it will appear to be impossible now to move the figure in its 

 own plane ') in such a way, as to make it coincide with fig. 2. 

 We can, however, obtain fig. 2 from fig. 3 by reflecting the last 

 one in a mirror 5, placed perpendicular to the plane of the drawing; 

 the mirror-image of fig'. 3 now obtained, is really congruent with 

 fig. 2 itself, and it can now be brought into coincidence with it by 

 mere shifting and rotating. Because of this relation, we say that 



the plane figures 2 

 and 3 are each other's 

 mirror-images. Such 

 mirror-images, al- 

 though built up by 

 the same geometrical 

 elements, are evident- 

 ly not congruent, and 

 they can never be 

 made to coincide by 

 mere movement. 



The same is obser- 

 ved in tri-dimensional 

 space: there are nu- 

 merous objects, e. g. 

 "right" and "left" 

 hand or foot, screw- 

 threads and tendrils, 

 etc., which are wellknown instances of this kind. They are related 

 to each other as mirror-images, and they can never be brought to 

 coincidence by mere rotations or shifting. Only the "mirror-image" 

 of each of them will coincide with the other object itself in the way 

 described above. This is commonly expressed by saying that the 

 right and left extrimities, or the screw-threads, etc. are objects 

 which are different from their mirror-images. 



It must however be kept in mind that a number of objects are 

 not at all different from their mirror-images: our own body is a 

 good example of this. If we look into a mirror, we soon come to 

 the conviction that the mirror-image of our body is really congruent 



Fig. 3- 



'). The condition that this two-dimensional figure remains in its own 

 plane during its motions, is essential in this mode of argument. In a tri-di- 

 mensional space the figure would be brought to coincidence with itself by a 

 mere rotation through 180 round an axis situated in its own plane. 



