Um, so what is a new moon then? Isn't that also a shadow cast on the moon by the earth? Why don't we call that an eclipse too?
The dark part of a new moon is the shadow cast on the moon by the moon itself, if you like, but that might be a confusing way to describe it.
Imagine a ball brightly lit, half bright, half in shadow. When it's full, as it was on Tuesday, the sun is directly behind us, shining straight on to it in the direction we're looking, so it looks round and flat (because it's shadowless - or rather, we can't see the shadows).
(SUN) (EARTH)
(MOON)
Two weeks later the moon has moved half way around the earth till we're looking at the side in shadow, but it rises about the time the sun does, so we can't see it at all. (Only if it's exactly in front of the sun we have a solar eclipse.)
(SUN) (MOON)
(EARTH)
A day or two later when it's at a slight angle, we see a sliver of the bright half, and all but a sliver of the dark half. That is the new moon.
(SUN) (EARTH)
(MOON)
(There is no permanently "dark side of the moon", though the same side always faces us; when our side is dark, the other side is lit.)
Sometimes the light reflected off the earth is bright enough to reflect back off the dark part of the new moon and back to us, and we can see "the old moon in the new moon's arms".
This stuff really ought to be taught in school. It's fairly basic to understanding our place in the Universe.
