viii TRANSLATOR S INTRODUCTION. 



Sir Henry Savile, in his Praelectiones on 

 Kiu-lid, Oxford, 1621, p. 140, says: &quot;In pul- 

 cherrimo Geometriae corpore duo sunt naevi, 

 duae labes ...&quot; etc., and these two blemishes 

 are the theory of parallels and the doctrine of 

 proportion; the very points in the Elements 

 which now arouse our wondering admiration. 

 But down to our very nineteenth century an 

 ever renewing stream of mathematicians tried 

 to wash away the first of these supposed stains 

 from the most beauteous body of Geometry. 



The year 1799 finds two extraordinary young 

 men striving thus 



&quot;To gild refined gold, to paint the lily, 

 To cast a perfume o er the violet.&quot; 



At the end of that year Gauss from Braun 

 schweig writes to Bolyai Parkas in Khiusen- 

 burg (Kolozsvar) as follows: [Abhandlungen 

 der Koetriglichea Gesellschaft der Wis&amp;gt;m- 

 schaften zu Goettingen, Bd. 22, 1877.] 



4i I very much regret, that I did not make use 

 of our former proximity, to find out more 

 about your inve-i i Cations in regard to the first 

 grounds of geometry; I should certainly theivbv 

 have spared m\ self much vain labor, and would 

 have heroine more restful than anv one, such 



