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But this has never happened as if you try, you will see it does not work that way. This is also a story written hundreds of years later ;)

This very week did the same experiment with different classes: to find the density of a stone without using a balance, using the two laws of displacement of water for an object floating and sinking.

Let me rephrase myself: you can get a result, but the uncertainty on it is huge compared to other ways to get the result :)

Yeah that's right but this was the only way they could do it 2300 years ago