TRANSLATOR'S INTRODUCTION, xxiii 



pinnacle embraces in the same view the 

 and the abysses, wrote that he was sur- 

 r ised to see accomplished what he had be- 

 gun, only to leave it behind in his papers." 



This refers to 1832. The only other record 

 that Gauss ever mentioned the book is a letter 

 from Gerling, written October 31st, 1851, to 

 Wolfgang Boylai, on receipt of a copy of 

 "Kurzer Grundriss." Gerling, a scholar of 

 Gauss, had been from 1817 Professor of As- 

 tronomy at Marburg. He writes : 4 ' I do not 

 mention my earlier occupation with the theory 

 of parallels, for already in the year 1810-1812 

 with Gauss, as earlier 1809 with J. F. Pfaff I 

 had learned to perceive how all previous at- 

 tempts to prove the Euclidean axiom had mis- 

 carried. I had then also obtained preliminary 

 knowledge of your works, and so, when I first 

 [1820] had to print something of my view 

 thereon, I wrote it exactly as it yet stands 

 to read on page 187 of the latest edition. 



"We had about this time [1819] here a law 

 professor, Schweikart, who was formerly in 

 Charkov, and had attained to similar ideas, 

 since without help of the Euclidean axiom he 

 developed in its beginnings a geometry which 

 he called Astralgeometry. What he commun- 

 icated to me thereon I sent to Gauss, who 



