186

Further complications in the derived shadows.

Why the intersections at n being composed of two compound derived shadows, forms a compound shadow and not a simple one, as happens with other intersections of compound shadows. This occurs, according to the 2nd [diagram] of this [prop.] which says:—The intersection of derived shadows when produced by the intersection of columnar shadows caused by a single light does not produce a simple shadow. And this is the corollary of the 1st [prop.] which says:—The intersection of simple derived shadows never results in a deeper shadow, because the deepest shadows all added together cannot be darker than one by itself. Since, if many deepest shadows increased in depth by their duplication, they could not be called the deepest shadows, but only part-shadows. But if such intersections are illuminated by a second light placed between the eye and the intersecting bodies, then those shadows would become compound shadows and be uniformly dark just as much at the intersection as throughout the rest. In the 1st and 2nd above, the intersections i k will not be doubled in depth as it is doubled in quantity. But in this 3rd, at the intersections g n they will be double in depth and in quantity.

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.
. . .
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
On reverberation.
205
Reflection on water.
206
. . .