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<p>The aim of this article is to study the result of the sphere demonstrated by Euclid in <i>Elements</i> XII, 16–18 and the result of the sphere demonstrated by Archimedes in <i>Sphere and Cylinder</i>, I, 33–34. The focus of this work is to offer a structural reconstruction of both proofs and, based on this, to conduct a comparative reading of the mathematical techniques and logical structure used. Finally, based on this structural reconstruction and historical and philological arguments, a correlative reading among these demonstrations will be proposed, in which there is a suggestion that Archimedes adapted the techniques of Euclid.</p>

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A comparative study between the approaches of Archimedes and Euclid to the sphere

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Guilherme Luiz Grüdtner

摘要

The aim of this article is to study the result of the sphere demonstrated by Euclid in Elements XII, 16–18 and the result of the sphere demonstrated by Archimedes in Sphere and Cylinder, I, 33–34. The focus of this work is to offer a structural reconstruction of both proofs and, based on this, to conduct a comparative reading of the mathematical techniques and logical structure used. Finally, based on this structural reconstruction and historical and philological arguments, a correlative reading among these demonstrations will be proposed, in which there is a suggestion that Archimedes adapted the techniques of Euclid.