217—Hannibal, with great celerity, crossed the Pyrenees and the Alps—having first completed the conquest of Spain—and defeated the Romans in the battle of Ticinus, and again at Trebia. 217—The Achaian confederacy, now in the height of its glory in maintaining the liberties of Greece, united all the Greeks in a confederacy under the influence of Philip, king of Macedon, with the hope of arresting the power and ambition of Rome. 216—Hannibal inflicted a dreadful defeat on the Romans near the Thrasymenean Lake. The Romans were greatly alarmed, and made Fabius Maximus dictator, whose habit of refusing a pitched battle, wearing out his adversary by skirmishes and cutting off his supplies, is called “The Fabian Policy.” This plan is, by maneuvering and delay, to wear out and destroy an invader in detail without peril of defeat in battle. The Romans kept armies in Spain to prevent the Carthaginians from sending reinforcements to Hannibal. 215—At the close of this year Fabius resigned his dictatorship and the consuls appointed to succeed him abandoned his policy. They offered battle to Hannibal at Cannæ and the army was annihilated. 40,000 Romans were slain on the field. These defeats had destroyed the flower of their fighting population, but Roman courage and resolution always rose with defeat. They did not despair, but raised a fresh army and put Fabius again at its head, against whom the talents of Hannibal were vain. They fomented disturbances in Greece to keep Philip, King of Macedon at home, and besieged Syracuse in Sicily, which had joined the Carthaginians, 212—for three years, and then took it by stratagem. Archimedes, a celebrated mathematician of Syracuse, who had protracted the siege by his ingenious and powerful engines was killed in the sack of the city. Soon 210—after the whole island was subdued and remained a Roman province. 206—Asdrubal, the brother of Hannibal, general of the Carthaginian forces in Spain, crossed the Pyrenees and the Alps to reinforce Hannibal, but was defeated by the Romans and slain before Hannibal knew of his march.