Leonardo Da Vinci - The Notebooks of Leonardo Da Vinci - [PDF Document] (2024)

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

1/96

Volume I

Translated by Jean Paul Richter

1888

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

2/96

PREFACE.

A singular fatality has ruled the destiny of nearly all themost

famous of Leonardo da Vinci's works. Two of the three mostimportantwere never completed, obstacles having arisen during hislife-time,

which obliged him to leave them unfinished; namely theSforza

Monument and the Wall-painting of the Battle of Anghiari, whilethethird--the picture of the Last Supper at Milan--has suffered

irremediable injury from decay and the repeated restorationsto

which it was recklessly subjected during the XVIIth andXVIIIth

centuries. Nevertheless, no other picture of the Renaissancehasbecome so wellknown and popular through copies of everydescription.

Vasari says, and rightly, in his Life of Leonardo, "that helaboured

much more by his word than in fact or by deed", and thebiographer

evidently had in his mind the numerous works in Manuscriptwhichhave been preserved to this day. To us, now, it seemsalmost

inexplicable that these valuable and interesting originaltexts

should have remained so long unpublished, and indeed forgotten.It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 notmerelyby the prices which they commanded, but also by theexceptional

interest which has been attached to the change of ownershipof

merely a few pages of Manuscript.

That, notwithstanding this eagerness to possess theManuscripts,

their contents remained a mystery, can only be accounted for bythemany and great difficulties attending the task of decipheringthem.

The handwriting is so peculiar that it requires considerable

practice to read even a few detached phrases, much more tosolve

with any certainty the numerous difficulties ofalternativereadings, and to master the sense as a connected whole.Vasari

observes with reference to Leonardos writing: "he wrotebackwards,

in rude characters, and with the left hand, so that any one whois not practised in reading them, cannot understand them". The aidof a

mirror in reading reversed handwriting appears to me availableonly

for a first experimental reading. Speaking from my ownexperience,the persistent use of it is too fatiguing andinconvenient to be

practically advisable, considering the enormous mass ofManuscripts

to be deciphered. And as, after all, Leonardo's handwritingruns

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

3/96

backwards just as all Oriental character runs backwards--thatisto say from right to left--the difficulty of reading direct fromthe

writing is not insuperable. This obvious peculiarity in thewriting

is not, however, by any means the only obstacle in the wayofmastering the text. Leonardo made use of an orthography peculiarto

himself; he had a fashion of amalgamating several short wordsintoone long one, or, again, he would quite arbitrarily divide along word into two separate halves; added to this there is nopunctuation

whatever to regulate the division and construction of thesentences,

nor are there any accents--and the reader may imagine thatsuchdifficulties were almost sufficient to make the task seem a

desperate one to a beginner. It is therefore not surprising thatthe

good intentions of some of Leonardo s most reverent admirersshould have failed.

Leonardos literary labours in various departments both of Artand of

Science were those essentially of an enquirer, hence theanalyticalmethod is that which he employs in arguing out hisinvestigations

and dissertations. The vast structure of his scientific theoriesisconsequently built up of numerous separate researches, and itis

much to be lamented that he should never have collated andarranged

them. His love for detailed research--as it seems to me--wasthereason that in almost all the Manuscripts, the differentparagraphs

appear to us to be in utter confusion; on one and the samepage,

observations on the most dissimilar subjects follow eachotherwithout any connection. A page, for instance, will begin withsome

principles of astronomy, or the motion of the earth; then comethelaws of sound, and finally some precepts as to colour. Anotherpage

will begin with his investigations on the structure of the

intestines, and end with philosophical remarks as to therelationsof poetry to painting; and so forth.

Leonardo himself lamented this confusion, and for that reason Ido

not think that the publication of the texts in the order inwhich

they occur in the originals would at all fulfil his intentions.No

reader could find his way through such a labyrinth; Leonardohimself

could not have done it.

Added to this, more than half of the five thousand manuscriptpages

which now remain to us, are written on loose leaves, and atpresentarranged in a manner which has no justification beyond thefancy of

the collector who first brought them together to make volumesof

more or less extent. Nay, even in the volumes, the pages ofwhich were numbered by Leonardo himself, their order, so far asthe

connection of the texts was concerned, was obviously a matterof

indifference to him. The only point he seems to have kept inview,

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

4/96

when first writing down his notes, was that each observationshould be complete to the end on the page on which it was begun.The

exceptions to this rule are extremely few, and it iscertainly

noteworthy that we find in such cases, in bound volumes withhisnumbered pages, the written observations: "turn over", "This isthe

continuation of the previous page", and the like. Is notthissufficient to prove that it was only in quite exceptional casesthat the writer intended the consecutive pages to remain connected,when

he should, at last, carry out the often planned arrangement ofhis

writings?

What this final arrangement was to be, Leonardo has in mostcases

indicated with considerable completeness. In other casesthisauthoritative clue is wanting, but the difficulties arisingfrom

this are not insuperable; for, as the subject of theseparate

paragraphs is always distinct and well defined in itself, itis

quite possible to construct a well-planned whole, out ofthescattered materials of his scientific system, and I may ventureto

state that I have devoted especial care and thought to thedueexecution of this responsible task.

The beginning of Leonardo's literary labours dates from abouthisthirty-seventh year, and he seems to have carried them onwithout

any serious interruption till his death. Thus the Manuscriptsthat

remain represent a period of about thirty years. Within thisspaceof time his handwriting altered so little that it isimpossible to

judge from it of the date of any particular text. The exactdates,indeed, can only be assigned to certain note-books in whichthe year

is incidentally indicated, and in which the order of the leaveshas

not been altered since Leonardo used them. The assistancetheseafford for a chronological arrangement of the Manuscriptsis

generally self evident. By this clue I have assigned to theoriginal

Manuscripts now scattered through England, Italy and France,theorder of their production, as in many matters of detail it ishighly

important to be able to verify the time and place at whichcertain

observations were made and registered. For this purposetheBibliography of the Manuscripts given at the end of Vol. II, maybe regarded as an Index, not far short of complete, of all Leonardos

literary works now extant. The consecutive numbers (from 1 to1566)

at the head of each passage in this work, indicate their logicalsequence 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 particularpassageis to be found. Thus the reader, by referring to the Listof

Manuscripts at the beginning of Volume I, and to theBibliography at

the end of Volume II, can, in every instance, easily ascertain,not

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

5/96

merely the period to which the passage belongs, but alsoexactlywhere it stood in the original document. Thus, too, byfollowing the

sequence of the numbers in the Bibliographical index, the readermay

reconstruct the original order of the Manuscripts and recomposethevarious texts to be found on the original sheets--so much ofit,

that is to say, as by its subject-matter came within the scopeofthis work. It may, however, be here observed that LeonardosManuscripts contain, besides the passages here printed, agreat

number of notes and dissertations on Mechanics, Physics, andsome

other subjects, many of which could only be satisfactorilydealtwith by specialists. I have given as complete a review ofthese

writings as seemed necessary in the Bibliographical notes.

In 1651, Raphael Trichet Dufresne, of Paris, published aselection

from Leonardo's writings on painting, and this treatise becameso

popular that it has since been reprinted about two-and-twentytimes,

and in six different languages. But none of these editionswerederived from the original texts, which were supposed to havebeen

lost, but from early copies, in which Leonardo's text had beenmore or less mutilated, and which were all fragmentary. The oldestand on

the whole the best copy of Leonardo's essays and precepts on

Painting is in the Vatican Library; this has been twiceprinted,first by Manzi, in 1817, and secondly by Ludwig, in 1882.Still,

this ancient copy, and the published editions of it, containmuch

for which it would be rash to hold Leonardo responsible, andsome portions--such as the very important rules for the proportionsof

the human figure--are wholly wanting; on the other hand theycontainpassages which, if they are genuine, cannot now be verifiedfrom any

original Manuscript extant. These copies, at any rate neithergive

us the original order of the texts, as written by Leonardo, nordo they afford any substitute, by connecting them on a rationalscheme;

indeed, in their chaotic confusion they are anything ratherthan

satisfactory reading. The fault, no doubt, rests with thecompilerof the Vatican copy, which would seem to be the sourcewhence all

the published and extensively known texts were derived; for,instead

of arranging the passages himself, he was satisfied withrecording asuggestion for a final arrangement of them into eightdistinctparts, without attempting to carry out his scheme. Underthe

mistaken idea that this plan of distribution might be that, notof

the compiler, but of Leonardo himself, the various editors, downtothe present day, have very injudiciously continued to adoptthis

order--or rather disorder.

I, like other enquirers, had given up the original Manuscript ofthe

Trattato della Pittura for lost, till, in the beginning of 1880,I

was enabled, by the liberality of Lord Ashburnham, to inspecthis

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

6/96

Manuscripts, and was so happy as to discover among them theoriginaltext of the best-known portion of the Trattato in hismagnificent

library at Ashburnham Place. Though this discovery was of afragment

only--but a considerable fragment--inciting me to furthersearch,it gave the key to the mystery which had so long envelopedthe first

origin of all the known copies of the Trattato. Theextensiveresearches I was subsequently enabled to prosecute, andthe resultsof which are combined in this work, were only renderedpossible by

the unrestricted permission granted me to investigate allthe

Manuscripts by Leonardo dispersed throughout Europe, andtoreproduce the highly important original sketches they contain,by

the process of "photogravure". Her Majesty the Queengraciously

accorded me special permission to copy for publicationtheManuscripts at the Royal Library at Windsor. The CommissionCentrale

Administrative de l'Institut de France, Paris, gave me, in themost

liberal manner, in answer to an application from SirFrederic

Leighton, P. R. A., Corresponding member of the Institut,freepermission to work for several months in their privatecollection at

deciphering the Manuscripts preserved there. The same favourwhichLord Ashburnham had already granted me was extended to me bythe

Earl of Leicester, the Marchese Trivulsi, and the Curators ofthe

Ambrosian Library at Milan, by the Conte Manzoni at Rome and byother private owners of Manuscripts of Leonardo's; as also bythe

Directors of the Louvre at Paris; the Accademia at Venice;the

Uffizi at Florence; the Royal Library at Turin; and theBritishMuseum, and the South Kensington Museum. I am also greatlyindebted

to the Librarians of these various collections for muchassistancein my labours; and more particularly to Monsieur LouisLalanne, of

the Institut de France, the Abbate Ceriani, of the Ambrosian

Library, Mr. Maude Thompson, Keeper of Manuscripts at theBritishMuseum, Mr. Holmes, the Queens Librarian at Windsor, theRevd Vere

Bayne, Librarian of Christ Church College at Oxford, and theRevd 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.Thetranslation, under many difficulties, of the Italian textinto

English, is mainly due to Mrs. R. C. Bell; while the renderingof

several of the most puzzling and important passages,particularly inthe second half of Vol. I, I owe to theindefatigable interest taken

in this work by Mr. E. J. Poynter R. A. Finally I must expressmy

thanks to Mr. Alfred Marks, of Long Ditton, who has mostkindlyassisted me throughout in the revision of the proofsheets.

The notes and dissertations on the texts on Architecture in Vol.II

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

7/96

I owe to my friend Baron Henri de Geymuller, of Paris.

I may further mention with regard to the illustrations, thatthe

negatives for the production of the "photo-gravures" byMonsieurDujardin of Paris were all taken direct from theoriginals.

It is scarcely necessary to add that most of the drawingsherereproduced in facsimile have never been published before. As Iam

now, on the termination of a work of several years' duration, ina

position to review the general tenour of Leonardos writings, Imayperhaps be permitted to add a word as to my own estimate ofthe

value of their contents. I have already shown that it is dueto

nothing but a fortuitous succession of unfortunatecirc*mstances,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 principlesand

discoveries were infinitely more in accord with the teachingsofmodern science, than with the views of his contemporaries. Forthis

reason his extraordinary gifts and merits are far more likely tobe appreciated in our own time than they could have been duringthe

preceding centuries. He has been unjustly accused of having

squandered his powers, by beginning a variety of studies andthen, having hardly begun, throwing them aside. The truth is thatthe

labours of three centuries have hardly sufficed for theelucidation

of some of the problems which occupied his mighty mind.

Alexander von Humboldt has borne witness that "he was the firstto start on the road towards the point where all the impressions ofour

senses converge in the idea of the Unity of Nature" Nay, yetmore

may be said. The very words which are inscribed on the monumentofAlexander von Humboldt himself, at Berlin, are perhaps themost

appropriate in which we can sum up our estimate ofLeonardo's

genius:

"Majestati naturae par ingenium."

LONDON, April 1883.

F. P. R.

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

8/96

CONTENTS OF VOLUME I.

PROLEGOMENA AND GENERAL INTRODUCTION TO THE BOOK ONPAINTING

Clavis Sigillorum and Index of Manuscripts.--The author'sintentionto publish his MSS. (1).--The preparation of the MSS.for

publication (2).--Admonition to readers (3).--The disorder inthe

MSS. (4).--Suggestions for the arrangement of MSS. treatingofparticular subjects (5--8).--General introductions to the bookon

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).--Variabilityof the eye (24).--Focus of sight(25).--Differences of perception by

one eye and by both eyes (26--29).--The comparative size oftheimage 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).--Thenature of the outline (49).--Definition ofperspective (50).--The

perception of the object depends on the direction of the eye

(51).--Experimental proof of the existence of the pyramid ofsight(52--55).--The relations of the distance point to thevanishing

point (55--56).--How to measure the pyramid of vision(57).--The

production of the pyramid of vision (58--64).--Proof byexperiment(65--66).--General conclusions (67).--That the contraryis

impossible (68).--A parallel case (69).--The function of theeye, as

explained by the camera obscura (70--71).--The practice of

perspective (72--73).--Refraction of the rays falling upon theeye(74--75).--The inversion of the images (76).--The intersectionof

the rays (77--82).--Demonstration of perspective by means ofa

vertical glass plane (83--85.)--The angle of sight varies withthedistance (86--88).--Opposite pyramids in juxtaposition(89).--On

simple and complex perspective (90).--The proper distance ofobjects

from the eye (91--92).--The relative size of objects with regardtotheir distance from the eye (93--98).--The apparent size ofobjects

denned by calculation (99--106).--On natural perspective(107--109).

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

9/96

III.

SIX BOOKS ON LIGHT AND SHADE

GENERAL INTRODUCTION.--Prolegomena (110).--Scheme of the bookson

light and shade (111).--Different principles and plans oftreatment(112--116).--Different sorts of light(117--118).--Definition ofthe nature of shadows (119--122).--Of thevarious kinds of shadows

(123--125).--Of the various kinds of light(126--127).--General

remarks (128--129).--FIRST BOOK ON LIGHT AND SHADE.--On thenatureof light (130--131).--The difference between light andlustre

(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 ofthe

eye (141--145).--The law of the incidence of light

(146--147).--SECOND BOOK ON LIGHT AND SHADE.--Gradations ofstrength

in the shadows (148--149).--On the intensity of shadows asdependenton the distance from the light (150--152).--On theproportion of

light and shadow (153--157).--THIRD BOOK ON LIGHTANDSHADE.--Definition of derived shadow (158--159).--Differentsorts of

derived shadows (160--162).--On the relation of derived andprimary

shadow (163--165).--On the shape of derived shadows(166--174).--Onthe relative intensity of derived shadows(175--179).--Shadow as

produced by two lights of different size (180--181).--The effectof

light at different distances (182).--Further complications inthederived shadows (183--187).--FOURTH BOOK ON LIGHT AND SHADE.--Onthe

shape of cast shadows (188--191).--On the outlines of castshadows(192--195).--On the relative size of cast shadows (196.

197).--Effects on cast shadows by the tone of the background

(198).--A disputed proposition (199).--On the relative depthofcast shadows (200--202).--FIFTH BOOK ON LIGHT AND

SHADE.--Principles of reflection (203. 204).--Onreverberation

(205).--Reflection on water (206. 207).--Experiments with themirror(208--210).--Appendix:--On shadows in movement(211--212).--SIXTH

BOOK ON LIGHT AND SHADE.--The effect of rays passing throughholes

(213. 214).--On gradation of shadows (215. 216).--Onrelative

proportion of light and shadows (216--221).

IV.

PERSPECTIVE OF DISAPPEARANCE

Definition (222. 223).--An illustration by experiment(224).--Aguiding rule (225).---An experiment (226).--Onindistinctness at

short distances (227--231).--On indistinctness at greatdistances

(232--234).--The importance of light and shade in theProspettiva

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

10/96

de' perdimenti (235--239).--The effect of light or darkbackgroundson 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 oppositeeach

other (263--271).--Combination of different colours in castshadows(272).--The effect of colours in the camera obscura (273.274).--On

the colours of derived shadows (275. 276).--On the nature ofcolours

(277. 278).--On gradations in the depth of colours (279.280).--Onthe reflection of colours (281--283).--On the use of darkand light

colours in painting (284--286).--On the colours of therainbow

(287--288).

VI.

PERSPECTIVE OF COLOUR AND AERIAL PERSPECTIVE

General rules (289--291).--An exceptional case (292).--Anexperiment(293).--The practice of the Prospettiva de' colori(294).--The rules

of aerial perspective (295--297).--On the relative density ofthe

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 headand

face (310--318).--Proportions of the head seen in front

(319--321).--Proportions of the foot(322--323).--Relativeproportions 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 thefoot(337).--The proportions of the whole figure (338--341).--Thetorso

from the front and back (342).--Vitruvius' scheme ofproportions

(343).--The arm and head (344).--Proportions of thearm(345--349).--The movement of the arm (350--354).--The movementof

the torso (355--361).--The proportions vary at differentages

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

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

11/96

walking up and down (375--379).--On the human body inaction(380--388).--On hair falling down in curls (389).--Ondraperies

(390--392).

VIII.

BOTANY FOR PAINTERS, AND ELEMENTS OF LANDSCAPE PAINTING

Classification of trees (393).--The relative thickness ofthebranches to the trunk (394--396).--The law of proportion inthe

growth of the branches (397--402).--The direction of growth

(403--407).--The forms of trees (408--411).--The insertion oftheleaves (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 shadeand

colour in leaves (430--434).--A classification of treesaccording totheir colours (435).--The proportions of light andshade in trees

(436--440).--The distribution of light and shade with referencetothe position of the spectator (441--443).--The effects ofmorning

light (444--448).--The effects of midday light (449).--The

appearance of trees in the distance (450--451).--The cast shadowoftrees (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 oftowns(465--469).--The effect of wind on trees (470--473).--Lightand

shade on clouds (474--477).--On images reflected in water(478).--Ofrainbows and rain (479. 480).--Of flower seeds (481).

IX.

THE PRACTICE OF PAINTING

I. MORAL PRECEPTS FOR THE STUDENT OF PAINTING.--How to ascertainthe

dispositions for an artistic career (482).--The course of

instruction for an artist (483--485).--The study of theantique

(486. 487).--The necessity of anatomical knowledge (488.489).--Howto acquire practice (490).--Industry and thoroughness thefirst

conditions (491--493.)--The artist's private life and choiceof

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 acquireuniversality

(503--506).--Useful games and exercises (507. 508).--II.THEARTIST'S STUDIO.--INSTRUMENTS AND HELPS FOR THE APPLICATIONOF

PERSPECTIVE.--ON JUDGING OF A PICTURE.--On the size of thestudio

(509).--On the construction of windows (510--512).--On thebest

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

12/96

light for painting (513--520).--On various helps in preparingapicture (521--530).--On the management of works (531. 532).--Onthe

limitations of painting (533--535).--On the choice of aposition

(536. 537).--The apparent size of figures in a picture(538.539).--The right position of the artist, when painting and ofthe

spectator (540--547).--III. THE PRACTICAL METHODS OF LIGHT ANDSHADEAND AERIAL PERSPECTIVE.--Gradations of light and shade(548).--Onthe choice of light for a picture (549--554).--Thedistribution of

light and shade (555--559).--The juxtaposition of light andshade

(560. 561).--On the lighting of the background (562--565).--Onthelighting of white objects (566).--The methods of aerialperspective

(567--570).--IV. OF PORTRAIT AND FIGURE PAINTING.--Ofsketching

figures and portraits (571. 572).--The position of thehead(573).--Of the light on the face (574--576).--Generalsuggestions

for historical pictures (577--581).--How to represent the

differences of age and sex (582. 583).--Of representing theemotions

(584).--Of representing imaginary animals (585).--The selectionofforms (586--591).--How to pose figures (592).--Of appropriate

gestures (593--600).--V. SUGGESTIONS FOR COMPOSITIONS.--Ofpaintingbattle-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.THEARTIST'S MATERIALS.--Of chalk and paper (612--617).--On the

preparation and use of colours (618--627).--Of preparing thepanel

(628).--The preparation of oils (629--634).--On varnishes(635--637).--On chemical _materials (638--650).--VII. PHILOSOPHYAND

HISTORY OF THE ART OF PAINTING.--The relation of art andnature(651. 652).--Painting is superior to poetry (653.654).--Painting is

superior to sculpture (655. 656).--Aphorisms (657--659).--Onthe

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'sportrait(664).--Notes on the Last Supper (665--668).--On the battleofAnghiari (669).--Allegorical representations referring to theduke

of Milan (670--673).--Allegorical representations

(674--678).--Arrangement of a picture (679).--List ofdrawings(680).--Mottoes and Emblems (681--702).

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

13/96

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 remainingunder water and how long I can remain without eating. And I do notpublish

nor divulge these, by reason of the evil nature of men, whowould

use them for assassinations at the bottom of the sea bydestroying ships, and sinking them, together with the men in them.Nevertheless

I will impart others, which are not dangerous because the mouthof

the tube through which you breathe is above the water, supportedonair sacks or cork.

[Footnote: The leaf on which this passage is written, is headedwith

the words _Casi_ 39, and most of these cases begin with theword'_Come_', like the two here given, which are the 26th and 27th.7.

_Sughero_. In the Codex Antlanticus 377a; 1170a there is asketch, drawn with the pen, representing a man with a tube in hismouth, 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, inorder

that this science may not be useless.--

[Footnote: A comparatively small portion of Leonardo's noteson

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 mywork.

The disorder in the MSS.

4.

Begun at Florence, in the house of Piero di Braccio Martelli, onthe

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

14/96

22nd day of March 1508. And this is to be a collectionwithoutorder, taken from many papers which I have copied here,hoping to

arrange them later each in its place, according to the subjectsof

which they may treat. But I believe that before I am at the endofthis [task] I shall have to repeat the same things severaltimes;

for which, O reader! do not blame me, for the subjects are manyand memory cannot retain them [all] and say: 'I will not writethisbecause I wrote it before.' And if I wished to avoid fallinginto

this fault, it would be necessary in every case when I wantedto

copy [a passage] that, not to repeat myself, I should read overallthat had gone before; and all the more since the intervals arelong

between one time of writing and the next.

[Footnote: 1. In the history of Florence in the early part ofthe

XVIth century _Piero di Braccio Martelli_ is frequentlymentioned as

_Commissario della Signoria_. He was famous for his learning andat

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.,NewSeries Vol. I., where this passage is printed, _Barto_ hasbeen

wrongly given for Braccio.

2. _addi 22 di marzo 1508_. The Christian era was computedin

Florence at that time from the Incarnation (Lady day, March25th).

Hence this should be 1509 by our reckoning.

3. _racolto tratto di molte carte le quali io ho qui copiate_.Wemust suppose that Leonardo means that he has copied out his ownMSS.

and not those of others. The first thirteen leaves of the MS. inthe

Brit. Mus. are a fair copy of some notes on physics.]

Suggestions for the arrangement of MSS treating ofparticular

subjects.(5-8).

5.

Of digging a canal. Put this in the Book of useful inventionsand in proving them bring forward the propositions already proved.And this

is the proper order; since if you wished to show the usefulnessof

any plan you would be obliged again to devise new machines toproveits utility and thus would confuse the order of the fortyBooks and

also the order of the diagrams; that is to say you would have tomix

up practice with theory, which would produce a confusedandincoherent work.

6.

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

15/96

I am not to blame for putting forward, in the course of my workon

science, any general rule derived from a previousconclusion.

7.

The Book of the science of Mechanics must precede the Book ofusefulinventions.--Have your books on anatomy bound! [Footnote: 4.The

numerous notes on anatomy written on loose leaves and now inthe

Royal collection at Windsor can best be classified in fourBooks,corresponding to the different character and size of thepaper. When

Leonardo speaks of '_li tua libri di notomia_', he probablymeans

the MSS. which still exist; if this hypothesis is correctthepresent condition of these leaves might seem to prove that heonly

carried out his purpose with one of the Books on anatomy. Aborrowed

book on Anatomy is mentioned in F.O.]

8.

The order of your book must proceed on this plan: firstsimple

beams, then (those) supported from below, then suspended inpart,

then wholly [suspended]. Then beams as supporting otherweights[Footnote: 4. Leonardo's notes on Mechanics areextraordinarily

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 usefulorpleasing--since the men who have come before me have taken fortheir

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 ofproviding

himself than by taking all the things already seen by otherbuyers,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 abouttodistribute it, not indeed in great cities, but in the poorertowns,

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' acovertirony. In the second and third prefaces, Leonardocharacterises his

rivals and opponents more closely. His protest is directedagainst

Neo-latinism as professed by most of the humanists of his time;its

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

16/96

futility is now no longer questioned.]

10.

INTRODUCTION.

I know that many will call this useless work [Footnote: 3.questaessere opera inutile. By opera we must here understand librodi

pittura and particularly the treatise on Perspective.]; andthey

will be those ofwhom Demetrius [Footnote: 4. Demetrio. "Withregardto the passage attributed to Demetrius", Dr. H. MULLERSTRUBING

writes, "I know not what to make of it. It is certainly not

Demetrius Phalereus that is meant and it can hardly beDemetriusPoliorcetes. Who then can it be--for the name is a verycommon one?

It may be a clerical error for Demades and the maxim is quite inthe

spirit of his writings I have not however been able to findany

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 somedataas to the time where these introductions were written.]declared

that he took no more account of the wind that came out theirmouth

in words, than of that they expelled from their lower parts: menwho desire nothing but material riches and are absolutely devoid ofthat

of wisdom, which is the food and the only true riches of themind.For so much more worthy as the soul is than the body, so muchmore

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,Iwonder that he does not put it to his nose, like a monkey, or askme

if it is something good to eat.

[Footnote: In the original, the Proemio di prospettiva cioe

dell'uffitio dell'occhio (see No. 21) stands between this andthe

preceding one, No. 9.]

INTRODUCTION.

I am fully concious that, not being a literary man,certainpresumptuous persons will think that they may reasonablyblame me;

alleging that I am not a man of letters. Foolish folks! do theynot

know that I might retort as Marius did to the RomanPatricians[Footnote 21: _Come Mario disse ai patriti Romani_. "I amunable to

find the words here attributed by Leonardo to Marius, eitherin

Plutarch's Life of Marius or in the Apophthegmata(_Moralia_,

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

17/96

p.202). Nor do they occur in the writings of Valerius Maximus(whofrequently mentions Marius) nor in Velleius Paterculus (II, 11to

43), Dio Cassius, Aulus Gellius, or Macrobius. Professor E.

MENDELSON of Dorpat, the editor of Herodian, assures me that nosuchpassage is the found in that author" (communication from Dr.MULLER

STRUBING). Leonardo evidently meant to allude to some wellknownincident in Roman history and the mention of Marius is theresultprobably of some confusion. We may perhaps read, forMarius,

Menenius Agrippa, though in that case it is true we mustalter

Patriti to Plebei. The change is a serious one. but it wouldrender the passage perfectly clear.] by saying: That they, whodeck

themselves out in the labours of others will not allow me myown.

They will say that I, having no literary skill, cannotproperlyexpress that which I desire to treat of [Footnote 26: _lemie cose

.... che d'altra parola_. This can hardly be reconciled withMons.

RAVAISSON'S estimate of L. da Vinci's learning. "_Leonard deVinci

etait un admirateur et un disciple des anciens, aussi biendansl'art que dans la science et il tenait a passer pour tel memeaux

yeux de la posterite._" _Gaz. des Beaux arts. Oct. 1877.]; buttheydo not know that my subjects are to be dealt with byexperience

rather than by words [Footnote 28: See Footnote 26]; and

[experience] has been the mistress of those who wrote well. Andso,as mistress, I will cite her in all cases.

11.

Though I may not, like them, be able to quote other authors, Ishall rely on that which is much greater and more worthy:--onexperience,

the mistress of their Masters. They go about puffed up andpompous,

dressed and decorated with [the fruits], not of their ownlabours,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 arenot

inventors but vaunters and declaimers of the works ofothers--beblamed.

INTRODUCTION.

And those men who are inventors and interpreters between Natureand

Man, as compared with boasters and declaimers of the worksof

others, must be regarded and not otherwise esteemed than astheobject in front of a mirror, when compared with its image seenin

the mirror. For the first is something in itself, and theother

nothingness.--Folks little indebted to Nature, since it is onlyby chance that they wear the human form and without it I mightclass

them with the herds of beasts.

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

18/96

12.

Many will think they may reasonably blame me by alleging thatmy

proofs are opposed to the authority of certain men held inthehighest reverence by their inexperienced judgments; notconsidering

that my works are the issue of pure and simple experience, whoisthe one true mistress. These rules are sufficient to enable youtoknow the true from the false--and this aids men to look onlyfor

things that are possible and with due moderation--and not towrap

yourself in ignorance, a thing which can have no good result, sothat in despair you would give yourself up to melancholy.

13.

Among all the studies of natural causes and reasons Lightchiefly

delights the beholder; and among the great features ofMathematics

the certainty of its demonstrations is what preeminently (tendsto)elevate the mind of the investigator. Perspective, therefore,must

be preferred to all the discourses and systems of humanlearning. Inthis branch [of science] the beam of light is explainedon those

methods of demonstration which form the glory not so much of

Mathematics as of Physics and are graced with the flowers ofboth [Footnote: 5. Such of Leonardo's notes on Optics or onPerspective

as bear exclusively on Mathematics or Physics could not beincluded

in the arrangement of the _libro di pittura_ which is herepresentedto the reader. They are however but few.]. But its axiomsbeing laid

down at great length, I shall abridge them to a conclusivebrevity,arranging them on the method both of their natural orderand of

mathematical demonstration; sometimes by deduction of theeffects

from the causes, and sometimes arguing the causes from theeffects;adding also to my own conclusions some which, though notincluded in

them, may nevertheless be inferred from them. Thus, if theLord--who

is the light of all things--vouchsafe to enlighten me, I willtreatof Light; wherefore I will divide the present work into 3Parts

[Footnote: 10. In the middle ages--for instance, by ROGER BACON,by

VITELLONE, with whose works Leonardo was certainly familiar, andby

all the writers of the Renaissance Perspective and Optics werenotregarded as distinct sciences. Perspective, indeed, is in itswidest

application the science of seeing. Although to Leonardo thetwo

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 ofthe

_libro di pittura_ propositions in Perspective and in Opticsstandside by side or occur alternately. Although this particularchapter

deals only with Optics, it is not improbable that the words_partiro

la presente opera in 3 parti_ may refer to the same divisioninto

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

19/96

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 withthe

reasons of the (apparent) diminution of objects as they recedefromthe eye, and is known as Diminishing Perspective.--Thesecond

contains the way in which colours vary as they recede from theeye.

The third and last is concerned with the explanation of howtheobjects [in a picture] ought to be less finished in proportionas

they are remote (and the names are as follows):

Linear Perspective. The Perspective of Colour. The PerspectiveofDisappearance.

[Footnote: 13. From the character of the handwriting I inferthat

this passage was written before the year 1490.].

15.

ON PAINTING AND PERSPECTIVE.

The divisions of Perspective are 3, as used in drawing; ofthese, the first includes the diminution in size of opaque objects;the

second treats of the diminution and loss of outline in suchopaque

objects; the third, of the diminution and loss of colour at longdistances.

[Footnote: The division is here the same as in the previouschapter No. 14, and this is worthy of note when we connect it withthe fact

that a space of about 20 years must have intervened betweenthe

writing of the two passages.]

16.

THE DISCOURSE ON PAINTING.

Perspective, as bearing on drawing, is divided into threeprincipal

sections; of which the first treats of the diminution in thesize ofbodies at different distances. The second part is that whichtreats

of the diminution in colour in these objects. The third [dealswith]

the diminished distinctness of the forms and outlines displayedby

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

20/96

the objects at various distances.

17.

ON THE SECTIONS OF [THE BOOK ON] PAINTING.

The first thing in painting is that the objects it representsshould appear in relief, and that the grounds surrounding them atdifferent

distances shall appear within the vertical plane of theforeground

of the picture by means of the 3 branches of Perspective, whichare:the diminution in the distinctness of the forms of the objects,the

diminution in their magnitude; and the diminution in theircolour.

And of these 3 classes of Perspective the first results from[the structure of] the eye, while the other two are caused bythe

atmosphere which intervenes between the eye and the objects seenby

it. The second essential in painting is appropriate action and adue

variety in the figures, so that the men may not all looklikebrothers, &c.

[Footnote: This and the two foregoing chapters must havebeen

written in 1513 to 1516. They undoubtedly indicate the schemewhich

Leonardo wished to carry out in arranging his researches onPerspective as applied to Painting. This is important because itis

an evidence against the supposition of H. LUDWIG and others,that

Leonardo had collected his principles of Perspective in one bookso

early as before 1500; a Book which, according to thehypothesis,

must have been lost at a very early period, or destroyedpossibly,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; sinceevery

man makes some mistakes in his first compositions and he whoknows

them not, cannot amend them. But you, knowing your errors, willcorrect your works and where you find mistakes amend them, and

remember never to fall into them again. But if you try toapply

these rules in composition you will never make an end, and willproduce confusion in your works.

These rules will enable you to have a free and sound judgment;sincegood judgment is born of clear understanding, and a clear

understanding comes of reasons derived from sound rules, andsound

rules are the issue of sound experience--the common mother ofall

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

21/96

the sciences and arts. Hence, bearing in mind the precepts of myrules, you will be able, merely by your amended judgment, to

criticise and recognise every thing that is out of proportion ina

work, whether in the perspective or in the figures or anythingelse.

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 likethe

sailor who gets into a ship without rudder or compass and whonever

can be certain whether he is going. Practice must always befounded

on sound theory, and to this Perspective is the guide andthegateway; and without this nothing can be done well in the matterof

drawing.

20.

The painter who draws merely by practice and by eye, withoutany

reason, is like a mirror which copies every thing placed infront 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 THEEYE.

Behold here O reader! a thing concerning which we cannot trustour forefathers, the ancients, who tried to define what the Souland

Life are--which are beyond proof, whereas those things, whichcan at

any time be clearly known and proved by experience, remainedfor

many ages unknown or falsely understood. The eye, whose functionweso certainly know by experience, has, down to my own time,been

defined by an infinite number of authors as one thing; but Ifind,

by experience, that it is quite another. [Footnote 13: Comparethenote to No. 70.]

[Footnote: In section 13 we already find it indicated that thestudy of Perspective and of Optics is to be based on that of thefunctions

of the eye. Leonardo also refers to the science of the eye, inhis

astronomical researches, for instance in MS. F 25b '_Ordinedel

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

22/96

provare la terra essere una stella: Imprima difiniscel'occhio'_,&c. Compare also MS. E 15b and F 60b. The principlesof astronomical

perspective.]

22.

Here [in the eye] forms, here colours, here the character ofevery part of the universe are concentrated to a point; and thatpoint is

so marvellous a thing ... Oh! marvellous, O stupendousNecessity--by

thy laws thou dost compel every effect to be the direct resultofits cause, by the shortest path. These [indeed] aremiracles;...

In so small a space it can be reproduced and rearranged in itswholeexpanse. Describe in your anatomy what proportion there isbetween

the diameters of all the images in the eye and the distancefrom

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; whichare:--Darkness, Light, Solidity and Colour, Form and Position,

Distance and Propinquity, Motion and Rest. This little work ofmine

will be a tissue [of the studies] of these attributes, remindingthepainter of the rules and methods by which he should use his artto

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 theincrease

of light which is reflected in it. 2nd. The pupil of the eyeexpands

in proportion to the diminution in the day light, or any otherlight, that is reflected in it. 3rd. [Footnote: 8. The subjectof

this third proposition we find fully discussed in MS. G. 44a.].The

eye perceives and recognises the objects of its vision withgreaterintensity in proportion as the pupil is more widely dilated;and

this can be proved by the case of nocturnal animals, such ascats,

and certain birds--as the owl and others--in which the pupilvariesin a high degree from large to small, &c., when in thedark or in

the light. 4th. The eye [out of doors] in an illuminatedatmosphere

sees darkness behind the windows of houses which [nevertheless]are

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

23/96

light. 5th. All colours when placed in the shade appear of anequal degree of darkness, among themselves. 6th. But all colourswhen

placed in a full light, never vary from their true andessential

hue.

25.

OF THE EYE.

Focus of sight.

If the eye is required to look at an object placed too near toit,

it cannot judge of it well--as happens to a man who tries to seethetip of his nose. Hence, as a general rule, Nature teaches usthat an

object can never be seen perfectly unless the space between itand

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, thatobject

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 makesit

seem as though the object at rest had acquired the motion ofthe

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_, andif

you look at it with the eye _g_, _h_ will appear to be at _m_.Apicture can never contain in itself both aspects.

29.

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

24/96

Let the object in relief _t_ be seen by both eyes; if you willlook

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 ifyoushut the right eye and open the left, the object (will occupythe)

space _b_; and if you open both eyes, the object will nolongerappear at _a_ or _b_, but at _e_, _r_, _f_. Why will not apictureseen by both eyes produce the effect of relief, as [real]relief

does when seen by both eyes; and why should a picture seen withone

eye give the same effect of relief as real relief would underthe 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 thereforesuppose

that the face in which the eyes _m_ and _n_ are placed isopposite

to the spectator.]

30.

The comparative size of the image depends on the amount oflight

(30-39).

The eye will hold and retain in itself the image of a luminousbody

better than that of a shaded object. The reason is that the eyeis

in itself perfectly dark and since two things that are alikecannot be distinguished, therefore the night, and other darkobjects cannot

be seen or recognised by the eye. Light is totally contrary andgives more distinctness, and counteracts and differs from theusual

darkness of the eye, hence it leaves the impression of itsimage.

31.

Every object we see will appear larger at midnight than atmidday, and larger in the morning than at midday.

This happens because the pupil of the eye is much smaller atmidday

than at any other time.

32.

The pupil which is largest will see objects the largest. Thisis

evident when we look at luminous bodies, and particularly atthose

in the sky. When the eye comes out of darkness and suddenlylooks upat these bodies, they at first appear larger and thendiminish; and

if you were to look at those bodies through a small opening,you

would see them smaller still, because a smaller part of thepupil

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

25/96

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 luminousbody,it will appear much larger at first sight than after longlooking at

it. The illuminated object will look larger and more brilliant,when

seen with two eyes than with only one. A luminous object willappearsmaller in size, when the eye sees it through a smalleropening. A

luminous body of an oval form will appear rounder in proportionas

it is farther from the eye.

34.

Why when the eye has just seen the light, does the half lightlookdark to it, and in the same way if it turns from the darknessthe

half light look very bright?

35.

ON PAINTING.

If the eye, when [out of doors] in the luminous atmosphere, seesaplace in shadow, this will look very much darker than it reallyis.

This happens only because the eye when out in the air contractsthepupil in proportion as the atmosphere reflected in it ismore

luminous. And the more the pupil contracts, the less luminous dothe

objects appear that it sees. But as soon as the eye enters intoashady place the darkness of the shadow suddenly seems todiminish.

This occurs because the greater the darkness into which thepupil

goes the more its size increases, and this increase makesthe

darkness seem less.

[Footnote 14: _La luce entrera_. _Luce_ occurs here in the senseof

pupil of the eye as in no 51: C. A. 84b; 245a; I--5; and inmanyother places.]

36.

ON PERSPECTIVE.

The eye which turns from a white object in the light of the sunand

goes into a less fully lighted place will see everything asdark.

And this happens either because the pupils of the eyes whichhave

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

26/96

rested on this brilliantly lighted white object have contractedsomuch that, given at first a certain extent of surface, theywill

have lost more than 3/4 of their size; and, lacking in size,they

are also deficient in [seeing] power. Though you might say tome: A little bird (then) coming down would see comparativelylittle, and

from the smallness of his pupils the white might seem black! Tothis I should reply that here we must have regard to the proportionofthe mass of that portion of the brain which is given up to thesense

of sight and to nothing else. Or--to return--this pupil inMan

dilates and contracts according to the brightness or darknessof(surrounding) objects; and since it takes some time to dilateand

contract, it cannot see immediately on going out of the lightand

into the shade, nor, in the same way, out of the shade into thelight, and this very thing has already deceived me in paintingan

eye, and from that I learnt it.

37.

Experiment [showing] the dilatation and contraction of thepupil,from the motion of the sun and other luminaries. Inproportion as

the sky is darker the stars appear of larger size, and if youwere

to light up the medium these stars would look smaller; andthisdifference arises solely from the pupil which dilates andcontracts

with the amount of light in the medium which is interposedbetween

the eye and the luminous body. Let the experiment be made,byplacing a candle above your head at the same time that you lookat a

star; then gradually lower the candle till it is on a level withtheray that comes from the star to the eye, and then you will seethe

star diminish so much that you will almost lose sight of it.

[Footnote: No reference is made in the text to the letters onthe

accompanying diagram.]

38.

The pupil of the eye, in the open air, changes in size witheverydegree of motion from the sun; and at every degree of itschangesone and the same object seen by it will appear of adifferent size;

although most frequently the relative scale of surroundingobjects

does not allow us to detect these variations in any singleobject we may look at.

39.

The eye--which sees all objects reversed--retains the imagesfor

some time. This conclusion is proved by the results; because,the

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

27/96

eye having gazed at light retains some impression of it.Afterlooking (at it) there remain in the eye images of intense

brightness, that make any less brilliant spot seem dark un tilthe

eye has lost the last trace of the impression of the strongerlight.

_II.

Linear Perspective.

We see clearly from the concluding sentence of section 49, wherethe author directly addresses the painter, that he must certainlyhave

intended to include the elements of mathematics in his Book onthe

art of Painting. They are therefore here placed at thebeginning. In section 50 the theory of the "Pyramid of Sight" isdistinctly and

expressly put forward as the fundamental principle of linear

perspective, and sections 52 to 57 treat of it fully. Thistheory of

sight can scarcely be traced to any author of antiquity. Suchpassages as occur in Euclid for instance, may, it is true, have

proved suggestive to the painters of the Renaissance, but itwouldbe rash to say any thing decisive on this point.

Leon Battista Alberti treats of the "Pyramid of Sight" atsomelength in his first Book of Painting; but his explanationdiffers

widely from Leonardo's in the details. Leonardo, like Alberti,may

have borrowed the broad lines of his theory from some viewscommonlyaccepted among painters at the time; but he certainlyworked out its

application in a perfectly original manner.

The axioms as to the perception of the pyramid of rays arefollowed

by explanations of its origin, and proofs of itsuniversalapplication (58--69). The author recurs to the subjectwith endless

variations; it is evidently of fundamental importance in his

artistic theory and practice. It is unnecessary to discuss howfarthis theory has any scientific value at the present day; so muchas

this, at any rate, seems certain: that from the artist's pointof

view it may still claim to be of immense practical utility.

According to Leonardo, on one hand, the laws of perspective arean

inalienable condition of the existence of objects in space; onthe

other hand, by a natural law, the eye, whatever it sees andwherever it turns, is subjected to the perception of the pyramid ofrays in

the form of a minute target. Thus it sees objects inperspective

independently of the will of the spectator, since the eyereceivesthe images by means of the pyramid of rays "just as amagnet

attracts iron".

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

28/96

In connection with this we have the function of the eyeexplained bythe Camera obscura, and this is all the moreinteresting and

important because no writer previous to Leonardo had treated ofthis

subject_ (70--73). _Subsequent passages, of no less specialinterest,betray his knowledge of refraction and of the inversion ofthe image

in the camera and in the eye_ (74--82).

_From the principle of the transmission of the image to the eyeand

to the camera obscura he deduces the means of producing an

artificial construction of the pyramid of rays or--which is thesamething--of the image. The fundamental axioms as to the angle ofsight

and the vanishing point are thus presented in a manner which isas

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 objectsat

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 isflat

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 termsof

mathematicians, which are:--the point, the line, the angle,the

superficies and the solid. The point is unique of its kind. Andthe point has neither height, breadth, length, nor depth, whence itis

to be regarded as indivisible and as having no dimensions inspace.

The line is of three kinds, straight, curved and sinuous and ithas neither breadth, height, nor depth. Hence it isindivisible,

excepting in its length, and its ends are two points. The angleis

the junction of two lines in a point.

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

29/96

43.

A point is not part of a line.

44.

OF THE NATURAL POINT.

The smallest natural point is larger than all mathematicalpoints,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 civilee

militare"_ &c. by FRANCESCO DI GIORGIO; opposite a passagewhere theauthor says: _'In prima he da sapere che punto e quellaparie della

quale he nulla--Linia he luncheza senza apieza; &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 thelimitation

of one body is that which begins another. 3, that which is notpart of any body is nothing. Nothing is that which fills nospace.

If one single point placed in a circle may be the starting pointof

an infinite number of lines, and the termination of aninfinite

number of lines, there must be an infinite number ofpointsseparable from this point, and these when reunited become oneagain;

whence it follows that the part may be equal to the whole.

46.

The point, being indivisible, occupies no space. That whichoccupies

no space is nothing. The limiting surface of one thing isthebeginning of another. 2. That which is no part of any body iscalled

nothing. 1. That which has no limitations, has no form. The

limitations of two conterminous bodies are interchangeablythesurface of each. All the surfaces of a body are not parts ofthat

body.

Of the line (47-48).

47.

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

30/96

DEFINITION OF THE NATURE OF THE LINE.

The line has in itself neither matter nor substance and mayrather be called an imaginary idea than a real object; and thisbeing its

nature it occupies no space. Therefore an infinite number oflinesmay be conceived of as intersecting each other at a point,which hasno dimensions and is only of the thickness (if thicknessit may be

called) of one single line.

HOW WE MAY CONCLUDE THAT A SUPERFICIES TERMINATES IN APOINT?

An angular surface is reduced to a point where it terminates inan angle. Or, if the sides of that angle are produced in astraight

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 ofevery object, and the character of their undulations. And these

undulations must be separately studied, as to whether the curvesare

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 athing is

a surface, which is not part of the body contained withinthatsurface; nor is it part of the air surrounding that body, butis the

medium interposted between the air and the body, as is proved inits

place. But the lateral boundaries of these bodies is theline

forming the boundary of the surface, which line is ofinvisiblethickness. Wherefore O painter! do not surround yourbodies with

lines, and above all when representing objects smaller thannature;

for not only will their external outlines become indistinct,buttheir parts will be invisible from distance.

50.

Definition of Perspective.

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

31/96

[Drawing is based upon perspective, which is nothing else thanathorough knowledge of the function of the eye. And thisfunction

simply consists in receiving in a pyramid the forms and coloursof

all the objects placed before it. I say in a pyramid, becausethereis no object so small that it will not be larger than the spotwhere

these pyramids are received into the eye. Therefore, if youextendthe lines from the edges of each body as they converge youwillbring them to a single point, and necessarily the said linesmust

form a pyramid.]

[Perspective is nothing more than a rational demonstrationapplied

to the consideration of how objects in front of the eyetransmit

their image to it, by means of a pyramid of lines. The _Pyramid_isthe name I apply to the lines which, starting from the surfaceand

edges of each object, converge from a distance and meet in asingle

point.]

[Perspective is a rational demonstration, by which we may

practically and clearly understand how objects transmit theirownimage, by lines forming a Pyramid (centred) in the eye.]

Perspective is a rational demonstration by which experienceconfirmsthat every object sends its image to the eye by a pyramidof lines;

and bodies of equal size will result in a pyramid of largeror

smaller size, according to the difference in their distance,onefrom the other. By a pyramid of lines I mean those which startfrom

the surface and edges of bodies, and, converging from a distancemeet in a single point. A point is said to be that which [havingno

dimensions] cannot be divided, and this point placed in theeye

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 thewriter;

but they serve as a commentary on the final paragraph, lines22-29.]

51.

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

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

Supposing that the ball figured above is the ball of the eye andletthe 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 faceof

the eye, by means of the pupil, pass on at once and enter thepupil,

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

32/96

passing through the crystalline humour, which does not interfereinthe pupil with the things seen by means of the light. And thepupil

having received the objects, by means of the light,immediately

refers them and transmits them to the intellect by the line _ab_.And you must know that the pupil transmits nothing perfectly tothe

intellect or common sense excepting when the objects presentedto itby means of light, reach it by the line _a b;_ as, forinstance, bythe 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 donot

coincide with the line _a b_. And the proof is this: If theeye,shown above, wants to count the letters placed in front, theeye

will be obliged to turn from letter to letter, because itcannot

discern them unless they lie in the line _a b;_ as, forinstance, in the line _a c_. All visible objects reach the eye bythe lines of a

pyramid, and the point of the pyramid is the apex and centre ofit,

in the centre of the pupil, as figured above.

[Footnote: 51. In this problem the eye is conceived of as fixedand

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 byexperience,that all objects transmit their image to the eye by apyramid of

lines.

By a pyramid of lines I understand those lines which start fromthe

edges of the surface of bodies, and converging from a distance,meet in a single point; and this point, in the present instance, Iwill

show to be situated in the eye which is the universal judge ofall

objects. By a point I mean that which cannot be divided intoparts;

therefore this point, which is situated in the eye, being

indivisible, no body is seen by the eye, that is not largerthan

this point. This being the case it is inevitable that the lineswhich come from the object to the point must form a pyramid. Andifany man seeks to prove that the sense of sight does not residein

this point, but rather in the black spot which is visible inthe

middle of the pupil, I might reply to him that a small objectcouldnever diminish at any distance, as it might be a grain ofmillet or

of oats or of some similar thing, and that object, if it werelarger

than the said [black] spot would never be seen as a whole; asmay beseen in the diagram below. Let _a_. be the seat of sight, _be_ the

lines which reach the eye. Let _e d_ be the grains of milletwithin

these lines. You plainly see that these will never diminishby

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

33/96

distance, and that the body _m n_ could not be entirely coveredbyit. Therefore you must confess that the eye contains withinitself

one single indivisible point _a_, to which all the pointsconverge

of the pyramid of lines starting from an object, as is shownbelow. Let _a_. _b_. be the eye; in the centre of it is the pointabove

mentioned. If the line _e f_ is to enter as an image into sosmallan opening in the eye, you must confess that the smallerobject cannot enter into what is smaller than itself unless itis

diminished, and by diminishing it must take the form of apyramid.

53.

PERSPECTIVE.

Perspective comes in where judgment fails [as to the distance]in

objects which diminish. The eye can never be a true judgefor

determining with exactitude how near one object is to anotherwhichis equal to it [in size], if the top of that other is on thelevel

of the eye which sees them on that side, excepting by means ofthevertical plane which is the standard and guide of perspective.Let

_n_ be the eye, _e f_ the vertical plane above mentioned. Let _ab c

d_ be the three divisions, one below the other; if the lines _an_and _c n_ are of a given length and the eye _n_ is in thecentre,

then _a b_ will look as large as _b c. c d_ is lower and fartheroff

from _n_, therefore it will look smaller. And the same effectwillappear in the three divisions of a face when the eye of thepainter

who is drawing it is on a level with the eye of the person heispainting.

54.

TO PROVE HOW OBJECTS REACH THE EYE.

If you look at the sun or some other luminous body and thenshut

your eyes you will see it again inside your eye for a longtime.

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, andthe

nearer to the eye these pyramids are intersected the smallerwill

the image appear of the objects which cause them. Therefore, youmay

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

34/96

intersect the pyramid with a vertical plane [Footnote 4:_Pariete_.Compare the definitions in 85, 2-5, 6-27. These linesrefer

exclusively to the third diagram. For the better understandingof

this it should be observed that _c s_ must be regardedasrepresenting 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 containcertainpreliminary observations to guide the reader inunderstanding the

diagram; the last three seem to have been added as asupplement.

Leonardo's mistake in writing _t denota_ (line 6) for _f denota_has been rectified.] which reaches the base of the pyramid as isshown

in the plane _a n_.

The eye _f_ and the eye _t_ are one and the same thing; but theeye

_f_ marks the distance, that is to say how far you are standingfrom

the object; and the eye _t_ shows you the direction of it; thatis

whether you are opposite, or on one side, or at an angle totheobject you are looking at. And remember that the eye _f_ and theeye

_t_ must always be kept on the same level. For example if youraiseor lower the eye from the distance point _f_ you must do thesame

with the direction point _t_. And if the point _f_ shows how farthe

eye is distant from the square plane but does not show on whichsideit is placed--and, if in the same way, the point _t_ show _s_the

direction and not the distance, in order to ascertain both youmust

use both points and they will be one and the same thing. If theeye_f_ could see a perfect square of which all the sides were equalto

the distance between _s_ and _c_, and if at the nearest end oftheside towards the eye a pole were placed, or some otherstraight

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 thatisnearest 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 youat

the height of the point _n_ on the vertical plane. Thus, bythisexample, you can understand that if the eye is above a numberof

objects all placed on the same level, one beyond another, themore

remote they are the higher they will seem, up to the level oftheeye, but no higher; because objects placed upon the level onwhich your feet stand, so long as it is flat--even if it beextended into

infinity--would never be seen above the eye; since the eye hasin

itself the point towards which all the cones tend and convergewhich convey the images of the objects to the eye. And this pointalways

coincides with the point of diminution which is the extreme ofall

we can see. And from the base line of the first pyramid as farasthe diminishing point

[Footnote: The two diagrams above the chapter are explained bythe

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

35/96

first five lines. They have, however, more letters than arereferredto in the text, a circ*mstance we frequently find occasionto

remark.]

56.

there are only bases without pyramids which constantly diminishupto this point. And from the first base where the vertical planeis

placed towards the point in the eye there will be onlypyramids

without bases; as shown in the example given above. Now, let _ab_ be the said vertical plane and _r_ the point of the pyramid

terminating in the eye, and _n_ the point of diminution whichis

always in a straight line opposite the eye and always moves astheeye moves--just as when a rod is moved its shadow moves, andmoves

with it, precisely as the shadow moves with a body. And eachpoint

is the apex of a pyramid, all having a common base with the

intervening vertical plane. But although their bases are equaltheirangles are not equal, because the diminishing point is the

termination of a smaller angle than that of the eye. If you askme: "By what practical experience can you show me these points?"I

reply--so far as concerns the diminishing point which moves withyou

--when you walk by a ploughed field look at the straightfurrowswhich come down with their ends to the path where you arewalking,

and you will see that each pair of furrows will look as thoughthey

tried to get nearer and meet at the [farther] end.

[Footnote: For the easier understanding of the diagram and ofits connection with the preceding I may here remark that thesquare

plane shown above in profile by the line _c s_ is here indicatedby

_e d o p_. According to lines 1, 3 _a b_ must be imagined as aplaneof 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 intelligiblebythis: If you look into the eye of another person you will seeyour

own image. Now imagine 2 lines starting from your ears and goingto

the ears of that image which you see in the other man's eye;youwill understand that these lines converge in such a way thatthey

would meet in a point a little way beyond your own imagemirrored in

the eye. And if you want to measure the diminution of thepyramid in the air which occupies the space between the object seenand 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 backwardsand

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

36/96

forwards till its ends correspond with those of the tower[Footnote9: _I sua stremi .. della storre_ (its ends ... of thetower) this

is the case at _e f_.]; then bring it nearer to the eye, at _cd_

and you will see that the image of the tower seems smaller, asat _ro_. Then [again] bring it closer to the eye and you will seethe rod

project far beyond the image of the tower from _a_ to _b_ andfrom_t_ to _b_, and so you will discern that, a little fartherwithin, 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 withan

infinite number of images which are produced by the variousbodiesand colours assembled in it. And the eye is the target, aloadstone,

of these images.

59.

The whole surface of opaque bodies displays its whole image inall

the illuminated atmosphere which surrounds them on allsides.

60.

That the atmosphere attracts to itself, like a loadstone, allthe

images of the objects that exist in it, and not their formsmerely

but their nature may be clearly seen by the sun, which is a hotandluminous body. All the atmosphere, which is theall-pervading

matter, absorbs light and heat, and reflects in itself the imageof

the source of that heat and splendour and, in each minutestportion, does the same. The Northpole does the same as theloadstone shows;

and the moon and the other planets, without suffering any

diminution, do the same. Among terrestrial things musk does thesame

and other perfumes.

61.

All bodies together, and each by itself, give off to thesurrounding

air an infinite number of images which are all-pervading andeach

complete, each conveying the nature, colour and form of the bodywhich produces it.

It can clearly be shown that all bodies are, by theirimages,

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

37/96

all-pervading in the surrounding atmosphere, and each completeinitself as to substance form and colour; this is seen by theimages

of the various bodies which are reproduced in one singleperforation

through which they transmit the objects by lines which intersectandcause reversed pyramids, from the objects, so that they areupside

down on the dark plane where they are first reflected. Thereason ofthis is--

[Footnote: The diagram intended to illustrate the statement (Pl.II

No. i) occurs in the original between lines 3 and 4. Thethreecircles must be understood to represent three luminous bodieswhich

transmit their images through perforations in a wall into adark

chamber, according to a law which is more fully explained in75?81. So far as concerns the present passage the diagram is onlyintended

to explain that the images of the three bodies may be madeto

coalesce at any given spot. In the circles are written,

giallo--yellow, biacho--white, rosso--red.

The text breaks off at line 8. The paragraph No.40 follows hereinthe 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 samelines converge to a pyramid [imaging] both the colour and form.No

sooner is a form created or compounded than suddenly infinitelines and angles are produced from it; and these lines,distributing

themselves and intersecting each other in the air, give rise toan

infinite number of angles opposite to each other. Given a base,each opposite angle, will form a triangle having a form andproportion

equal to the larger angle; and if the base goes twice into eachof

the 2 lines of the pyramid the smaller triangle will do thesame.

63.

Every body in light and shade fills the surrounding airwithinfinite images of itself; and these, by infinite pyramidsdiffused

in the air, represent this body throughout space and on everyside.

Each pyramid that is composed of a long assemblage of raysincludes within itself an infinite number of pyramids and each hasthe same

power as all, and all as each. A circle of equidistant pyramidsof

vision will give to their object angles of equal size; and aneye ateach point will see the object of the same size. The body ofthe

atmosphere is full of infinite pyramids composed ofradiating

straight lines, which are produced from the surface of thebodies in

8/4/2019 Leonardo Da Vinci - The Notebooks of Leonardo DaVinci

38/96

light and shade, existing in the air; and the farther they arefromthe object which produces them the more acute they becomeand

although in their distribution they intersect and cross theynever

mingle together, but pass through all the surroundingair,independently converging, spreading, and diffused. And they areall

of equal power [and value]; all equal to each, and each equaltoall. By these the images of objects are transmitted throughallspace and in every direction, and each pyramid, in itself,includes,

in each minutest part, the whole form of the body causingit.

64.

The body of the atmosphere is full of infinite radiatingpyramidsproduced by the objects existing in it. These intersect andcross

each other with independent convergence without interferingwith

each other and pass through all the surrounding atmosphere; andare

of equal force and value--all being equal to each, each to all.Andby means of these, images of the body are transmitted everywhereand

on all sides, and each receives in itself every minutest portionofthe object that produces it.

Proof by experiment (65-66).

65.

PERSPECTIVE.

The air is filled with endless images of the objects distributedin

it; and all are represented in all, and all in one, and all ineach,