209.

Describe how it is that no object has its limitation in the mirror but in the eye which sees it in the mirror.  For if you look at your face in the mirror, the part resembles the whole in as much as the part is everywhere in the mirror, and the whole is in every part of the same mirror; and the same is true of the whole image of any object placed opposite to this mirror, &c.

210.

No man can see the image of another man in a mirror in its proper place with regard to the objects; because every object falls on [the surface of] the mirror at equal angles.  And if the one man, who sees the other in the mirror, is not in a direct line with the image he will not see it in the place where it really falls; and if he gets into the line, he covers the other man and puts himself in the place occupied by his image.  Let n o be the mirror, b the eye of your friend and d your own eye.  Your friend’s eye will appear to you at a, and to him it will seem that yours is at c, and the intersection of the visual rays will occur at m, so that either of you touching m will touch the eye of the other man which shall be open.  And if you touch the eye of the other man in the mirror it will seem to him that you are touching your own.

Appendix:—­On shadows in movement (211. 212).

211.

OF THE SHADOW AND ITS MOTION.

When two bodies casting shadows, and one in front of the other, are between a window and the wall with some space between them, the shadow of the body which is nearest to the plane of the wall will move if the body nearest to the window is put in transverse motion across the window.  To prove this let a and b be two bodies placed between the window n m and the plane surface o p with sufficient space between them as shown by the space a b.  I say that if the body a is moved towards s the shadow of the body b which is at c will move towards d.

212.

OF THE MOTION OF SHADOWS.

The motion of a shadow is always more rapid than that of the body which produces it if the light is stationary.  To prove this let a be the luminous body, and b the body casting the shadow, and d the shadow.  Then I say that in the time while the solid body moves from b to c, the shadow d will move to e; and this proportion in the rapidity of the movements made in the same space of time, is equal to that in the length of the space moved over.  Thus, given the proportion of the space moved over by the body b to c, to that moved over by the shadow d to e, the proportion in the rapidity of their movements will be the same.

But if the luminous body is also in movement with a velocity equal to that of the solid body, then the shadow and the body that casts it will move with equal speed.  And if the luminous body moves more rapidly than the solid body, the motion of the shadow will be slower than that of the body casting it.