Pappus's centroid theorems were discovered 17 centuries ago, when calculus wasn't invented yet. How are these theorems proved without using calculus?(adsbygoogle = window.adsbygoogle || []).push({});

"The first theorem states that the surface areaAof a surface of revolution generated by rotating a plane curveCabout an axis external toCand on the same plane is equal to the product of the arc lengthsofCand the distancedtraveled by its geometric centroid."

The centroid of an object is its center of mass supposing its density is uniform.

"The second theorem states that the volumeVof a solid of revolution generated by rotating a plane figureFabout an external axis is equal to the product of the areaAofFand the distancedtraveled by its geometric centroid."

Quotes from https://en.wikipedia.org/wiki/Pappus's_centroid_theorem

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# I Prove Pappus's centroid theorems without calculus

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