so no account is taken of whether someone who is not present could see it.

The second factor:

Visibility varies with the number of observers. When they are numerous, it is more likely that one of them will see it because of his keen eyesight, his familiarity with where it rises, and his intent gaze in that direction. When they are few, this may not occur. Thus, when someone supposes that it will be visible, the observers may be few and unable to see it. Conversely, when he says that it will not be visible, there may be many observers, including someone capable of perceiving what others cannot.

The third factor:

Visibility varies according to the observation point. Someone at a higher elevation—in a minaret, on a high rooftop, or on a mountaintop—is not in the same position as someone on level ground or down in a valley. Likewise, one observer may have a building, mountain, or similar object in front of him that usually still allows him to see it, though it sometimes obstructs his view; another may have nothing in front of him.

Thus, if it is said without qualification that the crescent will be visible, someone at a lower elevation or in a similar position may not see it. If it is said that it will not be visible, someone at a higher elevation or in a similar position may see it. These circumstances plainly affect visibility.

The fourth factor:

Visibility varies according to the time of observation. Those who perform the calculations customarily report its separation from the sun at sunset, and at that