[565] a. Of the boundaries of the compound shadow.

The compound derivative shadow is of infinite length, being pyramidal, of a pyramid originating at its point; and this is proved because, at whatever part its pyramidal length be cut, its angle will never be destroyed, as happens in the simple derivative shadow.

[566] b. Of the boundary of the simple shadow.

The simple derivative shadow is of brief course compared with the compound derivative, because the compound, as said, has its origin from its angle, while this one has its origin from its base; and this is made manifest because, at whatever part that pyramid be cut by the shadowy body, that division never destroys its base.

[567] c. What shadow the light equal to the shadowy body makes in the figure of its shadows.

If the shadowy body be equal to the luminous body, then the simple shadow will be parallel and infinite in length; but the compound shadow and light will be pyramidal, with an angle looking toward the luminous body.

[568] What shadow the shadowy body larger than the luminous makes.

If the shadowy body be larger than its luminous body, then the simple derivative shadow will have its sides converging to the potential angle beyond the luminous body; and the angles of the compound shadow and light will look toward the whole luminous body.