Pseudo-Archimedes Pseudo-Archimedes Pseudo-Archimedes is a name given to pseudo-anonymous authors writing under the name of 'Archimedes' as quoted by various sources of the Islamic Golden Age such as Al-Jazari for the construction of water clocks. Archimedes himself is not known to have written any such manuscript. The only surviving manuscript from a Pseudo-Archimedes is an Arabic treatise not listed among Archimedes' works. Donald Routledge Hill is of the opinion that the original manuscript may have been Greek but that most of the manuscript was written by later Arabic authors. The scholar A.G. Drachmann believes that the manuscript was assembled from Arabic
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