11. If the arcs of great circles joining a point P on the surface of a sphere with
two other points A and C on the surface of the sphere, which are not at opposite
extremities of a diameter, be each of them equal to a quadrant, P is a pole of
the great circle through A and C. (See the figure of Art. 7.)
For suppose PA and PC to be quadrants, and O the centre of the sphere;
then since PA and PC are quadrants, the angles POC and POA are right
angles. Hence PO is at right angles to the plane AOC, and P is a pole of the
great circle AC.
I am having some difficulties understanding what is being proven by this article.
Thanks in advance...