The Last Quarter is the phase at which half the disc appears lit, the left half as seen from the northern hemisphere, and the illumination is decreasing toward the dark. Its name marks the Moon's completion of three quarters of its monthly circuit; again the Sun, Earth, and Moon stand at a right angle, the mirror of the first quarter. The last-quarter Moon rises around midnight and sets around midday, seen in the late night and morning sky. Traditionally it is read as a phase of letting go, reckoning, and clearing away in preparation for the new cycle. These are the astronomical facts of the phase together with the meanings traditions attach to it; the half disc is our side-on view of the sunlit hemisphere, lit now on the opposite side from the first quarter.
Islamic, Hebrew and other lunisolar calendars pay closer attention to the crescents that open and close the month than to the quarters, but the last-quarter Moon has its own long-noted calendrical role: in the Hebrew calendar it falls near the midpoint between the full moon that fixes major festivals and the new moon that opens the next month, and its right-angle geometry, the same configuration astrologers call a square, has made it a natural marker of transition in traditions that track the sky closely. The last quarter rises around midnight and is visible through the second half of the night into morning, the mirror image of the first quarter's evening prominence, so that a culture without artificial light experienced the two quarters as opposite halves of the twenty-four-hour day rather than as simply two points partway through a month.
Sources AstronomyAndrew Fraknoi, David Morrison, and Sidney C. Wolff (OpenStax) with Calendar and Community: A History of the Jewish Calendar, Second Century BCE to Tenth Century CESacha Stern