An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

10 THE EARTH.
the sphere, namely, the distance from the pole to the circuln
ference of the circle, must be 90~. If two great circles cut eabl'
other at right angles, the poles of each circle lie in the circumference of the other circle. For each circle passes through the
axis of the other.
20. All great circles of the sphere cut each other in two
points diametrically opposite, and consequently their points of
section are 180~ apart. For the line of common section is a
diameter in both circles, and therefore bisects both.
21. A great circle which passes through the pole of another
great circle, cuts the latter at right angles. For, since it
passes through the pole and the center of the circle, it must
pass,through the axis; which being at right angles to the
plane of the circle, every plane which passes through it is at
right angles to the same plane.
The great circle which passes through the pole of another
great circle, and is at right angles to it, is called a secondary
to that circle.
22. The angle made by two great circles on the surface of the
sphere, is measured by the are of another great circle, of which
the angular point is the pole, being the are of that great circle
intercepted between those two circles. For this arc is the measure of the angle formed at the center of the sphere by two radii,
drawn at right angles to the line of common section of the two
circles, one in one plane and the other in the other, which angle
is therefore that of the inclination of those planes.
23. In order to fix the position of any plane, either on tie
surface of the earth or in the heavens, both the earth and the
heavens are conceived to be divided into separate portions by
circles, which are imagined to cut through them in various ways.
The earth, thus intersected, is called the terrestrial, and the
heavens, the celestial sphere. The learner will remark that these
circles have no existence in nature, but are mere landmarks,
artificially contrived, for convenience of reference. On account
of the immense distance of the heavenly bodies, they appear to
us, wherever we are placed, to be fixed in the same concave