161.

OF SIMPLE DERIVED SHADOWS.

The simple derived shadow is of two kinds:  one kind which has its length defined, and two kinds which are undefined; and the defined shadow is pyramidal.  Of the two undefined, one is a column and the other spreads out; and all three have rectilinear outlines.  But the converging, that is the pyramidal, shadow proceeds from a body that is smaller than the light, and the columnar from a body equal in size to the light, and the spreading shadow from a body larger than the light; &c.

OF COMPOUND DERIVED SHADOWS.

Compound derived shadows are of two kinds; that is columnar and spreading.

162.

OF SHADOW.

Derived shadows are of three kinds of which one is spreading, the second columnar, the third converging to the point where the two sides meet and intersect, and beyond this intersection the sides are infinitely prolonged or straight lines.  And if you say, this shadow must terminate at the angle where the sides meet and extend no farther, I deny this, because above in the first on shadow I have proved:  that a thing is completely terminated when no portion of it goes beyond its terminating lines.  Now here, in this shadow, we see the converse of this, in as much as where this derived shadow originates we obviously have the figures of two pyramids of shadow which meet at their angles.  Hence, if, as [my] opponent says, the first pyramid of shadow terminates the derivative shadow at the angle whence it starts, then the second pyramid of shadow—­so says the adversary—­must be caused by the angle and not from the body in shadow; and this is disproved with the help of the 2nd of this which says:  Shadow is a condition produced by a body casting a shadow, and interposed between this shadow and the luminous body.  By this it is made clear that the shadow is not produced by the angle of the derived shadow but only by the body casting the shadow; &c.  If a spherical solid body is illuminated by a light of elongated form the shadow produced by the longest portion of this light will have less defined outlines than that which is produced by the breadth of the same light.  And this is proved by what was said before, which is:  That a shadow will have less defined outlines in proportion as the light which causes it is larger, and conversely, the outlines are clearer in proportion as it is smaller.

[Footnote:  The two diagrams to this chapter are on Plate IV, No. 1.]

On the relation of derived and primary shadow (163-165).

163.

The derived shadow can never resemble the body from which it proceeds unless the light is of the same form and size as the body causing the shadow.

The derived shadow cannot be of the same form as the primary shadow unless it is intercepted by a plane parallel to it.

164.

HOW A CAST SHADOW CAN NEVER BE OF THE SAME SIZE AS THE BODY THAT
CASTS IT.