, cap. IV, says:
"Lionardo Vinci … dimostro anco in figura tutte le proporzioni dei membri
del corpo umano".

The Vatican copy includes but very few sections of the "Universale
misura del huomo" _and until now nothing has been made known of the
original MSS. on the subject which have supplied the very extensive
materials for this portion of the work. The collection at Windsor, belonging
to her Majesty the Queen, includes by far the most important part of
Leonardo's investigations on this subject, constituting about half of the
whole of the materials here published; and the large number of original
drawings adds greatly to the interest which the subject itself must
command. Luca Paciolo would seem to have had these MSS. (which I have
distinguished by the initials W. P.) in his mind when he wrote the passage
quoted above. Still, certain notes of a later date—such as Nos. 360, 362 and
363, from MS. E, written in 1513—14, sufficiently prove that Leonardo did
not consider his earlier studies on the Proportions and Movements of the
Human Figure final and complete, as we might suppose from Luca
Paciolo's statement. Or else he took the subject up again at a subsequent
period, since his former researches had been carried on at Milan between
1490 and 1500. Indeed it is highly probable that the anatomical studies
which he was pursuing zvith so much zeal between 1510—16 should have
led him to reconsider the subject of Proportion.

Preliminary observations (308. 309).

308.

Every man, at three years old is half the full height he will grow to at last.

309.

If a man 2 braccia high is too small, one of four is too tall, the medium
being what is admirable. Between 2 and 4 comes 3; therefore take a man of
3 braccia in height and measure him by the rule I will give you. If you tell
me that I may be mistaken, and judge a man to be well proportioned who
does not conform to this division, I answer that you must look at many men
of 3 braccia, and out of the larger number who are alike in their limbs
choose one of those who are most graceful and take your measurements.
The length of the hand is 1/3 of a braccio [8 inches] and this is found 9
times in man. And the face [Footnote 7: The account here given of the
braccio is of importance in understanding some of the succeeding chapters.
Testa must here be understood to mean the face. The statements in this
section are illustrated in part on Pl. XI.] is the same, and from the pit of the
throat to the shoulder, and from the shoulder to the nipple, and from one
nipple to the other, and from each nipple to the pit of the throat.

Proportions of the head and face (310-318).

310.

The space between the parting of the lips [the mouth] and the base of the
nose is one-seventh of the face.

The space from the mouth to the bottom of the chin c d is the fourth part
of the face and equal to the width of the mouth.

The space from the chin to the base of the nose e f is the third part of the
face and equal to the length of the nose and to the forehead.

The distance from the middle of the nose to the bottom of the chin g h, is
half the length of the face.

The distance from the top of the nose, where the eyebrows begin, to the
bottom of the chin, i k, is two thirds of the face.

The space from the parting of the lips to the top of the chin l m, that is
where the chin ends and passes into the lower lip of the mouth, is the third
of the distance from the parting of the lips to the bottom of the chin and is
the twelfth part of the face. From the top to the bottom of the chin m n is the
sixth part of the face and is the fifty fourth part of a man's height.

From the farthest projection of the chin to the throat o p is equal to the
space between the mouth and the bottom of the chin, and a fourth of the
face.

The distance from the top of the throat to the pit of the throat below q r is
half the length of the face and the eighteenth part of a man's height.

From the chin to the back of the neck s t, is the same distance as between
the mouth and the roots of the hair, that is three quarters of the head.

From the chin to the jaw bone v x is half the head and equal to the
thickness of the neck in profile.

The thickness of the head from the brow to the nape is once and 3/4 that
of the neck.

[Footnote: The drawings to this text, lines 1-10 are on Pl. VII, No. I. The
two upper sketches of heads, Pl. VII, No. 2, belong to lines 11-14, and in
the original are placed immediately below the sketches reproduced on Pl.
VII, No. 1.]

311.

The distance from the attachment of one ear to the other is equal to that
from the meeting of the eyebrows to the chin, and in a fine face the width of
the mouth is equal to the length from the parting of the lips to the bottom of
the chin.

312.

The cut or depression below the lower lip of the mouth is half way
between the bottom of the nose and the bottom of the chin.

The face forms a square in itself; that is its width is from the outer corner
of one eye to the other, and its height is from the very top of the nose to the
bottom of the lower lip of the mouth; then what remains above and below
this square amounts to the height of such another square, a b is equal to the
space between c d; d n in the same way to n c, and likewise s r, q p, h k are
equal to each other.

It is as far between m and s as from the bottom of the nose to the chin.
The ear is exactly as long as the nose. It is as far from x to j as from the
nose to the chin. The parting of the mouth seen in profile slopes to the angle
of the jaw. The ear should be as high as from the bottom of the nose to the
top of the eye-lid. The space between the eyes is equal to the width of an
eye. The ear is over the middle of the neck, when seen in profile. The
distance from 4 to 5 is equal to that from s_ to r.

[Footnote: See Pl. VIII, No. I, where the text of lines 3-13 is also given in
facsimile.]

313.

(a b) is equal to (c d).

[Footnote: See Pl. VII, No. 3. Reference may also be made here to two
pen and ink drawings of heads in profile with figured measurements, of
which there is no description in the MS. These are given on Pl. XVII, No. 2.
—A head, to the left, with part of the torso [W. P. 5a], No. 1 on the same
plate is from MS. A 2b and in the original occurs on a page with wholly
irrelevant text on matters of natural history. M. RAVAISSON in his edition
of the Paris MS. A has reproduced this head and discussed it fully [note on
page 12]; he has however somewhat altered the original measurements. The
complicated calculations which M. RAVAISSON has given appear to me in
no way justified. The sketch, as we see it, can hardly have been intended for
any thing more than an experimental attempt to ascertain relative
proportions. We do not find that Leonardo made use of circular lines in any
other study of the proportions of the human head. At the same time we see
that the proportions of this sketch are not in accordance with the rules
which he usually observed (see for instance No. 310).]

The head a f 1/6 larger than n f.

315.

From the eyebrow to the junction of the lip with the chin, and the angle
of the jaw and the upper angle where the ear joins the temple will be a
perfect square. And each side by itself is half the head.

The hollow of the cheek bone occurs half way between the tip of the nose
and the top of the jaw bone, which is the lower angle of the setting on of the
ear, in the frame here represented.

From the angle of the eye-socket to the ear is as far as the length of the
ear, or the third of the face.

[Footnote: See Pl. IX. The text, in the original is written behind the head.
The handwriting would seem to indicate a date earlier than 1480. On the
same leaf there is a drawing in red chalk of two horsemen of which only a
portion of the upper figure is here visible. The whole leaf measures 22 1/2
centimetres wide by 29 long, and is numbered 127 in the top right-hand
corner.]

316.

From a to b—that is to say from the roots of the hair in front to the top of
the head—ought to be equal to c d;—that is from the bottom of the nose to
the meeting of the lips in the middle of the mouth. From the inner corner of
the eye m to the top of the head a is as far as from m down to the chin s. s c
f b are all at equal distances from each other.

[Footnote: The drawing in silver-point on bluish tinted paper—Pl. X—
which belongs to this chapter has been partly drawn over in ink by
Leonardo himself.]

317.

From the top of the head to the bottom of the chin is 1/9, and from the
roots of the hair to the chin is 1/9 of the distance from the roots of the hair
to the ground. The greatest width of the face is equal to the space between
the mouth and the roots of the hair and is 1/12 of the whole height. From
the top of the ear to the top of the head is equal to the distance from the
bottom of the chin to the lachrymatory duct of the eye; and also equal to the
distance from the angle of the chin to that of the jaw; that is the 1/16 of the
whole. The small cartilage which projects over the opening of the ear
towards the nose is half-way between the nape and the eyebrow; the
thickness of the neck in profile is equal to the space between the chin and

the eyes, and to the space between the chin and the jaw, and it is 1/18 of the
height of the man.

318.

a b, c d, e f, g h, i k are equal to each other in size excepting that d f is
accidental.

[Footnote: See Pl. XI.]

Proportions of the head seen in front (319-321).

319.

a n o f are equal to the mouth.

a c and a f are equal to the space between one eye and the other.

n m o f q r are equal to half the width of the eye lids, that is from the
inner [lachrymatory] corner of the eye to its outer corner; and in like
manner the division between the chin and the mouth; and in the same way
the narrowest part of the nose between the eyes. And these spaces, each in
itself, is the 19th part of the head, n o is equal to the length of the eye or of
the space between the eyes.

m c is 1/3 of n m measuring from the outer corner of the eyelids to the
letter c. b s will be equal to the width of the nostril.

[Footnote: See Pl. XII.]

320.

The distance between the centres of the pupils of the eyes is 1/3 of the
face. The space between the outer corners of the eyes, that is where the eye

ends in the eye socket which contains it, thus the outer corners, is half the
face.

The greatest width of the face at the line of the eyes is equal to the
distance from the roots of the hair in front to the parting of the lips.

[Footnote: There are, with this section, two sketches of eyes, not
reproduced here.]

321.

The nose will make a double square; that is the width of the nose at the
nostrils goes twice into the length from the tip of the nose to the eyebrows.
And, in the same way, in profile the distance from the extreme side of the
nostril where it joins the cheek to the tip of the nose is equal to the width of
the nose in front from one nostril to the other. If you divide the whole
length of the nose—that is from the tip to the insertion of the eyebrows, into
4 equal parts, you will find that one of these parts extends from the tip of
the nostrils to the base of the nose, and the upper division lies between the
inner corner of the eye and the insertion of the eyebrows; and the two
middle parts [together] are equal to the length of the eye from the inner to
the outer corner.

[Footnote: The two bottom sketches on Pl. VII, No. 4 face the six lines of
this section,—With regard to the proportions of the head in profile see No.
312.]

322.

The great toe is the sixth part of the foot, taking the measure in profile,
on the inside of the foot, from where this toe springs from the ball of the
sole of the foot to its tip a b; and it is equal to the distance from the mouth

to the bottom of the chin. If you draw the foot in profile from the outside,
make the little toe begin at three quarters of the length of the foot, and you
will find the same distance from the insertion of this toe as to the farthest
prominence of the great toe.

323.

For each man respectively the distance between a b is equal to c d.

324.

Relative proportion of the hand and foot.

The foot is as much longer than the hand as the thickness of the arm at
the wrist where it is thinnest seen facing.

Again, you will find that the foot is as much longer than the hand as the
space between the inner angle of the little toe to the last projection of the
big toe, if you measure along the length of the foot.

The palm of the hand without the fingers goes twice into the length of the
foot without the toes.

If you hold your hand with the fingers straight out and close together you
will find it to be of the same width as the widest part of the foot, that is
where it is joined onto the toes.

And if you measure from the prominence of the inner ancle to the end of
the great toe you will find this measure to be as long as the whole hand.

From the top angle of the foot to the insertion of the toes is equal to the
hand from wrist joint to the tip of the thumb.

The smallest width of the hand is equal to the smallest width of the foot
between its joint into the leg and the insertion of the toes.

The width of the heel at the lower part is equal to that of the arm where it
joins the hand; and also to the leg where it is thinnest when viewed in front.

The length of the longest toe, from its first division from the great toe to
its tip is the fourth of the foot from the centre of the ancle bone to the tip,
and it is equal to the width of the mouth. The distance between the mouth
and the chin is equal to that of the knuckles and of the three middle fingers
and to the length of their first joints if the hand is spread, and equal to the
distance from the joint of the thumb to the outset of the nails, that is the
fourth part of the hand and of the face.

The space between the extreme poles inside and outside the foot called
the ancle or ancle bone a b is equal to the space between the mouth and the
inner corner of the eye.

325.

The foot, from where it is attached to the leg, to the tip of the great toe is
as long as the space between the upper part of the chin and the roots of the
hair a b; and equal to five sixths of the face.

326.

a d is a head's length, c b is a head's length. The four smaller toes are all
equally thick from the nail at the top to the bottom, and are 1/13 of the foot.

[Footnote: See Pl. XIV, No. 1, a drawing of a foot with the text in three
lines below it.]

327.

The whole length of the foot will lie between the elbow and the wrist and
between the elbow and the inner angle of the arm towards the breast when
the arm is folded. The foot is as long as the whole head of a man, that is
from under the chin to the topmost part of the head[Footnote 2: nel modo
che qui i figurato. See Pl. VII, No. 4, the upper figure. The text breaks off at
the end of line 2 and the text given under No. 321 follows below. It may be
here remarked that the second sketch on W. P. 311 has in the original no
explanatory text.] in the way here figured.

Proportions of the leg (328-331).

328.

The greatest thickness of the calf of the leg is at a third of its height a b,
and is a twentieth part thicker than the greatest thickness of the foot.

a c is half of the head, and equal to d b and to the insertion of the five
toes e f. d k diminishes one sixth in the leg g h. g h is 1/3 of the head; m n
increases one sixth from a e and is 7/12 of the head, o p is 1/10 less than d k
and is 6/17 of the head. a is at half the distance between b q, and is 1/4 of
the man. r is half way between s and b[Footnote 11: b is here and later on
measured on the right side of the foot as seen by the spectator.]. The
concavity of the knee outside r is higher than that inside a. The half of the
whole height of the leg from the foot r, is half way between the prominence
s and the ground b. v is half way between t and b. The thickness of the thigh
seen in front is equal to the greatest width of the face, that is 2/3 of the
length from the chin to the top of the head; z r is 5/6 of 7 to v; m n is equal
to 7 v and is 1/4 of r b, x y goes 3 times into r b, and into r s.

[Footnote 22-35: The sketch illustrating these lines is on Pl. XIII,
No. 2.]

[Footnote 22: a b entra in c f 6 e 6 in c n. Accurate measurement however
obliges us to read 7 for 6.] a b goes six times into c f and six times into c n
and is equal to g h; i k l m goes 4 times into d f, and 4 times into d n and is
3/7 of the foot; p q r s goes 3 times into _d f, and 3 times into b n;
[Footnote: 25. y is not to be found on the diagram and x occurs twice; this
makes the passage very obscure.] x y is 1/8 of x f and is equal to n q. 3 7 is
1/9 of n f; 4 5 is 1/10 of n f [Footnote: 22-27. Compare with this lines 18-24
of No. 331, and the sketch of a leg in profile Pl. XV.].

I want to know how much a man increases in height by standing on tip-
toe and how much p g diminishes by stooping; and how much it increases at
n q likewise in bending the foot.

[Footnote 34: e f 4 dal cazo. By reading i for e the sense of this passage is
made clear.] e f is four times in the distance between the genitals and the
sole of the foot; [Footnote 35: 2 is not to be found in the sketch which
renders the passage obscure. The two last lines are plainly legible in the
facsimile.] 3 7 is six times from 3 to 2 and is equal to g h and i k.

[Footnote: The drawing of a leg seen in front Pl. XIII, No. 1 belongs to
the text from lines 3-21. The measurements in this section should be
compared with the text No. 331, lines 1-13, and the sketch of a leg seen in
front on Pl. XV.]

329.

The length of the foot from the end of the toes to the heel goes twice into
that from the heel to the knee, that is where the leg bone [fibula] joins the
thigh bone [femur].

330.

a n b are equal; c n d are equal; n c makes two feet; n d makes 2 feet.

[Footnote: See the lower sketch, Pl. XIV, No. 1.]

331.

m n o are equal. The narrowest width of the leg seen in front goes 8 times
from the sole of the foot to the joint of the knee, and is the same width as
the arm, seen in front at the wrist, and as the longest measure of the ear, and
as the three chief divisions into which we divide the face; and this
measurement goes 4 times from the wrist joint of the hand to the point of
the elbow. [14] The foot is as long as the space from the knee between a
and b; and the patella of the knee is as long as the leg between r and s.

[18] The least thickness of the leg in profile goes 6 times from the sole of
the foot to the knee joint and is the same width as the space between the
outer corner of the eye and the opening of the ear, and as the thickest part of
the arm seen in profile and between the inner corner of the eye and the
insertion of the hair.

a b c [d] are all relatively of equal length, c d goes twice from the sole of
the foot to the centre of the knee and the same from the knee to the hip.

[28]a b c are equal; a to b is 2 feet—that is to say measuring from the
heel to the tip of the great toe.

[Footnote: See Pl. XV. The text of lines 2-17 is to the left of the front
view of the leg, to which it refers. Lines 18-27 are in the middle column and
refer to the leg seen in profile and turned to the left, on the right hand side
of the writing. Lines 20-30 are above, to the left and apply to the sketch
below them.

Some farther remarks on the proportion of the leg will be found in
No. 336, lines 6, 7.]

On the central point of the whole body.

332.

In kneeling down a man will lose the fourth part of his height.

When a man kneels down with his hands folded on his breast the navel
will mark half his height and likewise the points of the elbows.

Half the height of a man who sits—that is from the seat to the top of the
head—will be where the arms fold below the breast, and below the
shoulders. The seated portion—that is from the seat to the top of the head—
will be more than half the man's [whole height] by the length of the
scrotum.

[Footnote: See Pl. VIII, No. 2.]

The relative proportions of the torso and of the whole figure.

333.

The cubit is one fourth of the height of a man and is equal to the greatest
width of the shoulders. From the joint of one shoulder to the other is two
faces and is equal to the distance from the top of the breast to the navel.
[Footnote 9: dalla detta somita. It would seem more accurate to read here
dal detto ombilico.] From this point to the genitals is a face's length.

[Footnote: Compare with this the sketches on the other page of the same
leaf. Pl. VIII, No. 2.]

The relative proportions of the head and of the torso.

334.

From the roots of the hair to the top of the breast a b is the sixth part of
the height of a man and this measure is equal.

From the outside part of one shoulder to the other is the same distance as
from the top of the breast to the navel and this measure goes four times
from the sole of the foot to the lower end of the nose.

The [thickness of] the arm where it springs from the shoulder in front
goes 6 times into the space between the two outside edges of the shoulders
and 3 times into the face, and four times into the length of the foot and three
into the hand, inside or outside.

[Footnote: The three sketches Pl. XIV, No. 2 belong to this text.]

The relative proportions of the torso and of the leg (335. 336).

335.

a b c are equal to each other and to the space from the armpit of the
shoulder to the genitals and to the distance from the tip of the fingers of the
hand to the joint of the arm, and to the half of the breast; and you must
know that c b is the third part of the height of a man from the shoulders to
the ground; d e f are equal to each other and equal to the greatest width of
the shoulders.

[Footnote: See Pl. XVI, No. 1.]

336.

—Top of the chin—hip—the insertion of the middle finger. The end of
the calf of the leg on the inside of the thigh.—The end of the swelling of the

shin bone of the leg. [6] The smallest thickness of the leg goes 3 times into
the thigh seen in front.

[Footnote: See Pl. XVII, No. 2, middle sketch.]

The relative proportions of the torso and of the foot.

337.

The torso a b in its thinnest part measures a foot; and from a to b is 2
feet, which makes two squares to the seat—its thinnest part goes 3 times
into the length, thus making 3 squares.

[Footnote: See Pl, VII, No. 2, the lower sketch.]

The proportions of the whole figure (338-341).

338.

A man when he lies down is reduced to 1/9 of his height.

339.

The opening of the ear, the joint of the shoulder, that of the hip and the
ancle are in perpendicular lines; a n is equal to m o.

[Footnote: See Pl. XVI, No. 2, the upper sketch.]

340.

From the chin to the roots of the hair is 1/10 of the whole figure. From
the joint of the palm of the hand to the tip of the longest finger is 1/10.
From the chin to the top of the head 1/8; and from the pit of the stomach to
the top of the breast is 1/6, and from the pit below the breast bone to the top

of the head 1/4. From the chin to the nostrils 1/3 Part of the face, the same
from the nostrils to the brow and from the brow to the roots of the hair, and
the foot is 1/6, the elbow 1/4, the width of the shoulders 1/4.

341.

The width of the shoulders is 1/4 of the whole. From the joint of the
shoulder to the hand is 1/3, from the parting of the lips to below the
shoulder-blade is one foot.

The greatest thickness of a man from the breast to the spine is one 8th of
his height and is equal to the space between the bottom of the chin and the
top of the head.

The greatest width is at the shoulders and goes 4.

The torso from the front and back.

342.

The width of a man under the arms is the same as at the hips.

A man's width across the hips is equal to the distance from the top of the
hip to the bottom of the buttock, when a man stands equally balanced on
both feet; and there is the same distance from the top of the hip to the
armpit. The waist, or narrower part above the hips will be half way between
the arm pits and the bottom of the buttock.

[Footnote: The lower sketch Pl. XVI, No. 2, is drawn by the side of line
1.]

Vitruvius' scheme of proportions.

343.

Vitruvius, the architect, says in his work on architecture that the
measurements of the human body are distributed by Nature as follows: that
is that 4 fingers make 1 palm, and 4 palms make 1 foot, 6 palms make 1
cubit; 4 cubits make a man's height. And 4 cubits make one pace and 24
palms make a man; and these measures he used in his buildings. If you open
your legs so much as to decrease your height 1/14 and spread and raise your
arms till your middle fingers touch the level of the top of your head you
must know that the centre of the outspread limbs will be in the navel and
the space between the legs will be an equilateral triangle.

The length of a man's outspread arms is equal to his height.

From the roots of the hair to the bottom of the chin is the tenth of a man's
height; from the bottom of the chin to the top of his head is one eighth of
his height; from the top of the breast to the top of his head will be one sixth
of a man. From the top of the breast to the roots of the hair will be the
seventh part of the whole man. From the nipples to the top of the head will
be the fourth part of a man. The greatest width of the shoulders contains in
itself the fourth part of the man. From the elbow to the tip of the hand will
be the fifth part of a man; and from the elbow to the angle of the armpit will
be the eighth part of the man. The whole hand will be the tenth part of the
man; the beginning of the genitals marks the middle of the man. The foot is
the seventh part of the man. From the sole of the foot to below the knee will
be the fourth part of the man. From below the knee to the beginning of the
genitals will be the fourth part of the man. The distance from the bottom of
the chin to the nose and from the roots of the hair to the eyebrows is, in
each case the same, and like the ear, a third of the face.

[Footnote: See Pl. XVIII. The original leaf is 21 centimetres wide and 33
1/2 long. At the ends of the scale below the figure are written the words diti
(fingers) and palmi (palms). The passage quoted from Vitruvius is Book III,

Cap. 1, and Leonardo's drawing is given in the editions of Vitruvius by FRA
GIOCONDO (Venezia 1511, fol., Firenze 1513, 8vo.) and by CESARIANO
(Como 1521).]

The arm and head.

344.

From b to a is one head, as well as from c to a and this happens when the
elbow forms a right angle.

[Footnote: See Pl. XLI, No. 1.]

Proportions of the arm (345-349).

345.

From the tip of the longest finger of the hand to the shoulder joint is four
hands or, if you will, four faces.

a b c are equal and each interval is 2 heads.

[Footnote: Lines 1-3 are given on Pl. XV below the front view of the leg;
lines 4 and 5 are below again, on the left side. The lettering refers to the
bent arm near the text.]

346.

The hand from the longest finger to the wrist joint goes 4 times from the
tip of the longest finger to the shoulder joint.

347.

a b c are equal to each other and to the foot and to the space between the
nipple and the navel d e will be the third part of the whole man.

f g is the fourth part of a man and is equal to g h and measures a cubit.

[Footnote: See Pl. XIX, No. 1. 1. mamolino (=bambino, little child) may
mean here the navel.]

348.

a b goes 4 times into a c and 9 into a m. The greatest thickness of the arm
between the elbow and the hand goes 6 times into a m and is equal to r f.
The greatest thickness of the arm between the shoulder and the elbow goes
4 times into c m, and is equal to h n g. The smallest thickness of the arm
above the elbow x y is not the base of a square, but is equal to half the space
h 3 which is found between the inner joint of the arm and the wrist joint.

[11]The width of the wrist goes 12 times into the whole arm; that is from
the tip of the fingers to the shoulder joint; that is 3 times into the hand and 9
into the arm.

The arm when bent is 4 heads.

The arm from the shoulder to the elbow in bending increases in length,
that is in the length from the shoulder to the elbow, and this increase is
equal to the thickness of the arm at the wrist when seen in profile. And the
space between the bottom of the chin and the parting of the lips, is equal to
the thickness of the 2 middle fingers, and to the width of the mouth and to
the space between the roots of the hair on the forehead and the top of the
head [Footnote: Queste cose. This passage seems to have been written on
purpose to rectify the foregoing lines. The error is explained by the
accompanying sketch of the bones of the arm.]. All these distances are

equal to each other, but they are not equal to the above-mentioned increase
in the arm.

The arm between the elbow and wrist never increases by being bent or
extended.

The arm, from the shoulder to the inner joint when extended.

When the arm is extended, p n is equal to n a. And when it is bent n a
diminishes 1/6 of its length and p n does the same. The outer elbow joint
increases 1/7 when bent; and thus by being bent it increases to the length of
2 heads. And on the inner side, by bending, it is found that whereas the arm
from where it joins the side to the wrist, was 2 heads and a half, in bending
it loses the half head and measures only two: one from the [shoulder] joint
to the end [by the elbow], and the other to the hand.

The arm when folded will measure 2 faces up to the shoulder from the
elbow and 2 from the elbow to the insertion of the four fingers on the palm
of the hand. The length from the base of the fingers to the elbow never
alters in any position of the arm.

If the arm is extended it decreases by 1/3 of the length between b and h;
and if—being extended—it is bent, it will increase the half of o e. [Footnote
59-61: The figure sketched in the margin is however drawn to different
proportions.] The length from the shoulder to the elbow is the same as from
the base of the thumb, inside, to the elbow a b c.

[Footnote 62-64: The arm sketch on the margin of the MS. is identically
the same as that given below on Pl. XX which may therefore be referred to
in this place. In line 62 we read therefore z c for m n.] The smallest
thickness of the arm in profile z c goes 6 times between the knuckles of the
hand and the dimple of the elbow when extended and 14 times in the whole

arm and 42 in the whole man [64]. The greatest thickness of the arm in
profile is equal to the greatest thickness of the arm in front; but the first is
placed at a third of the arm from the shoulder joint to the elbow and the
other at a third from the elbow towards the hand.

[Footnote: Compare Pl. XVII. Lines 1-10 and 11-15 are written in two
columns below the extended arm, and at the tips of the fingers we find the
words: fine d'unghie (ends of the nails). Part of the text—lines 22 to 25—is
visible by the side of the sketches on Pl. XXXV, No. 1.]

349.

From the top of the shoulder to the point of the elbow is as far as from
that point to the joints of the four fingers with the palm of the hand, and
each is 2 faces.

[5]a e is equal to the palm of the hand, r f and o g are equal to half a head
and each goes 4 times into a b and b c. From c to m is 1/2 a head; m n is 1/3
of a head and goes 6 times into c b and into b a; a b loses 1/7 of its length
when the arm is extended; c b never alters; o will always be the middle
point between a and s.

y l is the fleshy part of the arm and measures one head; and when the arm
is bent this shrinks 2/5 of its length; o a in bending loses 1/6 and so does o
r.

a b is 1/7 of r c. f s will be 1/8 of r c, and each of those 2 measurements
is the largest of the arm; k h is the thinnest part between the shoulder and
the elbow and it is 1/8 of the whole arm r c; o p is 1/5 of r l; c z goes 13
times into r c.

[Footnote: See Pl. XX where the text is also seen from lines 5-23.]

The movement of the arm (350-354).

350.

In the innermost bend of the joints of every limb the reliefs are converted
into a hollow, and likewise every hollow of the innermost bends becomes a
convexity when the limb is straightened to the utmost. And in this very
great mistakes are often made by those who have insufficient knowledge
and trust to their own invention and do not have recourse to the imitation of
nature; and these variations occur more in the middle of the sides than in
front, and more at the back than at the sides.

351.

When the arm is bent at an angle at the elbow, it will produce some
angle; the more acute the angle is, the more will the muscles within the
bend be shortened; while the muscles outside will become of greater length
than before. As is shown in the example; d c e will shrink considerably; and
b n will be much extended.

[Footnote: See Pl. XIX, No. 2.]

352.

OF PAINTING.

The arm, as it turns, thrusts back its shoulder towards the middle of the
back.

353.

The principal movements of the hand are 10; that is forwards, backwards,
to right and to left, in a circular motion, up or down, to close and to open,

and to spread the fingers or to press them together.

354.

OF THE MOTIONS OF THE FINGERS.

The movements of the fingers principally consist in extending and
bending them. This extension and bending vary in manner; that is,
sometimes they bend altogether at the first joint; sometimes they bend, or
extend, half way, at the 2nd joint; and sometimes they bend in their whole
length and in all the three joints at once. If the 2 first joints are hindered
from bending, then the 3rd joint can be bent with greater ease than before; it
can never bend of itself, if the other joints are free, unless all three joints are
bent. Besides all these movements there are 4 other principal motions of
which 2 are up and down, the two others from side to side; and each of
these is effected by a single tendon. From these there follow an infinite
number of other movements always effected by two tendons; one tendon
ceasing to act, the other takes up the movement. The tendons are made thick
inside the fingers and thin outside; and the tendons inside are attached to
every joint but outside they are not.

[Footnote 26: This head line has, in the original, no text to follow.] Of the
strength [and effect] of the 3 tendons inside the fingers at the 3 joints.

The movement of the torso (355-361).

355.

Observe the altered position of the shoulder in all the movements of the
arm, going up and down, inwards and outwards, to the back and to the
front, and also in circular movements and any others.

And do the same with reference to the neck, hands and feet and the breast
above the lips &c.

356.

Three are the principal muscles of the shoulder, that is b c d, and two are
the lateral muscles which move it forward and backward, that is a o; a
moves it forward, and o pulls it back; and bed raises it; a b c moves it
upwards and forwards, and c d o upwards and backwards. Its own weight
almost suffices to move it downwards.

The muscle d acts with the muscle c when the arm moves forward; and in
moving backward the muscle b acts with the muscle c.

[Footnote: See Pl. XXI. In the original the lettering has been written in
ink upon the red chalk drawing and the outlines of the figures have in most
places been inked over.]

357.

OF THE LOINS, WHEN BENT.

The loins or backbone being bent. The breasts are are always lower than
the shoulderblades of the back.

If the breast bone is arched the breasts are higher than the shoulderblades.

If the loins are upright the breast will always be found at the same level
as the shoulderblades.

[Footnote: See Pl. XXII, No. 1.]

358.

a b the tendon and ankle in raising the heel approach each other by a
finger's breadth; in lowering it they separate by a finger's breadth.

[Footnote: See Pl. XXII, No. 2. Compare this facsimile and text with
Pl. III, No. 2, and p. 152 of MANZI'S edition. Also with No. 274 of
LUDWIG'S edition of the Vatican Copy.]

359.

Just so much as the part d a of the nude figure decreases in this position
so much does the opposite part increase; that is: in proportion as the length
of the part d a diminishes the normal size so does the opposite upper part
increase beyond its [normal] size. The navel does not change its position to
the male organ; and this shrinking arises because when a figure stands on
one foot, that foot becomes the centre [of gravity] of the superimposed
weight. This being so, the middle between the shoulders is thrust above it
out of it perpendicular line, and this line, which forms the central line of the
external parts of the body, becomes bent at its upper extremity [so as to be]
above the foot which supports the body; and the transverse lines are forced
into such angles that their ends are lower on the side which is supported. As
is shown at a b c.

[Footnote: See Pl. XXII, No. 3.]

360.

OF PAINTING.

Note in the motions and attitudes of figures how the limbs vary, and their
feeling, for the shoulderblades in the motions of the arms and shoulders
vary the [line of the] back bone very much. And you will find all the causes
of this in my book of Anatomy.

361.

OF [CHANGE OF] ATTITUDE.

The pit of the throat is over the feet, and by throwing one arm forward
the pit of the throat is thrown off that foot. And if the leg is thrown forward
the pit of the throat is thrown forward; and. so it varies in every attitude.

362.

OF PAINTING.

Indicate which are the muscles, and which the tendons, which become
prominent or retreat in the different movements of each limb; or which do
neither [but are passive]. And remember that these indications of action are
of the first importance and necessity in any painter or sculptor who
professes to be a master &c.

And indicate the same in a child, and from birth to decrepitude at every
stage of its life; as infancy, childhood, boyhood, youth &c.

And in each express the alterations in the limbs and joints, which swell
and which grow thinner.

363.

O Anatomical Painter! beware lest the too strong indication of the bones,
sinews and muscles, be the cause of your becoming wooden in your
painting by your wish to make your nude figures display all their feeling.
Therefore, in endeavouring to remedy this, look in what manner the
muscles clothe or cover their bones in old or lean persons; and besides this,
observe the rule as to how these same muscles fill up the spaces of the
surface that extend between them, which are the muscles which never lose

their prominence in any amount of fatness; and which too are the muscles
of which the attachments are lost to sight in the very least plumpness. And
in many cases several muscles look like one single muscle in the increase of
fat; and in many cases, in growing lean or old, one single muscle divides
into several muscles. And in this treatise, each in its place, all their
peculiarities will be explained—and particularly as to the spaces between
the joints of each limb &c. Again, do not fail [to observe] the variations in
the forms of the above mentioned muscles, round and about the joints of the
limbs of any animal, as caused by the diversity of the motions of each limb;
for on some side of those joints the prominence of these muscles is wholly
lost in the increase or diminution of the flesh of which these muscles are
composed, &c.

[Footnote: DE ROSSI remarks on this chapter, in the Roman edition of
the Trattato, p. 504: "Non in questo luogo solo, ma in altri ancora osserverà
il lettore, che Lionardo va fungendo quelli che fanno abuso della loro
dottrina anatomica, e sicuramente con ciò ha in mira il suo rivale
Bonarroti, che di anatomia facea tanta pompa." Note, that Leonardo wrote
this passage in Rome, probably under the immediate impression of
MICHAELANGELO'S paintings in the Sistine Chapel and of RAPHAEL'S
Isaiah in Sant' Agostino.]

364.

OF THE DIFFERENT MEASUREMENTS OF BOYS AND MEN.

There is a great difference in the length between the joints in men and
boys for, in man, from the top of the shoulder [by the neck] to the elbow,
and from the elbow to the tip of the thumb and from one shoulder to the
other, is in each instance two heads, while in a boy it is but one because
Nature constructs in us the mass which is the home of the intellect, before
forming that which contains the vital elements.

365.

OF PAINTING.

Which are the muscles which subdivide in old age or in youth, when
becoming lean? Which are the parts of the limbs of the human frame where
no amount of fat makes the flesh thicker, nor any degree of leanness ever
diminishes it?

The thing sought for in this question will be found in all the external
joints of the bones, as the shoulder, elbow, wrists, finger-joints, hips, knees,
ankle-bone and toes and the like; all of which shall be told in its place. The
greatest thickness acquired by any limb is at the part of the muscles which
is farthest from its attachments.

Flesh never increases on those portions of the limb where the bones are
near to the surface.

At b r d a c e f the increase or diminution of the flesh never makes any
considerable difference. Nature has placed in front of man all those parts
which feel most pain under a blow; and these are the shin of the leg, the
forehead, and the nose. And this was done for the preservation of man,
since, if such pain were not felt in these parts, the number of blows to which
they would be exposed must be the cause of their destruction.

Describe why the bones of the arm and leg are double near the hand and
foot [respectively].

And where the flesh is thicker or thinner in the bending of the limbs.

366.

OF PAINTING.

Every part of the whole must be in proportion to the whole. Thus, if a
man is of a stout short figure he will be the same in all his parts: that is with
short and thick arms, wide thick hands, with short fingers with their joints
of the same character, and so on with the rest. I would have the same thing
understood as applying to all animals and plants; in diminishing, [the
various parts] do so in due proportion to the size, as also in enlarging.

367.

OF THE AGREEMENT OF THE PROPORTION OF THE LIMBS.

And again, remember to be very careful in giving your figures limbs, that
they must appear to agree with the size of the body and likewise to the age.
Thus a youth has limbs that are not very muscular not strongly veined, and
the surface is delicate and round, and tender in colour. In man the limbs are
sinewy and muscular, while in old men the surface is wrinkled, rugged and
knotty, and the sinews very prominent.

HOW YOUNG BOYS HAVE THEIR JOINTS JUST THE REVERSE OF THOSE OF MEN,
AS TO SIZE.

Little children have all the joints slender and the portions between them
are thick; and this happens because nothing but the skin covers the joints
without any other flesh and has the character of sinew, connecting the bones
like a ligature. And the fat fleshiness is laid on between one joint and the
next, and between the skin and the bones. But, since the bones are thicker at
the joints than between them, as a mass grows up the flesh ceases to have
that superfluity which it had, between the skin and the bones; whence the
skin clings more closely to the bone and the limbs grow more slender. But
since there is nothing over the joints but the cartilaginous and sinewy skin
this cannot dry up, and, not drying up, cannot shrink. Thus, and for this
reason, children are slender at the joints and fat between the joints; as may

be seen in the joints of the fingers, arms, and shoulders, which are slender
and dimpled, while in man on the contrary all the joints of the fingers, arms,
and legs are thick; and wherever children have hollows men have
prominences.

The movement of the human figure (368-375).

368.

Of the manner of representing the 18 actions of man. Repose, movement,
running, standing, supported, sitting, leaning, kneeling, lying down,
suspended. Carrying or being carried, thrusting, pulling, striking, being
struck, pressing down and lifting up.

[As to how a figure should stand with a weight in its hand [Footnote 8:
The original text ends here.] Remember].

369.

A sitting man cannot raise himself if that part of his body which is front
of his axis [centre of gravity] does not weigh more than that which is
behind that axis [or centre] without using his arms.

A man who is mounting any slope finds that he must involuntarily throw
the most weight forward, on the higher foot, rather than behind—that is in
front of the axis and not behind it. Hence a man will always, involuntarily,
throw the greater weight towards the point whither he desires to move than
in any other direction.

The faster a man runs, the more he leans forward towards the point he
runs to and throws more weight in front of his axis than behind. A man who
runs down hill throws the axis onto his heels, and one who runs up hill

throws it into the points of his feet; and a man running on level ground
throws it first on his heels and then on the points of his feet.

This man cannot carry his own weight unless, by drawing his body back
he balances the weight in front, in such a way as that the foot on which he
stands is the centre of gravity.

[Footnote: See Pl. XXII, No. 4.]

370.

How a man proceeds to raise himself to his feet, when he is sitting on
level ground.

371.

A man when walking has his head in advance of his feet.

A man when walking across a long level plain first leans [rather]
backwards and then as much forwards.

[Footnote 3-6: He strides forward with the air of a man going down hill;
when weary, on the contrary he walks like a man going up hill.]

372.

A man when running throws less weight on his legs than when standing
still. And in the same way a horse which is running feels less the weight of
the man he carries. Hence many persons think it wonderful that, in running,
the horse can rest on one single foot. From this it may be stated that when a
weight is in progressive motion the more rapid it is the less is the
perpendicular weight towards the centre.

373.

If a man, in taking a jump from firm ground, can leap 3 braccia, and
when he was taking his leap it were to recede 1/3 of a braccio, that would
be taken off his former leap; and so if it were thrust forward 1/3 of a
braccio, by how much would his leap be increased?

374.

OF DRAWING.

When a man who is running wants to neutralise the impetus that carries
him on he prepares a contrary impetus which is generated by his hanging
backwards. This can be proved, since, if the impetus carries a moving body
with a momentum equal to 4 and the moving body wants to turn and fall
back with a momentum of 4, then one momentum neutralises the other
contrary one, and the impetus is neutralised.

Of walking up and down (375-379)

375.

When a man wants to stop running and check the impetus he is forced to
hang back and take short quick steps. [Footnote: Lines 5-31 refer to the two
upper figures, and the lower figure to the right is explained by the last part
of the chapter.] The centre of gravity of a man who lifts one of his feet from
the ground always rests on the centre of the sole of the foot [he stands on].

A man, in going up stairs involuntarily throws so much weight forward
and on the side of the upper foot as to be a counterpoise to the lower leg, so
that the labour of this lower leg is limited to moving itself.

The first thing a man does in mounting steps is to relieve the leg he is
about to lift of the weight of the body which was resting on that leg; and
besides this, he gives to the opposite leg all the rest of the bulk of the whole

man, including [the weight of] the other leg; he then raises the other leg and
sets the foot upon the step to which he wishes to raise himself. Having done
this he restores to the upper foot all the weight of the body and of the leg
itself, and places his hand on his thigh and throws his head forward and
repeats the movement towards the point of the upper foot, quickly lifting
the heel of the lower one; and with this impetus he lifts himself up and at
the same time extends the arm which rested on his knee; and this extension
of the arm carries up the body and the head, and so straightens the spine
which was curved.

[32] The higher the step is which a man has to mount, the farther forward
will he place his head in advance of his upper foot, so as to weigh more on
a than on b; this man will not be on the step m. As is shown by the line g f.

[Footnote: See Pl. XXIII, No. 1. The lower sketch to the left belongs to
the four first lines.]

376.

I ask the weight [pressure] of this man at every degree of motion on these
steps, what weight he gives to b and to c.

[Footnote 8: These lines are, in the original, written in ink] Observe the
perpendicular line below the centre of gravity of the man.

[Footnote: See Pl. XXIII, No. 2.]

377.

In going up stairs if you place your hands on your knees all the labour
taken by the arms is removed from the sinews at the back of the knees.

[Footnote: See Pl. XXIII, No. 3.]

378.

The sinew which guides the leg, and which is connected with the patella
of the knee, feels it a greater labour to carry the man upwards, in proportion
as the leg is more bent; and the muscle which acts upon the angle made by
the thigh where it joins the body has less difficulty and has a less weight to
lift, because it has not the [additional] weight of the thigh itself. And
besides this it has stronger muscles, being those which form the buttock.

379.

A man coming down hill takes little steps, because the weight rests upon
the hinder foot, while a man mounting takes wide steps, because his weight
rests on the foremost foot.

[Footnote: See Pl. XXIII, No. 4.]

On the human body in action (380-388).

380.

OF THE HUMAN BODY IN ACTION.

When you want to represent a man as moving some weight consider what
the movements are that are to be represented by different lines; that is to say
either from below upwards, with a simple movement, as a man does who
stoops forward to take up a weight which he will lift as he straightens
himself. Or as a man does who wants to squash something backwards, or to
force it forwards or to pull it downwards with ropes passed through pullies
[Footnote 10: Compare the sketch on page 198 and on 201 (S. K. M. II.1
86b).]. And here remember that the weight of a man pulls in proportion as
his centre of gravity is distant from his fulcrum, and to this is added the
force given by his legs and bent back as he raises himself.

381.

Again, a man has even a greater store of strength in his legs than he
needs for his own weight; and to see if this is true, make a man stand on the
shore-sand and then put another man on his back, and you will see how
much he will sink in. Then take the man from off his back and make him
jump straight up as high as he can, and you will find that the print of his
feet will be made deeper by the jump than from having the man on his back.
Hence, here, by 2 methods it is proved that a man has double the strength he
requires to support his own body.

382.

OF PAINTING.

If you have to draw a man who is in motion, or lifting or pulling, or
carrying a weight equal to his own, in what way must you set on his legs
below his body?

[Footnote: In the MS. this question remains unanswered.]

383.

OF THE STRENGTH OF MAN.

A man pulling a [dead] weight balanced against himself cannot pull more
than his own weight. And if he has to raise it he will [be able to] raise as
much more than his weight as his strength may be more than that of other
men. [Footnote 7: The stroke at the end of this line finishes in the original in
a sort of loop or flourish, and a similar flourish occurs at the end of the
previous passage written on the same page. M. RAVAISSON regards these
as numbers (compare the photograph of page 30b in his edition of MS. A).
He remarks: "Ce chiffre 8 et, a la fin de l'alinea precedent, le chiffre 7 sont,

dans le manuscrit, des renvois."] The greatest force a man can apply, with
equal velocity and impetus, will be when he sets his feet on one end of the
balance [or lever] and then presses his shoulders against some stable body.
This will raise a weight at the other end of the balance [lever], equal to his
own weight and [added to that] as much weight as he can carry on his
shoulders.

384.

No animal can simply move [by its dead weight] a greater weight than
the sum of its own weight outside the centre of his fulcrum.

385.

A man who wants to send an arrow very far from the bow must be
standing entirely on one foot and raising the other so far from the foot he
stands on as to afford the requisite counterpoise to his body which is thrown
on the front foot. And he must not hold his arm fully extended, and in order
that he may be more able to bear the strain he must hold a piece of wood
which there is in all crossbows, extending from the hand to the breast, and
when he wishes to shoot he suddenly leaps forward at the same instant and
extends his arm with the bow and releases the string. And if he dexterously
does every thing at once it will go a very long way.

386.

When two men are at the opposite ends of a plank that is balanced, and if
they are of equal weight, and if one of them wants to make a leap into the
air, then his leap will be made down from his end of the plank and the man
will never go up again but must remain in his place till the man at the other
end dashes up the board.

[Footnote: See Pl. XXIV, No. 3.]

387.

Of delivering a blow to the right or left.

[Footnote: Four sketches on Pl. XXIV, No. 1 belong to this passage. The
rest of the sketches and notes on that page are of a miscellaneous nature.]

388.

Why an impetus is not spent at once [but diminishes] gradually in some
one direction? [Footnote 1: The paper has been damaged at the end of line
1.] The impetus acquired in the line a b c d is spent in the line d e but not so
completely but that some of its force remains in it and to this force is added
the momentum in the line d e with the force of the motive power, and it
must follow than the impetus multiplied by the blow is greater that the
simple impetus produced by the momentum d e.

[Footnote 8: The sketch No. 2 on Pl. XXIV stands, in the original,
between lines 7 and 8. Compare also the sketches on Pl. LIV.] A man who
has to deal a great blow with his weapon prepares himself with all his force
on the opposite side to that where the spot is which he is to hit; and this is
because a body as it gains in velocity gains in force against the object which
impedes its motion.

On hair falling down in curls.

389.

Observe the motion of the surface of the water which resembles that of
hair, and has two motions, of which one goes on with the flow of the
surface, the other forms the lines of the eddies; thus the water forms

eddying whirlpools one part of which are due to the impetus of the principal
current and the other to the incidental motion and return flow.

[Footnote: See Pl. XXV. Where also the text of this passage is given in
facsimile.]

On draperies (390—392).

390.

OF THE NATURE OF THE FOLDS IN DRAPERY.

That part of a fold which is farthest from the ends where it is confined
will fall most nearly in its natural form.

Every thing by nature tends to remain at rest. Drapery, being of equal
density and thickness on its wrong side and on its right, has a tendency to
lie flat; therefore when you give it a fold or plait forcing it out of its flatness
note well the result of the constraint in the part where it is most confined;
and the part which is farthest from this constraint you will see relapses most
into the natural state; that is to say lies free and flowing.

EXAMPLE.

[Footnote 13: a c sia. In the original text b is written instead of c—an
evident slip of the pen.] Let a b c be the fold of the drapery spoken of
above, a c will be the places where this folded drapery is held fast. I
maintain that the part of the drapery which is farthest from the plaited ends
will revert most to its natural form.

Therefore, b being farthest from a and c in the fold a b c it will be wider
there than anywhere else.

[Footnote: See Pl. XXVIII, No. 6, and compare the drawing from
Windsor Pl. XXX for farther illustration of what is here stated.]

391.

OF SMALL FOLDS IN DRAPERIES.

How figures dressed in a cloak should not show the shape so much as
that the cloak looks as if it were next the flesh; since you surely cannot wish
the cloak to be next the flesh, for you must suppose that between the flesh
and the cloak there are other garments which prevent the forms of the limbs
appearing distinctly through the cloak. And those limbs which you allow to
be seen you must make thicker so that the other garments may appear to be
under the cloak. But only give something of the true thickness of the limbs
to a nymph [Footnote 9: Una nifa. Compare the beautiful drawing of a
Nymph, in black chalk from the Windsor collection, Pl. XXVI.] or an angel,
which are represented in thin draperies, pressed and clinging to the limbs of
the figures by the action of the wind.

392.

You ought not to give to drapery a great confusion of many folds, but
rather only introduce them where they are held by the hands or the arms;
the rest you may let fall simply where it is its nature to flow; and do not let
the nude forms be broken by too many details and interrupted folds. How
draperies should be drawn from nature: that is to say if youwant to represent
woollen cloth draw the folds from that; and if it is to be silk, or fine cloth or
coarse, or of linen or of crape, vary the folds in each and do not represent
dresses, as many do, from models covered with paper or thin leather which
will deceive you greatly.

[Footnote: The little pen and ink drawing from Windsor (W. 102), given
on Pl. XXVIII, No. 7, clearly illustrates the statement made at the beginning
of this passage; the writing of the cipher 19 on the same page is in
Leonardo's hand; the cipher 21 is certainly not.]

VIII.

Botany for Painters and Elements of Landscape Painting.

The chapters composing this portion of the work consist of observations
on Form, Light and Shade in Plants, and particularly in Trees summed up
in certain general rules by which the author intends to guide the artist in
the pictorial representation of landscape.

With these the first principles of a Theory of Landscape painting are laid
down—a theory as profoundly thought out in its main lines as it is lucidly
worked out in its details. In reading these chapters the conviction is
irresistible that such a Botany for painters is or ought to be of similar
importance in the practice of painting as the principles of the Proportions
and Movements of the human figure i. e. Anatomy for painters.

There can be no doubt that Leonardo, in laying down these rules, did not
intend to write on Botany in the proper scientific sense—his own researches
on that subject have no place here; it need only be observed that they are
easily distinguished by their character and contents from those which are
here collected and arranged under the title 'Botany for painters'. In some
cases where this division might appear doubtful,—as for instance in No.
402—the Painter is directly addressed and enjoined to take the rule to heart
as of special importance in his art.

The original materials are principally derived from MS. G, in which we
often find this subject treated on several pages in succession without any of

that intermixture of other matters, which is so frequent in Leonardo's
writings. This MS., too, is one of the latest; when it was written, the great
painter was already more than sixty years of age, so we can scarcely doubt
that he regarded all he wrote as his final views on the subject. And the same
remark applies to the chapters from MSS. E and M which were also written
between 1513—15.

For the sake of clearness, however, it has been desirable to sacrifice—
with few exceptions—the original order of the passages as written, though it
was with much reluctance and only after long hesitation that I resigned
myself to this necessity. Nor do I mean to impugn the logical connection of
the author's ideas in his MS.; but it will be easily understood that the
sequence of disconnected notes, as they occurred to Leonardo and were
written down from time to time, might be hardly satisfactory as a systematic
arrangement of his principles. The reader will find in the Appendix an exact
account of the order of the chapters in the original MS. and from the data
there given can restore them at will. As the materials are here arranged, the
structure of the tree as regards the growth of the branches comes first (394-
411) and then the insertion of the leaves on the stems (412-419). Then
follow the laws of Light and Shade as applied, first, to the leaves (420-434),
and, secondly, to the whole tree and to groups of trees (435-457). After the
remarks on the Light and Shade in landscapes generally (458-464), we find
special observations on that of views of towns and buildings (465-469). To
the theory of Landscape Painting belong also the passages on the effect of
Wind on Trees (470-473) and on the Light and Shade of Clouds (474-477),
since we find in these certain comparisons with the effect of Light and
Shade on Trees (e. g.: in No. 476, 4. 5; and No. 477, 9. 12). The chapters
given in the Appendix Nos. 478 and 481 have hardly any connection with
the subjects previously treated.

Classification of trees.

393.

TREES.

Small, lofty, straggling, thick, that is as to foliage, dark, light, russet,
branched at the top; some directed towards the eye, some downwards; with
white stems; this transparent in the air, that not; some standing close
together, some scattered.

The relative thickness of the branches to the trunk (393—396).

394.

All the branches of a tree at every stage of its height when put together
are equal in thickness to the trunk [below them].

All the branches of a water [course] at every stage of its course, if they
are of equal rapidity, are equal to the body of the main stream.

395.

Every year when the boughs of a plant [or tree] have made an end of
maturing their growth, they will have made, when put together, a thickness
equal to that of the main stem; and at every stage of its ramification you
will find the thickness of the said main stem; as: i k, g h, e f, c d, a b, will
always be equal to each other; unless the tree is pollard—if so the rule does
not hold good.

All the branches have a direction which tends to the centre of the tree m.

[Footnote: The two sketches of leafless trees one above another on the
left hand side of Pl. XXVII, No. 1, belong to this passage.]

396.

If the plant n grows to the thickness shown at m, its branches will
correspond [in thickness] to the junction a b in consequence of the growth
inside as well as outside.

The branches of trees or plants have a twist wherever a minor branch is
given off; and this giving off the branch forms a fork; this said fork occurs
between two angles of which the largest will be that which is on the side of
the larger branch, and in proportion, unless accident has spoilt it.

[Footnote: The sketches illustrating this are on the right hand side of PI.
XXVII, No. I, and the text is also given there in facsimile.]

397.

There is no boss on branches which has not been produced by some
branch which has failed.

The lower shoots on the branches of trees grow more than the upper ones
and this occurs only because the sap that nourishes them, being heavy, tends
downwards more than upwards; and again, because those [branches] which
grow downwards turn away from the shade which exists towards the centre
of the plant. The older the branches are, the greater is the difference
between their upper and their lower shoots and in those dating from the
same year or epoch.

[Footnote: The sketch accompanying this in the MS. is so effaced that an
exact reproduction was impossible.]

398.

OF THE SCARS ON TREES.

The scars on trees grow to a greater thickness than is required by the sap
of the limb which nourishes them.

399.

The plant which gives out the smallest ramifications will preserve the
straightest line in the course of its growth.

[Footnote: This passage is illustrated by two partly effaced sketches. One
of these closely resembles the lower one given under No. 408, the other also
represents short closely set boughs on an upright trunk.]

400.

OF THE RAMIFICATION.

The beginning of the ramification [the shoot] always has the central line
[axis] of its thickness directed to the central line [axis] of the plant itself.

401.

In starting from the main stem the branches always form a base with a
prominence as is shown at a b c d.

402.

WHY, VERY FREQUENTLY, TIMBER HAS VEINS THAT ARE NOT STRAIGHT.

When the branches which grow the second year above the branch of the
preceding year, are not of equal thickness above the antecedent branches,
but are on one side, then the vigour of the lower branch is diverted to
nourish the one above it, although it may be somewhat on one side.

But if the ramifications are equal in their growth, the veins of the main
stem will be straight [parallel] and equidistant at every degree of the height
of the plant.

Wherefore, O Painter! you, who do not know these laws! in order to
escape the blame of those who understand them, it will be well that you
should represent every thing from nature, and not despise such study as
those do who work [only] for money.

The direction of growth (403-407).

403.

OF THE RAMIFICATIONS OF PLANTS.

The plants which spread very much have the angles of the spaces which
divide their branches more obtuse in proportion as their point of origin is
lower down; that is nearer to the thickest and oldest portion of the tree.
Therefore in the youngest portions of the tree the angles of ramification are
more acute. [Footnote: Compare the sketches on the lower portion of Pl.
XXVII, No. 2.]

404.

The tips of the boughs of plants [and trees], unless they are borne down
by the weight of their fruits, turn towards the sky as much as possible.

The upper side of their leaves is turned towards the sky that it may
receive the nourishment of the dew which falls at night.

The sun gives spirit and life to plants and the earth nourishes them with
moisture. [9] With regard to this I made the experiment of leaving only one
small root on a gourd and this I kept nourished with water, and the gourd

brought to perfection all the fruits it could produce, which were about 60
gourds of the long kind, andi set my mind diligently [to consider] this
vitality and perceived that the dews of night were what supplied it
abundantly with moisture through the insertion of its large leaves and gave
nourishment to the plant and its offspring—or the seeds which its offspring
had to produce—[21].

The rule of the leaves produced on the last shoot of the year will be that
they will grow in a contrary direction on the twin branches; that is, that the
insertion of the leaves turns round each branch in such a way, as that the
sixth leaf above is produced over the sixth leaf below, and the way they turn
is that if one turns towards its companion to the right, the other turns to the
left, the leaf serving as the nourishing breast for the shoot or fruit which
grows the following year.

[Footnote: A French translation of lines 9-12 was given by M.
RAVAISSON in the Gazette des Beaux Arts, Oct. 1877; his paper also
contains some valuable information as to botanical science in the ancient
classical writers and at the time of the Renaissance.]

405.

The lowest branches of those trees which have large leaves and heavy
fruits, such as nut-trees, fig-trees and the like, always droop towards the
ground.

The branches always originate above [in the axis of] the leaves.

406.

The upper shoots of the lateral branches of plants lie closer to the parent
branch than the lower ones.

407.

The lowest branches, after they have formed the angle of their separation
from the parent stem, always bend downwards so as not to crowd against
the other branches which follow them on the same stem and to be better
able to take the air which nourishes them. As is shown by the angle b a c;
the branch a c after it has made the corner of the angle a c bends
downwards to c d and the lesser shoot c dries up, being too thin.

The main branch always goes below, as is shown by the branch f n m,
which does not go to f n o.

The forms of trees (408—411).

408.

The elm always gives a greater length to the last branches of the year's
growth than to the lower ones; and Nature does this because the highest
branches are those which have to add to the size of the tree; and those at the
bottom must get dry because they grow in the shade and their growth would
be an impediment to the entrance of the solar rays and the air among the
main branches of the tree.

The main branches of the lower part bend down more than those above,
so as to be more oblique than those upper ones, and also because they are
larger and older.

409.

In general almost all the upright portions of trees curve somewhat turning
the convexity towards the South; and their branches are longer and thicker
and more abundant towards the South than towards the North. And this

occurs because the sun draws the sap towards that surface of the tree which
is nearest to it.

And this may be observed if the sun is not screened off by other plants.

410.

The cherry-tree is of the character of the fir tree as regards its
ramification placed in stages round its main stem; and its branches spring, 4
or five or 6 [together] opposite each other; and the tips of the topmost
shoots form a pyramid from the middle upwards; and the walnut and oak
form a hemisphere from the middle upwards.

411.

The bough of the walnut which is only hit and beaten when it has brought
to perfection…

[Footnote: The end of the text and the sketch in red chalk belonging to it,
are entirely effaced.]

The insertion of the leaves (412—419).

412.

OF THE INSERTION OF THE BRANCHES ON PLANTS.

Such as the growth of the ramification of plants is on their principal
branches, so is that of the leaves on the shoots of the same plant. These
leaves have [Footnote 6: Quattro modi (four modes). Only three are
described in the text, the fourth is only suggested by a sketch.

This passage occurs in MANZI'S edition of the Trattato, p. 399, but
without the sketches and the text is mutilated in an important part. The

whole passage has been commented on, from MANZI'S version, in Part I of
the Nuovo Giornale Botanico Italiano, by Prof. G. UZIELLI (Florence
1869, Vol. I). He remarks as to the 'four modes': "Leonardo, come si vede
nelle linie sententi da solo tre esempli. Questa ed altre inessattezze fanno
desiderare, sia esaminato di nuovo il manoscritto Vaticano". This has since
been done by D. KNAPP of Tubingen, and his accurate copy has been
published by H. LUDWIG, the painter. The passage in question occurs in
his edition as No. 833; and there also the drawings are wanting. The space
for them has been left vacant, but in the Vatican copy 'niente' has been
written on the margin; and in it, as well as in LUDWIG'S and MANZI'S
edition, the text is mutilated.] four modes of growing one above another.
The first, which is the most general, is that the sixth always originates over
the sixth below [Footnote 8: la sesta di sotto. "Disposizione 2/5 o 1/5.
Leonardo osservo probabilmente soltanto la prima" (UZIELLl).]; the
second is that two third ones above are over the two third ones below
[Footnote 10: terze di sotto: "Intende qui senza dubbio parlare di foglie
decussate, in cui il terzo verticello e nel piano del primo" (UZIELLI).]; and
the third way is that the third above is over the third below [Footnote 11: 3a
di sotto: "Disposizione 1/2" (UZIELLI).].

[Footnote: See the four sketches on the upper portion of the page
reproduced as fig. 2 on P1. XXVII.]

413.

A DESCRIPTION OF THE ELM.

The ramification of the elm has the largest branch at the top. The first and
the last but one are smaller, when the main trunk is straight.

The space between the insertion of one leaf to the rest is half the extreme
length of the leaf or somewhat less, for the leaves are at an interval which is

about the 3rd of the width of the leaf.

The elm has more leaves near the top of the boughs than at the base; and
the broad [surface] of the leaves varies little as to [angle and] aspect.

[Footnote: See Pl. XXVII, No. 3. Above the sketch and close under the
number of the page is the word 'olmo' (elm).]

414.

In the walnut tree the leaves which are distributed on the shoots of this
year are further apart from each other and more numerous in proportion as
the branch from which this shoot springs is a young one. And they are
inserted more closely and less in number when the shoot that bears them
springs from an old branch. Its fruits are borne at the ends of the shoots.
And its largest boughs are the lowest on the boughs they spring from. And
this arises from the weight of its sap which is more apt to descend than to
rise, and consequently the branches which spring from them and rise
towards the sky are small and slender [20]; and when the shoot turns
towards the sky its leaves spread out from it [at an angle] with an equal
distribution of their tips; and if the shoot turns to the horizon the leaves lie
flat; and this arises from the fact that leaves without exception, turn their
underside to the earth [29].

The shoots are smaller in proportion as they spring nearer to the base of
the bough they spring from.

[Footnote: See the two sketches on Pl XXVII, No. 4. The second refers to
the passage lines 20-30.]

415.

OF THE INSERTION OF THE LEAVES ON THE BRANCHES.

The thickness of a branch never diminishes within the space between one
leaf and the next excepting by so much as the thickness of the bud which is
above the leaf and this thickness is taken off from the branch above [the
node] as far as the next leaf.

Nature has so placed the leaves of the latest shoots of many plants that
the sixth leaf is always above the first, and so on in succession, if the rule is
not [accidentally] interfered with; and this occurs for two useful ends in the
plant: First that as the shoot and the fruit of the following year spring from
the bud or eye which lies above and in close contact with the insertion of
the leaf [in the axil], the water which falls upon the shoot can run down to
nourish the bud, by the drop being caught in the hollow [axil] at the
insertion of the leaf. And the second advantage is, that as these shoots
develop in the following year one will not cover the next below, since the 5
come forth on five different sides; and the sixth which is above the first is at
some distance.

416.

OF THE RAMIFICATIONS OF TREES AND THEIR FOLIAGE.

The ramifications of any tree, such as the elm, are wide and slender after
the manner of a hand with spread fingers, foreshortened. And these are seen
in the distribution [thus]: the lower portions are seen from above; and those
that are above are seen from below; and those in the middle, some from
below and some from above. The upper part is the extreme [top] of this
ramification and the middle portion is more foreshortened than any other of
those which are turned with their tips towards you. And of those parts of the
middle of the height of the tree, the longest will be towards the top of the
tree and will produce a ramification like the foliage of the common willow,
which grows on the banks of rivers.

Other ramifications are spherical, as those of such trees as put forth their
shoots and leaves in the order of the sixth being placed above the first.
Others are thin and light like the willow and others.

417.

You will see in the lower branches of the elder, which puts forth leaves
two and two placed crosswise [at right angles] one above another, that if the
stem rises straight up towards the sky this order never fails; and its largest
leaves are on the thickest part of the stem and the smallest on the slenderest
part, that is towards the top. But, to return to the lower branches, I say that
the leaves on these are placed on them crosswise like [those on] the upper
branches; and as, by the law of all leaves, they are compelled to turn their
upper surface towards the sky to catch the dew at night, it is necessary that
those so placed should twist round and no longer form a cross.

[Footnote: See Pl. XXVII, No. 5.]

418.

A leaf always turns its upper side towards the sky so that it may the better
receive, on all its surface, the dew which drops gently from the atmosphere.
And these leaves are so distributed on the plant as that one shall cover the
other as little as possible, but shall lie alternately one above another as may
be seen in the ivy which covers the walls. And this alternation serves two
ends; that is, to leave intervals by which the air and sun may penetrate
between them. The 2nd reason is that the drops which fall from the first leaf
may fall onto the fourth or—in other trees—onto the sixth.

419.

Every shoot and every fruit is produced above the insertion [in the axil]
of its leaf which serves it as a mother, giving it water from the rain and
moisture from the dew which falls at night from above, and often it protects
them against the too great heat of the rays of the sun.

LIGHT ON BRANCHES AND LEAVES (420—422).

420.

That part of the body will be most illuminated which is hit by the
luminous ray coming between right angles.

[Footnote: See Pl. XXVIII, No. 1.]

421.

Young plants have more transparent leaves and a more lustrous bark than
old ones; and particularly the walnut is lighter coloured in May than in
September.

422.

OF THE ACCIDENTS OF COLOURING IN TREES.

The accidents of colour in the foliage of trees are 4. That is: shadow,
light, lustre [reflected light] and transparency.

OF THE VISIBILITY OF THESE ACCIDENTS.

These accidents of colour in the foliage of trees become confused at a
great distance and that which has most breadth [whether light or shade, &c.]
will be most conspicuous.

The proportions of light and shade in a leaf (423-426).

423.

OF THE SHADOWS OF A LEAF.

Sometimes a leaf has three accidents [of light] that is: shade, lustre
[reflected light] and transparency [transmitted light]. Thus, if the light were
at n as regards the leaf s, and the eye at m, it would see a in full light, b in
shadow and c transparent.

424.

A leaf with a concave surface seen from the under side and up-side-down
will sometimes show itself as half in shade, and half transparent. Thus, if o
p is the leaf and the light m and the eye n, this will see o in shadow because
the light does not fall upon it between equal angles, neither on the upper nor
the under side, and p is lighted on the upper side and the light is transmitted
to its under side. [Footnote: See Pl. XXVIII, No. 2, the upper sketch on the
page. In the original they are drawn in red chalk.]

425.

Although those leaves which have a polished surface are to a great extent
of the same colour on the right side and on the reverse, it may happen that
the side which is turned towards the atmosphere will have something of the
colour of the atmosphere; and it will seem to have more of this colour of the
atmosphere in proportion as the eye is nearer to it and sees it more
foreshortened. And, without exception the shadows show as darker on the
upper side than on the lower, from the contrast offered by the high lights
which limit the shadows.

The under side of the leaf, although its colour may be in itself the same
as that of the upper side, shows a still finer colour—a colour that is green

verging on yellow—and this happens when the leaf is placed between

426.

the eye and the light which falls upon it from the opposite side.

And its shadows are in the same positions as those were of the opposite
side. Therefore, O Painter! when you do trees close at hand, remember that
if the eye is almost under the tree you will see its leaves [some] on the
upper and [some] on the under side, and the upper side will be bluer in
proportion as they are seen more foreshortened, and the same leaf
sometimes shows part of the right side and part of the under side, whence
you must make it of two colours.

Of the transparency of leaves (427-429).

427.

The shadows in transparent leaves seen from the under side are the same
shadows as there are on the right side of this leaf, they will show through to
the underside together with lights, but the lustre [reflected light] can never
show through.

428.

When one green has another [green] behind it, the lustre on the leaves
and their transparent [lights] show more strongly than in those which are
[seen] against the brightness of the atmosphere.

And if the sun illuminates the leaves without their coming between it and
the eye and without the eye facing the sun, then the reflected lights and the
transparent lights are very strong.

It is very effective to show some branches which are low down and dark
and so set off the illuminated greens which are at some distance from the
dark greens seen below. That part is darkest which is nearest to the eye or
which is farthest from the luminous atmosphere.

429.

Never paint leaves transparent to the sun, because they are confused; and
this is because on the transparency of one leaf will be seen the shadow of
another leaf which is above it. This shadow has a distinct outline and a
certain depth of shade and sometimes is [as much as] half or a third of the
leaf which is shaded; and consequently such an arrangement is very
confused and the imitation of it should be avoided.

The light shines least through a leaf when it falls upon it at an acute
angle.

The gradations of shade and colour in leaves (430-434).

430.

The shadows of plants are never black, for where the atmosphere
penetrates there can never be utter darkness.

431.

If the light comes from m and the eye is at n the eye will see the colour of
the leaves a b all affected by the colour of m —that is of the atmosphere;
and b c will be seen from the under side as transparent, with a beautiful
green colour verging on yellow.

If m is the luminous body lighting up the leaf s all the eyes that see the
under side of this leaf will see it of a beautiful light green, being

transparent.

In very many cases the positions of the leaves will be without shadow [or
in full light], and their under side will be transparent and the right side
lustrous [reflecting light].

432.

The willow and other similar trees, which have their boughs lopped every
3 or 4 years, put forth very straight branches, and their shadow is about the
middle where these boughs spring; and towards the extreme ends they cast
but little shade from having small leaves and few and slender branches.
Hence the boughs which rise towards the sky will have but little shade and
little relief; and the branches which are at an angle from the horizon,
downwards, spring from the dark part of the shadow and grow thinner by
degrees up to their ends, and these will be in strong relief, being in
gradations of light against a background of shadow.

That tree will have the least shadow which has the fewest branches and
few leaves.

433.

OF DARK LEAVES IN FRONT OF TRANSPARENT ONES.

When the leaves are interposed between the light and the eye, then that
which is nearest to the eye will be the darkest, and the most distant will be
the lightest, not being seen against the atmosphere; and this is seen in the
leaves which are away from the centre of the tree, that is towards the light.

[Footnote: See Pl. XXVIII, No. 2, the lower sketch.]

434.

OF THE LIGHTS ON DARK LEAVES.

The lights on such leaves which are darkest, will be most near to the
colour of the atmosphere that is reflected in them. And the cause of this is
that the light on the illuminated portion mingles with the dark hue to
compose a blue colour; and this light is produced by the blueness of the
atmosphere which is reflected in the smooth surface of these leaves and
adds to the blue hue which this light usually produces when it falls on dark
objects.

OF THE LIGHTS ON LEAVES OF A YELLOWISH GREEN.

But leaves of a green verging on yellow when they reflect the atmosphere
do not produce a reflection verging on blue, inasmuch as every thing which
appears in a mirror takes some colour from that mirror, hence the blue of
the atmosphere being reflected in the yellow of the leaf appears green,
because blue and yellow mixed together make a very fine green colour,
therefore the lustre of light leaves verging on yellow will be greenish
yellow.

A classification of trees according to their colours.

435.

The trees in a landscape are of various kinds of green, inasmuch as some
verge towards blackness, as firs, pines, cypresses, laurels, box and the like.
Some tend to yellow such as walnuts, and pears, vines and verdure. Some
are both yellowish and dark as chesnuts, holm-oak. Some turn red in
autumn as the service-tree, pomegranate, vine, and cherry; and some are
whitish as the willow, olive, reeds and the like. Trees are of various forms
…

The proportions of light and shade in trees (436-440).

436.

OF A GENERALLY DISTRIBUTED LIGHT AS LIGHTING UP TREES.

That part of the trees will be seen to lie in the least dark shadow which is
farthest from the earth.

To prove it let a p be the tree, n b c the illuminated hemisphere [the sky],
the under portion of the tree faces the earth p c, that is on the side o, and it
faces a small part of the hemisphere at c d. But the highest part of the
convexity a faces the greatest part of the hemisphere, that is b c. For this
reason—and because it does not face the darkness of the earth—it is in
fuller light. But if the tree has dense foliage, as the laurel, arbutus, box or
holm oak, it will be different; because, although a does not face the earth, it
faces the dark [green] of the leaves cut up by many shadows, and this
darkness is reflected onto the under sides of the leaves immediately above.
Thus these trees have their darkest shadows nearest to the middle of the
tree.

437.

OF THE SHADOWS OF VERDURE.

The shadows of verdure are always somewhat blue, and so is every
shadow of every object; and they assume this hue more in proportion as
they are remote from the eye, and less in proportion as they are nearer. The
leaves which reflect the blue of the atmosphere always present themselves
to the eye edgewise.

OF THE ILLUMINATED PART OF VERDURE AND OF MOUNTAINS.

The illuminated portion, at a great distance, will appear most nearly of its
natural colour where the strongest light falls upon it.

438.

OF TREES THAT ARE LIGHTED BY THE SUN AND BY THE ATMOSPHERE.

In trees that are illuminated [both] by the sun and the atmosphere and that
have leaves of a dark colour, one side will be illuminated by the atmosphere
[only] and in consequence of this light will tend to blueness, while on the
other side they will be illuminated by the atmosphere and the sun; and the
side which the eye sees illuminated by the sun will reflect light.

439.

OF DEPICTING A FOREST SCENE.

The trees and plants which are most thickly branched with slender
branches ought to have less dark shadow than those trees and plants which,
having broader leaves, will cast more shadow.

440.

ON PAINTING.

In the position of the eye which sees that portion of a tree illuminated
which turns towards the light, one tree will never be seen to be illuminated
equally with the other. To prove this, let the eye be c which sees the two
trees b d which are illuminated by the sun a; I say that this eye c will not
see the light in the same proportion to the shade, in one tree as in the other.
Because, the tree which is nearest to the sun will display so much the
stronger shadow than the more distant one, in proportion as one tree is
nearer to the rays of the sun that converge to the eye than the other; &c.

You see that the eye c sees nothing of the tree d but shadow, while the
same eye c sees thè tree b half in light and half in shade.

When a tree is seen from below, the eye sees the top of it as placed within
the circle made by its boughs[23].

Remember, O Painter! that the variety of depth of shade in any one
particular species of tree is in proportion to the rarity or density of their
branches.

[Footnote: The two lower sketches on the left of Pl XXVIII, No. 3, refer
to lines 21-23. The upper sketch has apparently been effaced by Leonardo
himself.]

The distribution of light and shade with reference to the position of the
spectator (441-443).

441.

The shadows of trees placed in a landscape do not display themselves in
the same position in the trees on the right hand and those on the left; still
more so if the sun is to the right or left. As is proved by the 4th which says:
Opaque bodies placed between the light and the eye display themselves
entirely in shadow; and by the 5th: The eye when placed between the
opaque body and the light sees the opaque body entirely illuminated. And
by the 6th: When the eye and the opaque body are placed between darkness
and light, it will be seen half in shadow and half in light.

[Footnote: See the figure on the right hand side of Pl. XXVIII, No. 3. The
first five lines of the text are written below the diagram and above it are the
last eight lines of the text, given as No. 461.]

442.

OF THE HERBS OF THE FIELD.

Of the plants which take a shadow from the plants which spring among
them, those which are on this side [in front] of the shadow have the stems
lighted up on a background of shadow, and the plants on which the shadows
fall have their stems dark on a light background; that is on the background
beyond the shadow.

OF TREES WHICH ARE BETWEEN THE EYE AND THE LIGHT.

Of the trees which are between the eye and the light the part in front will
be light; but this light will be broken by the ramifications of transparent
leaves—being seen from the under side—and lustrous leaves—being seen
from the upper side; and the background below and behind will be dark
green, being in shadow from the front portion of the said tree. This occurs
in trees placed above the eye.

443.

FROM WHENCE TO DEPICT A LANDSCAPE

Landscapes should be represented so that the trees may be half in light
and half in shadow; but it is better to do them when the sun is covered with
clouds, for then the trees are lighted by the general light of the sky, and the
general darkness of the earth. And then they are darkest in certain parts in
proportion as those parts are nearest to the middle of the tree and to the
earth.

The effects of morning light (444-448).

444.

OF TREES TO THE SOUTH.

When the sun is in the east the trees to the South and to the North have
almost as much light as shadow. But a greater share of light in proportion as
they lie to the West and a greater share of shadow in proportion as they lie
to the East.

OF MEADOWS.

If the sun is in the East the verdure of the meadows and of other small
plants is of a most beautiful green from being transparent to the sun; this
does not occur in the meadows to the West, and in those to the South and
North the grass is of a moderately brilliant green.

445.

OF THE 4 POINTS OF THE COMPASS [IN LANDSCAPES].

When the sun is in the East all the portions of plants lighted by it are of a
most lively verdure, and this happens because the leaves lighted by the sun
within the half of the horizon that is the Eastern half, are transparent; and
within the Western semicircle the verdure is of a dull hue and the moist air
is turbid and of the colour of grey ashes, not being transparent like that in
the East, which is quite clear and all the more so in proportion as it is
moister.

The shadows of the trees to the East cover a large portion of them and are
darker in proportion as the foliage of the trees is thicker.

446.

OF TREES IN THE EAST.

When the sun is in the East the trees seen towards the East will have the
light which surrounds them all round their shadows, excepting on the side

towards the earth; unless the tree has been pruned [below] in the past year.
And the trees to the South and North will be half in shade and half in light,
and more or less in shade or in light in proportion as they are more or less to
the East or to the West.

The [position of] the eye above or below varies the shadows and lights in
trees, inasmuch as the eye placed above sees the tree with the little shadow,
and the eye placed below with a great deal of shadow.

The colour of the green in plants varies as much as their species.

447.

OF THE SHADOWS IN TREES.

The sun being in the East [to the right], the trees to the West [or left] of
the eye will show in small relief and almost imperceptible gradations,
because the atmosphere which lies between the eye and those trees is very
dense [Footnote 7: per la 7a di questo. This possibly referred to something
written on the seventh page of this note book marked G. Unfortunately it
has been cut out and lost.], see the 7th of this—and they have no shade; for
though a shadow exists in every detail of the ramification, it results that the
images of the shade and light that reach the eye are confused and mingled
together and cannot be perceived on account of their minuteness. And the
principal lights are in the middle of the trees, and the shadows to wards the
edges; and their separation is shown by the shadows of the intervals
between the trees; but when the forests are thick with trees the thin edges
are but little seen.

448.

OF TREES TO THE EAST.

When the sun is in the East the trees are darker towards the middle while
their edges are light.

The effects of midday light.

449.

OBJECTS IN HIGH LIGHT SHOW BUT LITTLE, BUT BETWEEN LIGHT AND SHADOW
THEY STAND OUT WELL.

To represent a landscape choose that the sun shall be at noon and look
towards the West or East and then draw. And if you turn towards the North,
every object placed on that side will have no shadow, particularly those
which are nearest to the [direction of the] shadow of your head. And if you
turn towards the South every object on that side will be wholly in shadow.
All the trees which are towards the sun and have the atmosphere for their
background are dark, and the other trees which lie against that darkness will
be black [very dark] in the middle and lighter towards the edges.

The appearance of trees in the distance (450. 451).

450.

OF THE SPACES [SHOWING THE SKY] IN TREES THEMSELVES.

The spaces between the parts in the mass of trees, and the spaces between
the trees in the air, are, at great distances, invisible to the eye; for, where it
is an effort [even] to see the whole it is most difficult to discern the parts.—
But a confused mixture is the result, partaking chiefly of the [hue] which
predominates. The spaces between the leaves consist of particles of
illuminated air which are very much smaller than the tree and are lost sight
of sooner than the tree; but it does not therefore follow that they are not
there. Hence, necessarily, a compounded [effect] is produced of the sky and