consistently reliable method other than sighting itself. They have pursued various methods, as did the earlier practitioners, some of whom could determine its course only by averaging—a procedure which those who calculate agree is not consistently reliable.

It is merely an approximation, such as saying: “If it is seen on the morning of the twenty-eighth, the month is full; if it is not seen on the morning of the eighth, the month is short.” This assumes that the moon remains invisible for two nights, which is incorrect: sometimes it remains invisible for one night, and at other times for three. Their statement rests on the assumption that each night it spends exactly six-sevenths of an hour in its lunar station, neither more nor less. Thus, it sets at midnight on the seventh night; on the fourteenth night, it rises at the beginning of the night and remains up until sunrise; on the twenty-first night, it rises at midnight; and if it is invisible on the twenty-eighth night, the month is short, otherwise it is full. This is its usual course, but it may move faster or slower.

As for rational considerations, know that all the meticulous specialists in astronomical calculation agree that sighting cannot be determined by calculation in such a way as to establish, with consistent reliability, that the crescent will certainly be seen or will certainly not be seen. Rather, sighting may occur at certain times, or it may be impossible. For this reason, those devoted to this science among the various nations—the Romans, Indians, Persians, Arabs, and others, such as Ptolemy, their foremost authority, and those who followed them before and after Islam—have not attributed to him a single statement concerning sighting, nor have they defined it as they defined the conjunction of the two discs. Only some of them among the people of Islam discussed it, such as