In-and-circumscribed TViangle. 27 



or 



d(f> dcfJ 



where 



~ {a + lif-r'^' 

 Whence also 



It will be convenient for comparison with the formulce of 

 Richelot to write Z ACQ = 2-»/r; this gives 



2f = 'n—2(f). 



And the differential equation is 



Ji|r _ dylr' 



\^a^ + n^ -)-^^2aRco^2yJr ~ \/ a^ + R^-i-^-2aB.cos2^' 

 i. e. 



\/m — n cos 2'»/r V m — n cos 2-^^ 



tani|f=^tan Q, 



„, l-^tan^^ 

 ^«^^^= l+^nan^^ 



_ , (m — n) cos^ 0+ Cm + n] q^ siu^ d 



m—n cos 2\/r= -^— ^^ — \ ■ icr 



^ COS'' t' ■^-g'- %\v? 6 



Or if 



cos2 e + '-^^— ? sin^ ^ 



Ug^ = 



m-\-n' 



1_ J^sin*^ 

 7n + w 



s/ 



m — 71 



de 



, , m + n 



dY=- 



and 



l__2!Lsin20 



V m4-n\ / 1 



-»cos2>Ir , — — /I 2n TTT' 



V m + n 



