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

Spherical Triangles. 11
13. Since every great circle has two poles, it will be necessary to make some convention in order to distinguish them.
For this purpose we employ, as in so many other cases, the
terms positive and negative. Thus, if BC be an arc of a great
circle, its positive pole will be that round which tlie rotation
from B to C will be from left to right; that is, in the same
direction in which the hands of a watch move, and the other
will be the negative pole.
For example, if B, C be points on the equator, and C west
of B, the north pole will be the positive pole of BC, and the
south its negative pole.
DEF. XIV.-The spherical triangle, whose angular points are
the positive poles of the sides of a triangle ABC is called the
POLAR TRIANGLE of AB C.
14. If two spherical triangles ABC, A'B'C' be such that the
latter is the polar triangle of the former, the former is the polar
triangle of the latter.
A
C r= \
F _ _
E B
Fig. 6.
DEM.-Join A'C, B'C by arcs of great circles; then, because
A' is the pole of BC, A'C is a quadrant. Similarly, B'C is a
quadrant. Hence, since the arcs CA', CB' are quadrants, C is
the pole of A'B', and it is evidently the positive pole. Hence
the proposition is proved.