Screw pump different applications and handling fluids with varying characteristics. Each ‘screw pump' operates on the same basic principle of a screw turning to isolate a volume of fluid and convey it. However, the mechanical design of each is different. The primary difference is the number of screws: one, two, three or more. The screw pump was described by Archimedes on the occasion of his visit to Egypt. This suggests that the apparatus was unknown to the Greeks before Hellenistic times. A cuneiform inscription of Assyrian king Sennacherib (704–681 BC) has been interpreted by Stephanie Dalley to describe casting water screws in
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