De Olifant, Burdaard Archimedes' screw. This Archimedes' screw has an axle diameter of and is diameter overall. It is inclined at an angle of 17½°. Each revolution of the screw lifts of water. The drive to the smaller of the two Archimedes' screws that drain the polder is from a 36 cog gear wheel meshing with the "great spur wheel". This drives a 33-cog gear wheel which drives the Archimedes' screw via a 41-cog gear wheel on the axle of the Archimedes' screw. This Archimedes' screw has an axle diameter of and is diameter overall. It is inclined at an angle of 121°.
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