Cause of the Phases of the Moon
During new and full moon, the earth, moon, and sun are all in the same straight line, but, that during the first and last quarters, they are at right angles. The portions of the earth and moon turned toward the sun are illumined, the shaded portions are in the darkness. To an observer on the earth, the moon, at a, appears new, since the dark part is turned toward the person; at b, however, it must appear full, since the illumined portions are toward the person. At c, and d, the positions of the quarters, only one-half of the illumined half, or one quarter, is seen.