“Hence it follows that the heaven is spherical. For if it were cylindrical or conical, the stars upon the oblique circles, which cut the equator, would not in the revolution of the heaven always appear to be divided into semicircles; but the visible segment would sometimes be greater and sometimes less than a semicircle. For if a cone or a cylinder were cut by a plane not parallel to the base, the section is that of an acute-angled cone, which resembles a shield (an ellipse). It is, therefore, evident that if a figure of this description is cut in the middle both in length and breath, its segments will be unequal. But the appearances of the heaven agree with none of these results. Therefore the heaven must be supposed to be spherical, and to revolve equally round an axis of which one pole above the earth is visible and the other below the earth is invisible. “The Horizon is the plane reaching from our station to the heaven, and bounding the hemisphere visible above the earth. It is a circle; for if a sphere be cut by a plane the section is a circle. “The Meridian is a circle passing through the poles of the sphere, and at right angles to the horizon. “The Tropics are circles which touch the zodiacal circle, and have the same poles as the sphere. The zodiacal and the equinoctial are both great circles, for they bisect one another. For the beginning of Aries and the beginning of the Claws (or Scorpio) are upon the same diameter; and when they are both upon the equinoctial, they rise and set in conjunction, having between their beginnings six of the twelve signs and two semicircles of the equinoctial; inasmuch as each beginning, being upon the equinoctial, performs its movement above and below the earth in equal times. If a sphere revolves equally round its axis, all the points on its surface pass through similar axes of the parallel circles in equal times. Therefore these signs pass through equal axes of the equinoctial, one above and the other below the earth; consequently the axes are equal, and each is a semicircle; for the circuit from east to east and from west to west is an entire circle. Consequently the zodiacal and equinoctial circles bisect one another; each will be a great circle. Therefore the zodiacal and equinoctial are great circles. The horizon is likewise a great circle; for it bisects the zodiacal and equinoctial, both great circles. For it always has six of the twelve signs above the earth, as well as a semicircle of the equator. The stars above the horizon which rise and set together reappear in equal times, some moving from east to west, and some from west to east.” We have given this long extract in justice to the men of old, containing as it does many of those geometrical principles which all our modern instruments must and actually do fulfil.