CHAPTER I. 



Introductory Remarks. The Symmetry-Principle in General. 

 Its Aesthetic Value. Definition of Symmetrical Figures. - 

 Symmetry-Properties and Symmetry-Character. 



yu.p ast SVTGS f) ysw^erptx^ yvwai? eor/v- 



Plato, Respub., 7,527,b. 



1. Of the numerous theories suggested to explain natural 

 phenomena, those have proved particularly efficient, which 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 

 most obvious features in the relationship of the natural phenomena 

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

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

 the observed facts in their logical connections. 



In this mathematical outlining of nature, human science makes 

 use of a number of fundamental notions and principles which, as a 

 rule, after a long period of error or opposition have been accepted 

 in the end. The methods of mathematical physics wijh its classical 

 mechanics as well as its recent views on electromagnetics, are 

 wellknown illustrations of this. Such fundamental notions are 

 finally adopted generally, if they prove to be extremely effective 

 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 as 

 one of the most remarkable and interesting. 



