CHAPTER I. 



Introductory Remarks. The Symmetry-Principle in General. 

 Its Aesthetic Value. - Definition of Symmetrical Figures. - 

 Symmetry-Properties and Symmetry-Character. 



TOU yap v.gt Svrog ft yjw/xST^/xtj yvtavif twv. 

 Plato, Pol. 7.527.0. 



1. Of the numerous theories suggested to explain natural 

 phenomena, such have proved particularly efficient, as allow of 

 mathematical treatment, and therefore are especially suited for the 

 outlining of repeatedly observed facts in their mutual dependence. 



Not before such a summarising mathematical description of the 

 ino>t obvious features in the relationship of the natural phenomena 

 considered, or between groups of them, has been performed as 

 euneisely as possible, --can we claim to have really understood 

 tlu- observed facts in their logical connections. 



In this mathematical outlining of nature, human science mako 

 use of a number of fundamental notions and principles which, com- 

 monly after a long period of error or opposition, have been generally 

 accepted in the end. The methods of mathematical physics with its 

 classical mechanics, as well as its recent views on electromagnetics, 

 an- well-known illustrations of this. Such fundamental notions 

 are at last adopted generally, if they prove to be extremely 

 eltrrtive in the further theoretical development and schematising 

 of natural phenomena. 



Among ideas of this kind playing an important role in modern 

 science, the principle of symmetry may certainly be considered a> 



ie of the most remarkable and interesting. 



