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should have remained so long unpublished, and indeed forgotten.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