So, why would I be wondering about it? Well, what I couldn't figure out was if the moon was exactly half illuminated by the sun, the sun had to be directly west of it, since it was the west side of the moon that was bright. But, it was going on 23:00 and the sun had set a long time before. Now, if you don't believe me, draw a picture. Draw a big round circle to represent the earth, a smaller one directly above the big one to represent the moon. Now draw a line vertically through the moon and blacken in the left half. Then directly way off to the right of the moon, draw another circle to represent the sun. This sketch would represent what I believed I saw last night.
Now here is the problem as I see it. Draw a line from the center of the sun to the center of the earth. Then draw a line perpendicular to that line through the center of the earth. Darken in the side of the earth away from the sun. Now, if you were at the top of the earth looking straight up at the moon so that your would see the moon half illuminated by the sun, you would be standing in the illuminated part of the earth!! Yes, but it was eleven pm last night and it was dark. . . take my word for it, except for the moonlight.