Introductory Astronomical Writings of the Ancients

[winter tropic] circle is cut by the horizon in such a way that the smaller segment is above the earth, and the larger segment is beneath the earth. The inequality of these segments has the same variation in all climates as occurred in the case of the summer tropic circle; for the alternating segments of the tropic circles are at all times equal to one another; for which reason the greatest diurnal [arc] is equal to the greatest nocturnal [arc]; and the shortest diurnal is equal to the shortest nocturnal. The antarctic circle is entirely hidden beneath the horizon.

Concerning the magnitude of the five parallel circles.

Of the aforementioned five parallel circles, the magnitudes of some remain the same throughout the entire inhabited world, while the magnitudes of others shift according to the climates, and the circles become larger for some and smaller for others. For the tropic circles and the equator are equal in magnitude throughout the entire inhabited world; but the arctic circles shift in magnitude, and become larger for some and smaller for others. For the arctic circles become larger for those dwelling toward the north. For as the pole appears more elevated, it is necessary that the arctic circle, which touches the horizon, always becomes proportionally larger. And for those dwelling even further toward the north, the summer tropic circle sometimes becomes the arctic circle, such that the two circles coincide with one another—the summer tropic circle and the arctic—and assume a single position. And for those in more northerly regions, [they become] even larger than the summer tropic circle.