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cylinder = 2(sphere) + 2(cone AEF).
Now also
cylinder = 3(cone AEF); [Eucl. XII.10]
therefore
cone AEF = 2(sphere).
But, since
EF = 2BD,
cone AEF = 8(cone ABD);
therefore
sphere = 4(cone ABD).
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A R C H I M E D E S |
The Method Proposition 2 | |
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That is, cylinder = 2(sphere) + 2(cone AEF). Now also cylinder = 3(cone AEF); [Eucl. XII.10] therefore cone AEF = 2(sphere). But, since EF = 2BD, cone AEF = 8(cone ABD); therefore sphere = 4(cone ABD). |
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