The diurnal motion of the celestial sphere, and the motion of the moon in the circle of the signs, gave rise to a mathematical science, _the Doctrine of the Sphere_, which was one of the earliest branches of applied mathematics. A number of technical conceptions and terms were soon introduced. The _Sphere_ of the heavens was conceived to be complete, though we see but a part of it; it was supposed to turn about the visible _pole_ and another pole opposite to this, and these poles were connected by an imaginary _Axis_. The circle which divided the sphere exactly midway between these poles was called the _Equator_ (ἰσημέρινος). {131} The two circles parallel to this which bounded the sun's path among the stars were called _Tropics_ (τροπικαί), because the sun _turns_ back again towards the equator when he reaches them. The stars which never set are bounded by a circle called the _Arctic Circle_ (ἄρκτικος, from ἄρκτος, the Bear, the constellation to which some of the principal stars within that circle belong.) A circle about the opposite pole is called _Antarctic_, and the stars which are within it can never rise to us.[41\3] The sun's path or circle of the signs is called the _Zodiac_, or circle of animals; the points where this circle meets the equator are the _Equinoctial Points_, the days and nights being equal when the sun is in them; the _Solstitial Points_ are those where the sun's path touches the tropics; his motion to the south or to the north ceases when he is there, and he appears in that respect to stand still. The _Colures_ (κόλουροι, mutilated) are circles which pass through the poles and through the equinoctial and solstitial points; they have their name because they are only visible in part, a portion of them being below the horizon. [Note 41\3: The Arctic and Antarctic Circles of modern astronomers are different from these.]