And calculation can determine the moon’s disappearance and fullness, corresponding to conjunction and opposition. People describe these phenomena in terms of what is visible: the crescent’s disappearance at the end of the month, its appearance at the beginning, and the fullness of its light in the middle. Astronomical calculators, however, describe them in terms of what is hidden: the conjunction of the two discs, which occurs when the moon disappears, and the opposition of the sun and moon, which occurs at the full moon. These can be determined precisely by calculation.

As for the crescent’s first appearance, they have no precise way of determining it by calculation. It cannot be determined through a known calculation as the times of solar and lunar eclipses can. According to the established order Allah has appointed for the sun, a solar eclipse occurs only when the moon is hidden, when it comes between the sun and people’s sight in a precise alignment. Likewise, a lunar eclipse occurs only on the nights of the full moon, in a precise alignment, when the earth comes between the moon and the sun. For someone whose calculations are correct, knowing when solar and lunar eclipses will occur is like anyone’s knowing that the crescent must appear on the thirty-first night of the month; uncertainty arises only on the thirtieth night.

We therefore say: the most an astronomical calculator can determine, provided his calculations are correct, is, for example, that the two discs came into conjunction at a particular hour and that, by sunset, the moon will have moved away from the sun by, say, ten degrees, or less or more. A degree is one of the three hundred and sixty divisions of the celestial sphere.