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Welcome To The World of Free Plain Vanilla Electronic Texts<\/strong><\/p>\n eBooks Readable By Both Humans and By Computers, Since 1971<\/strong><\/p>\n *****These eBooks Were Prepared By Thousands of Volunteers!*****<\/p>\n Title: The Notebooks of Leonardo Da Vinci, Complete<\/p>\n Author: Leonardo Da Vinci<\/p>\n Release Date: Jan, 2004 [EBook #5000] Edition: 09<\/p>\n Language: English<\/p>\n Character set encoding: UTF-8<\/p>\n *** START OF THE PROJECT GUTENBERG EBOOK, THE NOTEBOOKS OF LEONARDO DA VINCI, COMPLETE ***<\/p>\n CONTENTS OF VOLUME I.<\/p>\n 1.<\/p>\n How by a certain machine many may stay some time under water. And [Footnote: The leaf on which this passage is written, is headed with The preparation of the MSS. for publication.<\/p>\n 2.<\/p>\n When you put together the science of the motions of water, remember [Footnote: A comparatively small portion of Leonardo’s notes on Admonition to readers.<\/p>\n 3.<\/p>\n Let no man who is not a Mathematician read the elements of my work.<\/p>\n The disorder in the MSS.<\/p>\n 4.<\/p>\n Begun at Florence, in the house of Piero di Braccio Martelli, on the [Footnote: 1. In the history of Florence in the early part of the racolto tratto di molte carte le quali io ho qui copiate<\/em>. We Suggestions for the arrangement of MSS treating of particular 5.<\/p>\n Of digging a canal. Put this in the Book of useful inventions and in 6.<\/p>\n I am not to blame for putting forward, in the course of my work on 7.<\/p>\n The Book of the science of Mechanics must precede the Book of useful 8.<\/p>\n The order of your book must proceed on this plan: first simple General introductions to the book on Painting (9-13).<\/p>\n 9.<\/p>\n INTRODUCTION.<\/p>\n Seeing that I can find no subject specially useful or 10.<\/p>\n INTRODUCTION.<\/p>\n I know that many will call this useless work [Footnote: 3. questa The same passage occurs as a simple Memorandum in the MS. Tr. 57, [Footnote: In the original, the Proemio d\u00c3\u00ac prospettiva cio\u00c3\u00a8 INTRODUCTION.<\/p>\n I am fully concious that, not being a literary man, certain 11.<\/p>\n Though I may not, like them, be able to quote other authors, I shall INTRODUCTION.<\/p>\n And those men who are inventors and interpreters between Nature and 12.<\/p>\n Many will think they may reasonably blame me by alleging that my 13.<\/p>\n Among all the studies of natural causes and reasons Light chiefly The plan of the book on Painting (14–17).<\/p>\n 14.<\/p>\n ON THE THREE BRANCHES OF PERSPECTIVE.<\/p>\n There are three branches of perspective; the first deals with the Linear Perspective. The Perspective of Colour. The Perspective of [Footnote: 13. From the character of the handwriting I infer that 15.<\/p>\n ON PAINTING AND PERSPECTIVE.<\/p>\n The divisions of Perspective are 3, as used in drawing; of these, [Footnote: The division is here the same as in the previous chapter 16.<\/p>\n THE DISCOURSE ON PAINTING.<\/p>\n Perspective, as bearing on drawing, is divided into three principal 17.<\/p>\n ON THE SECTIONS OF [THE BOOK ON] PAINTING.<\/p>\n The first thing in painting is that the objects it represents should [Footnote: This and the two foregoing chapters must have been The use of the book on Painting.<\/p>\n 18.<\/p>\n These rules are of use only in correcting the figures; since every These rules will enable you to have a free and sound judgment; since Necessity of theoretical knowledge (19. 20).<\/p>\n 19.<\/p>\n OF THE MISTAKES MADE BY THOSE WHO PRACTISE WITHOUT KNOWLEDGE.<\/p>\n Those who are in love with practice without knowledge are like the 20.<\/p>\n The painter who draws merely by practice and by eye, without any The function of the eye (21-23).<\/p>\n 21.<\/p>\n INTRODUCTION TO PERSPECTIVE:–THAT IS OF THE FUNCTION OF THE EYE.<\/p>\n Behold here O reader! a thing concerning which we cannot trust our [Footnote: In section 13 we already find it indicated that the study 22.<\/p>\n Here [in the eye] forms, here colours, here the character of every In so small a space it can be reproduced and rearranged in its whole 23.<\/p>\n OF THE 10 ATTRIBUTES OF THE EYE, ALL CONCERNED IN PAINTING.<\/p>\n Painting is concerned with all the 10 attributes of sight; which 24.<\/p>\n ON PAINTING.<\/p>\n Variability of the eye.<\/p>\n 1st. The pupil of the eye contracts, in proportion to the increase 25.<\/p>\n OF THE EYE.<\/p>\n Focus of sight.<\/p>\n If the eye is required to look at an object placed too near to it, Differences of perception by one eye and by both eyes (26-29).<\/p>\n 26.<\/p>\n OF THE EYE.<\/p>\n When both eyes direct the pyramid of sight to an object, that object 27.<\/p>\n Objects seen by one and the same eye appear sometimes large, and 28.<\/p>\n The motion of a spectator who sees an object at rest often makes it ON PAINTING.<\/p>\n Objects in relief, when seen from a short distance with one eye, 29.<\/p>\n Let the object in relief t<\/em> be seen by both eyes; if you will look [Footnote: In the sketch, m<\/em> is the left eye and n<\/em> the right, 30.<\/p>\n The comparative size of the image depends on the amount of light The eye will hold and retain in itself the image of a luminous body 31.<\/p>\n Every object we see will appear larger at midnight than at midday, This happens because the pupil of the eye is much smaller at midday 32.<\/p>\n The pupil which is largest will see objects the largest. This is [Footnote: 9. buso<\/em> in the Lomb. dialect is the same as buco<\/em>.]<\/p>\n 33.<\/p>\n When the eye, coming out of darkness suddenly sees a luminous body, 34.<\/p>\n Why when the eye has just seen the light, does the half light look 35.<\/p>\n ON PAINTING.<\/p>\n If the eye, when [out of doors] in the luminous atmosphere, sees a [Footnote 14: La luce entrer\u00c3\u00a0<\/em>. Luce<\/em> occurs here in the sense of 36.<\/p>\n ON PERSPECTIVE.<\/p>\n The eye which turns from a white object in the light of the sun and 37.<\/p>\n Experiment [showing] the dilatation and contraction of the pupil, [Footnote: No reference is made in the text to the letters on the 38.<\/p>\n The pupil of the eye, in the open air, changes in size with every 39.<\/p>\n The eye–which sees all objects reversed–retains the images for _II.<\/p>\n Linear Perspective.<\/p>\n We see clearly from the concluding sentence of section 49, where the Leon Battista Alberti treats of the “Pyramid of Sight” at some The axioms as to the perception of the pyramid of rays are followed According to Leonardo, on one hand, the laws of perspective are an In connection with this we have the function of the eye explained by From the principle of the transmission of the image to the eye and Leonardo distinguishes between simple and complex perspective<\/em> (90, General remarks on perspective (40-41).<\/p>\n 40.<\/p>\n ON PAINTING.<\/p>\n Perspective is the best guide to the art of Painting.<\/p>\n [Footnote: 40. Compare 53, 2.]<\/p>\n 41.<\/p>\n The art of perspective is of such a nature as to make what is flat The elements of perspective–Of the Point (42-46).<\/p>\n 42.<\/p>\n All the problems of perspective are made clear by the five terms of 43.<\/p>\n A point is not part of a line.<\/p>\n 44.<\/p>\n OF THE NATURAL POINT.<\/p>\n The smallest natural point is larger than all mathematical points, [Footnote: This definition was inserted by Leonardo on a MS. copy on 45.<\/p>\n 1, The superficies is a limitation of the body. 2, and the If one single point placed in a circle may be the starting point of 46.<\/p>\n The point, being indivisible, occupies no space. That which occupies Of the line (47-48).<\/p>\n 47.<\/p>\n DEFINITION OF THE NATURE OF THE LINE.<\/p>\n The line has in itself neither matter nor substance and may rather HOW WE MAY CONCLUDE THAT A SUPERFICIES TERMINATES IN A POINT?<\/p>\n An angular surface is reduced to a point where it terminates in an 48.<\/p>\n OF DRAWING OUTLINE.<\/p>\n Consider with the greatest care the form of the outlines of every 49.<\/p>\n The nature of the outline.<\/p>\n The boundaries of bodies are the least of all things. The 50.<\/p>\n Definition of Perspective.<\/p>\n [Drawing is based upon perspective, which is nothing else than a [Perspective is nothing more than a rational demonstration applied [Perspective is a rational demonstration, by which we may Perspective is a rational demonstration by which experience confirms [Footnote: 50. 1-5. Compare with this the Proem. No. 21. The 51.<\/p>\n IN WHAT WAY THE EYE SEES OBJECTS PLACED IN FRONT OF IT.<\/p>\n The perception of the object depends on the direction of the eye.<\/p>\n Supposing that the ball figured above is the ball of the eye and let [Footnote: 51. In this problem the eye is conceived of as fixed and Experimental proof of the existence of the pyramid of sight (52-55).<\/p>\n 52.<\/p>\n Perspective is a rational demonstration, confirmed by experience, By a pyramid of lines I understand those lines which start from the 53.<\/p>\n PERSPECTIVE.<\/p>\n Perspective comes in where judgment fails [as to the distance] in 54.<\/p>\n TO PROVE HOW OBJECTS REACH THE EYE.<\/p>\n If you look at the sun or some other luminous body and then shut The relations of the distance points to the vanishing point (55-56).<\/p>\n 55.<\/p>\n ELEMENTS OF PERSPECTIVE.<\/p>\n All objects transmit their image to the eye in pyramids, and the The eye f<\/em> and the eye t<\/em> are one and the same thing; but the eye [Footnote: The two diagrams above the chapter are explained by the 56.<\/p>\n there are only bases without pyramids which constantly diminish up [Footnote: For the easier understanding of the diagram and of its 57.<\/p>\n How to measure the pyramid of vision.<\/p>\n As regards the point in the eye; it is made more intelligible by The Production of pyramid of Vision (58-60).<\/p>\n 58.<\/p>\n PERSPECTIVE.<\/p>\n The instant the atmosphere is illuminated it will be filled with an 59.<\/p>\n The whole surface of opaque bodies displays its whole image in all 60.<\/p>\n That the atmosphere attracts to itself, like a loadstone, all the 61.<\/p>\n All bodies together, and each by itself, give off to the surrounding It can clearly be shown that all bodies are, by their images, [Footnote: The diagram intended to illustrate the statement (Pl. II The text breaks off at line 8. The paragraph No.40 follows here in 62.<\/p>\n Every point is the termination of an infinite number of lines, which 63.<\/p>\n Every body in light and shade fills the surrounding air with 64.<\/p>\n The body of the atmosphere is full of infinite radiating pyramids Proof by experiment (65-66).<\/p>\n 65.<\/p>\n PERSPECTIVE.<\/p>\n The air is filled with endless images of the objects distributed in 66.<\/p>\n The images of objects are all diffused through the atmosphere which 67.<\/p>\n General conclusions.<\/p>\n All objects project their whole image and likeness, diffused and 68.<\/p>\n That the contrary is impossible.<\/p>\n It is impossible that the eye should project from itself, by visual [Footnote: The view here refuted by Leonardo was maintained among Circa il primo modo che si fa con ragione, per essere la cosa in It is worthy of note that Leonardo had made his memorandum refuting 69.<\/p>\n A parallel case.<\/p>\n Just as a stone flung into the water becomes the centre and cause of [Footnote: Compare LIBRI, Histoire des sciences math\u00c3\u00a9matiques en The function of the eye as explained by the camera obscura (70. 71).<\/p>\n 70.<\/p>\n If the object in front of the eye sends its image to the eye, the PROVE HOW ALL OBJECTS, PLACED IN ONE POSITION, ARE ALL EVERYWHERE I say that if the front of a building–or any open piazza or [Footnote: 70. 15–23. This section has already been published in the 71.<\/p>\n HOW THE IMAGES OF OBJECTS RECEIVED BY THE EYE INTERSECT WITHIN THE An experiment, showing how objects transmit their images or [Footnote: This chapter is already known through a translation into The practice of perspective (72. 73).<\/p>\n 72.<\/p>\n In the practice of perspective the same rules apply to light and to 73.<\/p>\n The object which is opposite to the pupil of the eye is seen by that Refraction of the rays falling upon the eye (74. 75)<\/p>\n 74.<\/p>\n The lines sent forth by the image of an object to the eye do not 75.<\/p>\n If the judgment of the eye is situated within it, the straight lines The intersection of the rays (76-82).<\/p>\n 76.<\/p>\n The inversion of the images.<\/p>\n All the images of objects which pass through a window [glass pane] 77.<\/p>\n THE PRINCIPLE ON WHICH THE IMAGES OF BODIES PASS IN BETWEEN THE What difference is there in the way in which images pass through OF THE MOVEMENT OF THE EDGE AT THE RIGHT OR LEFT, OR THE UPPER, OR If you move the right side of the opening the image on the left will [Footnote: 77. 2. In the first of the three diagrams Leonardo had 78.<\/p>\n Necessity has provided that all the images of objects in front of 79.<\/p>\n OF THE CENTRAL LINE OF THE EYE.<\/p>\n Only one line of the image, of all those that reach the visual According to my adversary, necessity requires that the central line 80.<\/p>\n AS TO WHETHER THE CENTRAL LINE OF THE IMAGE CAN BE INTERSECTED, OR It is impossible that the line should intersect itself; that is, 81.<\/p>\n HOW THE INNUMERABLE RAYS FROM INNUMERABLE IMAGES CAN CONVERGE TO A Just as all lines can meet at a point without interfering with each Read the marginal text on the other side.<\/p>\n In proportion as the opening is smaller than the shaded body, so It is impossible that the images of objects should be seen between When the images are made double by mutually crossing each other they [Footnote: 81. On the original diagram at the beginning of this [Footnote: 15–23. These lines stand between the diagrams I and III.]<\/p>\n [Footnote: 24–53. These lines stand between the diagrams I and II.]<\/p>\n [Footnote: 54–97 are written along the left side of diagram I.]<\/p>\n 82.<\/p>\n An experiment showing that though the pupil may not be moved from If you look at an object at some distance from you and which is How the above mentioned facts prove that the pupil acts upside down [Footnote: 82. 14–17. The subject indicated by these two headings is Demostration of perspective by means of a vertical glass plane 83.<\/p>\n OF THE PLANE OF GLASS.<\/p>\n Perspective is nothing else than seeing place [or objects] behind a 84.<\/p>\n Pictorial perspective can never make an object at the same distance,
\n[Yes, we are more than one year ahead of schedule]
\n[This file was first posted on April 10, 2002]<\/p>\n
\nLeonardo da Vinci Notebook<\/h1>\n
\nhow and wherefore I do not describe my method of remaining under
\nwater and how long I can remain without eating. And I do not publish
\nnor divulge these, by reason of the evil nature of men, who would
\nuse them for assassinations at the bottom of the sea by destroying
\nships, and sinking them, together with the men in them. Nevertheless
\nI will impart others, which are not dangerous because the mouth of
\nthe tube through which you breathe is above the water, supported on
\nair sacks or cork.<\/p>\n
\nthe words Casi<\/em> 39, and most of these cases begin with the word
\n‘Come<\/em>‘, like the two here given, which are the 26th and 27th. 7.
\nSughero<\/em>. In the Codex Antlanticus 377a; 1170a there is a sketch,
\ndrawn with the pen, representing a man with a tube in his mouth, and
\nat the farther end of the tube a disk. By the tube the word
\n‘Channa<\/em>‘ is written, and by the disk the word ‘sughero<\/em>‘.]<\/p>\n
\nto include under each proposition its application and use, in order
\nthat this science may not be useless.–<\/p>\n
\nwater-power was published at Bologna in 1828, under the title: “Del
\nmoto e misura dell’Acqua, di L. da Vinci<\/em>“.]<\/p>\n
\n22nd day of March 1508. And this is to be a collection without
\norder, taken from many papers which I have copied here, hoping to
\narrange them later each in its place, according to the subjects of
\nwhich they may treat. But I believe that before I am at the end of
\nthis [task] I shall have to repeat the same things several times;
\nfor which, O reader! do not blame me, for the subjects are many and
\nmemory cannot retain them [all] and say: ‘I will not write this
\nbecause I wrote it before.’ And if I wished to avoid falling into
\nthis fault, it would be necessary in every case when I wanted to
\ncopy [a passage] that, not to repeat myself, I should read over all
\nthat had gone before; and all the more since the intervals are long
\nbetween one time of writing and the next.<\/p>\n
\nXVIth century Piero di Braccio Martelli<\/em> is frequently mentioned as
\nCommissario della Signoria<\/em>. He was famous for his learning and at
\nhis death left four books on Mathematics ready for the press; comp.
\nLITTA, Famiglie celebri Italiane<\/em>, Famiglia Martelli di
\nFirenze<\/em>.–In the Official Catalogue of MSS. in the Brit. Mus., New
\nSeries Vol. I., where this passage is printed, Barto<\/em> has been
\nwrongly given for Braccio.<\/p>\n\n
\nFlorence at that time from the Incarnation (Lady day, March 25th).
\nHence this should be 1509 by our reckoning.<\/p>\n<\/li>\n
\nmust suppose that Leonardo means that he has copied out his own MSS.
\nand not those of others. The first thirteen leaves of the MS. in the
\nBrit. Mus. are a fair copy of some notes on physics.]<\/p>\n<\/li>\n<\/ol>\n
\nsubjects.(5-8).<\/p>\n
\nproving them bring forward the propositions already proved. And this
\nis the proper order; since if you wished to show the usefulness of
\nany plan you would be obliged again to devise new machines to prove
\nits utility and thus would confuse the order of the forty Books and
\nalso the order of the diagrams; that is to say you would have to mix
\nup practice with theory, which would produce a confused and
\nincoherent work.<\/p>\n
\nscience, any general rule derived from a previous conclusion.<\/p>\n
\ninventions.–Have your books on anatomy bound! [Footnote: 4. The
\nnumerous notes on anatomy written on loose leaves and now in the
\nRoyal collection at Windsor can best be classified in four Books,
\ncorresponding to the different character and size of the paper. When
\nLeonardo speaks of ‘li tua libri di notomia<\/em>‘, he probably means
\nthe MSS. which still exist; if this hypothesis is correct the
\npresent condition of these leaves might seem to prove that he only
\ncarried out his purpose with one of the Books on anatomy. A borrowed
\nbook on Anatomy is mentioned in F.O.]<\/p>\n
\nbeams, then (those) supported from below, then suspended in part,
\nthen wholly [suspended]. Then beams as supporting other weights
\n[Footnote: 4. Leonardo’s notes on Mechanics are extraordinarily
\nnumerous; but, for the reasons assigned in my introduction, they
\nhave not been included in the present work.].<\/p>\n
\npleasing–since the men who have come before me have taken for their
\nown every useful or necessary theme–I must do like one who, being
\npoor, comes last to the fair, and can find no other way of providing
\nhimself than by taking all the things already seen by other buyers,
\nand not taken but refused by reason of their lesser value. I, then,
\nwill load my humble pack with this despised and rejected
\nmerchandise, the refuse of so many buyers; and will go about to
\ndistribute it, not indeed in great cities, but in the poorer towns,
\ntaking such a price as the wares I offer may be worth. [Footnote: It
\nneed hardly be pointed out that there is in this ‘Proemio’ a covert
\nirony. In the second and third prefaces, Leonardo characterises his
\nrivals and opponents more closely. His protest is directed against
\nNeo-latinism as professed by most of the humanists of his time; its
\nfutility is now no longer questioned.]<\/p>\n
\nessere opera inutile. By opera we must here understand libro di
\npittura and particularly the treatise on Perspective.]; and they
\nwill be those of whom Demetrius [Footnote: 4. Demetrio. “With regard
\nto the passage attributed to Demetrius”, Dr. H. M\u00c3\u0153LLER STR\u00c3\u0153BING
\nwrites, “I know not what to make of it. It is certainly not
\nDemetrius Phalereus that is meant and it can hardly be Demetrius
\nPoliorcetes. Who then can it be–for the name is a very common one?
\nIt may be a clerical error for Demades and the maxim is quite in the
\nspirit of his writings I have not however been able to find any
\ncorresponding passage either in the ‘Fragments’ (C. MULLER, Orat.
\nAtt.<\/em>, II. 441) nor in the Supplements collected by DIETZ (Rhein.
\nMus.<\/em>, vol. 29, p. 108).”<\/p>\n
\napparently as a note for this ‘Proemio<\/em>‘ thus affording some data
\nas to the time where these introductions were written.] declared
\nthat he took no more account of the wind that came out their mouth
\nin words, than of that they expelled from their lower parts: men who
\ndesire nothing but material riches and are absolutely devoid of that
\nof wisdom, which is the food and the only true riches of the mind.
\nFor so much more worthy as the soul is than the body, so much more
\nnoble are the possessions of the soul than those of the body. And
\noften, when I see one of these men take this work in his hand, I
\nwonder that he does not put it to his nose, like a monkey, or ask me
\nif it is something good to eat.<\/p>\n
\ndell’uffitio dell’occhio (see No. 21) stands between this and the
\npreceding one, No. 9.]<\/p>\n
\npresumptuous persons will think that they may reasonably blame me;
\nalleging that I am not a man of letters. Foolish folks! do they not
\nknow that I might retort as Marius did to the Roman Patricians
\n[Footnote 21: Come Mario disse ai patriti Romani<\/em>. “I am unable to
\nfind the words here attributed by Leonardo to Marius, either in
\nPlutarch’s Life of Marius or in the Apophthegmata (Moralia<\/em>,
\np.202). Nor do they occur in the writings of Valerius Maximus (who
\nfrequently mentions Marius) nor in Velleius Paterculus (II, 11 to
\n43), Dio Cassius, Aulus Gellius, or Macrobius. Professor E.
\nMENDELSON of Dorpat, the editor of Herodian, assures me that no such
\npassage is the found in that author” (communication from Dr. MULLER
\nSTRUBING). Leonardo evidently meant to allude to some well known
\nincident in Roman history and the mention of Marius is the result
\nprobably of some confusion. We may perhaps read, for Marius,
\nMenenius Agrippa, though in that case it is true we must alter
\nPatriti to Plebei. The change is a serious one. but it would render
\nthe passage perfectly clear.] by saying: That they, who deck
\nthemselves out in the labours of others will not allow me my own.
\nThey will say that I, having no literary skill, cannot properly
\nexpress that which I desire to treat of [Footnote 26: le mie cose
\n…. che d’altra parola<\/em>. This can hardly be reconciled with Mons.
\nRAVAISSON’S estimate of L. da Vinci’s learning. “Leonard de Vinci
\netait un admirateur et un disciple des anciens, aussi bien dans
\nl’art que dans la science et il tenait a passer pour tel meme aux
\nyeux de la posterite.<\/em>” _Gaz. des Beaux arts. Oct. 1877.]; but they
\ndo not know that my subjects are to be dealt with by experience
\nrather than by words [Footnote 28: See Footnote 26]; and
\n[experience] has been the mistress of those who wrote well. And so,
\nas mistress, I will cite her in all cases.<\/p>\n
\nrely on that which is much greater and more worthy:–on experience,
\nthe mistress of their Masters. They go about puffed up and pompous,
\ndressed and decorated with [the fruits], not of their own labours,
\nbut of those of others. And they will not allow me my own. They will
\nscorn me as an inventor; but how much more might they–who are not
\ninventors but vaunters and declaimers of the works of others–be
\nblamed.<\/p>\n
\nMan, as compared with boasters and declaimers of the works of
\nothers, must be regarded and not otherwise esteemed than as the
\nobject in front of a mirror, when compared with its image seen in
\nthe mirror. For the first is something in itself, and the other
\nnothingness.–Folks little indebted to Nature, since it is only by
\nchance that they wear the human form and without it I might class
\nthem with the herds of beasts.<\/p>\n
\nproofs are opposed to the authority of certain men held in the
\nhighest reverence by their inexperienced judgments; not considering
\nthat my works are the issue of pure and simple experience, who is
\nthe one true mistress. These rules are sufficient to enable you to
\nknow the true from the false–and this aids men to look only for
\nthings that are possible and with due moderation–and not to wrap
\nyourself in ignorance, a thing which can have no good result, so
\nthat in despair you would give yourself up to melancholy.<\/p>\n
\ndelights the beholder; and among the great features of Mathematics
\nthe certainty of its demonstrations is what preeminently (tends to)
\nelevate the mind of the investigator. Perspective, therefore, must
\nbe preferred to all the discourses and systems of human learning. In
\nthis branch [of science] the beam of light is explained on those
\nmethods of demonstration which form the glory not so much of
\nMathematics as of Physics and are graced with the flowers of both
\n[Footnote: 5. Such of Leonardo’s notes on Optics or on Perspective
\nas bear exclusively on Mathematics or Physics could not be included
\nin the arrangement of the libro di pittura<\/em> which is here presented
\nto the reader. They are however but few.]. But its axioms being laid
\ndown at great length, I shall abridge them to a conclusive brevity,
\narranging them on the method both of their natural order and of
\nmathematical demonstration; sometimes by deduction of the effects
\nfrom the causes, and sometimes arguing the causes from the effects;
\nadding also to my own conclusions some which, though not included in
\nthem, may nevertheless be inferred from them. Thus, if the Lord–who
\nis the light of all things–vouchsafe to enlighten me, I will treat
\nof Light; wherefore I will divide the present work into 3 Parts
\n[Footnote: 10. In the middle ages–for instance, by ROGER BACON, by
\nVITELLONE, with whose works Leonardo was certainly familiar, and by
\nall the writers of the Renaissance Perspective and Optics were not
\nregarded as distinct sciences. Perspective, indeed, is in its widest
\napplication the science of seeing. Although to Leonardo the two
\nsciences were clearly separate, it is not so as to their names; thus
\nwe find axioms in Optics under the heading Perspective. According to
\nthis arrangement of the materials for the theoretical portion of the
\nlibro di pittura<\/em> propositions in Perspective and in Optics stand
\nside by side or occur alternately. Although this particular chapter
\ndeals only with Optics, it is not improbable that the words partir\u00c3\u00b2
\nla presente opera in 3 parti<\/em> may refer to the same division into
\nthree sections which is spoken of in chapters 14 to 17.].<\/p>\n
\nreasons of the (apparent) diminution of objects as they recede from
\nthe eye, and is known as Diminishing Perspective.–The second
\ncontains the way in which colours vary as they recede from the eye.
\nThe third and last is concerned with the explanation of how the
\nobjects [in a picture] ought to be less finished in proportion as
\nthey are remote (and the names are as follows):<\/p>\n
\nDisappearance.<\/p>\n
\nthis passage was written before the year 1490.].<\/p>\n
\nthe first includes the diminution in size of opaque objects; the
\nsecond treats of the diminution and loss of outline in such opaque
\nobjects; the third, of the diminution and loss of colour at long
\ndistances.<\/p>\n
\nNo. 14, and this is worthy of note when we connect it with the fact
\nthat a space of about 20 years must have intervened between the
\nwriting of the two passages.]<\/p>\n
\nsections; of which the first treats of the diminution in the size of
\nbodies at different distances. The second part is that which treats
\nof the diminution in colour in these objects. The third [deals with]
\nthe diminished distinctness of the forms and outlines displayed by
\nthe objects at various distances.<\/p>\n
\nappear in relief, and that the grounds surrounding them at different
\ndistances shall appear within the vertical plane of the foreground
\nof the picture by means of the 3 branches of Perspective, which are:
\nthe diminution in the distinctness of the forms of the objects, the
\ndiminution in their magnitude; and the diminution in their colour.
\nAnd of these 3 classes of Perspective the first results from [the
\nstructure of] the eye, while the other two are caused by the
\natmosphere which intervenes between the eye and the objects seen by
\nit. The second essential in painting is appropriate action and a due
\nvariety in the figures, so that the men may not all look like
\nbrothers, &c.<\/p>\n
\nwritten in 1513 to 1516. They undoubtedly indicate the scheme which
\nLeonardo wished to carry out in arranging his researches on
\nPerspective as applied to Painting. This is important because it is
\nan evidence against the supposition of H. LUDWIG and others, that
\nLeonardo had collected his principles of Perspective in one book so
\nearly as before 1500; a Book which, according to the hypothesis,
\nmust have been lost at a very early period, or destroyed possibly,
\nby the French (!) in 1500 (see H. LUDWIG. L. da Vinci: Das Buch van
\nder Malerei<\/em>. Vienna 1882 III, 7 and 8).]<\/p>\n
\nman makes some mistakes in his first compositions and he who knows
\nthem not, cannot amend them. But you, knowing your errors, will
\ncorrect your works and where you find mistakes amend them, and
\nremember never to fall into them again. But if you try to apply
\nthese rules in composition you will never make an end, and will
\nproduce confusion in your works.<\/p>\n
\ngood judgment is born of clear understanding, and a clear
\nunderstanding comes of reasons derived from sound rules, and sound
\nrules are the issue of sound experience–the common mother of all
\nthe sciences and arts. Hence, bearing in mind the precepts of my
\nrules, you will be able, merely by your amended judgment, to
\ncriticise and recognise every thing that is out of proportion in a
\nwork, whether in the perspective or in the figures or any thing
\nelse.<\/p>\n
\nsailor who gets into a ship without rudder or compass and who never
\ncan be certain whether he is going. Practice must always be founded
\non sound theory, and to this Perspective is the guide and the
\ngateway; and without this nothing can be done well in the matter of
\ndrawing.<\/p>\n
\nreason, is like a mirror which copies every thing placed in front of
\nit without being conscious of their existence.<\/p>\n
\nforefathers, the ancients, who tried to define what the Soul and
\nLife are–which are beyond proof, whereas those things, which can at
\nany time be clearly known and proved by experience, remained for
\nmany ages unknown or falsely understood. The eye, whose function we
\nso certainly know by experience, has, down to my own time, been
\ndefined by an infinite number of authors as one thing; but I find,
\nby experience, that it is quite another. [Footnote 13: Compare the
\nnote to No. 70.]<\/p>\n
\nof Perspective and of Optics is to be based on that of the functions
\nof the eye. Leonardo also refers to the science of the eye, in his
\nastronomical researches, for instance in MS. F 25b ‘Ordine del
\nprovare la terra essere una stella: Imprima difinisce l’occhio’<\/em>,
\n&c. Compare also MS. E 15b and F 60b. The principles of astronomical
\nperspective.]<\/p>\n
\npart of the universe are concentrated to a point; and that point is
\nso marvellous a thing … Oh! marvellous, O stupendous Necessity–by
\nthy laws thou dost compel every effect to be the direct result of
\nits cause, by the shortest path. These [indeed] are miracles;…<\/p>\n
\nexpanse. Describe in your anatomy what proportion there is between
\nthe diameters of all the images in the eye and the distance from
\nthem of the crystalline lens.<\/p>\n
\nare:–Darkness, Light, Solidity and Colour, Form and Position,
\nDistance and Propinquity, Motion and Rest. This little work of mine
\nwill be a tissue [of the studies] of these attributes, reminding the
\npainter of the rules and methods by which he should use his art to
\nimitate all the works of Nature which adorn the world.<\/p>\n
\nof light which is reflected in it. 2nd. The pupil of the eye expands
\nin proportion to the diminution in the day light, or any other
\nlight, that is reflected in it. 3rd. [Footnote: 8. The subject of
\nthis third proposition we find fully discussed in MS. G. 44a.]. The
\neye perceives and recognises the objects of its vision with greater
\nintensity in proportion as the pupil is more widely dilated; and
\nthis can be proved by the case of nocturnal animals, such as cats,
\nand certain birds–as the owl and others–in which the pupil varies
\nin a high degree from large to small, &c., when in the dark or in
\nthe light. 4th. The eye [out of doors] in an illuminated atmosphere
\nsees darkness behind the windows of houses which [nevertheless] are
\nlight. 5th. All colours when placed in the shade appear of an equal
\ndegree of darkness, among themselves. 6th. But all colours when
\nplaced in a full light, never vary from their true and essential
\nhue.<\/p>\n
\nit cannot judge of it well–as happens to a man who tries to see the
\ntip of his nose. Hence, as a general rule, Nature teaches us that an
\nobject can never be seen perfectly unless the space between it and
\nthe eye is equal, at least, to the length of the face.<\/p>\n
\nbecomes clearly seen and comprehended by the eyes.<\/p>\n
\nsometimes small.<\/p>\n
\nseem as though the object at rest had acquired the motion of the
\nmoving body, while the moving person appears to be at rest.<\/p>\n
\nlook like a perfect picture. If you look with the eye a<\/em>, b<\/em> at
\nthe spot c<\/em>, this point c<\/em> will appear to be at d<\/em>, f<\/em>, and if
\nyou look at it with the eye g<\/em>, h<\/em> will appear to be at m<\/em>. A
\npicture can never contain in itself both aspects.<\/p>\n
\nat the object with the right eye m<\/em>, keeping the left eye n<\/em> shut,
\nthe object will appear, or fill up the space, at a<\/em>; and if you
\nshut the right eye and open the left, the object (will occupy the)
\nspace b<\/em>; and if you open both eyes, the object will no longer
\nappear at a<\/em> or b<\/em>, but at e<\/em>, r<\/em>, f<\/em>. Why will not a picture
\nseen by both eyes produce the effect of relief, as [real] relief
\ndoes when seen by both eyes; and why should a picture seen with one
\neye give the same effect of relief as real relief would under the
\nsame conditions of light and shade?<\/p>\n
\nwhile the text reverses this lettering. We must therefore suppose
\nthat the face in which the eyes m<\/em> and n<\/em> are placed is opposite
\nto the spectator.]<\/p>\n
\n(30-39).<\/p>\n
\nbetter than that of a shaded object. The reason is that the eye is
\nin itself perfectly dark and since two things that are alike cannot
\nbe distinguished, therefore the night, and other dark objects cannot
\nbe seen or recognised by the eye. Light is totally contrary and
\ngives more distinctness, and counteracts and differs from the usual
\ndarkness of the eye, hence it leaves the impression of its image.<\/p>\n
\nand larger in the morning than at midday.<\/p>\n
\nthan at any other time.<\/p>\n
\nevident when we look at luminous bodies, and particularly at those
\nin the sky. When the eye comes out of darkness and suddenly looks up
\nat these bodies, they at first appear larger and then diminish; and
\nif you were to look at those bodies through a small opening, you
\nwould see them smaller still, because a smaller part of the pupil
\nwould exercise its function.<\/p>\n
\nit will appear much larger at first sight than after long looking at
\nit. The illuminated object will look larger and more brilliant, when
\nseen with two eyes than with only one. A luminous object will appear
\nsmaller in size, when the eye sees it through a smaller opening. A
\nluminous body of an oval form will appear rounder in proportion as
\nit is farther from the eye.<\/p>\n
\ndark to it, and in the same way if it turns from the darkness the
\nhalf light look very bright?<\/p>\n
\nplace in shadow, this will look very much darker than it really is.
\nThis happens only because the eye when out in the air contracts the
\npupil in proportion as the atmosphere reflected in it is more
\nluminous. And the more the pupil contracts, the less luminous do the
\nobjects appear that it sees. But as soon as the eye enters into a
\nshady place the darkness of the shadow suddenly seems to diminish.
\nThis occurs because the greater the darkness into which the pupil
\ngoes the more its size increases, and this increase makes the
\ndarkness seem less.<\/p>\n
\npupil of the eye as in no 51: C. A. 84b; 245a; I–5; and in many
\nother places.]<\/p>\n
\ngoes into a less fully lighted place will see everything as dark.
\nAnd this happens either because the pupils of the eyes which have
\nrested on this brilliantly lighted white object have contracted so
\nmuch that, given at first a certain extent of surface, they will
\nhave lost more than 3\/4 of their size; and, lacking in size, they
\nare also deficient in [seeing] power. Though you might say to me: A
\nlittle bird (then) coming down would see comparatively little, and
\nfrom the smallness of his pupils the white might seem black! To this
\nI should reply that here we must have regard to the proportion of
\nthe mass of that portion of the brain which is given up to the sense
\nof sight and to nothing else. Or–to return–this pupil in Man
\ndilates and contracts according to the brightness or darkness of
\n(surrounding) objects; and since it takes some time to dilate and
\ncontract, it cannot see immediately on going out of the light and
\ninto the shade, nor, in the same way, out of the shade into the
\nlight, and this very thing has already deceived me in painting an
\neye, and from that I learnt it.<\/p>\n
\nfrom the motion of the sun and other luminaries. In proportion as
\nthe sky is darker the stars appear of larger size, and if you were
\nto light up the medium these stars would look smaller; and this
\ndifference arises solely from the pupil which dilates and contracts
\nwith the amount of light in the medium which is interposed between
\nthe eye and the luminous body. Let the experiment be made, by
\nplacing a candle above your head at the same time that you look at a
\nstar; then gradually lower the candle till it is on a level with the
\nray that comes from the star to the eye, and then you will see the
\nstar diminish so much that you will almost lose sight of it.<\/p>\n
\naccompanying diagram.]<\/p>\n
\ndegree of motion from the sun; and at every degree of its changes
\none and the same object seen by it will appear of a different size;
\nalthough most frequently the relative scale of surrounding objects
\ndoes not allow us to detect these variations in any single object we
\nmay look at.<\/p>\n
\nsome time. This conclusion is proved by the results; because, the
\neye having gazed at light retains some impression of it. After
\nlooking (at it) there remain in the eye images of intense
\nbrightness, that make any less brilliant spot seem dark until the
\neye has lost the last trace of the impression of the stronger light.<\/p>\n
\nauthor directly addresses the painter, that he must certainly have
\nintended to include the elements of mathematics in his Book on the
\nart of Painting. They are therefore here placed at the beginning. In
\nsection 50 the theory of the “Pyramid of Sight” is distinctly and
\nexpressly put forward as the fundamental principle of linear
\nperspective, and sections 52 to 57 treat of it fully. This theory of
\nsight can scarcely be traced to any author of antiquity. Such
\npassages as occur in Euclid for instance, may, it is true, have
\nproved suggestive to the painters of the Renaissance, but it would
\nbe rash to say any thing decisive on this point.<\/p>\n
\nlength in his first Book of Painting; but his explanation differs
\nwidely from Leonardo’s in the details. Leonardo, like Alberti, may
\nhave borrowed the broad lines of his theory from some views commonly
\naccepted among painters at the time; but he certainly worked out its
\napplication in a perfectly original manner.<\/p>\n
\nby explanations of its origin, and proofs of its universal
\napplication (58–69). The author recurs to the subject with endless
\nvariations; it is evidently of fundamental importance in his
\nartistic theory and practice. It is unnecessary to discuss how far
\nthis theory has any scientific value at the present day; so much as
\nthis, at any rate, seems certain: that from the artist’s point of
\nview it may still claim to be of immense practical utility.<\/p>\n
\ninalienable condition of the existence of objects in space; on the
\nother hand, by a natural law, the eye, whatever it sees and wherever
\nit turns, is subjected to the perception of the pyramid of rays in
\nthe form of a minute target. Thus it sees objects in perspective
\nindependently of the will of the spectator, since the eye receives
\nthe images by means of the pyramid of rays “just as a magnet
\nattracts iron”.<\/p>\n
\nthe Camera obscura, and this is all the more interesting and
\nimportant because no writer previous to Leonardo had treated of this
\nsubject_ (70–73). Subsequent passages, of no less special interest,
\nbetray his knowledge of refraction and of the inversion of the image
\nin the camera and in the eye<\/em> (74–82).<\/p>\n
\nto the camera obscura he deduces the means of producing an
\nartificial construction of the pyramid of rays or–which is the same
\nthing–of the image. The fundamental axioms as to the angle of sight
\nand the vanishing point are thus presented in a manner which is as
\ncomplete as it is simple and intelligible<\/em> (86–89).<\/p>\n
\n91). The last sections treat of the apparent size of objects at
\nvarious distances and of the way to estimate it<\/em> (92–109).<\/p>\n
\nappear in relief and what is in relief flat.<\/p>\n
\nmathematicians, which are:–the point, the line, the angle, the
\nsuperficies and the solid. The point is unique of its kind. And the
\npoint has neither height, breadth, length, nor depth, whence it is
\nto be regarded as indivisible and as having no dimensions in space.
\nThe line is of three kinds, straight, curved and sinuous and it has
\nneither breadth, height, nor depth. Hence it is indivisible,
\nexcepting in its length, and its ends are two points. The angle is
\nthe junction of two lines in a point.<\/p>\n
\nand this is proved because the natural point has continuity, and any
\nthing that is continuous is infinitely divisible; but the
\nmathematical point is indivisible because it has no size.<\/p>\n
\nparchment of the well-known “Trattato d’Architettura civile e
\nmilitare”<\/em> &c. by FRANCESCO DI GIORGIO; opposite a passage where the
\nauthor says: _’In prima he da sapere che punto \u00c3\u00a8 quella parie della
\nquale he nulla–Linia he luncheza senza \u00c3\u00a0pieza; &c.]<\/p>\n
\nlimitation of a body is no part of that body. 4, and the limitation
\nof one body is that which begins another. 3, that which is not part
\nof any body is nothing. Nothing is that which fills no space.<\/p>\n
\nan infinite number of lines, and the termination of an infinite
\nnumber of lines, there must be an infinite number of points
\nseparable from this point, and these when reunited become one again;
\nwhence it follows that the part may be equal to the whole.<\/p>\n
\nno space is nothing. The limiting surface of one thing is the
\nbeginning of another. 2. That which is no part of any body is called
\nnothing. 1. That which has no limitations, has no form. The
\nlimitations of two conterminous bodies are interchangeably the
\nsurface of each. All the surfaces of a body are not parts of that
\nbody.<\/p>\n
\nbe called an imaginary idea than a real object; and this being its
\nnature it occupies no space. Therefore an infinite number of lines
\nmay be conceived of as intersecting each other at a point, which has
\nno dimensions and is only of the thickness (if thickness it may be
\ncalled) of one single line.<\/p>\n
\nangle. Or, if the sides of that angle are produced in a straight
\nline, then–beyond that angle–another surface is generated,
\nsmaller, or equal to, or larger than the first.<\/p>\n
\nobject, and the character of their undulations. And these
\nundulations must be separately studied, as to whether the curves are
\ncomposed of arched convexities or angular concavities.<\/p>\n
\nproposition is proved to be true, because the boundary of a thing is
\na surface, which is not part of the body contained within that
\nsurface; nor is it part of the air surrounding that body, but is the
\nmedium interposted between the air and the body, as is proved in its
\nplace. But the lateral boundaries of these bodies is the line
\nforming the boundary of the surface, which line is of invisible
\nthickness. Wherefore O painter! do not surround your bodies with
\nlines, and above all when representing objects smaller than nature;
\nfor not only will their external outlines become indistinct, but
\ntheir parts will be invisible from distance.<\/p>\n
\nthorough knowledge of the function of the eye. And this function
\nsimply consists in receiving in a pyramid the forms and colours of
\nall the objects placed before it. I say in a pyramid, because there
\nis no object so small that it will not be larger than the spot where
\nthese pyramids are received into the eye. Therefore, if you extend
\nthe lines from the edges of each body as they converge you will
\nbring them to a single point, and necessarily the said lines must
\nform a pyramid.]<\/p>\n
\nto the consideration of how objects in front of the eye transmit
\ntheir image to it, by means of a pyramid of lines. The Pyramid<\/em> is
\nthe name I apply to the lines which, starting from the surface and
\nedges of each object, converge from a distance and meet in a single
\npoint.]<\/p>\n
\npractically and clearly understand how objects transmit their own
\nimage, by lines forming a Pyramid (centred) in the eye.]<\/p>\n
\nthat every object sends its image to the eye by a pyramid of lines;
\nand bodies of equal size will result in a pyramid of larger or
\nsmaller size, according to the difference in their distance, one
\nfrom the other. By a pyramid of lines I mean those which start from
\nthe surface and edges of bodies, and, converging from a distance
\nmeet in a single point. A point is said to be that which [having no
\ndimensions] cannot be divided, and this point placed in the eye
\nreceives all the points of the cone.<\/p>\n
\nparagraphs placed in brackets: lines 1-9, 10-14, and 17–20, are
\nevidently mere sketches and, as such, were cancelled by the writer;
\nbut they serve as a commentary on the final paragraph, lines 22-29.]<\/p>\n
\nthe small portion of the ball which is cut off by the line s t<\/em> be
\nthe pupil and all the objects mirrored on the centre of the face of
\nthe eye, by means of the pupil, pass on at once and enter the pupil,
\npassing through the crystalline humour, which does not interfere in
\nthe pupil with the things seen by means of the light. And the pupil
\nhaving received the objects, by means of the light, immediately
\nrefers them and transmits them to the intellect by the line a b<\/em>.
\nAnd you must know that the pupil transmits nothing perfectly to the
\nintellect or common sense excepting when the objects presented to it
\nby means of light, reach it by the line a b;<\/em> as, for instance, by
\nthe line b c<\/em>. For although the lines m n<\/em> and f g<\/em> may be seen
\nby the pupil they are not perfectly taken in, because they do not
\ncoincide with the line a b<\/em>. And the proof is this: If the eye,
\nshown above, wants to count the letters placed in front, the eye
\nwill be obliged to turn from letter to letter, because it cannot
\ndiscern them unless they lie in the line a b;<\/em> as, for instance, in
\nthe line a c<\/em>. All visible objects reach the eye by the lines of a
\npyramid, and the point of the pyramid is the apex and centre of it,
\nin the centre of the pupil, as figured above.<\/p>\n
\nimmovable; this is plain from line 11.]<\/p>\n
\nthat all objects transmit their image to the eye by a pyramid of
\nlines.<\/p>\n
\nedges of the surface of bodies, and converging from a distance, meet
\nin a single point; and this point, in the present instance, I will
\nshow to be situated in the eye which is the universal judge of all
\nobjects. By a point I mean that which cannot be divided into parts;
\ntherefore this point, which is situated in the eye, being
\nindivisible, no body is seen by the eye, that is not larger than
\nthis point. This being the case it is inevitable that the lines
\nwhich come from the object to the point must form a pyramid. And if
\nany man seeks to prove that the sense of sight does not reside in
\nthis point, but rather in the black spot which is visible in the
\nmiddle of the pupil, I might reply to him that a small object could
\nnever diminish at any distance, as it might be a grain of millet or
\nof oats or of some similar thing, and that object, if it were larger
\nthan the said [black] spot would never be seen as a whole; as may be
\nseen in the diagram below. Let a<\/em>. be the seat of sight, b e<\/em> the
\nlines which reach the eye. Let e d<\/em> be the grains of millet within
\nthese lines. You plainly see that these will never diminish by
\ndistance, and that the body m n<\/em> could not be entirely covered by
\nit. Therefore you must confess that the eye contains within itself
\none single indivisible point a<\/em>, to which all the points converge
\nof the pyramid of lines starting from an object, as is shown below.
\nLet a<\/em>. b<\/em>. be the eye; in the centre of it is the point above
\nmentioned. If the line e f<\/em> is to enter as an image into so small
\nan opening in the eye, you must confess that the smaller object
\ncannot enter into what is smaller than itself unless it is
\ndiminished, and by diminishing it must take the form of a pyramid.<\/p>\n
\nobjects which diminish. The eye can never be a true judge for
\ndetermining with exactitude how near one object is to another which
\nis equal to it [in size], if the top of that other is on the level
\nof the eye which sees them on that side, excepting by means of the
\nvertical plane which is the standard and guide of perspective. Let
\nn<\/em> be the eye, e f<\/em> the vertical plane above mentioned. Let a b c
\nd<\/em> be the three divisions, one below the other; if the lines a n<\/em>
\nand c n<\/em> are of a given length and the eye n<\/em> is in the centre,
\nthen a b<\/em> will look as large as b c. c d<\/em> is lower and farther off
\nfrom n<\/em>, therefore it will look smaller. And the same effect will
\nappear in the three divisions of a face when the eye of the painter
\nwho is drawing it is on a level with the eye of the person he is
\npainting.<\/p>\n
\nyour eyes you will see it again inside your eye for a long time.
\nThis is evidence that images enter into the eye.<\/p>\n
\nnearer to the eye these pyramids are intersected the smaller will
\nthe image appear of the objects which cause them. Therefore, you may
\nintersect the pyramid with a vertical plane [Footnote 4: Pariete<\/em>.
\nCompare the definitions in 85, 2-5, 6-27. These lines refer
\nexclusively to the third diagram. For the better understanding of
\nthis it should be observed that c s<\/em> must be regarded as
\nrepresenting the section or profile of a square plane, placed
\nhorizontally (comp. lines 11, 14, 17) for which the word pianura<\/em>
\nis subsequently employed (20, 22). Lines 6-13 contain certain
\npreliminary observations to guide the reader in understanding the
\ndiagram; the last three seem to have been added as a supplement.
\nLeonardo’s mistake in writing t denota<\/em> (line 6) for f denota<\/em> has
\nbeen rectified.] which reaches the base of the pyramid as is shown
\nin the plane a n<\/em>.<\/p>\n
\nf<\/em> marks the distance, that is to say how far you are standing from
\nthe object; and the eye t<\/em> shows you the direction of it; that is
\nwhether you are opposite, or on one side, or at an angle to the
\nobject you are looking at. And remember that the eye f<\/em> and the eye
\nt<\/em> must always be kept on the same level. For example if you raise
\nor lower the eye from the distance point f<\/em> you must do the same
\nwith the direction point t<\/em>. And if the point f<\/em> shows how far the
\neye is distant from the square plane but does not show on which side
\nit is placed–and, if in the same way, the point t<\/em> show s<\/em> the
\ndirection and not the distance, in order to ascertain both you must
\nuse both points and they will be one and the same thing. If the eye
\nf<\/em> could see a perfect square of which all the sides were equal to
\nthe distance between s<\/em> and c<\/em>, and if at the nearest end of the
\nside towards the eye a pole were placed, or some other straight
\nobject, set up by a perpendicular line as shown at r s<\/em>–then, I
\nsay, that if you were to look at the side of the square that is
\nnearest to you it will appear at the bottom of the vertical plane r
\ns<\/em>, and then look at the farther side and it would appear to you at
\nthe height of the point n<\/em> on the vertical plane. Thus, by this
\nexample, you can understand that if the eye is above a number of
\nobjects all placed on the same level, one beyond another, the more
\nremote they are the higher they will seem, up to the level of the
\neye, but no higher; because objects placed upon the level on which
\nyour feet stand, so long as it is flat–even if it be extended into
\ninfinity–would never be seen above the eye; since the eye has in
\nitself the point towards which all the cones tend and converge which
\nconvey the images of the objects to the eye. And this point always
\ncoincides with the point of diminution which is the extreme of all
\nwe can see. And from the base line of the first pyramid as far as
\nthe diminishing point<\/p>\n
\nfirst five lines. They have, however, more letters than are referred
\nto in the text, a circumstance we frequently find occasion to
\nremark.]<\/p>\n
\nto this point. And from the first base where the vertical plane is
\nplaced towards the point in the eye there will be only pyramids
\nwithout bases; as shown in the example given above. Now, let a b<\/em>
\nbe the said vertical plane and r<\/em> the point of the pyramid
\nterminating in the eye, and n<\/em> the point of diminution which is
\nalways in a straight line opposite the eye and always moves as the
\neye moves–just as when a rod is moved its shadow moves, and moves
\nwith it, precisely as the shadow moves with a body. And each point
\nis the apex of a pyramid, all having a common base with the
\nintervening vertical plane. But although their bases are equal their
\nangles are not equal, because the diminishing point is the
\ntermination of a smaller angle than that of the eye. If you ask me:
\n“By what practical experience can you show me these points?” I
\nreply–so far as concerns the diminishing point which moves with you
\n–when you walk by a ploughed field look at the straight furrows
\nwhich come down with their ends to the path where you are walking,
\nand you will see that each pair of furrows will look as though they
\ntried to get nearer and meet at the [farther] end.<\/p>\n
\nconnection with the preceding I may here remark that the square
\nplane shown above in profile by the line c s<\/em> is here indicated by
\ne d o p<\/em>. According to lines 1, 3 a b<\/em> must be imagined as a plane
\nof glass placed perpendicularly at o p<\/em>.]<\/p>\n
\nthis: If you look into the eye of another person you will see your
\nown image. Now imagine 2 lines starting from your ears and going to
\nthe ears of that image which you see in the other man’s eye; you
\nwill understand that these lines converge in such a way that they
\nwould meet in a point a little way beyond your own image mirrored in
\nthe eye. And if you want to measure the diminution of the pyramid in
\nthe air which occupies the space between the object seen and the
\neye, you must do it according to the diagram figured below. Let m
\nn<\/em> be a tower, and e f<\/em> a, rod, which you must move backwards and
\nforwards till its ends correspond with those of the tower [Footnote
\n9: I sua stremi .. della storre<\/em> (its ends … of the tower) this
\nis the case at e f<\/em>.]; then bring it nearer to the eye, at c d<\/em>
\nand you will see that the image of the tower seems smaller, as at r
\no<\/em>. Then [again] bring it closer to the eye and you will see the rod
\nproject far beyond the image of the tower from a<\/em> to b<\/em> and from
\nt<\/em> to b<\/em>, and so you will discern that, a little farther within,
\nthe lines must converge in a point.<\/p>\n
\ninfinite number of images which are produced by the various bodies
\nand colours assembled in it. And the eye is the target, a loadstone,
\nof these images.<\/p>\n
\nthe illuminated atmosphere which surrounds them on all sides.<\/p>\n
\nimages of the objects that exist in it, and not their forms merely
\nbut their nature may be clearly seen by the sun, which is a hot and
\nluminous body. All the atmosphere, which is the all-pervading
\nmatter, absorbs light and heat, and reflects in itself the image of
\nthe source of that heat and splendour and, in each minutest portion,
\ndoes the same. The Northpole does the same as the loadstone shows;
\nand the moon and the other planets, without suffering any
\ndiminution, do the same. Among terrestrial things musk does the same
\nand other perfumes.<\/p>\n
\nair an infinite number of images which are all-pervading and each
\ncomplete, each conveying the nature, colour and form of the body
\nwhich produces it.<\/p>\n
\nall-pervading in the surrounding atmosphere, and each complete in
\nitself as to substance form and colour; this is seen by the images
\nof the various bodies which are reproduced in one single perforation
\nthrough which they transmit the objects by lines which intersect and
\ncause reversed pyramids, from the objects, so that they are upside
\ndown on the dark plane where they are first reflected. The reason of
\nthis is–<\/p>\n
\nNo. i) occurs in the original between lines 3 and 4. The three
\ncircles must be understood to represent three luminous bodies which
\ntransmit their images through perforations in a wall into a dark
\nchamber, according to a law which is more fully explained in 75?81.
\nSo far as concerns the present passage the diagram is only intended
\nto explain that the images of the three bodies may be made to
\ncoalesce at any given spot. In the circles are written,
\ngiallo–yellow, bi\u00c3\u00a0cho–white, rosso–red.<\/p>\n
\nthe original MS.]<\/p>\n
\ndiverge to form a base, and immediately, from the base the same
\nlines converge to a pyramid [imaging] both the colour and form. No
\nsooner is a form created or compounded than suddenly infinite lines
\nand angles are produced from it; and these lines, distributing
\nthemselves and intersecting each other in the air, give rise to an
\ninfinite number of angles opposite to each other. Given a base, each
\nopposite angle, will form a triangle having a form and proportion
\nequal to the larger angle; and if the base goes twice into each of
\nthe 2 lines of the pyramid the smaller triangle will do the same.<\/p>\n
\ninfinite images of itself; and these, by infinite pyramids diffused
\nin the air, represent this body throughout space and on every side.
\nEach pyramid that is composed of a long assemblage of rays includes
\nwithin itself an infinite number of pyramids and each has the same
\npower as all, and all as each. A circle of equidistant pyramids of
\nvision will give to their object angles of equal size; and an eye at
\neach point will see the object of the same size. The body of the
\natmosphere is full of infinite pyramids composed of radiating
\nstraight lines, which are produced from the surface of the bodies in
\nlight and shade, existing in the air; and the farther they are from
\nthe object which produces them the more acute they become and
\nalthough in their distribution they intersect and cross they never
\nmingle together, but pass through all the surrounding air,
\nindependently converging, spreading, and diffused. And they are all
\nof equal power [and value]; all equal to each, and each equal to
\nall. By these the images of objects are transmitted through all
\nspace and in every direction, and each pyramid, in itself, includes,
\nin each minutest part, the whole form of the body causing it.<\/p>\n
\nproduced by the objects existing in it. These intersect and cross
\neach other with independent convergence without interfering with
\neach other and pass through all the surrounding atmosphere; and are
\nof equal force and value–all being equal to each, each to all. And
\nby means of these, images of the body are transmitted everywhere and
\non all sides, and each receives in itself every minutest portion of
\nthe object that produces it.<\/p>\n
\nit; and all are represented in all, and all in one, and all in each,
\nwhence it happens that if two mirrors are placed in such a manner as
\nto face each other exactly, the first will be reflected in the
\nsecond and the second in the first. The first being reflected in the
\nsecond takes to it the image of itself with all the images
\nrepresented in it, among which is the image of the second mirror,
\nand so, image within image, they go on to infinity in such a manner
\nas that each mirror has within it a mirror, each smaller than the
\nlast and one inside the other. Thus, by this example, it is clearly
\nproved that every object sends its image to every spot whence the
\nobject itself can be seen; and the converse: That the same object
\nmay receive in itself all the images of the objects that are in
\nfront of it. Hence the eye transmits through the atmosphere its own
\nimage to all the objects that are in front of it and receives them
\ninto itself, that is to say on its surface, whence they are taken in
\nby the common sense, which considers them and if they are pleasing
\ncommits them to the memory. Whence I am of opinion: That the
\ninvisible images in the eyes are produced towards the object, as the
\nimage of the object to the eye. That the images of the objects must
\nbe disseminated through the air. An instance may be seen in several
\nmirrors placed in a circle, which will reflect each other endlessly.
\nWhen one has reached the other it is returned to the object that
\nproduced it, and thence–being diminished–it is returned again to
\nthe object and then comes back once more, and this happens
\nendlessly. If you put a light between two flat mirrors with a
\ndistance of 1 braccio between them you will see in each of them an
\ninfinite number of lights, one smaller than another, to the last. If
\nat night you put a light between the walls of a room, all the parts
\nof that wall will be tinted with the image of that light. And they
\nwill receive the light and the light will fall on them, mutually,
\nthat is to say, when there is no obstacle to interrupt the
\ntransmission of the images. This same example is seen in a greater
\ndegree in the distribution of the solar rays which all together, and
\neach by itself, convey to the object the image of the body which
\ncauses it. That each body by itself alone fills with its images the
\natmosphere around it, and that the same air is able, at the same
\ntime, to receive the images of the endless other objects which are
\nin it, this is clearly proved by these examples. And every object is
\neverywhere visible in the whole of the atmosphere, and the whole in
\nevery smallest part of it; and all the objects in the whole, and all
\nin each smallest part; each in all and all in every part.<\/p>\n
\nreceives them; and all on every side in it. To prove this, let a c
\ne<\/em> be objects of which the images are admitted to a dark chamber by
\nthe small holes n p<\/em> and thrown upon the plane f i<\/em> opposite to
\nthese holes. As many images will be produced in the chamber on the
\nplane as the number of the said holes.<\/p>\n
\nmingled in the whole of the atmosphere, opposite to themselves. The
\nimage of every point of the bodily surface, exists in every part of
\nthe atmosphere. All the images of the objects are in every part of
\nthe atmosphere. The whole, and each part of the image of the
\natmosphere is [reflected] in each point of the surface of the bodies
\npresented to it. Therefore both the part and the whole of the images
\nof the objects exist, both in the whole and in the parts of the
\nsurface of these visible bodies. Whence we may evidently say that
\nthe image of each object exists, as a whole and in every part, in
\neach part and in the whole interchangeably in every existing body.
\nAs is seen in two mirrors placed opposite to each other.<\/p>\n
\nrays, the visual virtue, since, as soon as it opens, that front
\nportion [of the eye] which would give rise to this emanation would
\nhave to go forth to the object and this it could not do without
\ntime. And this being so, it could not travel so high as the sun in a
\nmonth’s time when the eye wanted to see it. And if it could reach
\nthe sun it would necessarily follow that it should perpetually
\nremain in a continuous line from the eye to the sun and should
\nalways diverge in such a way as to form between the sun and the eye
\nthe base and the apex of a pyramid. This being the case, if the eye
\nconsisted of a million worlds, it would not prevent its being
\nconsumed in the projection of its virtue; and if this virtue would
\nhave to travel through the air as perfumes do, the winds would bent
\nit and carry it into another place. But we do [in fact] see the mass
\nof the sun with the same rapidity as [an object] at the distance of
\na braccio, and the power of sight is not disturbed by the blowing of
\nthe winds nor by any other accident.<\/p>\n
\nothers by Bramantino, Leonardo’s Milanese contemporary. LOMAZZO
\nwrites as follows in his Trattato dell’ Arte della pittura &c.
\n(Milano 1584. Libr. V cp. XXI): Sovviemmi di aver gi\u00c3\u00a0 letto in certi
\nscritti alcune cose di Bramantino milanese, celebratissimo pittore,
\nattenente alla prospettiva, le quali ho voluto riferire, e quasi
\nintessere in questo luogo, affinch\u00c3\u00a8 sappiamo qual fosse l’opinione
\ndi cosi chiaro e famoso pittore intorno alla prospettiva . . Scrive
\nBramantino che la prospettiva \u00c3\u00a8 una cosa che contraf\u00c3\u00a0 il naturale, e
\nche ci\u00c3\u00b2 si fa in tre modi<\/p>\n
\npoche parole conclusa da Bramantino in maniera che giudico non
\npotersi dir meglio, contenendovi si tutta Parte del principio al
\nfine, io riferir\u00c3\u00b2 per appunto le proprie parole sue (cp. XXII, Prima
\nprospettiva di Bramantino). La prima prospettiva fa le cose di
\npunto, e l’altra non mai, e la terza pi\u00c3\u00b9 appresso. Adunque la prima
\nsi dimanda prospettiva, cio\u00c3\u00a8 ragione, la quale fa l’effetto dell’
\nocchio, facendo crescere e calare secondo gli effetti degli occhi.
\nQuesto crescere e calare non procede della cosa propria, che in se
\nper esser lontana, ovvero vicina, per quello effetto non pu\u00c3\u00b2
\ncrescere e sminuire, ma procede dagli effetti degli occhi, i quali
\nsono piccioli, e perci\u00c3\u00b2 volendo vedere tanto gran cosa_, bisogna che
\nmandino fuora la virt\u00c3\u00b9 visiva, la quale si dilata in tanta
\nlarghezza, che piglia tutto quello che vuoi vedere, ed<\/em> arrivando a
\nquella cosa la vede dove \u00c3\u00a8: e da lei agli occhi per quello circuito
\nfino all’ occhio, e tutto quello termine \u00c3\u00a8 pieno di quella cosa<\/em>.<\/p>\n
\nthis view, at Milan in 1492]<\/p>\n
\nmany circles, and as sound diffuses itself in circles in the air: so
\nany object, placed in the luminous atmosphere, diffuses itself in
\ncircles, and fills the surrounding air with infinite images of
\nitself. And is repeated, the whole every-where, and the whole in
\nevery smallest part. This can be proved by experiment, since if you
\nshut a window that faces west and make a hole [Footnote: 6. Here the
\ntext breaks off.] . .<\/p>\n
\nItalie<\/em>. Tome III, p. 43.]<\/p>\n
\neye, on the other hand, sends its image to the object, and no
\nportion whatever of the object is lost in the images it throws off,
\nfor any reason either in the eye or the object. Therefore we may
\nrather believe it to be the nature and potency of our luminous
\natmosphere which absorbs the images of the objects existing in it,
\nthan the nature of the objects, to send their images through the
\nair. If the object opposite to the eye were to send its image to the
\neye, the eye would have to do the same to the object, whence it
\nmight seem that these images were an emanation. But, if so, it would
\nbe necessary [to admit] that every object became rapidly smaller;
\nbecause each object appears by its images in the surrounding
\natmosphere. That is: the whole object in the whole atmosphere, and
\nin each part; and all the objects in the whole atmosphere and all of
\nthem in each part; speaking of that atmosphere which is able to
\ncontain in itself the straight and radiating lines of the images
\nprojected by the objects. From this it seems necessary to admit that
\nit is in the nature of the atmosphere, which subsists between the
\nobjects, and which attracts the images of things to itself like a
\nloadstone, being placed between them.<\/p>\n
\nAND ALL IN EACH PART.<\/p>\n
\nfield–which is illuminated by the sun has a dwelling opposite to
\nit, and if, in the front which does not face the sun, you make a
\nsmall round hole, all the illuminated objects will project their
\nimages through that hole and be visible inside the dwelling on the
\nopposite wall which may be made white; and there, in fact, they will
\nbe upside down, and if you make similar openings in several places
\nin the same wall you will have the same result from each. Hence the
\nimages of the illuminated objects are all everywhere on this wall
\nand all in each minutest part of it. The reason, as we clearly know,
\nis that this hole must admit some light to the said dwelling, and
\nthe light admitted by it is derived from one or many luminous
\nbodies. If these bodies are of various colours and shapes the rays
\nforming the images are of various colours and shapes, and so will
\nthe representations be on the wall.<\/p>\n
\n“Saggio delle Opere di Leonardo da Vinci<\/em>” Milan 1872, pp. 13, 14.
\nG. Govi observes upon it, that Leonardo is not to be regarded as the
\ninventor of the Camera obscura, but that he was the first to explain
\nby it the structure of the eye. An account of the Camera obscura
\nfirst occurs in CESARE CESARINI’s Italian version of Vitruvius, pub.
\n1523, four years after Leonardo’s death. Cesarini expressly names
\nBenedettino Don Papnutio as the inventor of the Camera obscura. In
\nhis explanation of the function of the eye by a comparison with the
\nCamera obscura Leonardo was the precursor of G. CARDANO, Professor
\nof Medicine at Bologna (died 1576) and it appears highly probable
\nthat this is, in fact, the very discovery which Leonardo ascribes to
\nhimself in section 21 without giving any further details.]<\/p>\n
\nCRYSTALLINE HUMOUR OF THE EYE.<\/p>\n
\npictures, intersecting within the eye in the crystalline humour, is
\nseen when by some small round hole penetrate the images of
\nilluminated objects into a very dark chamber. Then, receive these
\nimages on a white paper placed within this dark room and rather near
\nto the hole and you will see all the objects on the paper in their
\nproper forms and colours, but much smaller; and they will be upside
\ndown by reason of that very intersection. These images being
\ntransmitted from a place illuminated by the sun will seem actually
\npainted on this paper which must be extremely thin and looked at
\nfrom behind. And let the little perforation be made in a very thin
\nplate of iron. Let a b e d e<\/em> be the object illuminated by the sun
\nand o r<\/em> the front of the dark chamber in which is the said hole at
\nn m<\/em>. Let s t<\/em> be the sheet of paper intercepting the rays of the
\nimages of these objects upside down, because the rays being
\nstraight, a<\/em> on the right hand becomes k<\/em> on the left, and e<\/em> on
\nthe left becomes f<\/em> on the right; and the same takes place inside
\nthe pupil.<\/p>\n
\nFrench by VENTURI. Compare his ‘Essai sur les ouvrages
\nphysico-math\u00c3\u00a9matiques de L. da Vinci avec des fragments tir\u00c3\u00a9s de ses
\nManuscrits, apport\u00c3\u00a9s de l’Italie. Lu a la premiere classe de
\nl’Institut national des Sciences et Arts.’ Paris, An V<\/em> (1797).]<\/p>\n
\nthe eye.<\/p>\n
\npupil and that which is opposite to the eye is seen by the pupil.<\/p>\n
\nreach the point within the eye in straight lines.<\/p>\n
\nof the images are refracted on its surface because they pass through
\nthe rarer to the denser medium. If, when you are under water, you
\nlook at objects in the air you will see them out of their true
\nplace; and the same with objects under water seen from the air.<\/p>\n
\nfrom the free outer air to the air confined within walls, are seen
\non the opposite side; and an object which moves in the outer air
\nfrom east to west will seem in its shadow, on the wall which is
\nlighted by this confined air, to have an opposite motion.<\/p>\n
\nMARGINS OF THE OPENINGS BY WHICH THEY ENTER.<\/p>\n
\nnarrow openings and through large openings, or in those which pass
\nby the sides of shaded bodies? By moving the edges of the opening
\nthrough which the images are admitted, the images of immovable
\nobjects are made to move. And this happens, as is shown in the 9th
\nwhich demonstrates: [Footnote 11: per la 9a che dicie<\/em>. When
\nLeonardo refers thus to a number it serves to indicate marginal
\ndiagrams; this can in some instances be distinctly proved. The ninth
\nsketch on the page W. L. 145 b corresponds to the middle sketch of
\nthe three reproduced.] the images of any object are all everywhere,
\nand all in each part of the surrounding air. It follows that if one
\nof the edges of the hole by which the images are admitted to a dark
\nchamber is moved it cuts off those rays of the image that were in
\ncontact with it and gets nearer to other rays which previously were
\nremote from it &c.<\/p>\n
\nLOWER EDGE.<\/p>\n
\nmove [being that] of the object which entered on the right side of
\nthe opening; and the same result will happen with all the other
\nsides of the opening. This can be proved by the 2nd of this which
\nshows: all the rays which convey the images of objects through the
\nair are straight lines. Hence, if the images of very large bodies
\nhave to pass through very small holes, and beyond these holes
\nrecover their large size, the lines must necessarily intersect.<\/p>\n
\ndrawn only one of the two margins, et m<\/em>.]<\/p>\n
\nthe eye shall intersect in two places. One of these intersections is
\nin the pupil, the other in the crystalline lens; and if this were
\nnot the case the eye could not see so great a number of objects as
\nit does. This can be proved, since all the lines which intersect do
\nso in a point. Because nothing is seen of objects excepting their
\nsurface; and their edges are lines, in contradistinction to the
\ndefinition of a surface. And each minute part of a line is equal to
\na point; for smallest<\/em> is said of that than which nothing can be
\nsmaller, and this definition is equivalent to the definition of the
\npoint. Hence it is possible for the whole circumference of a circle
\nto transmit its image to the point of intersection, as is shown in
\nthe 4th of this which shows: all the smallest parts of the images
\ncross each other without interfering with each other. These
\ndemonstrations are to illustrate the eye. No image, even of the
\nsmallest object, enters the eye without being turned upside down;
\nbut as it penetrates into the crystalline lens it is once more
\nreversed and thus the image is restored to the same position within
\nthe eye as that of the object outside the eye.<\/p>\n
\nvirtue, has no intersection; and this has no sensible dimensions
\nbecause it is a mathematical line which originates from a
\nmathematical point, which has no dimensions.<\/p>\n
\nof every image that enters by small and narrow openings into a dark
\nchamber shall be turned upside down, together with the images of the
\nbodies that surround it.<\/p>\n
\nNOT, WITHIN THE OPENING.<\/p>\n
\nthat its right should cross over to its left side, and so, its left
\nside become its right side. Because such an intersection demands two
\nlines, one from each side; for there can be no motion from right to
\nleft or from left to right in itself without such extension and
\nthickness as admit of such motion. And if there is extension it is
\nno longer a line but a surface, and we are investigating the
\nproperties of a line, and not of a surface. And as the line, having
\nno centre of thickness cannot be divided, we must conclude that the
\nline can have no sides to intersect each other. This is proved by
\nthe movement of the line a f<\/em> to a b<\/em> and of the line e b<\/em> to e
\nf<\/em>, which are the sides of the surface a f e b<\/em>. But if you move
\nthe line a b<\/em> and the line e f<\/em>, with the frontends a e<\/em>, to the
\nspot c<\/em>, you will have moved the opposite ends f b<\/em> towards each
\nother at the point d<\/em>. And from the two lines you will have drawn
\nthe straight line c d<\/em> which cuts the middle of the intersection of
\nthese two lines at the point n<\/em> without any intersection. For, you
\nimagine these two lines as having breadth, it is evident that by
\nthis motion the first will entirely cover the other–being equal
\nwith it–without any intersection, in the position c d<\/em>. And this
\nis sufficient to prove our proposition.<\/p>\n
\nPOINT.<\/p>\n
\nother–being without breadth or thickness–in the same way all the
\nimages of surfaces can meet there; and as each given point faces the
\nobject opposite to it and each object faces an opposite point, the
\nconverging rays of the image can pass through the point and diverge
\nagain beyond it to reproduce and re-magnify the real size of that
\nimage. But their impressions will appear reversed–as is shown in
\nthe first, above; where it is said that every image intersects as it
\nenters the narrow openings made in a very thin substance.<\/p>\n
\nmuch less will the images transmitted through this opening intersect
\neach other. The sides of images which pass through openings into a
\ndark room intersect at a point which is nearer to the opening in
\nproportion as the opening is narrower. To prove this let a b<\/em> be an
\nobject in light and shade which sends not its shadow but the image
\nof its darkened form through the opening d e<\/em> which is as wide as
\nthis shaded body; and its sides a b<\/em>, being straight lines (as has
\nbeen proved) must intersect between the shaded object and the
\nopening; but nearer to the opening in proportion as it is smaller
\nthan the object in shade. As is shown, on your right hand and your
\nleft hand, in the two diagrams a<\/em> b<\/em> c<\/em> n<\/em> m<\/em> o<\/em> where, the
\nright opening d<\/em> e<\/em>, being equal in width to the shaded object a<\/em>
\nb<\/em>, the intersection of the sides of the said shaded object occurs
\nhalf way between the opening and the shaded object at the point c<\/em>.
\nBut this cannot happen in the left hand figure, the opening o<\/em>
\nbeing much smaller than the shaded object n<\/em> m<\/em>.<\/p>\n
\nthe objects and the openings through which the images of these
\nbodies are admitted; and this is plain, because where the atmosphere
\nis illuminated these images are not formed visibly.<\/p>\n
\nare invariably doubly as dark in tone. To prove this let d<\/em> e<\/em> h<\/em>
\nbe such a doubling which although it is only seen within the space
\nbetween the bodies in b<\/em> and i<\/em> this will not hinder its being
\nseen from f<\/em> g<\/em> or from f<\/em> m<\/em>; being composed of the images a<\/em>
\nb<\/em> i<\/em> k<\/em> which run together in d<\/em> e<\/em> h<\/em>.<\/p>\n
\nchapter Leonardo has written “azurro<\/em>” (blue) where in the
\nfacsimile I have marked A<\/em>, and “giallo<\/em>” (yellow) where B<\/em>
\nstands.]<\/p>\n
\nits position the objects seen by it may appear to move from their
\nplaces.<\/p>\n
\nbelow the eye, and fix both your eyes upon it and with one hand
\nfirmly hold the upper lid open while with the other you push up the
\nunder lid–still keeping your eyes fixed on the object gazed at–you
\nwill see that object double; one [image] remaining steady, and the
\nother moving in a contrary direction to the pressure of your finger
\non the lower eyelid. How false the opinion is of those who say that
\nthis happens because the pupil of the eye is displaced from its
\nposition.<\/p>\n
\nin seeing.<\/p>\n
\nfully discussed in the two chapters that follow them in the
\noriginal; but it did not seem to me appropriate to include them
\nhere.]<\/p>\n
\n(83-85).<\/p>\n
\nplane of glass, quite transparent, on the surface of which the
\nobjects behind that glass are to be drawn. These can be traced in
\npyramids to the point in the eye, and these pyramids are intersected
\non the glass plane.<\/p>\n
\nlook of the same size as it appears to the eye. You see that the
\napex of the pyramid f c d<\/em> is as far from the object c<\/em> d<\/em> as the
\nsame point f<\/em> is from the object a<\/em> b<\/em>; and yet c<\/em> d<\/em>, which is
\nthe base made by the painter’s point, is smaller than a<\/em>