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by Dio Cassius (c. AD 155-235 )
A portion of Book XV of this work deals with the siege of Syracuse, but it survives only in the form of the following two paraphrases by the 12th century Byzantine authors John Zonaras and John Tzetzes:
John Zonaras, Epitome ton Istorion 9, 4
. . . Marcellus crossed into Sicily and proceeded to besiege Syracuse. The city had submitted to him, but then had revolted again as the result of a false message sent by the treachery of certain men. Now he would have subdued it very speedily, as the result of a joint assault upon the wall by land and sea, had not Archimedes with his inventions enabled the inhabitants to resist for a very long time. For this man by his devices suspended stones and heavy-armed soldiers in the air, and these he would let down suddenly, and presently draw them up again. And he would lift up ships, even those equipped with towers, by means of other appliances which he dropped upon them; and raising them aloft, would let them drop suddenly, so that when they fell into the water they were sunk by the impact. At last in an incredible manner he burned up the whole Roman fleet. For by tilting a kind of mirror toward the sun he concentrated the sun's beam upon it; and owing to the thickness and smoothness of the mirror he ignited the air from this beam and kindled a great flame, the whole of which he directed upon the ships that lay at anchor in the path of the fire, until he consumed them all.
Marcellus, therefore, despairing of capturing the city on account of the inventiveness of Archimedes, planned to take it by famine after a regular investment.
John Tzetzes, Book of Histories (Chiliades) 2, 109-128
And when once Marcellus, the Roman general, was assaulting Syracuse by land and sea, this man [Archimedes] first by his engines drew up some merchantmen [ships], and lifting them up against the wall of Syracuse dropped them again and sent them every one to the bottom, crews and all. Again, when Marcellus removed his ships to a little distance, the old man gave all the Syracusans the power to lift stones of a waggon's size, and hurling them one at a time, to sink the ships. When Marcellus withdrew them a bow-shot thence, the old man constructed a kind of hexagonal mirror, and at an interval proportionate to to the size of the mirror, he set similar small mirrors with four edges, moving by links and by a kind of hinge, and made the glass the centre of the sun's beams--its noontide beam, whether in summer or in the dead of winter. So after that, when the beams were reflected into this, a terrible kindling of flame arose upon the ships, and he reduced them to ashes a bow-shot off. Thus by his contrivances did the old man vanquish Marcellus.
DIO'S ROMAN HISTORY
(Volume II: Fragments of Books XII - XXV)
Translated by E. Cary
Loeb Classical Library, Harvard University Press, Cambridge, 1914