• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.371-388
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• 2013

In ${\ll}$The Method${\gg}$, Archimedes presented the famous heuristic technique for calculating areas, volumes and centers of gravity of various plane and solid figures, utilizing the law of the lever. In that treatise, Archimedes used the fact that the center of gravity of a cone lies one-quarter of the way from the center of the base to the vertex, but the proof of this is not extant in his works. This study analyzes the propositions and their relations of ${\ll}$The Method${\gg}$ focusing on the procedural characteristics of the 'method' of Archimedes. According to the result of that analysis, this study discusses the likely approach which was taken for Archimedes to find out the center of gravity of a cone.