On Analytical Geometry. 289 
we peer “4 mG oid Se 
From (8) we have =ate", Or developi ; 
shay Ee Waar P= 
—V¥I1//B\? 1/B\? 1/B\? | . . 
papa (la) sala). tela) 2-8)» « nisascon a 
Or ite 9 for the real factor of the second member, and a= 
eV —1, (9 designating the angle BAC,) it ‘appears, from the 
equation oi b Sa ~s (if x designate the angle B/AC) ‘that 
atl +x) =V—1: the sum of these angles is thus seen to 
: Constant and ‘to have opposite signs. Put 9’, and 9”, to repre 
sent the angles ABC, BAC, and equations (1), (2) and (3), ial 
cat yt ay at? 1g PY Haas, (ay 
hs Wh het — zal ee wV =A) ye, ay re 
: pais = a(atee’Y <1 gee “ly Lge, (3) 
i (4), (5) and (6) become 
2a —(aPPY Ay FRY Ay (gt VN 4 Gr “hoy 
if 1 Qo =1, 
Leader vet 9 jz 
ae wi 329V=1 
aan A, ava yet gee V5 ly ne-46) 
and since A te — , (7).is changed to 
We sat : 
2 gta ee qi2ev —1 r (teeY ai gv —1 ne. 4 ee 
= (7s. 
y~ im =1 are puyy 1 , “tee’Y — ge’ 1 
Resolving ‘ibe first. members of (ay into two factors of the first 
degree and we have the following equations. : 
teey — <9 +n \ 
v— ya = =z0- (12) 
a yar? —1_. anf 
epee agtteV hy ce +n’ | 
oe (13) 
if 
j 
eB “ie + y=zat” 
Pie 
