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

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

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

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

      137

      SHOWS HOW LIGHT FROM ANY SIDE CONVERGES TO ONE POINT.

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

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

      138

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

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

      139

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

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

      140

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

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

      141

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

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

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

      142

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

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

      143

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

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

      144

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

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

      145

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

      If the sun is in the East and you look towards the West you will see every thing in full light and totally without shadow because you see them from the same side as the sun: and if you look towards the South or North you will see all objects in light and shade, because you see both the side towards the sun and the side away from it; and if you look towards the coming of the sun all objects will show you their shaded side, because on that side the sun cannot fall upon them.

      The law of the incidence of light.

      146

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

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

      147

      OF PAINTING.

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

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

      SECOND BOOK ON LIGHT AND SHADE

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

      148

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

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

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

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