xx 5v TRANSLATOR S INTROIH VTION. 



then informed me how much farther alre; 

 had been attained on this way, and later 

 expressed himself about the u lvat acquisitio 

 which is offered to the few expert judges ii. 

 the Appendix to your hook.&quot; 



The &quot;latest edition&quot; mentioned appeared 

 in 1S51, and the pas.- Ferred to is: &quot;This 



]&amp;gt;roof of the parallel-axiom] has been sought 

 in manifold wavs by acute mathematicians, 

 hut yet until now not found with complete 

 sufticieiicv. So lon^- as it fails, the theorem, 

 as all founded on it, remains a hypothesis, 

 whose validity for our life indeed is suftici- 

 entlv proven bv experience, whose general, 

 necessary exactness, however, could he 

 doubted without absurdity.&quot; 



Alas! that this feeble utterance should have 

 seemed sufficient for more- than thirty years 

 to the associate of (iauss and Schweikart, the 

 latter certainlv one of the independent discov 

 erers of the non-Euclidean geometry. Hut 

 then, since neither of these suflicicntly real 

 ized the transcendent importance of the mat 

 ter to publish any of their thoughts on the 

 subject, a more ad conception of the 



LSSUes at stake could scarcely he expected of 

 the scholar and colleague. How different with 

 lJi\ai JaiK.s and Lobachevski, who claimed 



