Archimedes' screw Archimedes' screw An Archimedes' screw, also known by the name the Archimedean screw or screw pump, is a machine used for transferring water from a low-lying body of water into irrigation ditches. Water is pumped by turning a screw-shaped surface inside a pipe. The screw pump is commonly attributed to Archimedes, on the occasion of his visit to Egypt. This tradition may reflect only that the apparatus was unknown to the Greeks before Hellenistic times and was introduced in Archimedes's lifetime by unknown engineers. Depictions of Greek and Roman water screws show them being powered by a human treading on
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