Page:Spherical Trigonometry (1914).djvu/22

4 7. The arc of a great circle which is drawn from a pole of a great circle to any point in its circumference is a quadrant.



Let $$P$$ be a pole of the great circle $$ABC$$; then the arc $$PA$$ is a quadrant.

For let $$O$$ be the centre of the sphere, and draw $$PO$$. Then $$PO$$ is at right angles to the plane $$ABC$$, because $$P$$ is the pole of $$ABC$$, therefore $$P \widehat O A$$ is a right angle, and the arc $$PA$$ is a quadrant.

8. The angle subtended at the centre of a sphere by the arc of a great circle which joins the poles of two great circles is equal to the inclination of the planes of the great circles.



Let $$O$$ be the centre of the sphere, $$CD$$, $$CE$$ the great circles intersecting at $$C$$, $$A$$ and $$B$$ the poles of $$CD$$ and $$CE$$ respectively.