The Sphere. Spherical Distances and Angles. The Spheroid. Earth's Axis and Equator. Terrestrial Latitude and Longitude. The Sphere of the Heavens, Zenith and Horizon. Celestial Pole and Equator. The Ecliptic. The Zodiac. Right Ascension and Declination. Celestial Longitude and Latitude. Parallax. Terms defining the Orbit of a Planet. Sidereal and Apparent Time.
§ 1. A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
The radius of a sphere is a straight line drawn from the centre to a point in the surface; the diameter, or axis, is a line passing through the centre, and terminated each way by the surface.
All the radii of a sphere are equal; all the diameters are also equal, and double the radius.
§ 2. Every section of a sphere made by a plane is a circle.
If a sphere is cut by a plane which passes through the centre, the section is called a great circle of the sphere; the radius of such a section being the greatest possible, the same, namely, with the radius of the sphere.
From this definition it is evident that a great circle may be made to pass through any two points in the surface of a sphere; and that, if the two points be not opposite extremities of a diameter, only one great circle can be made