Of shadow.

The derivative shadows are of three natures, of which one is dilatable, the other columnar, the third concurrent at the site of the intersection of its sides, which after such intersection are of infinite length or straightness (rigour). And if you should say that such a shadow is terminated at the angle of the joining of its sides and does not pass further, this is denied, because in the first proposition of shadows it was proved: "that thing is entirely terminated of which no part exceeds its boundaries." The which here in such a shadow one sees the contrary, since, when such a derivative shadow arises, there manifestly arises the figure of two shadowy pyramids, which are joined at their angles. Therefore, if, for the adversary, the first shadowy pyramid is the terminator of the derivative shadow with its angle, whence then arises the second shadowy pyramid? The adversary says it is caused by the angle and not by the shadowing body, and this is denied with the help of the second proposition of this book, which says: "the shadow is an accident created by shadowing bodies interposed between the site of that shadow and the luminous body"; and by this it is clarified that the shadow is not generated by the angle of the derivative shadow, but only by the shadowing body, etc.

If the spherical shadowing body is illuminated by a luminous body of long shape, the shadow generated by the length of that luminous body will be of less distinct boundaries than the one generated by its width. And this is proved by the foregoing, which said: "that shadow is of less distinct boundaries which is created by a larger luminous body," and conversely: "that is of less distinct boundaries which is illuminated by a smaller light."

Of corrected shadows.

Corrected shadows are those which are seen by bright walls or another luminous body.

That shadow shows itself darker which is in a whiter field.

The boundaries of that derivative shadow will be more distinct which are nearer to the primitive shadow.

The derivative shadow will have the boundaries of its impression more distinct which are cut between more equal angles on its wall.

That part of one and the same shadow will show itself darker which has darker objects against it. And it will show itself less dark which is seen by a brighter object; and the bright object which is larger will brighten it the more; and the dark object which is of greater quantity will darken the derivative shadow the more in the site of its striking.