288 On Analytical Geometry. 
1 ~ mi 4 as 
- —Aiv —1+B?=at”’ 
bs Le > “4 at" ate : 
4 and consequently A?=——3—— a 
2 “ ue : é - : se \ be 
" ‘ "¢ dB s : at at” — qt". 
oo. WII 
: at —at 
A?= = 
Sadie SMe] 
3 on = at! 
B= 
— 
Cig the 1st equation of (8) multiplied by —v —1, and the au 
by YW —1, with the second and first of (9) and giv azattV a1 
Hlavating (8) and (9) to the power m, and abridging the i 
members and their results, 
oun T=atm, ‘ i 
*_ DIV Li=ate, sag 
sal i4D?=ate, 
—~C?V 14D? =a, | 
\ yim a +mn 
=a ot Sng ae 
‘ be atmn — gem 
Dt = 
av 1" . 
Finns +mni rs 
pane ae a ys 
2f — 
een 
It is thus seen that ct, and D?, are the same functions of mn, OF 
: ATS BD 
ma’, that A® and B® are of n, or n’, and consequently if gy OQ - 
| aan 
oe ps Ace sian 
subtends the angle BAC or n, “J or» will, when not gveater t 
unity, subtend the angle mn. 
