Vertical circles are those which pass through the poles of the horizon, (the zenith and nadir,) perpendicular to it.
The meridian is that vertical circle which passes through the north and south points.
The prime vertical is that vertical circle which passes through the east and west points.
The altitude of a body is its elevation above the horizon, measured on a vertical circle.
The azimuth of a body is its distance, measured on the horizon, from the meridian to a vertical circle passing through that body.
The amplitude of a body is its distance, on the horizon, from the prime vertical to a vertical circle passing through the body.
Azimuth is reckoned ninety degrees from either the north or south point; and amplitude ninety degrees from either the east or west point. Azimuth and amplitude are mutually complements of each other, for one makes up what the other wants of ninety degrees. When a point is on the horizon, it is only necessary to count the number of degrees of the horizon between that point and the meridian, in order to find its azimuth; but if the point is above the horizon, then its azimuth is estimated by passing a vertical circle through it, and reckoning the azimuth from the point where this circle cuts the horizon.
The zenith distance of a body is measured on a vertical circle passing through that body. It is the complement of the altitude.
The axis of the earth is the diameter on which the earth is conceived to turn in its diurnal revolution. The same line, continued until it meets the starry concave, constitutes the axis of the celestial sphere.
The poles of the earth are the extremities of the earth's axis: the poles of the heavens, the extremities of the celestial axis.