What is the cause which makes the outlines of the shadow vague and
confused?

Whether it is possible to give clear and definite outlines to the
edges of shadows.

On the relative size of shadows (196. 197).

196.

THE BODY WHICH IS NEAREST TO THE LIGHT CASTS THE LARGEST SHADOW, AND
WHY?

If an object placed in front of a single light is very close to it
you will see that it casts a very large shadow on the opposite wall,
and the farther you remove the object from the light the smaller
will the image of the shadow become.

WHY A SHADOW LARGER THAN THE BODY THAT PRODUCES IT BECOMES OUT OF
PROPORTION.

The disproportion of a shadow which is larger than the body
producing it, results from the light being smaller than the body, so
that it cannot be at an equal distance from the edges of the body
[Footnote 11: H. LUDWIG in his edition of the old copies, in the
Vatican library--in which this chapter is included under Nos. 612,
613 and 614 alters this passage as follows: _quella parte ch'e piu
propinqua piu cresce che le distanti_, although the Vatican copy
agrees with the original MS. in having _distante_ in the former and
_propinque_ in the latter place. This supposed amendment seems to me
to invert the facts. Supposing for instance, that on Pl. XXXI No. 3.
_f_ is the spot where the light is that illuminates the figure there
represented, and that the line behind the figure represents a wall
on which the shadow of the figure is thrown. It is evident, that in
that case the nearest portion, in this case the under part of the
thigh, is very little magnified in the shadow, and the remoter
parts, for instance the head, are more magnified.]; and the portions
which are most remote are made larger than the nearer portions for
this reason [Footnote 12: See Footnote 11].

WHY A SHADOW WHICH IS LARGER THAN THE BODY CAUSING IT HAS
ILL-DEFINED OUTLINES.

The atmosphere which surrounds a light is almost like light itself
for brightness and colour; but the farther off it is the more it
loses this resemblance. An object which casts a large shadow and is
near to the light, is illuminated both by that light by the luminous
atmosphere; hence this diffused light gives the shadow ill-defined
edges.

197.

A luminous body which is long and narrow in shape gives more
confused outlines to the derived shadow than a spherical light, and
this contradicts the proposition next following: A shadow will have
its outlines more clearly defined in proportion as it is nearer to
the primary shadow or, I should say, the body casting the shadow;
[Footnote 14: The lettering refers to the lower diagram, Pl. XLI,
No. 5.] the cause of this is the elongated form of the luminous body
_a c_, &c. [Footnote 16: See Footnote 14].

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

198.

OF MODIFIED SHADOWS.

Modified shadows are those which are cast on light walls or other
illuminated objects.

A shadow looks darkest against a light background. The outlines of a
derived shadow will be clearer as they are nearer to the primary
shadow. A derived shadow will be most defined in shape where it is
intercepted, where the plane intercepts it at the most equal angle.

Those parts of a shadow will appear darkest which have darker
objects opposite to them. And they will appear less dark when they
face lighter objects. And the larger the light object opposite, the
more the shadow will be lightened.

And the larger the surface of the dark object the more it will
darken the derived shadow where it is intercepted.

A disputed proposition.

199.

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


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