On this defiant note, a refusal was sent to Darius who also heard, through a eunuch escaped from camp, that his wife had died in childbirth and that Alexander had given her a magnificent funeral, a tribute which he had no political need to pay. The news of her death and Alexander's refusal of the peace offer finally determined Darius to muster a truly grand army from the Punjab to the Persian Gulf, a task which would take a whole year; it was evident that the Aegean offensive would now fail, as the Levantine fleets had surrendered, although his admirals still put up a resourceful struggle with the help of that scourge of Greek sailors and sea trade, the pirate. The coast of western Asia had been thoroughly harassed by land and sea in the past nine months, despite the attempted closure of its ports. Cos had been retaken and fifty pirate long-boats had helped raid even the apparent stronghold of Miletus, restoring a Persian governor and exacting badly-needed money. Ephesus's new democracy may have been similarly disturbed, and as if by design, the wild mountain tribes of three satrapies in Asia Minor had drawn off Alexander's generals in punitive expeditions. These were their last signal successes, for Alexander's second Greek fleet had finally put to sea. It at once cleared the Hellespont, then freed its islands and pursued the Persians southwards. Their henchmen were rooted out with them, not least the Athenian soldier of fortune, Chares, who had set himself up in Mitylene less than three years after he had crowned Alexander at Troy: he throve on chaos and disorder, but not for the first time he had changed sides too late and was expelled by the Macedonian admirals.

Back at Tyre, the next incident selected by the historians was centred on Alexander himself One July morning, after careful preparation behind screens of hide, the Tyrians sailed out in their thirteen smartest warships, meaning to surprise Alexander's Cypriot fleet which had been beached in the north harbour while its crews had left as usual for lunch. Their adventure began auspiciously. They approached in hushed silence, then raised their cox's call, plashed their oars and rammed three royal Cypriot quinqueremes to pieces before the crews could return. Alexander was lunching in the southern harbour but had not returned to his royal tent as usual; he hurried to his quinquereme on hearing of the sortie, and sped round the city with ships to the rescue, urging his crews to ram and sink the Tyrian attackers. His own role was conspicuous, its results important, for his surprise retaliation deprived Tyre of her swiftest ships. Their sortie was said to have been prompted by a festive bout of drinking, but it was more likely to have been inspired by hunger, as Alexander had long been mounting a blockade on both harbours. Without their best warships the Tyrians were now more hemmed in than ever. Even Carthage had withdrawn her offers of help.

After two days' rest, the Macedonians were able to follow up their naval victory. In keeping with Alexander's methods, the final blow was to be delivered by varied weapons at various places. Battering-ships were to breach given points in the wall, machine-bearing ships would give cover and two more shiploads of infantry were to emerge down newly devised drawbridges and storm a way through any breaches. Meanwhile the fleet was to attack both harbours, north and south; archers and catapults were to be carried round the island in a flotilla of warships in order to create an unpleasant diversion. Such a mixture of concentrated and diversionary tactics is the mark of a great general, able to see his decisive chance and seize it. As planned, walls were rammed until they tottered, artillery rounded off the damage, warships and archers drew off the defenders, drawbridges dropped downwards and the Shield Bearers poured into the breach, led by their captain Admetus, with Alexander heading the second wave. Admetus, first to mount the wall, died a hero's death. Alexander was quickly astride the battlements to fill his place. Conspicuous both in armour and performance, he speared some, stabbed others and hurled Tyrians down into the sea. As the infantry followed his lead Tyre fast fell to Macedonian hands, no longer having the ships to keep its attackers at bay. A last-ditch stand by the shrine of the city founder was to no avail.

Enraged by Tyrian atrocities and the seven-month length of the siege, Alexander's army killed some 8,000 of the citizens and enslaved a further 30,000 of those who had not already been shipped in safety to Carthage and Sidon; on Alexander's orders, 2,000 more were crucified along the shore. The cruelty was not wholly wanton, for as the army burst upon the city, a truce had been announced for all who might take refuge in shrines or temples. Though most of the Tyrians were now too stubborn to comply, those who did so were spared, including Azemilk, King of Tyre, and the thirty envoys from Carthage whom it would have been unwise to violate. Azemilk was to be restored to his kingship and the city was to be resettled with loyal garrison troops and native survivors; as a sign of the times, it was given a Greek constitution.

On the following day, Alexander paid his overdue sacrifice to Heracles or Melkarth, dedicating the catapult which had first broken the city walls and consecrating the sacred ship of Tyre which he himself had been responsible for sinking. Never can the god have received such a bloodstained sacrifice: 'Tyre', said a Macedonian historian, possibly Callisthenes, 'had fallen in the month of July when Aniketos was official magistrate at Athens.' But the magistrate's name is known to have been Nikeratos; the word Aniketos means Invincible and in a forgivable burst of enthusiasm, even the name-date of the year was altered to suit Alexander's invincibility as a besieger.

Encouraging, explaining, 'sharing the hardships in person', whether on the mole or among the cedars of Lebanon, Alexander had deserved his touch of historical glamour. As usual, the histories centre their story round the king, but there is one chance reminder that the new Achilles could no longer sack cities in the manner of his Homeric forbear, 'laying them low by the might of his own spear'. In a work on technical engineering, Diades the Greek from Thessaly, pupil to King Philip's inventor, is later described as the 'man who besieged Tyre with Alexander'. The fall of the city perhaps owed more to the drawing-board than will ever be known.

Once Tyre had fallen, Alexander could continue south through the coastal plains to Egypt, sure of the surrender of lesser cities in Syria and Palestine. Dor, Ashdod and Straton's Tower made terms because they depended on Tyre and Sidon, but a mere hundred miles south he ran into more obstinacy. Gaza, that large and ancient Philistine city, bestrode his route two miles from the sea, and from the Lebanon's trade of frankincense and the Arab's trade in spices, it had long grown very rich. It was garrisoned by hired Arabs, and it was urged to resist by its oriental governor Batis, who went down in history as ugly, fat and a eunuch.

Gaza's most formidable defence was its own mound, for like many cities in biblical lands it was perched on a 'tell' or heap of its earlier layers of habitation, from which it surveyed the open desert. It was well provisioned, and as soon as Alexander ordered the machinery which had been shipped from Tyre to be reassembled his engineers protested that the city was 'too high to take by force’. Undeterred, Alexander 'thought that the more impossible it seemed, the more it must be captured; the feat would be so extraordinary that it would greatly unnerve his enemies, whereas failure would be a disgrace if ever the Greeks or Darius should hear of it*. Gaza, like Tyre, was too strong to be left on Alexander's one route of communication, and this must have weighed as heavily as any attractions of the impossible.