A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

Poles and Polars. 109
DEM.-Let Y be the circumcircle of the colunar triangle
A C'B, and 00' the spherical centres of X and Y; and since
the angle C is right, the circles X, Y cut orthogonally; therefore A 0', O'B are tangents to X. Hence AB is the polar of
c
C
Fig. 41.
0', with respect to X; and since O'A = O'C', the locus of O' is
the radical axis of the circle X and the fixed point C'; and
therefore AB, the polar of O' with respect to X, passes through
a given point.
103. Every secant ( A0) passing through a given point O is eut
harmonically by the circle X and the harmonic polar of O.
Fig. 42.
DEM.-Let BC be the polar of 0, and let the sines of the