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All years are BC. All events are accurate to within one year unless followed by a question mark.

814 Carthage founded by Phoenician colonists? (traditional date)
753 Rome founded by unified Latin tribes? (traditional date)
734 Syracuse founded by Greek colonists from Corinth? (traditional date)
306 Birth of Hiero, king of Syracuse?
289 Reign of Hiketas, tyrant of Syracuse, begins.
279 Reign of Hiketas ends.
278 Pyrrhos, king of Greek city of Epirus, rules over Syracuse and the rest of Greek Sicily. (See Plutarch's Life of Pyrrhos.)
276 Pyrrhos leaves Sicily.
275 Hiero executes military takeover of Syracuse.
Hiero marries Philistis, daughter of Leptines, influential Syracusan?
270 Birth of Hiero's son Gelo?
268 Birth of Marcellus, consul of Rome and conqueror of Syracuse. (See Plutarch's Life of Marcellus.)
265 Hiero defeats Mamertines (Italic mercenaries) and is declared king of Syracuse.
264 Beginning of First Punic War for control of Sicily. Syracuse initially allied with Carthage against Rome.
263 Hiero signs peace treaty with Rome after Romans threaten Syracuse.
247 Birth of Hannibal, Carthaginian general.
241 End of First Punic War. Rome gains control of all of Sicily outside of a small area surrounding Syracuse.
240 Gelo begins co-rule with Hiero?
230 Birth of Gelo's son Hieronymos.
218 Beginning of Second Punic War.
Hannibal crosses the Alps and invades Italy.
216 Hannibal defeats Romans at Cannae.
Death of Gelo (at age 54?)
215 Death of Hiero (at age 91?)
Hieronymos assumes throne of Syracuse (at age 15).
Syracuse switches allegiance from Rome to Carthage.
214 Hieronymos assassinated at Leontini, Syracuse's Greek ally (at age 16).
Adranodoros (son-in-law of Hiero) and Themistos (son-in-law of Gelo) assassinated in Syracuse.
Five female members of Hiero's family put to death by a pro-Roman assembly.
Marcellus captures Leontini.
Hannibal's agents, Hippokrates and Epikydes, assume control of Syracuse.
213 Marcellus attacks Syracuse, but is defeated by Archimedes' military machines.
Marcellus begins blockade of Syracuse.
212 Syracuse captured and looted by Romans.
DEATH OF ARCHIMEDES (at age 75?) during sack of Syracuse.
208 Marcellus killed by Hannibal's forces in a minor skirmish (at age 60). (See Plutarch's Life of Marcellus.)
201 End of Second Punic War. Rome gains control of all Carthaginian territory outside of Africa.
183 Death of Hannibal (at age 64). He commits suicide to prevent capture by Roman forces.
146 Carthage is utterly destroyed at the end of Third Punic War, which began in 149 BC.
 75 Cicero discovers and restores Archimedes' tomb.