Origins of the names of the months:

September: September, (septem, Latin for 7) the seventh month in the Julian or Roman calendar, established in the reign of Julius Caesar,

October: Eighth month (octo, Latin for 8) in the Julian (Roman) calendar. The Gregorian calendar instituted by Pope Gregory XIII established January as the first month of the year,

November: Ninth Roman month (novem, Latin for 9)

December: Julian (Roman) year's tenth month (decem, Latin for 10)