(9) 



288 Oil Analytical Geometry. 



-aV'-Ti+b^ =«+'■' 



and consequently A-= ^ | 



B3= -=^ 



2\/-l J 



Comparing the 1st equation of (8) multiplied by — v^ — 1, and the 2d 



by v^ — 1, with the second and first of (9) and a+"'=+a-"'v/— 1. 



Elevating (8) and (9) to the power m, and abridging the first 

 members and their results, 



C2=- ■ ' 



2 



+r 



D 



-J a-'"'^— a"" 



2\/-l 



Xtnn/ j^+mn/ 



(.^_ «-'""'- « 



2x/t:i 



D2 = 



2 

 It IS thus seen that C^, and D , are the same functions of mn, or 



mn'} that A and B^ are of n, or w', and consequently \i -^ ot -^ 



C^ j)i 

 subtends the angle BAC or Wj -^ ^"^ ~2 ^ ^^^^' ^^^®" "°*- §f ^ater than 

 imity^ subtend the angle mn. 



