 Complete the following phrase:  The ancient Romans were certain of the day Rome was founded: April 21, the day of the festival sacred to Pales, goddess of shepherds, on which date they celebrated the Par ilia or Palilia. However they did not know, or they were uncertain of, the exact year the city had been founded; this is one reason they preferred to date their years by the presiding consuls rather than using the formula A.U.C. or Ab Urbe Condita. Several dates had been proposed by ancient authorities, and Dionysius of Halicarnassus records these: The Greek historian Timaeus, one of the first to write a history to include the Romans, stated that Rome was founded in the 38th year prior to the first Olympiad, or 8143 BC; Quintus Fabius Pictor, the first Roman to write the history of his people, in Greek, stated Rome was founded in the first year of the eighth Olympiad, or 7487 BC; Lucius Cincius Alimentus claimed Rome was founded in the fourth year of the twelfth Olympiad, or 7298 BC; and Cato the Elder calculated that Rome was founded 432 years after the Trojan War, which Dionysius states was equivalent to the first year of the seventh Olympiad, or 7521 BC. Dionysius himself provided calculations showing that Rome was founded in 751 BC, starting with the 