.\i\- TRANSLATOR S INTRODUCTION. 



ta&amp;gt;k; but his work swells to a quarto book of 

 101 pagr-. 



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 &quot;Aus 

 clem Li-ben xweier ungarischer Mathematiker, 

 Johann und Wolfgang Bolyai von Bolya.&quot; 

 Grunert a Archiv, Bd. 48, 1868, p. 217. 



In two communications &amp;gt;ent me in Sept-m- 

 ber and ( &amp;gt;ctober !S n 5, Ilerr Schmidt has very 

 kindly and graciously put at my disposal the 

 results of his subsequent researches, which 1 

 will hen- reproduce. But meantime I have 

 from entirely another source come most unex 

 pectedly into possession &amp;lt;f original documents 

 [tensive, so precious that I have determined 

 t&amp;lt;&amp;gt; iue them in a separate volume devoted 

 wholly to the life of the IJolyais; but these are 

 not used in the &amp;gt;ketch here given. 



liolyai Farkas was born February ( th, 1775, 

 at Bolya, in that part of Transylvania (Er- 



