Page:Spherical Trigonometry (1914).djvu/22

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.