xiv TRANSLATOR'S INTRODUCTION. 



task; but his work swells to a quarto book of 

 101 pages. 



Had he not been overawed by a conviction 

 of the absolute necessity of Euclid's system, 

 he might have anticipated Bolyai Janos, who 

 ninety years later not only discovered the new 

 world of mathematics but appreciated the 

 transcendent import of his discovery. 



Hitherto what was known of the Bolyais 

 came wholly from the published works of the 

 father Bolyai Farkas, and from a brief article 

 by Architect Fr. Schmidt of Budapest "Aus 

 dem Leben zweier ungarischer Mathematiker, 

 Johann und Wolfgang Bolyai von Bolya." 

 Grunert's Archiv, Bd. 48, 1868, p. 217. 



In two communications sent me in Septem- 

 ber and October 1895, Herr Schmidt has very 

 kindly and graciously put at my disposal the 

 results of his subsequent researches, which I 

 will here reproduce. But meantime I have 

 from entirely another source come most unex- 

 pectedly into possession of original documents 

 so extensive, so precious that I have determined 

 to issue them in a separate volume devoted 

 wholly to the life of the Bolyais; but these are 

 not used in the sketch here given. 



Bolyai Farkas was born February 9th, 1775, 

 at Bolya, in that part of Transylvania (Er- 



