ON THE 



OEIGIN AND SIGNIFICANCE 



OF 



GEOMETEICAL AXIOMS. 



Lecture delivered in the Docenten Verein in Heidelberg, 

 in the year 1870. 



THE fact that a science can exist and can be de- 

 veloped as has been the case with geometry, has 

 always attracted the closest attention among those 

 who are interested in questions relating to the bases of 

 the theory of cognition. Of all branches of human 

 knowledge, there is none which, like it, has sprung as 

 a completely armed Minerva from the head of Jupiter ; 

 none before whose death-dealing Aegis doubt and in- 

 consistency have so little dared to raise their eyes. It 

 escapes the tedious and troublesome task of collect- 

 ing experimental facts, which is the province of the 

 natural sciences in the strict sense of the word ; the 



