Motion and Spherical Trigonometry. 



729 



Fiff. 1. 



the circle AQD, cutting AD in L, the limiting point or 

 Landen point ; then 



(4) ED.EA = EL 2 , and HQ . HQ' = HL 2 , 



(5) QL 2 = (HQ-HL) 2 = HQ 2 -2HQ . HL + HQ . HQ' 



= (HQi-HQ'-2HL)HQ = (2HM-2HL)HQ 

 = 2LM.HQ = 2LC.KQ 

 = 2LC . AE . A 2 c/> = AL 2 . A 2 cf>. 

 Fisr. 2. 



2. Turn the vertical circle about the diameter AD through 

 a right angle, so as to bring DB to DO in fig. 2, and project 



