OF THE OPINION OF SOME THAT A TRIANGLE CASTS NO SHADOW ON A PLANE SURFACE.

Certain mathematicians have maintained that a triangle, of which the
base is turned to the light, casts no shadow on a plane; and this
they prove by saying [5] that no spherical body smaller than the
light can reach the middle with the shadow. The lines of radiant
light are straight lines [6]; therefore, suppose the light to be *g
h* and the triangle *l m n*, and let the plane be *i k*; they say
the light *g* falls on the side of the triangle *l n*, and the
portion of the plane *i q*. Thus again *h* like *g* falls on the
side *l m*, and then on *m n* and the plane *p k*; and if the whole
plane thus faces the lights *g h*, it is evident that the triangle
has no shadow; and that which has no shadow can cast none. This, in
this case appears credible. But if the triangle *n p g* were not
illuminated by the two lights *g* and *h*, but by *i p* and *g* and
*k* neither side is lighted by more than one single light: that is
*i p* is invisible to *h g* and *k* will never be lighted by *g*;
hence *p q* will be twice as light as the two visible portions that
are in shadow.

[Footnote: 5—6. This passage is so obscure that it would be rash to offer an explanation. Several words seem to have been omitted.]

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

. . .

Shadow as produced by two lights of different size.

180,

The effect of light at different distances.

Further complications in the derived shadows.

183,

184,

185,

186,

On the shape of the cast shadows.

188,

189,

190,

On the outlines of cast shadows.

192,

193,

194,

On the relative size of shadows.

196,

Effects on cast shadows by the tone of the back ground.

A disputed proposition.

On the relative depth of cast shadows.

200,

201,

Principles of reflection.

203,

On reverberation.

Reflection on water.

206,

Experiments with the mirror.

208,

209,

Appendix:--On shadows in movement.

211,

The effect of rays passing through holes.

213,

On gradation of shadows.

On relative proportion of light and shadows.

216,

217,

218,

. . .