14.3
he proceeded to attack the city by land and sea, Appius leading up the land forces, and he himself having a fleet of sixty quinqueremes filled with all sorts of arms and missiles. Moreover, he had erected an engine of artillery on a huge platform supported by eight galleys fastened together,See chapter xv. 3. According to Polybius (viii. 6). Marcellus had eight quinqueremes in pairs, and on each pair, lashed together, a sambuca (or harp) had been constructed. This was a pent-house for raising armed men on to the battlements of the besieged city. and with this sailed up to the city wall, confidently relying on the extent and splendour of his equipment and his own great fame. But all this proved to be of no account in the eyes of Archimedes and in comparison with the engines of Archimedes.
14.4
To these he had by no means devoted himself as work worthy of his serious effort, but most of them were mere accessories of a geometry practised for amusement, since in bygone days Hiero the king had eagerly desired and at last persuaded him to turn his art somewhat from abstract notions to material things, and by applying his philosophy somehow to the needs which make themselves felt, to render it more evident to the common mind.
14.5
For the art of mechanics, now so celebrated and admired, was first originated by Eudoxus and Archytas, who embellished geometry with its subtleties, and gave to problems incapable of proof by word and diagram, a support derived from mechanical illustrations that were patent to the senses. For instance, in solving the problem of finding two mean proportional lines, a necessary requisite for many geometrical figures, both mathematicians had recourse to mechanical arrangements, adapting to their purposes certain intermediate portions of curved lines and sections.
