Ancient roman dating calendars
The Romans did not count days in the month as a simple number, as we do, but backwards from one of three fixed points in the month: the Kalends, the Nones, and the Ides. The Nones fell on the 7th day of the long months (March, May, Quinctilis, October), and the 5th of the others.
But Aloysus Lilius, the Italian scientist who developed the system Pope Gregory would unveil in 1582, realized that the addition of so many days made the calendar slightly too long.
The confusion was compounded by political maneuvers.
The Pontifex Maximus and the College of Pontiffs had the authority to alter the calendar, and they sometimes did so to reduce or extend the term of a particular magistrate or other public official.
The months were 30 or 31 days in length, and to take care of the 6 hours, every fourth year was made a 366-day year.
Moreover, Caesar decreed the year began with the first of January, not with the vernal equinox in late March.