In relation to the story of the death of Achilles, Dictys the Cretan tells us, that Achilles having seen Polyxena, the daughter of Priam, along with Cassandra, as she was sacrificing to Apollo, fell in love with her, and demanded her in marriage and that Hector would not consent to it, except on condition of his betraying the Greeks. This demand, so injurious to his honour, provoked Achilles so much, that he forthwith slew Hector, and dragged his body round the walls of the city. He further says that when Priam went to demand the body of Hector, he took Polyxena with him, in order to soften Achilles. His design succeeded, and Priam then agreed to give her to him in marriage. On the day appointed for the solemnity in the temple of Apollo, Paris, concealing himself behind the altar, while Deiphobus pretended to embrace Achilles, wounded him in the heel, and killed him on the spot, either because the arrow was poisoned, or because he was wounded on the great tendon, which has since been called 'tendon Achillis,' a spot where a wound might very easily be mortal.
This story of the death of Achilles does not seem to have been known to Homer; for he appears, in the twenty-fourth book of the Odyssey, to insinuate that that hero died in battle, fighting for the Grecian cause.
After his death Achilles was honoured as a Demigod, and Strabo says that he had a temple near the promontory of Sigæum. Pausanias and Pliny the Elder make mention of an island in the Euxine Sea, where the memory of Achilles was expressly honoured, from which circumstances it had the name of Achillea.
After the death of Achilles, Ajax and Ulysses contend for his armour; the Greek chiefs having adjudged it to the last, Ajax kills himself in despair, and his blood is changed into a flower. When Ulysses has brought Philoctetes, who is possessed of the arrows of Hercules, to the siege, and the destinies of Troy are thereby accomplished, the city is taken and sacked, and Hecuba becomes the slave of Ulysses.
The chiefs were seated; and a ring of the common people standing { around}, Ajax, the lord of the seven-fold shield, arose before them. And as he was impatient in his wrath, with stern features he looked back upon the Sigæan shores, and the fleet upon the shore, and, stretching out his hands, he said, "We are pleading,[1] O Jupiter, our cause before the ships, and Ulysses vies with me! But he did not hesitate to yield to the flames of Hector, which I withstood, { and} which I drove from this fleet. It is safer, therefore, for him to contend with artful words than with his { right} hand. But neither does my talent lie in speaking, nor his[2] in acting; and as great ability as I have in fierce warfare, so much has he in talking. Nor do I think, O Pelasgians, that my deeds need be related to you; for you have been eye-witnesses of them. Let Ulysses recount his, which he has performed without any witness, { and} of which night alone[3] is conscious. I own that the prize that is sought is great; but the rival of Ajax lessens its value. It is no proud thing, great though it may be, to possess any thing which Ulysses has hoped for. Already has he obtained the reward of this contest, in which, when he shall have been worsted, he will be said to have contended with me. And I, if my prowess were to be questioned, should prevail by the nobleness of my birth, being the son of Telamon, who took the city[4] of Troy under the valiant Hercules, and entered the Colchian shores in the Pagasæan ship. Æacus was his father, who there gives laws to the silent { shades}, where the heavy stone urges { downward} Sisyphus,[5] the son of Æolus.