Here he invokes the argument well known among mathematicians who study the configuration of the celestial spheres and the earth—that is, their form and shape. They argue that the sun, moon, and stars rise in the east of the earth before rising in the west, and set in the east before setting in the west. Thus, night and day begin in the east before they begin in the west.

The month, however, begins in the west before it begins in the east, because its beginning depends on the appearance of the crescent. The crescent becomes more readily visible as its separation from the sun increases and the sun is concealed, allowing the crescent’s light to be seen. The sun sets later in the west than in the east, so its separation from the crescent increases correspondingly, making the crescent’s light stronger. Once the sun has set, the rays below the crescent weaken because of the increased distance. Thus, the factor conducive to sighting it is strengthened, while the impediment is weakened.

They use lunar eclipses as evidence for this, since people can observe an eclipse at night at the same instant. They can thereby know that it occurs earlier for those in the east than for those in the west, and ascertain its extent in the various regions of the earth. Such evidence is not confined to lunar eclipses; solar eclipses can also be used, and even conjunctions of the stars