Introductory Astronomical Writings of the Ancients

The tropic is cut by the horizon in such a way that the smaller of the sections is held to be above the earth, and the larger beneath the earth. Indeed, the inequality of the sections has the same variation in all climates as we also mentioned regarding the solstitial tropic: for the sections corresponding to one another on opposite sides of the tropics are always equal to each other. And it comes about that the longest day becomes equal to the longest night, and the shortest day to the shortest night. The antarctic circle, however, lies entirely hidden beneath the horizon.

Concerning the magnitude of the parallels.

But of the five circles already mentioned, the magnitudes of some remain the same for themselves throughout the whole globe of the earth, while others change according to the climates, and the circles become larger for some and smaller for others. For the tropics and the equator maintain equal magnitudes throughout the whole globe; the arctics vary in magnitude, since they are observed to be larger in one place and smaller in another. Indeed, for those who dwell toward the north, the northern [circles] become larger, since with the pole elevated higher, it is necessary that the arctic circle, which touches the horizon, constantly becomes larger. But for those who lean even more toward the north, sometimes the solstitial tropic passes completely into the arctic; and it happens that the two circles, the northern and the tropic, coalesce and are held as one. Thus, when one approaches even closer to the north, [they become] larger than the solstitial