The Notebooks of Leonardo Da Vinci. Complete. Leonardo da Vinci

it unless every portion of that surface is equidistant from the luminous body. This is proved by the 7th which says:—The shadow will appear lighter or stronger as it is surrounded by a darker or a lighter background. And by the 8th of this:—The background will be in parts darker or lighter, in proportion as it is farther from or nearer to the luminous body. And:—Of various spots equally distant from the luminous body those will always be in the highest light on which the rays fall at the smallest angles: The outline of the shadow as it falls on inequalities in the surface will be seen with all the contours similar to those of the body that casts it, if the eye is placed just where the centre of the light was.

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

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

      192

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

      193

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

      194

      OF SHADOWS WHICH NEVER COME TO AN END.

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

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

      195

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

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

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

      196

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

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

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

      The disproportion of a shadow which is larger than the body producing it, results from the light being smaller than the body, so that it cannot be at an equal distance from the edges of the body [Footnote 11: H. LUDWIG in his edition of the old copies, in the Vatican library—in which this chapter is included under Nos. 612, 613 and 614 alters this passage as follows: quella parte ch'e piu propinqua piu cresce che le distanti, although the Vatican copy agrees with the original MS. in having distante in the former and propinque in the latter place. This supposed amendment seems to me to invert the facts. Supposing for instance, that on Pl. XXXI No. 3. f is the spot where the light is that illuminates the figure there represented, and that the line behind the figure represents a wall on which the shadow of the figure is thrown. It is evident, that in that case the nearest portion, in this case the under part of the thigh, is very little magnified in the shadow, and the remoter parts, for instance the head, are more magnified.]; and the portions which are most remote are made larger than the nearer portions for this reason [Footnote 12: See Footnote 11].

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

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

      197

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

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

      198

      OF MODIFIED SHADOWS.

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

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

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

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

      A disputed proposition.

      199

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

      Certain mathematicians have maintained that a triangle, of which the base is turned to the light, casts no shadow on a plane; and this they prove by saying [5] that no spherical body smaller than the light can reach the middle with the shadow. The lines of radiant light are straight lines [6]; therefore, suppose the light to be g h and the triangle l m n, and let the plane be i k; they say the light g falls on the side of the triangle l n, and the portion of the plane i q. Thus again h like g falls on the side l m, and then on m n and the plane p k; and if the whole plane thus faces the lights g h, it is evident that the triangle has no shadow; and that which has no shadow can cast none. This, in this case appears credible. But if the triangle n p g were not illuminated by the two lights g and h, but by i p and g and k neither side is lighted by more than one single light: that is i p is invisible to h g and k will never be lighted by g; hence p q will be twice as light as the two visible portions that are in shadow.

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

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

      200

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

      201

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

      202

      The shadow cast by an object on a plane will be smaller in proportion as that object is lighted by feebler rays. Let d e be the object and d c the plane surface; the number of times that d e will go into f g gives the proportion of light