Rectification of the Conic Sections. 259 



two elliptic arcs. This beautiful theorem was discovered by 

 Landen, and is now for the first time demonstrated geometri- 

 cally ; but the manner in which it is stated by him and by suc- 

 ceeding writers differs from the above, and is much more 

 complicated. The different forms under which they have pre- 

 sented it may be easily deduced from the preceding, by means 

 of the theorem of Fagnani, of which a geometrical demonstra- 

 tion was first given in vol. ix. of the Transactions of the Royal 

 Irish Academy, by the Lord Bishop of Cloyne. 



December 23; 1829. 



S 2 



