The Romans gave dates according to the number of days there were to go to certain set days in the month. These were the Kalends, the Nones and the Ides. The set day itself was included in the counting. The year was written as A.U C for 'ab urbe condita' ( from the founding of the city) the legendary date of the city of Rome's beginning.. In the case of 22nd August 2003 the date would have been written XI Kal. Sep MMDCCLVI, that is 'eleven days to the Kalends of September in the year which is 2756 years from the foundation of the city '. As you see they counted on to the next set date even though that meant going into the next month; they did not count back to the nearest date in the month they were in.