Claw of Archimedes Claw of Archimedes The Claw (, "harpágē", "snatcher") of Archimedes (also known as the "iron hand") was an ancient weapon devised by Archimedes to defend the seaward portion of Syracuse's city wall against amphibious assault. Although its exact nature is unclear, the accounts of ancient historians seem to describe it as a sort of crane equipped with a grappling hook that was able to lift an attacking ship partly out of the water, then either cause the ship to capsize or suddenly drop it. These machines featured prominently during the Second Punic War in 214 BC, when the Roman Republic
Archimedes Palimpsest a parabola and one of its secant lines. (For explicit details, see Archimedes' use of infinitesimals.) When rigorously proving theorems, Archimedes often used what are now called Riemann sums. In "On the Sphere and Cylinder," he gives upper and lower bounds for the surface area of a sphere by cutting the sphere into sections of equal width. He then bounds the area of each section by the area of an inscribed and circumscribed cone, which he proves have a larger and smaller area correspondingly. He adds the areas of the cones, which is a type of Riemann sum for the