The foregoing proposition can be clearly proved in this way.  Let us say that m q is the luminous body, then f g will be the opaque body; and let a e be the above-mentioned plane on which the said angles fall, showing [plainly] the nature and character of their bases.  Then:  a will be more luminous than b; the base of the angle a is larger than that of b and it therefore makes a greater angle which will be a m q; and the pyramid b p m will be narrower and m o c will be still finer, and so on by degrees, in proportion as they are nearer to e, the pyramids will become narrower and darker.  That portion of the wall will be the darkest where the breadth of the pyramid of shadow is greater than the breadth of the pyramid of light.

At the point a the pyramid of light is equal in strength to the pyramid of shadow, because the base f g is equal to the base r f.  At the point d the pyramid of light is narrower than the pyramid of shadow by so much as the base s f is less than the base f g.

Divide the foregoing proposition into two diagrams, one with the pyramids of light and shadow, the other with the pyramids of light [only].

261.

Among shadows of equal depth those which are nearest to the eye will look least deep.

262.

The more brilliant the light given by a luminous body, the deeper will the shadows be cast by the objects it illuminates.

V.

Theory of colours.

Leonardo’s theory of colours is even more intimately connected with his principles of light and shade than his Perspective of Disappearance and is in fact merely an appendix or supplement to those principles, as we gather from the titles to sections 264, 267_, and 276, while others again_ (Nos. 281, 282_) are headed_ Prospettiva.

A very few of these chapters are to be found in the oldest copies and editions of the Treatise on Painting, and although the material they afford is but meager and the connection between them but slight, we must still attribute to them a special theoretical value as well as practical utility—­all the more so because our knowledge of the theory and use of colours at the time of the Renaissance is still extremely limited.

The reciprocal effects of colours on objects placed opposite each other (263-272).

263.

OF PAINTING.

The hue of an illuminated object is affected by that of the luminous body.

264.

OF SHADOW.

The surface of any opaque body is affected by the colour of surrounding objects.

265.

A shadow is always affected by the colour of the surface on which it is cast.

266.

An image produced in a mirror is affected by the colour of the mirror.

267.