October (Roman month) did not number days of a month sequentially from the 1st through the last day. Instead, they counted back from the three fixed points of the month: the Nones (5th or 7th), the Ides (13th or 15th), and the Kalends (1st) of the following month. The Nones of October was the 7th, and the Ides was the 15th. The last day of October was the "pridie Kalendas Novembris," "day before the Kalends of November". Roman counting was inclusive; October 9 was "ante diem VII Idūs Octobris", "the 7th day before the Ides of October," usually abbreviated "a.d. VII Id. Oct."
December (Roman month) fixed points of the month: the Nones (5th or 7th), the Ides (13th or 15th), and the Kalends (1st) of the following month. The Nones of December was the 5th, and the Ides the 13th. The last day of December was the "pridie Kalendas Ianuarias," "day before the Januarian Kalends". Roman counting was inclusive; December 9 was "ante diem V Idūs Decembrīs", "the 5th day before the Ides of December," usually abbreviated "a.d. V Id. Dec." (or with the "a.d." omitted altogether); December 24 was "IX Kal. Ian.", "the 9th day before the Kalends of Ianuarius," on the Julian calendar