September, October, November and December are the ninth, tenth, eleventh and twelfth months of the year. However, they are formed from the Latin words for seven, eight, nine and ten. The reason is that the original calendar only had ten months. In the original calendar, the final month of the year, December, was the tenth month.
The months of January and February were later added to the calendar. The result was that the number of months increased from ten to twelve. However, the names of the ninth, tenth, eleventh and twelfth months did not change.
January and February are the first two months, but if they were the last two, September to December would remain months seven to ten of the year. However, January and February are the first two months of the year, so the names of September, October, November and December are inaccurate. Their names reflect that they were once the seventh, eighth, ninth and tenth months of the calendar.