Editing Democritus (section)

=== Mathematics ===
[[File:Plane intersecting cone 2.png|thumb|250px|right|Democritus argued that the circular cross-section of a cone would need step-like sides,{{sfn|Berryman|2016}} rather than being shaped like a cylinder.]]
Democritus was also a pioneer of mathematics and geometry in particular.{{sfn|Heath|1913|pp=121-122}} In ''[[The Method of Mechanical Theorems]]'',<ref>Archimedes, [[The Method of Mechanical Theorems]], Preface</ref>  [[Archimedes]] states that [[Eudoxus of Cnidus]], whose rigorous proof using the [[method of exhaustion]] that the volume of a cone is one-third the volume of cylinder is preserved in [[Euclid]]'s ''[[Euclid's Elements|Elements]]'',<ref>[[Euclid]], ''[[Euclid's Elements|Elements]]'', XII.7, 10</ref> was aided by the fact that Democritus had already asserted it to be true on the argument that this is true for the same reason that the pyramid has one-third the rectangular prism of the same base.{{sfn|Netz|2022|p=150-151}} [[Plutarch]] also reports<ref>[[Plutarch]], De Comm. 39</ref> that Democritus argued that the circular [[cross-section (geometry)|cross-section]] of a cone would need step-like sides, rather than being shaped like a cylinder, which [[Thomas Heath (classicist)|Thomas Heath]] suggests may be an early version of [[infinitesimal calculus]].{{sfn|Heath|1913|pp=121-122}}