De Marssumermolen, Marssum 57 cogs. This drives the "wallower" (31 cogs) at the top of the "upright shaft". At the bottom of the "upright shaft" there are two "crown wheels"' The upper "crown wheel", which has 17 cogs drives an Archimedes' screw. The axle of the Archimedes' screw is diameter and long. This screw is used to pump water into the polder. The lower "crown wheel", which has 43 cogs, drives a gearwheel with 38 cogs on the axle of an Archimedes' screw, which is used to drain the polder. The axle of the screw is diameter and long. The screw is diameter.
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