Introductory Astronomical Writings of the Ancients

It is fitting that the circles be understood as being without any width, perceivable by reason through the position of the stars, and delineated by the same sight of the dioptra and our intellect. For by sense, one Milky Way can be discerned in the heavens; all the rest, by reason.

Indeed, only five equidistant circles are accustomed to be described on the sphere; which, however, does not mean that these alone are equidistant in the world, since the sun, by the rotation of the world, traverses a circle equidistant to the equator daily (which can be perceived by sense). Whence it happens that it describes twice one hundred and eighty-two equidistant circles within the tropics; for just as many days are numbered within the turnings. Moreover, the stars themselves, one and all, are borne daily upon equidistant circles. Yet not all of these are employed on the sphere. Although they are useful for many other matters in astrology (since it is impossible for the stars to be properly located on the sphere without all the equidistant circles, or for the lengths of days and nights to be found with precision without them), nevertheless, because they have been judged not so useful for the first rudiments of astrology, it did not seem necessary to inscribe them on the sphere. But the five equidistant circles, on account of certain compendia, which for the tyro of astrology—