Where the shadow is larger, or smaller, or equal the body which casts it.

[First of the character of divided lights. [Footnote 14:  lumi divisi.  The text here breaks off abruptly.]

OF THE COMPOUND SHADOW F, R, C, H CAUSED BY A SINGLE LIGHT.

The shadow f r c h is under such conditions as that where it is farthest from its inner side it loses depth in proportion.  To prove this: 

Let d a, be the light and f n the solid body, and let a e be one of the side walls of the window that is d a.  Then I say—­according to the 2nd [proposition]:  that the surface of any body is affected by the tone of the objects surrounding it,—­that the side r c, which faces the dark wall a e must participate of its darkness and, in the same way that the outer surface which faces the light d a participates of the light; thus we get the outlines of the extremes on each side of the centre included between them.]

This is divided into four parts.  The first the extremes, which include the compound shadow, secondly the compound shadow between these extremes.

179.

THE ACTION OF THE LIGHT AS FROM ITS CENTRE.

If it were the whole of the light that caused the shadows beyond the bodies placed in front of it, it would follow that any body much smaller than the light would cast a pyramidal shadow; but experience not showing this, it must be the centre of the light that produces this effect.

[Footnote:  The diagram belonging to this passage is between lines 4 and 5 in the original.  Comp. the reproduction Pl.  IV, No. 4.  The text and drawing of this chapter have already been published with tolerable accuracy.  See M. JORDAN:  “Das Malerbuch des Leonardo da Vinci”.  Leipzig 1873, P. 90.]

PROOF.

Let a b be the width of the light from a window, which falls on a stick set up at one foot from a c [Footnote 6:  bastone (stick).  The diagram has a sphere in place of a stick.].  And let a d be the space where all the light from the window is visible.  At c e that part of the window which is between l b cannot be seen.  In the same way a m cannot be seen from d f and therefore in these two portions the light begins to fail.

Shadow as produced by two lights of different size (180. 181).

180.

A body in light and shade placed between two equal lights side by side will cast shadows in proportion to the [amount of] light.  And the shadows will be one darker than the other in proportion as one light is nearer to the said body than the other on the opposite side.

A body placed at an equal distance between two lights will cast two shadows, one deeper than the other in proportion, as the light which causes it is brighter than the other.

[Footnote:  In the MS. the larger diagram is placed above the first line; the smaller one between l. 4 & 5.]