184

Further complications in the derived shadows.

OF SIMPLE SHADOWS.

Why, at the intersections a, b of the two compound shadows e f and m e, is a simple shadow pfoduced as at e h and m g, while no such simple shadow is produced at the other two intersections c d made by the very same compound shadows?

ANSWER.

Compound shadow are a mixture of light and shade and simple shadows are simply darkness. Hence, of the two lights n and o, one falls on the compound shadow from one side, and the other on the compound shadow from the other side, but where they intersect no light falls, as at a b; therefore it is a simple shadow. Where there is a compound shadow one light or the other falls; and here a difficulty arises for my adversary since he says that, where the compound shadows intersect, both the lights which produce the shadows must of necessity fall and therefore these shadows ought to be neutralised; inasmuch as the two lights do not fall there, we say that the shadow is a simple one and where only one of the two lights falls, we say the shadow is compound, and where both the lights fall the shadow is neutralised; for where both lights fall, no shadow of any kind is produced, but only a light background limiting the shadow. Here I shall say that what my adversary said was true: but he only mentions such truths as are in his favour; and if we go on to the rest he must conclude that my proposition is true. And that is: That if both lights fell on the point of intersection, the shadows would be neutralised. This I confess to be true if [neither of] the two shadows fell in the same spot; because, where a shadow and a light fall, a compound shadow is produced, and wherever two shadows or two equal lights fall, the shadow cannot vary in any part of it, the shadows and the lights both being equal. And this is proved in the eighth [proposition] on proportion where it is said that if a given quantity has a single unit of force and resistance, a double quantity will have double force and double resistance.

Taken from The Notebooks of Leonardo da Vinci edited by Jean Paul Richter, 1880.

II * IV
Notebooks of Leonoardo da Vinci
III: Six books on Light and Shade.
. . .
164,
165
On the shape of derived shadows.
166,
167,
168,
169,
170,
171,
172,
173,
174
On the relative intensity of derived shadows.
175,
176,
177,
178,
179
Shadow as produced by two lights of different size.
180,
181
The effect of light at different distances.
182
Further complications in the derived shadows.
183,
184,
185,
186,
187
On the shape of the cast shadows.
188,
189,
190,
191
On the outlines of cast shadows.
192,
193,
194,
195
On the relative size of shadows.
196,
197
Effects on cast shadows by the tone of the back ground.
198
A disputed proposition.
199
On the relative depth of cast shadows.
200,
201,
202
Principles of reflection.
203,
204
. . .