The Gregorian calendar is a modification of the Julian calendar first used by the Romans. The Roman calendar originated as a lunisolar calendar and named many of its days after the syzygies of the moon: the new moon ("Kalendae" or calends, hence "calendar") and the full moon ("Idus" or ides). The "Nonae" or nones was not the first quarter moon but was exactly one "nundina" or Roman market week of nine days before the ides, inclusively counting the ides as the first of those nine days. This is what we would call a period of eight days. In 1825, Ideler believed that the lunisolar calendar was abandoned about 450 BC by the decemvirs, who implemented the Roman Republican calendar, used until 46 BC. The days of these calendars were counted down (inclusively) to the next named day, so February 24 was "ante diem sextum Kalendas Martias" ("the sixth day before the calends of March") often abbreviated a. d. VI Kal. Mart. The Romans counted days inclusively in their calendars, so this was actually the fifth day before March 1 when counted in the modern exclusive manner (not including the starting day).