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Overview
In noting the situations of the stars and planets, astronomers have been under the necessity of imagining various lines and circles on the sphere; and geographers have done the same for fixing the situation of places on the earth. The most remarkable of these are the following.
A great circle is that whose plane passes through the centre of the sphere; and a small circle is that whose plane does not pass through that centre.
A diameter of a sphere, perpendicular to any great circle, is called the axis of that circle; and the extremities of a diameter are called its poles. Hence the pole of a great circle is 90° from every point of it upon the surface of the sphere; but as the axis is perpendicular to the circle when it is perpendicular to any two radii, a point on the surface of a sphere 90° distant from any two points of a great circle will be the pole.
All angular distances on the surface of a sphere, to an eye at the centre, are measured by arcs of great circles. Hence all triangles formed upon the surface of a sphere, for the solution of spherical problems, must be formed by the arcs of great circles.
Secondaries to a great circle are great circles which pass through its poles, and consequently must be perpendicular to their great circles.