FIBST DISCOVERIES. 13 



die, or the human body; we can imagine a plane 

 passing through these objects which divides each of 

 them into two absolutely similar halves. Thus, a. 

 plane passing through the middle of the seat and of 

 the back of an arm-chair would have, on its right 

 and left, identical parts; in like manner a vertical 

 plane passing through the middle of the forehead, 

 nose, mouth, and chin of an individual, would have 

 similar parts to the right and to the left. All these 

 objects, and a multitude of similar ones, constitute 

 our first category. They have, as mathematicians 

 express it, one or several planes of symmetry. 



' But, as regards the repetition of similar parts, it 

 is far from being the case that all bodies are constituted 

 in the manner here described. Consider, for example, 

 your right hand : it is impossible to find for it a plane 

 of symmetry. Whatever be the position of a plane 

 which you imagine cutting the hand, you will never 

 find on the right of this plane exactly the same as 

 you find on its left. The same remark applies to 

 your left hand, to your right ear and to your left ear, 

 to your right eye and to your left eye ; to your two 

 arms, your two legs, and your two feet. The human 

 body, taken as a whole, has a plane of symmetry, 

 but none of the parts composing one or the other of 

 its halves has such a plane. The stalk of a plant 

 whose leaves are distributed spirally round its stem 

 has not a plane of symmetry, nor has a spiral stair- 



