78 
: IDA GID 
b 
But sin AB sin BAP =sin BL sin BLP, 
and sin CA sin CAP =sin CL sin CLP. 
Hence 
y sin VOQ _ sin CL kesmCA 
z smOQN sinBL b/lsin AB’ 
Tn like manner z pal Mees ZB : 
z chsnBC 
Also 
sin BC sinCA _ sm AB sin YZ sinZX _ sin Pe 
snd. smb. sin 0)’, sim) Sele gece 
and, since ABC is the polar triangle of XYZ, sin YZ=sin A, 
sin ZX=sin B, sin XY=sinC. Therefore the equations to 
OR, a normal to the face h& J, will be 
Ne 
he © BO” ie 
where a, @, y are three straight lines subject to one of the four 
indentical conditions 
Od. de VCs we py Ga) OB nica 
sin BC sinCA_ sin AB’ sin A sinB sinC’ 
an 68 cry an bB cry 
ain VS aS ZX Si XS OP Si 
It is evident that OR is the diagonal of a parallelopiped 
having its edges in the lines OA, OB, OC, and _ respectively 
proportional to hz, k8, ly. 
Let G be the pole 1 1 1. 
Then 
1M, il ie Thad Mowe 
“gin BAG = —sin CAG, —sin CBG=-sn ABG, 
b Cc Cc a 
Ie ibe 
—sin ACG =; sin BCG. 
a b 
Therefore 
sn BAP _,sin GAP. sn CBP. , sin ABP 
STAG C SCde: snCEG cmebee 
