GEOMETRY 



33 



The direction cosines of the two systems of axes are given by the following 

 scheme : 



2.050 Trilinear Coordinates. 



A point in a plane is denned if its distances 

 from two intersecting lines are given. Let CA, 

 CB (Fig. i) be these lines: 



PR = p, PS = q, PT = r. 



Taking CA and CB as the x-, y-axes, including 

 an angle C, 



sin C 



sinC 



S 



FIG. i 



Any curve f(x,y) = o becomes : 



f \s5Tc' sm~C/ = * 

 If s is the area of the triangle CAB (triangle of reference), 



25 = ap + bq + cr, 

 a = BC, 

 b =CA, 

 c = AB, 



and the equation of a curve may be written in the homogeneous form : 



, / 2sp f 2^7 \ = Q 



\(flP + bq + cr) sin C (ap + bq + cr) sin C/ 



2.060 Quadriplanar Coordinates. 



These are the analogue in 3 dimensions of trilinear coordinates in a plane 

 (2.050). 



