Archimedes and center of gravity of an triangle

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I want to know: how Archimedes determined the center of gravity of arbitrary triangle? Do you know the rigorous method?

If you know a website or document please tell me. I'm a looking for a reliable reference.

Thank you for your help.

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2 Answers

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Historical reference: On the Equilibria of Planes, Book I, Propositions 13-14.

Here is an online version (containing comments from Eutocius) translated by Henry Mendell, with pictures included.

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Although I don't have a historical reference, I'm sure he did it by noting that a line segment from a vertex to the mid-point of the opposite side bisects the triangle into triangles of equal area. So doing this construction from two vertices finds the centroid as the intersection of the constructed lines.

Of course, you can prove that this construction bisects area by the usual area formula $A =\frac{1}{2} bh$

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