Editing Archimedes (section)

==== ''The Method of Mechanical Theorems'' ====
{{Main|The Method of Mechanical Theorems}}
As with ''[[Archimedes's cattle problem|The Cattle Problem]]'', ''The Method of Mechanical Theorems'' was written in the form of a letter to [[Eratosthenes]] in [[Alexandria]].

In this work Archimedes uses a novel method, an early form of [[Cavalieri's principle]],<ref name="ArchimedesCalc">{{Cite web |last=Powers |first=J. |date=2020 |title=Did Archimedes do calculus? |url=https://old.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/2020-Jeffery%20Powers.pdf |access-date=14 April 2021 |website=maa.org}}; {{Citation |last=Jullien |first=V. |title=Archimedes and Indivisibles |date=2015 |work=Seventeenth-Century Indivisibles Revisited |volume=49 |pages=451–457 |editor-last=J. |editor-first=Vincent |series=Science Networks. Historical Studies |place=Cham |publisher=Springer International Publishing |doi=10.1007/978-3-319-00131-9_18 |isbn=978-3-319-00131-9}}; {{cite web |author1=O'Connor, J.J. |author2=Robertson, E.F. |date=February 1996 |title=A history of calculus |url=https://mathshistory.st-andrews.ac.uk/HistTopics/The_rise_of_calculus/ |access-date=7 August 2007 |publisher=[[University of St Andrews]]}}; {{Cite journal |last=Kirfel |first=Christoph |date=2013 |title=A generalisation of Archimedes' method |url=https://www.jstor.org/stable/24496758 |journal=The Mathematical Gazette |volume=97 |issue=538 |pages=43–52 |doi=10.1017/S0025557200005416 |issn=0025-5572 |jstor=24496758}}</ref> to rederive the results from the treatises sent to Dositheus (''Quadrature of the Parabola'', ''On the Sphere and Cylinder'', ''On Spirals'', ''On Conoids and Spheroids'') that he had previously used the [[method of exhaustion]] to prove,{{sfn|Netz|2022|p=131}} using the [[law of the lever]] he applied in ''On the Equilbrium of Planes'' in order to find the [[center of gravity]] of an object first, and reasoning geometrically from there in order to more easily derive the volume of an object.{{sfn|Netz|2022|pp=187-193}} Archimedes states that he used this method to derive the results in the treatises sent to Dositheus before he proved them more rigorously with the method of exhaustion, stating that it is useful to know that a result is true before proving it rigorously, much as [[Eudoxus of Cnidus]] was aided in proving that the volume of a cone is one-third the volume of cylinder by knowing that [[Democritus]] had already asserted it to be true on the argument that this is true by the fact that the pyramid has one-third the rectangular prism of the same base.{{sfn|Netz|2022|p=150-151}}

This treatise was thought lost until the discovery of the [[Archimedes Palimpsest]] in 1906.<ref>{{cite book |last1=Smith |first1=David Eugene |title=Geometrical Solutions Derived from Mechanics: A Treatise of Archimedes |date=1909 |publisher=Open Court Publishing Company |url=https://archive.org/details/geometricalsolu00smitgoog/mode/2up |access-date=4 May 2025 |language=English}}</ref>